the EOG
Grade 6 StudyText
Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Except as permitted under the United States Copyright Act, no part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior permission of the publisher. Send all inquiries to: Glencoe/McGraw-Hill 8787 Orion Place Columbus, OH 43240-4027 ISBN: 978-0-07-890673-2 MHID: 0-07-890673-3 Printed in the United States of America. 1 2 3 4 5 6 7 8 9 10 HSO 19 18 17 16 15 14 13 12 11 10
North Carolina Mastering the EOG, Grade 6
Contents in Brief Using Your North Carolina StudyText . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v Commonly-Used Mathematics Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Chapter-by-Chapter Contents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii North Carolina Essential Standards, Mathematics Grade 6 . . . . . . . . . .xxii Chapter Resources 1 Algebra: Number Patterns and Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Statistics and Graphs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Operations with Decimals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4 Fractions and Decimals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5 Operations with Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6 Ratio, Proportion, and Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7 Percent and Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8 Systems of Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 10 Measurement: Perimeter, Area, and Volume . . . . . . . . . . . . . . . . . . . . . . . . . 181 11 Integers and Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203 12 Algebra: Properties and Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 Mastering the EOG Diagnostic Test: Student Answer Document. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A1 Diagnostic Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A3 Practice by Essential Standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A17 Countdown to EOG. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A45 Practice Test: Student Answer Document . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A51 Practice Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A53
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iii
Using Your North Carolina StudyText North Carolina Mastering the EOG, Grade 6 Mathematics StudyText is a practice workbook designed to help you master the North Carolina Essential Standards for Grade 6 Mathematics. It is divided into two sections.
Chapter Resources • The Chapter-by-Chapter Contents lists all of the chapter resources, which Essential Standard(s) they address, and where to go in your textbook if you need more explanation. • Each chapter begins with two activities. The Anticipation Guide is an informal assessment of what you may think you know about the topics in the chapter. This can help you determine how well you are prepared for the content of the chapter. The Family Activity is a problem-solving opportunity to practice at home. Each question has a full solution to help you check your work. • The chapter contains four pages for each key lesson in for the chapter. Your teacher may ask you to complete one or more of these worksheets as an assignment in addition to your work in your textbook. • Each worksheet is labeled with the Essential Standard(s) that it practices.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Mastering the EOG This section of your StudyText is composed of different types of assessment and practice to prepare you for taking the EOG. • The Diagnostic Test can help you determine which Essential Standards you might need to review before taking the EOG. After taking the Diagnostic Test, your teacher can tell you which standard(s) you need to review. • The Practice by Essential Standard gives you more practice problems to help you become a better test-taker. The problems are organized by Essential Standard and can be used as review on a particular standard or as a general review of all the standards. • Countdown to EOG gives you one practice question per day for the six weeks prior to the EOG. • The Practice Test can be used to simulate what the Grade 6 EOG mathematics test might be like so that you will be better prepared to take the EOG in the spring.
Know Your Formulas On the next page you will see a list of formulas that are commonly used in the problems you solve in geometry in Grade 6. You can become a better problem-solver if you know these formulas by heart and do not have to look them up each time you need them to solve a problem.
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Commonly-Used Formulas Mathematics Grade 6 There are many formulas used in mathematics. You can become a better problem-solver if you know the formulas without having to look them up, so that you work more efficiently. It is recommended that you be very familiar with the following measurement formulas for Grade 6 Mathematics. Area of a Rectangle
Sum of Measures of Angles In a Triangle
w
2
1
A = w
3
m∠1 + m∠2 + m∠3 = 180°
Area of a Triangle
h
h
h b
b
2
Circumference of a Circle
d
C = πd
vi
r
C = 2πr
North Carolina, Grade 6
Area of a Circle
d
A=π
r
( _d ) 2
2
A = πr2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
b
1 A=_ bh
Chapter-by-Chapter Contents Chapter 1 Algebra: Number Patterns and Functions
Page
Lesson
1
Chapter 1 Anticipation Guide
2
Chapter 1 Family Activity
Focus on Essential Standard(s)
1A Powers and Exponents
32–36
3
Explore Through Reading
6.N.5.2, 6.N.5.3
4
Study Guide
6.N.5.2, 6.N.5.3
5
Homework Practice
6.N.5.2, 6.N.5.3
6
Problem-Solving Practice
6.N.5.2, 6.N.5.3
1B Scientific Notation
32–36
7
Study Guide
6.N.5.1
8
Skills Practice
6.N.5.1
9
Homework Practice
6.N.5.1
Problem-Solving Practice
6.N.5.1
10
1C Algebra: Area Formulas
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Learn More in Math Connects, Course 1 (pages)
63–67
11
Explore Through Reading
6.M.2.2
12
Study Guide
6.M.2.2
13
Homework Practice
6.M.2.2
14
Problem-Solving Practice
6.M.2.2
Additional Resources Math Triumphs, Grade 6 [Book 2]: Chapter 5 (Multiplication) Math Triumphs, Grade 6 [Book 3]: Chapter 10 (Formulas)
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Chapter 2 Statistics and Graphs
Page 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
Chapter 2 Anticipation Guide Chapter 2 Family Activity 2A Bar Graphs and Histograms Study Guide Skills Practice Homework Practice Problem-Solving Practice 2B Interpret Line Graphs Explore Through Reading Study Guide Homework Practice Problem-Solving Practice 2C Qualitative Graphs Study Guide Skills Practice Homework Practice Problem-Solving Practice 2D Stem-and-Leaf Plots Explore Through Reading Study Guide Homework Practice Problem-Solving Practice 2E Line Plots and Dot Plots Explore Through Reading Study Guide Homework Practice Problem-Solving Practice 2F Mean Explore Through Reading Study Guide Homework Practice Problem-Solving Practice 2G Median, Mode, and Range Explore Through Reading Study Guide Homework Practice Problem-Solving Practice 2H Interpret Data Study Guide Skills Practice Homework Practice Problem-Solving Practice 2I Integers and Graphing Explore Through Reading Study Guide Homework Practice Problem-Solving Practice
LA25–LA28 6.S.3.1 6.S.3.1 6.S.3.1 6.S.3.1 88–91 6.S.3.2, 6.S.3.4 6.S.3.2, 6.S.3.4 6.S.3.2, 6.S.3.4 6.S.3.2, 6.S.3.4 6.A.3.1, 6.A.3.2 6.A.3.1, 6.A.3.2 6.A.3.1, 6.A.3.2 6.A.3.1, 6.A.3.2 92–95 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 96–100 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 6.S.3.1, 6.S.3.2 102–106 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 108–113 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 6.S.3.2, 6.S.3.3 6.S.3.4 6.S.3.4 6.S.3.4 6.S.3.4 121–125 6.N.3.1 6.N.3.1 6.N.3.1 6.N.3.1
Additional Resource Math Triumphs, Grade 6 [Book 2]: Chapters 5 (Multiplication) and 6 (Division)
viii
North Carolina, Grade 6
Learn More in Math Connects, Course 1 (pages)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
33 34 35 36
Lesson
Focus on Essential Standard(s)
3 Operations with Decimals
Page 53 54
Lesson
Focus on Essential Standard(s)
Chapter 3 Anticipation Guide Chapter 3 Family Activity 3A Comparing and Ordering Decimals
142–145
55
Explore Through Reading
6.N.3.1
56
Study Guide
6.N.3.1
57
Homework Practice
6.N.3.1
58
Mini-Project
6.N.3.1
3B Adding and Subtracting Decimals
156–160
59
Explore Through Reading
6.N.2.1
60
Study Guide
6.N.2.1
61
Homework Practice
6.N.2.1
62
Problem-Solving Practice
6.N.2.1
3C Multiplying Decimals by Whole Numbers
163–166
63
Explore Through Reading
6.N.1.1
64
Study Guide
6.N.1.1
65
Homework Practice
6.N.1.1
66
Problem-Solving Practice
6.N.1.1
3D Multiplying Decimals
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Learn More in Math Connects, Course 1 (pages)
169–172
67
Explore Through Reading
6.N.1.1
68
Study Guide
6.N.1.1
69
Homework Practice
6.N.1.1
70
Problem-Solving Practice
6.N.1.1
3E Dividing Decimals by Whole Numbers
173–176
71
Explore Through Reading
6.N.1.1
72
Study Guide
6.N.1.1
73
Homework Practice
6.N.1.1
74
Problem-Solving Practice
6.N.1.1
3F Dividing by Decimals
179–183
75
Explore Through Reading
6.N.1.1
76
Study Guide
6.N.1.1
77
Homework Practice
6.N.1.1
78
Problem-Solving Practice
6.N.1.1
Additional Resources Math Triumphs, Grade 6 [Book 1]: Chapter 3 (Decimals), Chapter 4 (Operations with Decimals) Math Triumphs, Grade 6 [Book 2]: Chapter 5 (Multiplication) and 6 (Division)
North Carolina, Grade 6
ix
4 Fractions and Decimals
Page
Lesson
79
Chapter 4 Anticipation Guide
80
Chapter 4 Family Activity
Focus on Essential Standard(s)
4A Problem Solving Investigation: Make an Organized List 81
Explore Through Reading
6.S.2.2
82
Study Guide
6.S.2.2
83
Homework Practice
6.S.2.2
84
Problem-Solving Practice
6.S.2.2
4B Comparing and Ordering Fractions Explore Through Reading
6.N.3.1
86
Study Guide
6.N.3.1
87
Homework Practice
6.N.3.1
88
Problem-Solving Practice
6.N.3.1 225–228
89
Explore Through Reading
6.N.3.2
90
Study Guide
6.N.3.2
91
Homework Practice
6.N.3.2
92
Problem-Solving Practice
6.N.3.2
4D Writing Fractions as Decimals
229–232
Explore Through Reading
6.N.3.2
94
Study Guide
6.N.3.2
95
Homework Practice
6.N.3.2
96
Problem-Solving Practice
6.N.3.2
Additional Resource Math Triumphs, Grade 6 [Book 1]: Chapters 1 (Fractions) and 3 (Decimals)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
93
North Carolina, Grade 6
214–215
220–224
85
4C Writing Decimals as Fractions
x
Learn More in Math Connects, Course 1 (pages)
5 Operations with Fractions
Page 97 98
Lesson
Focus on Essential Standard(s)
Chapter 5 Anticipation Guide Chapter 5 Family Activity 5A Adding and Subtracting Fractions with Like Denominators
99
Explore Through Reading
6.N.2.1
100
Study Guide
6.N.2.1
101
Homework Practice
6.N.2.1
102
Mini-Project
6.N.2.1
256–260
5B Adding and Subtracting Fractions with Unlike Denominators 103
Explore Through Reading
6.N.2.1
104
Study Guide
6.N.2.1
105
Homework Practice
6.N.2.1
106
Problem-Solving Practice
6.N.2.1
263–268
5C Adding and Subtracting Mixed Numbers
270–274
107
Explore Through Reading
6.N.2.1
108
Study Guide
6.N.2.1
109
Homework Practice
6.N.2.1
110
Problem-Solving Practice
6.N.2.1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5D Multiplying Fractions
282–286
111
Explore Through Reading
6.N.1.2
112
Study Guide
6.N.1.2
113
Homework Practice
6.N.1.2
114
Problem-Solving Practice
6.N.1.2
5E Multiplying Mixed Numbers
287–290
115
Explore Through Reading
6.N.1.2
116
Study Guide
6.N.1.2
117
Homework Practice
6.N.1.2
118
Problem-Solving Practice
6.N.1.2
5F Dividing Fractions
293–297
119
Explore Through Reading
6.N.2.1
120
Study Guide
6.N.2.1
121
Homework Practice
6.N.2.1
122
Problem-Solving Practice
6.N.2.1
5G Dividing Mixed Numbers 123
Learn More in Math Connects, Course 1 (pages)
298–301
Explore Through Reading
6.N.1.2
124
Study Guide
6.N.1.2
125
Homework Practice
6.N.1.2
126
Problem-Solving Practice
6.N.1.2
Additional Resources Math Triumphs, Grade 6 [Book 1]: Chapter 2 (Operations with Fractions) Math Triumphs, Grade 6 [Book 2]: Chapters 5 (Multiplication) and 6 (Division)
North Carolina, Grade 6
xi
6 Ratio, Proportion, and Functions
Page
Lesson
127
Chapter 6 Anticipation Guide
128
Chapter 6 Family Activity
Focus on Essential Standard(s)
6A Ratios and Rates
Learn More in Math Connects, Course 1 (pages)
314–319
129
Explore Through Reading
6.N.4.2
130
Study Guide
6.N.4.2
131
Homework Practice
6.N.4.2
132
Problem-Solving Practice
6.N.4.2
6B Ratio Tables
322–327
133
Explore Through Reading
6.N.4.1
134
Study Guide
6.N.4.1
135
Homework Practice
6.N.4.1
136
Problem-Solving Practice
6.N.4.1
6C Proportions
329–333
137
Explore Through Reading
6.N.4.2
138
Study Guide
6.N.4.2
139
Homework Practice
6.N.4.2
140
Problem-Solving Practice
6.N.4.2
6D Algebra: Solving Proportions
334–339
Explore Through Reading
6.N.4.2
142
Study Guide
6.N.4.2
143
Homework Practice
6.N.4.2
144
Problem-Solving Practice
6.N.4.2
6E Sequences and Expressions
343–348
145
Explore Through Reading
6.A.2.1, 6.A.2.2, 6.A.2.3
146
Study Guide
6.A.2.1, 6.A.2.2, 6.A.2.3
147
Homework Practice
6.A.2.1, 6.A.2.2, 6.A.2.3
148
Problem-Solving Practice
6.A.2.1, 6.A.2.2, 6.A.2.3
Additional Resource Math Triumphs, Grade 6 [Book 2]: Chapters 5 (Multiplication), 6 (Division), and 7 (Ratios, Rates, and Unit Rates)
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North Carolina, Grade 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
141
7 Percent and Probability
Page
Lesson
149
Chapter 7 Anticipation Guide
150
Chapter 7 Family Activity
Focus on Essential Standard(s)
7A Percents and Fractions
365–369
151
Explore Through Reading
6.N.3.2
152
Study Guide
6.N.3.2
153
Homework Practice
6.N.3.2
154
Problem-Solving Practice
6.N.3.2
7B Percents and Decimals
377–380
155
Explore Through Reading
6.N.3.2
156
Study Guide
6.N.3.2
157
Homework Practice
6.N.3.2
158
Problem-Solving Practice
6.N.3.2
7C Probability
381–386
159
Explore Through Reading
6.S.1.1, 6.S.1.2
160
Study Guide
6.S.1.1, 6.S.1.2
161
Homework Practice
6.S.1.1, 6.S.1.2
162
Problem-Solving Practice
6.S.1.1, 6.S.1.2
7D Sample Spaces
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Learn More in Math Connects, Course 1 (pages)
389–393
163
Explore Through Reading
6.S.2.1
164
Study Guide
6.S.2.1
165
Homework Practice
6.S.2.1
166
Problem-Solving Practice
6.S.2.1
167
Explore Through Reading
6.S.2.1
168
Study Guide
6.S.2.1
169
Homework Practice
6.S.2.1
170
Problem-Solving Practice
6.S.2.1
7E Making Predictions
394–398
7F Estimating with Percents
401–405
171
Study Guide
6.N.3.2
172
Skills Practice
6.N.3.2
173
Homework Practice
6.N.3.2
174
Problem-Solving Practice
6.N.3.2
Additional Resource Math Triumphs, Grade 6 [Book 2]: Chapter 7 (Ratios, Rates, and Unit Rates).
North Carolina, Grade 6 xiii
8 Systems of Measurement
Page
Lesson
175
Chapter 8 Anticipation Guide
176
Chapter 8 Family Activity
Focus on Essential Standard(s)
Learn More in Math Connects, Course 1 (pages)
8A Converting Between Metric and Customary Units 177
Study Guide
6.M.1.1
178
Skills Practice
6.M.1.1
179
Homework Practice
6.M.1.1
180
Problem-Solving Practice
6.M.1.1
Additional Resource Math Triumphs, Grade 6 [Book 2]: Chapters 5 (Multiplication) and 6 (Division)
9 Geometry: Angles and Polygons
(OPTIONAL)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
xiv
North Carolina, Grade 6
10 Measurement: Perimeter, Area, and Volume
Page 181 182
Lesson
Focus on Essential Standard(s)
Chapter 10 Anticipation Guide Chapter 10 Family Activity 10A Perimeter
522–526
183
Explore Through Reading
6.M.2.1
184
Study Guide
6.M.2.1
185
Homework Practice
6.M.2.1
186
Problem-Solving Practice
6.M.2.1
10B Circles and Circumference
528–533
187
Explore Through Reading
6.M.3.1, 6.M.3.2
188
Study Guide
6.M.3.1, 6.M.3.2
189
Homework Practice
6.M.3.1, 6.M.3.2
190
Mini-Project
6.M.3.1, 6.M.3.2
10C Area of Circles
LA15–LA19
191
Study Guide
6.M.3.2
192
Skills Practice
6.M.3.2
193
Homework Practice
6.M.3.2
194
Problem-Solving Practice
6.M.3.2
10D Area of Parallelograms
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Learn More in Math Connects, Course 1 (pages)
534–538
195
Explore Through Reading
6.M.2.2
196
Study Guide
6.M.2.2
197
Homework Practice
6.M.2.2
198
Problem-Solving Practice
6.M.2.2
10E Area of Triangles
540–544
199
Explore Through Reading
6.M.2.2
200
Study Guide
6.M.2.2
201
Homework Practice
6.M.2.2
202
Mini-Project
6.M.2.2
Additional Resource Math Triumphs, Grade 6 [Book 3]: Chapter 10 (Formulas)
North Carolina, Grade 6
xv
11 Integers and Transformations
Page
Lesson
203
Chapter 11 Anticipation Guide
204
Chapter 11 Family Activity
Focus on Essential Standard(s)
11A Ordering Integers
Learn More in Math Connects, Course 1 (pages)
572–575
205
Explore Through Reading
6.N.3.1
206
Study Guide
6.N.3.1
207
Homework Practice
6.N.3.1
208
Problem-Solving Practice
6.N.3.1
11B The Coordinate Plane
599–603
209
Explore Through Reading
6.G.1.1
210
Study Guide
6.G.1.1
211
Homework Practice
6.G.1.1
212
Mini-Project
6.G.1.1
11C Intersections of Geometric Figures 213
Study Guide
6.G.1.2
214
Skills Practice
6.G.1.2
215
Homework Practice
6.G.1.2
216
Problem-Solving Practice
6.G.1.2
11D Translations
604–609
Explore Through Reading
6.G.1.3
218
Study Guide
6.G.1.3
219
Homework Practice
6.G.1.3
220
Problem-Solving Practice
6.G.1.3
11E Reflections
610–614
221
Explore Through Reading
6.G.1.4
222
Study Guide
6.G.1.4
223
Homework Practice
6.G.1.4
224
Problem-Solving Practice
6.G.1.4
Additional Resource Math Triumphs, Grade 6 [Book 3]: Chapter 9 (Variables and Expressions)
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North Carolina, Grade 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
217
12 Algebra: Properties and Equations
Page 225 226
Lesson
Focus on Essential Standard(s)
Chapter 12 Anticipation Guide Chapter 12 Family Activity 12A Simplifying Algebraic Expressions
636–641
227
Explore Through Reading
6.N.2.2
228
Study Guide
6.N.2.2
229
Homework Practice
6.N.2.2
230
Problem-Solving Practice
6.N.2.2
12B Solving Addition Equations
644–648
231
Explore Through Reading
6.A.1.1, 6.A.1.2
232
Study Guide
6.A.1.1, 6.A.1.2
233
Homework Practice
6.A.1.1, 6.A.1.2
234
Problem-Solving Practice
6.A.1.1, 6.A.1.2
12C Solving Subtraction Equations
651–654
235
Explore Through Reading
6.A.1.1, 6.A.1.2
236
Study Guide
6.A.1.1, 6.A.1.2
237
Homework Practice
6.A.1.1, 6.A.1.2
238
Mini-Project
6.A.1.1, 6.A.1.2
12D Solving Multiplication Equations
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Learn More in Math Connects, Course 1 (pages)
657–660
239
Explore Through Reading
6.A.1.1, 6.A.1.2
240
Study Guide
6.A.1.1, 6.A.1.2
241
Homework Practice
6.A.1.1, 6.A.1.2
242
Problem-Solving Practice
6.A.1.1, 6.A.1.2
12E Inequalities
749–750
243
Study Guide
6.A.1.1, 6.A.1.3
244
Skills Practice
6.A.1.1, 6.A.1.3
245
Homework Practice
6.A.1.1, 6.A.1.3
246
Problem-Solving Practice
6.A.1.1, 6.A.1.3
Additional Resources Math Triumphs, Grade 6 [Book 2]: Chapter 5 (Multiplication) Math Triumphs, Grade 6 [Book 3]: Chapter 8 (Properties), Chapter 9 (Variables and Expressions), and Chapter 10 (Formulas)
North Carolina, Grade 6 xvii
North Carolina Essential Standards Mathematics Grade 6 The diagram shows what each part of the standard means. 6 is the grade level
1 is the Essential Standard number and 2 tells which Clarifying Objective under that Essential Standard
6.N.1.2
N stands for Number and Operations
Number and Operations Use a variety of strategies (including models, pictures, mental computation) to solve problems involving multiplication and division of non-negative rational numbers.
6.N.1.1
Apply multiplication and division to non-negative decimal numbers.
6.N.1.2
Apply multiplication and division to non-negative fractions.
6.N.2
Use combinations of addition, subtraction, multiplication and division for non-negative rational numbers to solve multi-step problems.
6.N.2.1
Use formal algorithms for all four operations for non-negative rational numbers.
6.N.2.2
Understand when the associative and commutative properties hold true for non-negative rational numbers.
6.N.3
Understand the relationship between integers, non-negative decimals, fractions, and percents.
6.N.3.1
Compare integers and non-negative decimals, fractions and percents using the number line.
6.N.3.2
Represent percents as decimals and fractions; fractions as decimals and percents; and decimals as fractions and percents.
6.N.4
Use the concept of unit rate to solve problems.
6.N.4.1
Use ratio tables or graphs to represent unit rates.
6.N.4.2
Use unit rates to solve problems.
6.N.5
Understand large and small numbers using exponents and exponential notation.
6.N.5.1
Represent numbers using scientific notation.
6.N.5.2
Represent numbers as prime factors with exponents.
6.N.5.3
Compare numeric expressions using repeated multiplication and exponential notation.
Algebra 6.A.1
Apply mathematical operations and properties for non-negative rational numbers to solve one-step equations and inequalities.
6.A.1.1
Use verbal descriptions and algebraic equations and inequalities to represent problem situations.
6.A.1.2
Use mathematical operations and properties to solve one-step equations.
6.A.1.3
Use mathematical operations and properties to solve inequalities.
6.A.2
Analyze patterns to determine the rule that enables accurate predictions of missing numbers, including the nth term, of arithmetic sequences (x1, x2, x3, xn).
6.A.2.1
Analyze patterns of arithmetic sequences to determine the rule that defines the pattern.
6.A.2.2
Use the rule to predict the nth term of an arithmetic sequence.
6.A.2.3
Use a given rule to determine the pattern.
xviii
North Carolina, Grade 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6.N.1
North Carolina Essential Standards Mathematics Grade 6 (continued) 6.A.3
Analyze the data presented in qualitative graphs in terms of position, time, change and rate of change.
6.A.3.1
Represent the essential elements of a scenario in graphical form.
6.A.3.2
Analyze the data presented in a qualitative graph to solve problems or answer questions.
Geometry 6.G.1
Represent one- and two-dimensional geometric figures in the Cartesian coordinate system.
6.G.1.1
Identify the origin, axes, quadrants and coordinates on the Cartesian coordinate system.
6.G.1.2
Describe the intersection of two or more geometric figures in the Cartesian coordinate system (e.g. intersection of a circle and a line).
6.G.1.3
Summarize the effect of translations.
6.G.1.4
Summarize the effect of reflections across horizontal and vertical lines.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Measurement 6.M.1
Use the relationship between customary and metric measurements to estimate measures given in one system to its measure in the other system.
6.M.1.1
Use the relationships between customary and metric measurements to make estimates between systems.
6.M.2
Use attributes of polygons and formulas to determine perimeter and area.
6.M.2.1
Calculate the perimeter of polygons.
6.M.2.2
Calculate the area of polygons.
6.M.3
Use the appropriate value of π to calculate the circumference and area of circles.
6.M.3.1
Compare the ratio of the circumference to the diameter to identify an approximate value of π.
6.M.3.2
Use formulas to determine the area and circumference of circles.
Statistics and Probability 6.S.1
Understand the relationships between experimental and theoretical probabilities for simple events.
6.S.1.1
Predict the outcomes of probability experiments for simple events based on theoretical probability.
6.S.1.2
Compare the outcomes from random experiments (experimental probability) to an expected outcome based on a theoretical probability.
6.S.2
Use strategies to identify sample spaces and probabilities.
6.S.2.1
Use tree diagrams and Fundamental Counting Principle to identify sample space and identify probabilities.
6.S.2.2
Use organized lists to display a sample space and identify probabilities.
6.S.3
Understand graphical displays of data in terms of shape, measures of center and variability.
6.S.3.1
Represent data using dot plots, stem and leaf plots and histograms.
6.S.3.2
Interpret distributions of data in terms of measures of center (mean, median and mode), shape (clusters, peaks and gaps) and variability (range).
6.S.3.3
Compare the meanings and uses of means, medians and modes.
6.S.3.4
Interpret information from a data set in terms of supporting or refuting statements about the data group.
North Carolina, Grade 6 xix
NAME
1
DATE
PERIOD
Anticipation Guide Algebra: Number Patterns and Functions
STEP 1
Before you begin Chapter 1
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. An estimate is not a good indication of the answer to a problem because an estimate is not the exact answer. 2. To determine when an estimate can be used to answer a problem, look for words such as “about” that indicate an exact answer is not needed. 3. A prime number is any number with more than two factors. 4. 41 and 4 are equivalent.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. A number to the second power, such as 72, is said to be squared. 6. In using the order of operations to simplify an expression, all addition and subtraction should be done first. 7. In using the order of operations to simplify an expression, multiply and divide in order from left to right. 8. In the expression 3x + 4, x is called a variable. 9. Using a guess and check strategy to solve a math problem is never a good idea. 10. To solve the equation t - 5 = 12, subtract 5 from 12. 11. The area of a rectangle is found by multiplying the length by the width. 12. The dimensions of a rectangle with an area of 12 square units must be 4 and 3. STEP 2
After you complete Chapter 1
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible. Chapter 1
North Carolina, Grade 6
1
NAME
1
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. For the table below, find the expression that can be used to find term n in the sequence. Which expression can be used to find n? Position, n 1 2 3 4 5 n
Value of Term 6 8 10 12 14 ?
A 3n + 2
C 2n + 4
B 2n - 2
D 2n + 3
2. What is the prime factorization for 125? A 5 × 25 B 53 C 12 × 5 D 35
Fold here. Solution
Solution
While 3n + 2 will work for the second pair (3 × 2 + 2 = 8), it does not work with the rest of the number pairs (For example: 3 × 1 + 2 ≠ 6). 2n - 2 and 2n + 3 do not work for any of the pairs.
2. Hint: Prime factorization is the expression of a number as the product of prime numbers. A prime number is a number that is divisible only by one and itself. Both A and C are wrong because they contain numbers that are not prime. If you find the value of the remaining two choices, you will find that B (5 3 = 5 × 5 × 5) equals 125 while D (3 5 = 3 × 3 × 3 × 3 × 3) equals 243.
The expression that does work for all of them is 2n + 4. This is modeled below: 2 2 2 2 2
× × × × ×
1 2 3 4 5
+ + + + +
4 4 4 4 4
= = = = =
6 8 10 12 14 The answer is C.
2
North Carolina, Grade 6
The answer is B. Chapter 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Hint: Remember to test at least three of the number pairs in the expressions before deciding on an answer. Some expressions may work for one of the pairs, but not all of them.
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Explore Through Reading
6.N.5.2, 6.N.5.3
Powers and Exponents Get Ready for the Lesson Complete the Mini Lab at the top of page 32 in your textbook. Write your answers below. 1. What prime factors did you record?
2. How does the number of folds relate to the number of factors in the prime factorization of the number of holes?
3. Write the prime factorization of the number of holes made if you folded it eight times.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Describe the expression 2 5. In your description, use the terms power, base, and exponent.
5. In the power 3 5, what does the exponent 5 indicate?
6. Complete the following table. Expression 4
Words
3
72 96 8×8×8×8 3×3×3×3×3
Remember What You Learned 7. Explain how to find the value of 5 4.
Chapter 1
North Carolina, Grade 6
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Study Guide
6.N.5.2, 6.N.5.3
Powers and Exponents A product of prime factors can be written using exponents and a base. Numbers expressed using exponents are called powers. Powers
Words
42
4 to the second power or 4 squared
4×4
5
6
5 to the sixth power
5×5×5×5×5×5
7
4
7 to the fourth power
7×7×7×7
9
3
9 to the third power or 9 cubed
9×9×9
Example 1
Expression
Value 16 15,625 2,401 729
Write 6 × 6 × 6 using an exponent. Then find the value.
The base is 6. Since 6 is a factor 3 times, the exponent is 3. 6 × 6 × 6 = 6 3 or 216 Example 2
Write 2 4 as a product of the same factor. Then find the value.
The base is 2. The exponent is 4. So, 2 is a factor 4 times. 2 4 = 2 × 2 × 2 × 2 or 16 Example 3
Write the prime factorization of 225 using exponents.
The prime factorization of 225 can be written as 3 × 3 × 5 × 5, or 3 2 × 5 2. Example 4
Compare 8 5 and 8 × 8 × 8 × 8.
Bacause 8 × 8 × 8 × 8 can be rewritten as 8 4, 8 5 > 8 × 8 × 8 × 8. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Write each product using an exponent. Then find the value. 1. 2 × 2 × 2 × 2 × 2
2. 9 × 9
3. 3 × 3 × 3
4. 5 × 5 × 5
Write each power as a product of the same factor. Then find the value. 5. 7 2
6. 4 3
7. 8 4
8. 5 5
Write the prime factorization of each number using exponents. 9. 40
10. 75
11. 100
12. 147
Using >, <, or =, compare each set of numbers. 13. 6 × 6 × 6 × 6 × 6 15. 2 × 2 × 2 × 2
4
North Carolina, Grade 6
24
66
14. 3 5
3×3×3×3×3×3
16. 9 3
9×9
Chapter 1
NAME
1A
DATE
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Homework Practice
6.N.5.2, 6.N.5.3
Powers and Exponents Write each product using an exponent. 1. 6 × 6 2. 10 × 10 × 10 × 10 3. 4 × 4 × 4 × 4 × 4 4. 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 5. 5 × 5 × 5 × 5 × 5 × 5 6. 13 × 13 × 13 Write each power as a product of the same factor. Then find the value. 7. 10 1
8. 2 7
9. 8 3
10. 3 8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11. nine squared
12. four to the sixth power
Write the prime factorization of each number using exponents. 13. 32
14. 100
15. 63
16. 99
17. 52
18. 147
Using >, <, or =, compare each set of numbers. 19. 2 × 2 × 2 × 2
25
21. 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 23. 3 × 3 × 3 × 3 × 3 × 3 × 3
36
88
20. 4 8
4×4×4×4×4×4
22. 7 4
7×7×7×7×7
24. 5 7
5×5×5×5×5×5
25. LABELS A sheet of labels has 8 rows of labels with 8 labels in each row. How many total labels are on the sheet? Write your answer using exponents, and then find the value.
Chapter 1
North Carolina, Grade 6
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Problem-Solving Practice
PERIOD
6.N.5.2, 6.N.5.3
Powers and Exponents 2. WEIGHT A 100-pound person on Earth would weigh about 4 · 4 · 4 · 4 pounds on Jupiter. Write 4 · 4 · 4 · 4 using an exponent. Then find the value of the power. How much would a 100-pound person weigh on Jupiter?
3. ELECTIONS In the year 2000, the governor of Washington, Gary Locke, received about 10 6 votes to win the election. Write this as a product. How many votes did Gary Locke receive?
4. SPACE The diameter of Mars is about 9 4 kilometers. Write 9 4 as a product. Then find the value of the product.
5. SPACE The length of one day on Venus is 3 5 Earth days. Express this exponent as a product. Then find the value of the product:
6. GEOGRAPHY The area of San Bernardino County, California, the largest county in the U.S., is about 3 9 square miles. Write this as a product. What is the area of San Bernardino County?
7. GEOMETRY The volume of the block shown can be found by multiplying the width, length, and height. Write the volume using an exponent. Find the volume.
8. SPACE A day on Jupiter lasts about 10 hours. Write a product and an exponent to show how many hours are in 10 Jupiter days. Then find the value of the power.
North Carolina, Grade 6
2 in.
2 in.
2 in.
Chapter 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6
1. SPACE The Sun is about 10 · 10 million miles away from Earth. Write 10 · 10 using an exponent. Then find the value of the power. How many miles away is the Sun?
NAME
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Study Guide
6.N.5.1
Scientific Notation A number in scientific notation is written as the product of a factor that is at least one but less than ten and a power of ten.
Example 1
Write 8.65 × 10 7 in standard form.
8.65 × 10 7 = 8.65 × 10,000,000 = 86,500,000 Example 2
Move the decimal point 7 places to the right.
Write 9.2 × 10 -3 in standard form.
1 9.2 × 10 -3 = 9.2 × _ 3 10
1 10 -3 = _ 3 10
= 9.2 × 0.001
1 1 _ =_ or 0.001
= 0.0092
Move the decimal point 3 places to the left.
Example 3
= 7.625 × 10 4 Example 4
10 3
1,000
Write 76,250 in scientific notation.
76,250 = 7.625 × 10,000
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10 7 = 10 · 10 · 10 · 10 · 10 · 10 · 10 or 10,000,000
The decimal point moves 4 places. The exponent is positive.
Write 0.00157 in scientific notation.
0.00157 = 1.57 × 0.001 = 1.57 × 10 -3
The decimal point moves 3 places. The exponent is negative.
Exercises Write each number in standard form. 1. 5.3 × 10 1
2. 9.4 × 10 3
3. 7.07 × 10 5
4. 2.6 × 10 -3
5. 8.651 × 10 -2
6. 6.7 × 10 -6
Write each number in scientific notation. 7. 561 9. 56,400,000 11. 0.0064
Chapter 1
8. 14 10. 0.752 12. 0.000581
North Carolina, Grade 6
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Skills Practice
PERIOD
6.N.5.1
Scientific Notation Write each number in standard form. 1. 6.7 × 10 1
2. 6.1 × 10 4
3. 1.6 × 10 3
4. 3.46 × 10 2
5. 2.91 × 10 5
6. 8.651 × 10 7
7. 3.35 × 10 -1
8. 7.3 × 10 -6
9. 1.49 × 10 -7
10. 4.0027 × 10 -4
11. 5.2277 × 10 -3
12. 8.50284 × 10 -2
Write each number in scientific notation. 14. 273
15. 79,700
16. 6,590
17. 4,733,800
18. 2,204,000,000
19. 0.00916
20. 0.29
21. 0.00000571
22. 0.0008331
23. 0.0121
24. 0.00000018
North Carolina, Grade 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
13. 34
Chapter 1
NAME
1B
DATE
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Homework Practice
6.N.5.1
Scientific Notation Write each number in standard form. 1. 9.03 × 10 2
2. 7.89 × 10 3
3. 4.115 × 10 5
4. 3.201 × 10 6
5. 5.1 × 10 -2
6. 7.7 × 10 -5
7. 3.85 × 10 -4
8. 1.04 × 10 -3
Write each number in scientific notation. 9. 4,400
10. 75,000
11. 69,900,000
12. 575,000,000
13. 0.084
14. 0.0099
15. 0.000000515
16. 0.0000307
17. Which number is greater: 3.5 × 10 4 or 2.1 × 10 6?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
18. Which number is less: 7.2 × 10 7 or 9.9 × 10 5? 19. POPULATION The table lists the populations of five countries. List the countries from least to greatest population.
Country Australia Brazil Egypt Luxembourg Singapore
Population 2 × 10 7 1.9 × 10 8 7.7 × 10 7 4.7 × 10 5 4.4 × 10 6
Source: The World Factbook
20. SOLAR SYSTEM Pluto is 3.67 × 10 9 miles from the Sun. Write this number in standard form. 21. MEASUREMENT One centimeter is equal to about 0.0000062 mile. Write this number in scientific notation. 22. DISASTERS In 2005, Hurricane Katrina caused over $125 billion in damage in the southern United States. Write $125 billion in scientific notation.
Chapter 1
North Carolina, Grade 6
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NAME
1B
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Problem-Solving Practice
PERIOD
6.N.5.1
Scientific Notation 2. POPULATION In the year 2000, the population of Rahway, New Jersey, was 26,500. Write this number in scientific notation.
3. MEASUREMENT There are 5,280 feet in one mile. Write this number in scientific notation.
4. PHYSICS The speed of light is about 1.86 × 10 5 miles per second. Write this number in standard notation.
5. COMPUTERS A CD can store about 650,000,000 bytes of data. Write this number in scientific notation.
6. SPACE The diameter of the Sun is about 1.39 × 10 9 meters. Write this number in standard notation.
7. ECONOMICS The U.S. Gross Domestic Product in the year 2004 was 1.17 × 10 13 dollars. Write this number in standard notation.
8. MASS The mass of planet Earth is about 5.98 × 10 24 kilograms. Write this number in standard notation.
North Carolina, Grade 6
Chapter 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10
1. MEASUREMENT There are about 25.4 millimeters in one inch. Write this number in scientific notation.
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1C
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Explore Through Reading
6.M.2.2
Algebra: Area Formulas Get Ready for the Lesson Complete the activity at the top of page 63 in your textbook. Write your answers below. 1. Draw as many rectangles as you can on grid paper so that each one has an area of 20 square units. Find the distance around each one.
2. Which rectangle from Question 1 has the greatest distance around it? the least?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Look up the word area in a dictionary. Write the meaning of the word as used in this lesson.
4. In order to find the area of a surface, what two measurements do you need to know? 5. On page 63, the textbook says that the area of a figure is the number of square units needed to cover a surface. If the length and width are measured in inches, in what units will the area be expressed?
6. What unit of measure is indicated by m 2? How large is one unit?
Remember What You Learned 7. With a partner, measure a surface in your classroom. Explain how to find its area. Then find the area in the appropriate square units.
Chapter 1
North Carolina, Grade 6
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Study Guide
6.M.2.2
Algebra: Area Formulas The area of a figure is the number of square units needed to cover a surface. You can use a formula to find the area of a rectangle. The formula for finding the area of a rectangle is A = × w. In this formula, A represents area, represents the length of the rectangle, and w represents the width of the rectangle.
Example 1
Find the area of a rectangle with length 8 feet and width 7 feet.
A=×w Area of a rectangle Replace with 8 and w with 7. A=8×7 A = 56 The area is 56 square feet.
Example 2
Find the area of a square with side length 5 inches.
Area of a square A = s2 2 Replace s with 5. A=5 A = 25 The area is 25 square inches.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Find the area of each figure. 1.
2.
5 ft
3.
7 cm
8 ft
3 cm
6 yd
4.
6 yd
5. What is the area of a rectangle with a length of 10 meters and a width of 7 meters?
6. What is the area of a square with a side length of 15 inches?
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North Carolina, Grade 6
Chapter 1
NAME
1C
DATE
PERIOD
Homework Practice
6.M.2.2
Algebra: Area Formulas Find the area of each rectangle. 1.
2.
3. 15 mm
7m
4 ft 10 ft
24 mm
9m
4. Find the area of a rectangle with a length of 35 inches and a width of 21 inches. Find the area of each square. 5.
6.
7.
13 in.
2 cm
8 ft 2 cm
8 ft
13 in.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. What is the area of a square with a side length of 21 yards? Find the area of each shaded region. 10.
11.
10 cm
12.
6 yd
8 ft 18 ft
4 cm
21 ft
6 yd 12 yd 3 cm 10 cm 14 yd
13. REMODELING The Crofts are covering the floor in their living room and in their bedroom with carpeting. The living room is 16 feet long and 12 feet wide. The bedroom is a square with 10 feet on each side. How many square feet of carpeting should the Crofts buy?
23 ft
150 ft
150 ft
14. GARDENING The diagram shows a park’s lawn with a sandy playground in the corner. If a bag of fertilizer feeds 5,000 square feet of lawn, how many bags of fertilizer are needed to feed the lawn area of the park? Chapter 1
50 ft 50 ft
North Carolina, Grade 6
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Problem-Solving Practice
6.M.2.2
Algebra: Area Formulas FLOOR PLANS For Exercises 1–6, use the diagram that shows the floor
plan for a house. 7 ft
Bath
2 ft
10 ft
Closet
13 ft
2 ft Closet
9 ft
6 ft
Bedroom 1
Bedroom 2
13 ft
Hall
12 ft
Kitchen
Living/Dining Room 12 ft
14
18 ft
1. What is the area of the floor in the kitchen?
2. Find the area of the living/dining room.
3. What is the area of the bathroom?
4. Find the area of Bedroom 1.
5. Which two parts of the house have the same area?
6. How much larger is Bedroom 2 than Bedroom 1?
North Carolina, Grade 6
Chapter 1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
12 ft
NAME
2
DATE
PERIOD
Anticipation Guide Statistics and Graphs
STEP 1
Before you begin Chapter 2
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. A table can be used to help solve a problem when there is a multiple number of data in the problem. 2. A bar graph or a line graph can be used to display a set of data. 3. A stem-and-leaf plot is a graph that looks similar in shape to a tree. 4. The mean and the average of a set of numbers are the same.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. The median of an ordered set of numbers is the middle number. 6. The range of a set of numbers is the sum of the numbers divided by the number of pieces of data. 7. Graphs are always accurate displays of data because they contain facts about the data. 8. Integers are the set of all positive whole numbers. 9. Positive integers are to the right of zero on a number line. 10. Opposite numbers are numbers that are the same distance from zero in opposite directions on the number line. STEP 2
After you complete Chapter 2
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
Chapter 2
North Carolina, Grade 6
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NAME
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work.
12 71 55 33
15 13 54 15
14 67 12 12
39 11 14 51
45 14 15 25
15 13 10 23
Which selection includes all of the correct answers? A mean = 27; median = 15; modes = 12 and 14; range = 81
2. Refer to the table below. During which month were U.S. citizens least likely to be unemployed?
Unemployment Rate
1. Use the data on the table below to calculate the mean, median, mode, and range of the ages of people who worked at Whetstone Middle School’s Spring Festival.
5.5 5 4.5 4 3.5 3 2.5
U.S. Unemployment Rates (%)
2 1.5 1 0.5 0
Aug. Sept. Oct. Nov. Dec. Jan. 2005 2005 2005 2005 2005 2006
B mean = 28; median = 15; modes = 12 and 14; range = 61
Source: U.S. Department of Labor
C mean = 27; median = 15; mode = 15; range = 61
A Aug., 2005
C Sept., 2005
B Jan., 2006
D Nov., 2005
Fold here. Solution
Solution 1. Hint: It is always best to sort a large set of numbers from least to greatest when finding mean, median, mode, and range. To find the mean, add all the numbers then divide by how many numbers are in the set. There are 24 numbers, and the sum is 648. The mean is 648 ÷ 24 or 27. This eliminates choice B. You need not calculate the median since all answer choices have the same value. The mode is the number or numbers that occur(s) most often in the set. In this set, 15 occurs most often. Only choice C has a mean of 27 and a mode of 15. The answer is C.
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North Carolina, Grade 6
2. U.S. Citizens are least likely to be unemployed when the employment rate is lowest, which corresponds with the shortest bar on the graph above. The shortest bar occurs in January, so that is when citizens are least likely to be unemployed.
The answer is B. Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
D mean = 27; median = 15; modes = 12 and 14; range = 61
Months
NAME
2A
DATE
PERIOD
Study Guide
6.S.3.1
Bar Graphs and Histograms A bar graph is one method of comparing data by using solid bars to represent quantities. A histogram is a special kind of bar graph. It uses bars to represent the frequency of numerical data that have been organized into intervals. SIBLINGS Make a bar graph to display the data in the table below.
Student Sue Isfu Margarita Akira
Number of Siblings 1 6 3 2
Number of Siblings
Example 1
7 6 5 4 3 2 1 0
Siblings
Sue
Istu Margarita Akira
Student
Step 1 Draw a horizontal and a vertical axis. Label the axes as shown. Add a title. Step 2 Draw a bar to represent each student. In this case, a bar is used to represent the number of siblings for each student. Example 2
SIBLINGS The number of siblings of 17 students have been
Number of Siblings 0–1 2–3 4–5 6–7
Frequency 4 10 2 1
Frequency
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
organized into a table. Make a histogram of the data. Siblings
10 8 6 4 2 0
0–1 2–3 4–5
6–7
Number of Siblings
Step 1 Draw and label horizontal and vertical axes. Add a title. Step 2 Draw a bar to represent the frequency of each interval. Exercises 1. Make a bar graph for the data in the table. Student Luis Laura Opal Gad
Chapter 2
Number of Free Throws 6 10 4 14
2. Make a histogram for the data in the table. Number of Free Throws 0–1 2–3 4–5 6–7
Frequency 1 5 10 4
North Carolina, Grade 6
17
NAME
2A
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Skills Practice
6.S.3.1
Bar Graphs and Histograms ZOOS For Exercises 1 and 2, use the table. It shows
the number of species at several zoological parks. 1. Make a bar graph of the data. Animal Species in Zoos
Zoo Los Angeles Lincoln Park Cincinnati Bronx Oklahoma City
Species 350 290 700 530 600
2. Which zoological park has the most species? ZOOS For Exercises 3 and 4, use the table at the right. It shows the number of species at 37 major U.S. public zoological parks.
Animal Species in Zoos
4. Which interval has the largest frequency?
5. What does each bar represent?
6. Determine whether the graph is a bar graph or a histogram. Explain how you know.
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North Carolina, Grade 6
Calories Consumed
HEALTH For Exercises 5 and 6, use the graph at the right.
3,000 2,750 2,500 2,250 2,000 1,750 1,500 1,250 1,000 0
Calories in One Day
Clara
Drew
Bly
Akira
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Make a histogram of the data. Use intervals of 101–200, 201–300, 301–400, 401–500, 501–600, 601–700, and 701–800 for the horizontal axis.
Number of Species 200 700 290 600 681 300 643 350 794 400 360 600 134 200 800 305 384 500 330 250 530 715 303 200 475 465 340 347 300 708 184 800 375 350 450 337 221
NAME
2A
DATE
PERIOD
Homework Practice
6.S.3.1
Bar Graphs and Histograms Select the appropriate graph to display each set of data: bar graph or histogram. Then display the data in the appropriate graph. 2.
Home Run Derby 2007 Round 1 Home Runs Player Home Runs Vladimir Guerrero 5 Alex Rios 5 Matt Holliday 5 Albert Pujols 4 Justin Morneau 4 Source: Baseball Almanac
POPULATION For Exercises 3–5, use
the bar graph that shows the number of males and females in the world for the years 1970, 1980, 1990, 2000, 2005. 3. By how much did the number of females increase from 1970 to 1980? 4. By how much did the number of females increase from 2000 to 2005?
Males and Females 160 140
# (in millions)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Ages of Children Taking Swimming Lessons Age Children 0–2 8 3–5 12 6–8 18 9–11 17 12–14 12 15–17 13
Males
120 100
Females
80 60 40 20 0 1970
1980
1990
2000
2005
year
5. Between which years did the number of females increase the most?
Chapter 2
North Carolina, Grade 6
19
NAME
2A
DATE
PERIOD
Problem-Solving Practice
6.S.3.1
Bar Graphs and Histograms PUPPIES For Exercises 1 and 2, use the
EARTH SCIENCE In Exercises 3–6, use
table below. It shows the results of a survey in which students were asked what name they would most like to give a new pet puppy.
the table below. It shows the highest wind speeds in 30 U.S. cities.
Name Max Tiger Lady Shadow Molly Buster
Votes 15 5 13 10 9 2
1. Make a bar graph to display the data. Favorite New Puppy Names
Highest Wind Speeds
5. How many cities recorded wind speeds of 80 miles per hour or more?
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North Carolina, Grade 6
Speeds 54 91 46 73 49 56
(mph) 60 81 58 46 51 49 51 54 51
2. Use your bar graph from Exercise 1. Compare the number of votes the name Shadow received to the number of votes the name Tiger received.
4. What is the top wind speed of most of the cities?
6. How many cities recorded their highest wind speeds at 60 miles per hour or more? Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Make a histogram of the data.
Highest Wind 52 75 60 80 55 53 73 46 76 53 57 58 56 47 65
NAME
2B
DATE
PERIOD
Explore Through Reading
6.S.3.2, 6.S.3.4
Interpret Line Graphs Get Ready for the Lesson Complete the activity at the top of page 88 in your textbook. Write your answers below. 1. Describe the trends in the winning amounts.
2. Predict how much the 2008 winner received. Research and compare to the actual 2008 amount. 3. The Masters Tournament is held once a year. If a line graph is made of these data, will there be any realistic data values between years? Explain.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Refer to the sentence just below the activity at the top of page 88: “Line graphs are often used to predict future events because they show trends over time.” 3. The word predict comes from two Latin words that mean “to tell in advance.” Look up the word predict in a dictionary. What meaning is given for the word?
4. Look up the word trend in a dictionary. What meaning is given for the word as it is used in the definition of line graph?
5. Look at the line graph at the bottom of page 88. In terms of trends, what happened between 2005 and 2008? What is the difference between prediction and data or statistics?
Remember What You Learned 6. Find two line graphs, one where you feel you can predict the future with confidence and one where you cannot. Explain the difference.
Chapter 2
North Carolina, Grade 6
21
NAME
2B
DATE
PERIOD
Study Guide
6.S.3.2, 6.S.3.4
Interpret Line Graphs Because they show trends over time, line graphs are often used to predict future events.
Example 1 The graph shows the time Ruben spends each day practicing piano scales. Predict how much time he will spend practicing his scales on Friday.
Piano Scale Practice Times
Hours
2
Continue the graph with a dotted line in the same direction until you reach a vertical position for Friday. By extending the graph, you see that Ruben will probably spend half an hour practicing piano scales on Friday.
1
Sa t. Su n. M on Tu . e W . ed Th . ur . Fr i.
0
Day
Exercises MONEY Use the graph that shows the price of a ticket to a local high school football game over the last few years.
9 8 7 6 5 4 3
2. Predict the price of a ticket in year 6 if the trend continues.
2 1 0
3. In what year do you think the price will reach $9.00 if the trend continues?
1
2
3
4
5
6
7
8
Year
BANKS Use the graph that shows the interest rate for a savings account over the last few years.
Interest Rates 6% 5%
4. What does the graph tell you about interest rates? Rate
4%
5. If the trend continues, when will the interest rate reach 1 percent?
3% 2% 1% 0
1
2
3
4
5
6
7
8
Year
22
North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Price ($)
1. Has the price been increasing or decreasing? Explain.
Football Tickets
NAME
2B
DATE
PERIOD
Homework Practice
6.S.3.2, 6.S.3.4
Interpret Line Graphs SPORTS For Exercises 1–3, use the graph at the right.
Swimsuit Sales 90
1. Describe the change in the number of swimsuits sold.
80
2. Predict the number of swimsuits sold in December. Explain your reasoning.
Number
70 60 50 40 30 Ju ne Ju l Se Aug y pt us em t O be N cto r ov be em r be r
0
3. Predict the number of swimsuits sold in May. How did you reach this conclusion?
Month
Average Monthly Temperature
WEATHER For Exercises 4–7, use the graph at the right.
110 100 90
Temperature (°F)
4. Predict the average temperature for Juneau in February.
6. What do you think is the average temperature for San Francisco in October?
80 70 60 50 40 30 20
San Francisco, CA
Juneau, AK
ar c Ap h ri M l ay Ju ne Ju A Se u ly pt gu em st be r
0
7. How much colder would you expect it to be in Juneau than in Mobile in October?
M
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Predict the average temperature for Mobile in October.
Mobile, AL
Month
BASEBALL For Exercises 8–10, use the table that shows the number of games won by the Florida Gators men’s baseball team from 2002 to 2007.
Florida Gators Baseball Statistics Year 2002 2003 2004 2005 2006 Games Won 46 37 43 48 28
Source: The World Almanac
2007 29
8. Make a line graph of the data. 9. In what year did the team have the greatest increase in the number of games won? 10. Explain the disadvantages of using this line graph to make a prediction about the number of games that the team will win in 2009.
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NAME
2B
DATE
PERIOD
Problem-Solving Practice
6.S.3.2, 6.S.3.4
Interpret Line Graphs FITNESS For Exercises 1–3, use Graph A. For Exercises 4–6, use Graph B.
Graph A
Graph B Cara’s Sit-ups
14
80
12
70
Number of Sit-ups
Number of Students
Aerobics Class
10 8 6 4 2
60 50 40 30 20 10
0
1
2
3
4
5
6
Week
0
1
2
3
4
5
6
7
8
Week
2. Predict how many students will be in the aerobics class in week 6 if the trend continues.
3. Predict how many students will be in the aerobics class in week 8.
4. Describe the change in the number of sit-ups Cara can do.
5. Predict how many sit-ups Cara will be able to do in week 6 if the trend continues.
6. Predict the week in which Cara will be able to do 80 sit-ups if the trend continues.
North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
24
1. Refer to Graph A. Describe the change in the number of students taking the aerobics class.
NAME
2C
DATE
PERIOD
Study Guide
6.A.3.1, 6.A.3.2
Qualitative Graphs Qualitative graphs are graphs that are used to represent situations that do not necessarily have numerical values. Qualitative graphs represent the essential elements of a situation in a graphical form.
Describe a situation that could be represented by the graph shown.
Step 1 Look at the labels of the horizontal and vertical axes. Think of a situation that could be represented using the given labels. • The labels of the axes are Time and Distance from Floor. Step 2 Look at each section of the graph and decide whether it is increasing, decreasing, or constant.
Distance from Floor
Example 1
Time
• The first part of the graph decreases. • The second part of the graph increases but not to the original height. It then decreases and repeats. Step 3 Describe an event or action that could be represented by the graph. • You drop a ball onto a hard surface, it bounces twice, and then you stop it.
Step 1 Analyze the problem to determine the labels for your axes. Step 2 Determine what shape the graph will take. Are the values increasing or decreasing? Sketch the graph. • The temperature of the soup will increase sharply during heating, level off, and then gradually decrease until it reaches room temperature.
Temperature
• The values that vary are temperature and time.
Time
Exercises Describe a situation that could be represented by each graph. 1.
Water Level
2. Speed
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2 FOOD You heat up a bowl of soup for lunch. It is too hot to eat so you let it sit until it cools off. Sketch a qualitative graph to represent the situation.
Time
Time
3. FOOD Simone put frozen burgers into the refrigerator to thaw. Sketch a qualitative graph to represent the situation.
Chapter 2
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NAME
2C
DATE
Skills Practice
PERIOD
6.A.3.1, 6.A.3.2
Qualitative Graphs For Exercises 1–4, match each description with the most appropriate graph. Graph B
Temperature
Temperature
Graph A
Time
Time
Graph D
Temperature
Temperature
Graph C
Time
Time
1. In August, you enter a hot house and turn on the air conditioning.
3. You put ice cubes in your water and then drink it slowly.
4. You put a cup of water in the microwave and heat it for one minute, then let it cool.
For Exercises 5–7, sketch a qualitative graph to represent the situation. 5. TOYS A remote controlled car moves along and then crashes against a wall.
6. SPORTS The height of a basketball that was thrown for a three-point shot compared to the distance the basketball is from the basket.
7. BICYCLES Tamar is riding her bicycle uphill at a steady rate. At the top of the hill, she rides along flat land at the same rate, then coasts downhill.
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Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. In February, you enter a cold house and turn the thermostat up to 68°F.
NAME
2C
DATE
PERIOD
Homework Practice
6.A.3.1, 6.A.3.2
Qualitative Graphs 1. Identify the graph that represents the following situation: A bus frequently stops to pick up passengers. Graph B
Graph C
Time
Speed
Speed
Speed
Graph A
Time
Time
For Exercises 2–5, describe a situation that could be represented by each graph. 3. Speed
Distance from Ground
2.
Time
5.
Money in Account
4. Water Level
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Time
Time
Time
For Exercises 6 and 7, sketch a qualitative graph to represent the situation. 6. CARS A car approaches a traffic light that turns red. 7. CARDS Jamaal collects and trades sports cards. One week he purchases a large amount of cards. Over the next month, he sells most of them on the Internet.
Chapter 2
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NAME
2C
DATE
PERIOD
Problem-Solving Practice
6.A.3.1, 6.A.3.2
Qualitative Graphs 2. INCOME Mr. Bashara creates a graph that shows the relationship between a person’s annual income and age.
Temperature
Annual Income
1. ILLNESS The graph shows Kelli’s temperature over the course of a day she missed shool due to illness.
Time of Day
Write a story about Kelli’s illness.
Write a story about the person’s income.
4. CARS Write a story about a situation with a car that will produce a graph like the one shown.
Sketch a graph that shows the relationship of the height of the water to the amount of water used.
5. TRAVEL Eric drives from home to work in the morning. On the way home, he drives to a grocery store that is further from home than his office. Then he drives home. Sketch a graph that shows the relationship between Eric’s distance from home and time.
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North Carolina, Grade 6
Time
6. WEATHER When Bryan woke up the outside temperature was cool. The temperature rose steadily to 85° at 3 P.M., then dropped steadily to 65° at 8 P.M. Sketch a graph that shows the relationship of the temperature and the time of day.
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Speed
3. FLOWERS Mrs. Coates is filling the vase shown below with water.
Age
NAME
2D
DATE
PERIOD
Explore Through Reading
6.S.3.1, 6.S.3.2
Stem-and-Leaf Plots Get Ready for the Lesson Complete the activity at the top of page 92 in your textbook. Write your answers below. 1. What were the least and greatest number of instant messages sent?
2. Which number of instant messages occurred most often?
Read the Lesson 3. In a stem-and-leaf plot, in what order are the data?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. In a stem-and-leaf plot of two-digit numbers, how are the data represented?
5. Look at the stem-and-leaf plot at the top of page 93. Of the twenty tallest waterfalls, how many are between 600 and 699 feet tall? Using the stemand-leaf plot, how can you tell that this height-range is most common?
Remember What You Learned 6. Write the steps for making a stem-and-leaf plot. Show someone what a stem-and-leaf plot is, how to read one, and how to make one.
Chapter 2
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NAME
2D
DATE
Study Guide
PERIOD
6.S.3.1, 6.S.3.2
Stem-and-Leaf Plots Sometimes it is hard to read data in a table. You can use a stem-and-leaf plot to display the data in a more readable way. In a stem-and-leaf plot, you order the data from least to greatest. Then you organize the data by place value.
Example 1 Make a stem-and-leaf plot of the data in the table. Then write a few sentences that analyze the data. Step 1 Order the data from least to greatest. 41 51 52 53 55 60 65 65 67 68 70 72 Step 2 Draw a vertical line and write the tens digits from least to greatest to the left of the line. Step 3 Write the ones digits to the right of the line with the corresponding stems.
In this data set, the tens digits form the stems.
⎧ ⎨ ⎩
Stem 4 5 6 7
Leaf 1 1235 05578 02
⎫ ⎬ ⎭
Money Earned Mowing Lawn ($) 60 55 53 41 67 72 65 68 65 70 52 51
The ones digits of the data form the leaves.
6|5 = $65 Key
even if it repeats.
Step 4 Include a key that explains the stems and leaves. By looking at the plot, it is easy to see that the least amount of money earned was $41 and the greatest amount was $72. You can also see that most of the data fall between $51 and $68. Exercise Make a stem-and-leaf plot for the set of data below. Write a few sentences that analyze the data. Points scored: 34 44 51 48 55 41 47 22 55
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North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Always write each leaf,
NAME
2D
DATE
PERIOD
Homework Practice
6.S.3.1, 6.S.3.2
Stem-and-Leaf Plots Make a stem-and-leaf plot for each set of data. 1. Minutes on the bus to school: 10, 5, 21, 30, 7, 12, 15, 21, 8, 12, 12, 20, 31, 10, 23, 31
2. Employee’s ages: 22, 52, 24, 19, 25, 36, 30, 32, 19, 26, 28, 33, 53, 24, 35, 26
SHOPPING For Exercises 3–5, use the stem-and-leaf plot
at the right that shows costs for various pairs of jeans. 3. How much is the most expensive pair of jeans? 4. How many pairs cost less than $20?
Stem 1 2 3 4
Leaf 667889999 135 223 2|3 = $23
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Write a sentence or two that analyzes the data.
6. Construct a stem-and-leaf plot for the set of test scores 81, 55, 55, 62, 73, 49, 56, 91, 55, 64, 72, 62, 64, 53, 56, and 57. Then write sentences explaining how a teacher might use the plot.
7. Display the amounts $104, $120, $99, $153, $122, $116, $114, $139, $102, $95, $123, $116, $152, $104 and $115 in a stem-and-leaf plot. (Hint: Use the hundreds and tens digits to form the stems.)
Chapter 2
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NAME
2D
DATE
PERIOD
Problem-Solving Practice
6.S.3.1, 6.S.3.2
Stem-and-Leaf Plots TRAFFIC For Exercises 1 and 2, use the table. For Exercises 3 and 4, use
the stem-and-leaf plot. Number of Trucks Passing Through the Intersection Each Hour 5 15 6 42 34 28 19 18 19 22 23 21 32 26 34 19 29 21 10 6 8 40 14 17
Stem 1 2 3 4 5
Leaf 89 489 3444 2555578 00334667 3|4 = 34 birds
1. Mr. Chin did a traffic survey. He wrote down the number of trucks that passed through an intersection each hour. Make a stem-and-leaf plot of his data.
2. Refer to your stem-and-leaf plot from Exercise 1. Mr. Chin needs to know the range of trucks passing through the intersection in one hour into which the greatest number of trucks fall.
3. What is the least number of birds at the watering hole in one hour? What is the greatest number?
4. What is the most frequent number of birds to be at the watering hole in one hour?
5. RVs Make a stem-and-leaf plot for the number of RVs Mr. Chin counted in 12 hours: 3, 4, 9, 13, 7, 9, 8, 5, 4, 6, 1, 11.
6. RVs Write a few sentences that analyze the RV data for Mr. Chin’s report in Exercise 5.
North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
32
Number of Birds at a Watering Hole Each Hour
NAME
2E
DATE
PERIOD
Explore Through Reading
6.S.3.1, 6.S.3.2
Line Plots and Dot Plots Get Ready for the Lesson Read the introduction at the top of page 96 in your textbook. Write your answers below. 1. How many of the animals have a life expectancy of 15 years? 2. How many animals have a life expectancy from 5 to 10 years, including 10? 3. What is the longest life expectancy represented? 4. What is the shortest life expectancy represented?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. How is a line plot similar to plotting points on a number line?
6. Describe one benefit of plotting data on a line plot.
7. Explain how you can use the shape of a line plot (clusters, peaks, and gaps) to describe the data.
Remember What You Learned 8. Work with a partner. Find a set of data from a survey, newspaper, or the Internet that can be used in a line plot. Create a line plot of the data along with two questions about the data. Switch your line plot and questions with another group. Use the line plots to answer the questions about the data.
Chapter 2
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NAME
2E
DATE
PERIOD
Study Guide
6.S.3.1, 6.S.3.2
Line Plots and Dot Plots A line plot is a diagram that shows the frequency of data on a number line. A line plot is created by drawing a number line and then placing an × above a data value each time that data occurs. If your line plot is made up of dots instead of “×”s, it is called a dot plot.
Example 1 Make a line plot of the data in the table at the right.
Time Spent Traveling to School (minutes) 5 6 3 10 12 15 5 10
5
8
12
5
5
8
Draw a number line. The smallest value is 3 minutes and the largest value is 15 minutes. So, you can use a scale of 0 to 15. Put an × above the number that represents the travel time of each student in the table. Be sure to include a title.
0
5
10
Example 2
15
How many students spend 5 minutes traveling to school each day?
Exercises AGES For Exercises 1–3, use the data below.
Ages of Lifeguards at Brookville Swim Club 16 18 16 20 22 18 18
17
18
25
17
19
1. Make a dot plot of the data.
2. Are there any peaks in the dot plot? What does this tell you? 3. What is the age difference between the oldest and youngest lifeguard at Brookville Swim Club?
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Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Locate 5 on the number line and count the number of ×’s above it. There are 5 students that travel 5 minutes to school each day.
NAME
2E
DATE
PERIOD
Homework Practice
6.S.3.1, 6.S.3.2
Line Plots and Dot Plots PRESIDENTS For Exercises 1–4, use the line plot below. It shows the ages of the first ten Presidents of the United States when they first took office. Age of First Ten Presidents at Inauguration
50
55
60
65
70
Years
Source: Time Almanac
1. How many Presidents were 54 when they took office? 2. Which age was most common among the first ten Presidents when they took office? How can you tell by looking at the line plot? 3. How many Presidents were in their 60s when they first took office?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. What is the difference between the age of the oldest and youngest President represented in the line plot? 5. EXERCISE Make a dot plot for the set of data. Interpret any clusters, peaks, or gaps.
Miles Walked this Week 16 21 11 24 8
14
16
11
21
10
8
14
11
24
12
18
18
27
11
14
BIRDS For Exercises 6 and 7, use the line plot below. It shows the number of mockingbirds each bird watcher saw on a bird walk.
20
25
30
35
40
45
50
6. How many more bird watchers saw 36 mockingbirds than saw 46 mockingbirds? 7. How many bird watchers are represented in the line plot? Chapter 2
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NAME
2E
DATE
PERIOD
Problem-Solving Practice
6.S.3.1, 6.S.3.2
Line Plots and Dot Plots ANIMALS For Exercises 1–4, use the dot plot below about the maximum speed of several animals. Maximum Speed of Animals (miles per hour)
30
40
45
50
55
60
65
70
1. How many animals represented in the dot plot have a maximum speed of 45 miles per hour?
2. What speed is most common that is represented in the dot plot?
3. What is the difference between the greatest speed and least speed represented in the dot plot?
4. Write one or two sentences that analyze the data.
5. LAWN SERVICE Make a line plot for the amount of money Kyle earned this summer with each lawn service job: $20, $25, $30, $15, $22, $25, $25, $30, $18, $15, $25, $20.
6. MAGAZINES Make a line plot for the selling price of several popular magazines: $3, $4, $5, $4, $3, $2, $4, $5, $3, $7, $9, $3, $4, $5.
North Carolina, Grade 6
Chapter 2
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36
35
NAME
2F
DATE
PERIOD
Explore Through Reading
6.S.3.2, 6.S.3.3
Mean Get Ready for the Lesson Complete the Mini Lab at the top of page 102 in your textbook. Write your answers below. 1. On average, how many inches did it snow per day in five days? Explain your reasoning. 2. Suppose on the sixth day it snowed 9 inches. If you moved the cubes again, how many cubes would be in each stack?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Look up the word mean in a dictionary. Write the meaning that fits the way the word is used in this lesson.
Look at the paragraph below the activity at the top of page 102 in your textbook. A number that helps describe all of the data in a data set is an average. An average is also referred to as a measure of central tendency. 4. Is the mean a good measure of central tendency when there is no outlier? Give an example.
5. Is the mean a good measure of central tendency when there is an outlier? Give an example.
Remember What You Learned 6. Explain one problem with using the mean as a measure of central tendency.
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NAME
2F
DATE
PERIOD
Study Guide
6.S.3.2, 6.S.3.3
Mean The mean is the most common measure of central tendency. It is an average, so it describes all of the data in a data set.
Example 1 The picture graph shows the number of members on four different swim teams. Find the mean number of members for the four different swim teams.
Swim Team Members Amberly Carlton
Simplify an expression. mean =
___
9 + 11 + 6 + 10 4
Hamilton
36 or 9 =_
Westhigh
4
A set of data may contain very high or very low values. These values are called outliers.
Example 2 Find the mean for the snowfall data with and without the outlier. Then tell how the outlier affects the mean of the data.
Month Snowfall (in.) Nov. 20 Dec. 19 Jan. 20 Feb. 17 Mar. 4
Compared to the other values, 4 inches is low. So, it is an outlier.
mean =
____
20 + 19 + 20 + 17 + 4 5
80 or 16 =_ 5
mean without outlier mean =
____
20 + 19 + 20 + 17 4
76 =_ or 19 4
With the outlier, the mean is less than the values of most of the data. Without the outlier, the mean is close in value to the data. Exercises SHOPPING For Exercises 1–3, use the bar graph
Jacket Prices
at the right.
2. Which jacket price is an outlier? 3. Find the mean of the data if the outlier is not included.
Price ($)
1. Find the mean of the data.
30 25 20 15 10 5 0
22
25
28 21 9
A
B
C
D
E
Jacket
4. How does the outlier affect the mean of the data?
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North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
mean with outlier
NAME
2F
DATE
PERIOD
Homework Practice
6.S.3.2, 6.S.3.3
Mean Find the mean of the data represented in each model. Number of Toys Collected
2.
Ling Kathy Lucita
Ages of Dance Instructors Ages (Years)
1.
32 30 28 26 24 22 20
30 26
21 Curtis
Terrell
NATURE For Exercises 3–6, use the table that shows
the heights of the tallest waterfalls along Oregon’s Columbia River Gorge. 3. Find the mean of the data. 4. Identify the outlier.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
25
23
5. Find the mean if Multnomah Falls is not included in the data set.
Joy
Ken
Nida David
Instructors
Falls Bridal Veil Horsetail Latourell Metlako Multnomah Wahkeena
Height (ft) 153 176 249 150 620 242
Source: U.S. Forest Service
6. How does the outlier affect the mean of the data?
GARDENING For Exercises 7–9, use the following information.
Alan earned $23, $26, $25, $24, $23, $24, $6, $24, and $23 gardening. 7. What is the mean of the amounts he earned? 8. Which amount is an outlier? 9. How does the outlier affect the mean of the data?
Find the mean for number of cans collected. Explain the method you used. 10. 57, 59, 60, 58, 58, 56 Chapter 2
North Carolina, Grade 6
39
NAME
2F
DATE
Problem-Solving Practice
PERIOD
6.S.3.2, 6.S.3.3
Mean ANIMALS For Exercises 1–3, use the table about bears.
Bear Alaskan Brown Black Grizzly Polar
1. You are writing a report on bears. You are analyzing the data on heights and weights in the table above. First look for outliers. Identify the outlier for the height data. Identify the outlier for the weight data.
2. Find the mean of the bear weight data with and without the outlier.
3. Describe how the outlier affects the mean of the bear weight data.
4. WORK Carlos earned $23, $29, $25, $16, and $17 working at an ice cream shop after school. What is the mean amount he earned?
5. CARS The cost of a tank of gas at nine different gas stations is shown below. What was the mean cost of a tank of gas?
6. SCHOOL Sally received scores on math quizzes as shown below. Find her mean score with and without both outliers.
Cost of Gas: $17, $18, $22, $15, $17, $16, $25, $21, and $20
Quiz Scores: 84, 85, 91, 81, 52, 92, 99, 91, and 45
North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
40
Average Height (ft) Average Weight (lb) 8 1,500 6 338 7 588 7 850
NAME
2G
DATE
PERIOD
Explore Through Reading
6.S.3.2, 6.S.3.3
Median, Mode, and Range Get Ready for the Lesson Complete the activity at the top of page 108 in your textbook. Write your answers below. 1. Order the data from least to greatest. Which piece of data is in the middle of this list? 2. Compare this number to the mean of the data.
Read the Lesson 3. How are mean, median, and mode similar? How are they different?
Look at Example 4 on page 110.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. How would you find the average of the data? What is another term for the average of the data?
5. What is causing the mean to be so high?
6. If there were two deserts of 250,000 square miles, how would this affect the mean?
7. Does this example illustrate the statement, “Some averages may describe a data set better than other averages”?
Remember What You Learned 8. You may already know that a median strip refers to the concrete or landscaped divider that runs down the center of many roads. How does this idea of median relate to the meaning of median in this lesson?
Chapter 2
North Carolina, Grade 6
41
NAME
2G
DATE
PERIOD
Study Guide
6.S.3.2, 6.S.3.3
Median, Mode, and Range The median is the middle number of the data put in order, or the mean of the middle two numbers. The mode is the number or numbers that occur most often.
Example 1 The table shows the costs of seven different books. Find the mean, median, and mode of the data. mean:
Book Cost ($) 22 13 11 16 14 14 16
22 + 13 + 11 + 16 + 14 + 13 + 16 105 ______ =_ or 15 7
7
To find the median, write the data in order from least to greatest. median: 11, 13, 13, 14, 16, 16, 22 To find the mode, find the number or numbers that occur most often. mode: 11, 13, 13, 14, 16, 16, 22 The mean is $15. The median is $14. There are two modes, $13 and $16. Whereas the measures of central tendency describe the average of a set of data, the range of a set of data describes how the data vary.
Example 2 Find the range of the data in the stem-and-leaf plot. Then write a sentence describing how the data vary. The greatest value is 63. The least value is 32. So, the range is 63° - 32° or 31°. The range is large. It tells us that the data vary greatly in value.
Leaf 2 0 05 03 3|2 = 32°
Exercises Find the mean, median, mode, and range of each set of data. 1. hours worked: 14, 13, 14, 16, 8
Quiz Scores
3. 100
Score
80
4.
Snowfall (inches) 3 3 3 3 3 3 3 3 3 3
86
80
72
2. points scored by football team: 29, 31, 14, 21, 31, 22, 20
72
68
60
3
60
0
40
1
2
3
4
5
6
7
8
9 10
20
42
ka ra Ta
an
s cu ar
Ry
a
North Carolina, Grade 6
M
n
ish Le
ia Br
Ab i
ga
il
0
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stem 3 4 5 6
NAME
2G
DATE
PERIOD
Homework Practice
6.S.3.2, 6.S.3.3
Median, Mode, and Range Find the median, mode, and range for each set of data. 1. minutes spent practicing violin: 25, 15, 30, 25, 20, 15, 24
2. snow in inches: 40, 28, 24, 37, 43, 26, 30, 36
Find the mean, median, mode, and range of the data represented in each statistical graph.
Student’s Favorite Music
6.
4
0
1
2
3
4
5
6
7
Day
WEATHER For Exercises 7–9, refer to the table at the right.
7. Compare the median low temperatures.
al sic as
ue Bl
0
s
2
11
er
6
11
th
8
19 15
O
10
27
25
30 25 20 15 10 5 0
ae
Number of Students
12
Laps Swam
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
14
gg
Kai-Yo’s Swimming Schedule
5.
zz
45
Re
40
Leaf 1244 24 134777788 223 012456 5|4 = $54
Ja
35
Stem 4 5 6 7 8
try
3 3
4.
un
30
3 333 333
Co
3 3 3
3 3
Cl
3.
Type of Music
Daily Low Temperatures (°F) Charleston Atlanta 33 34 33 35 48 41 43 40 36 35 34 45 35 37
8. Find the range for each data set. 9. Write a statement that compares the daily low temperatures for the two cities.
Chapter 2
North Carolina, Grade 6
43
NAME
2G
DATE
Problem-Solving Practice
PERIOD
6.S.3.2, 6.S.3.3
Median, Mode, and Range SCIENCE For Exercises 1–3, use Table A. For Exercises 4–6, use Table B.
Table A shows the number of days it took for some seeds to germinate after planting. Table B shows how tall the plants were after 60 days. Table B
Number of Days for Seeds to Germinate 15 20 30 15 16 9 21 21 15
Height (in.) of Plants After 60 Days 17 19 13 17 20 15 17 21 14
1. Refer to Table A. You are doing some experiments with germinating seeds. You are preparing a report on your findings to a seed company. What are the mean, median, and mode of the data?
2. Use your answer from Exercise 1. Which measure of central tendency best describes the data? Explain.
3. What is the range of the seed germination data? Describe how the data vary.
4. What are the mean, median, and mode of the plant height data?
5. Refer to your answer in Exercise 4. Which measure of central tendency best describes the data? Explain.
6. What is the range of the plant height data? Describe how the data vary.
North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
44
Table A
NAME
2H
DATE
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Study Guide
6.S.3.4
Interpret Data Data can be represented graphically using displays or numerically using measures of center and variability. One way in which information in a data set can be interpreted is in terms of supporting and refuting statements about the data group.
Example 1 SURVEYS Lamar surveyed the boys and girls in his middle school about their participation in after-school activities. The results are shown in the tables below. Boys Number of Number of Activities Students 0 10 1 21 2 12 3 or more 6
Girls Number of Number of Activities Students 0 15 1 30 2 9 3 or more 10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lamar concluded that more girls than boys participate in after-school activities. Explain how the data could refute his conclusion. The percent of boys who participate in at least one after-school activity is 39 out of 49 or about 80%. The percent of girls who participate is 49 out of 64 or about 77%. A greater percentage of boys participate. Example 2 SCHOOL On the first quiz in Ms. Hill’s science class, the median score was 80.2, with scores ranging from 61 to 90. The scores on the second quiz are shown below. 78, 73, 80, 91, 62, 63, 88, 91, 94, 84, 69, 70, 93, 75, 78, 85, 81 Mrs. Hill thought that the students performed better on the second quiz. Explain how the data could support her conclusion. On the first quiz, the lowest score was 61 and the highest score was 90. On the second quiz, the lowest score was 62 and highest score was 94. Exercises 1. Explain how the data in Example 1 could support Lamar’s conclusion.
2. Explain how the data in Example 2 could refute Mrs. Hill’s conclusion.
Chapter 2
North Carolina, Grade 6
45
NAME
2H
DATE
PERIOD
Skills Practice
6.S.3.4
Interpret Data WEATHER Annika researched the snowfall totals for three winter
seasons. Her results are shown in the graph at the right. Snowfall Totals Snowfall (in.)
1. Annika said that December is the month with the most snowfall. Use the information in the graph to support Annika’s conclusion.
15 10 5 0
14 9
8
12
10
8
4
6
4.5
Winter 1 Winter 2 Winter 3
Season
2. Annika’s cousin said that January is the month with the most snowfall. Use the information in the graph to support Annika’s cousin’s conclusion.
FOOD Grocery store customers
were asked to choose their favorite cereals in a taste test. The results are shown in the table at the right.
Dec
Jan
Feb
Cereal Taste Test Results Cereal Cereal A Cereal B Cereal C Number of People 7 5 4
4. A grocery store worker said that one less person preferred Cereal C than Cereal B. Use the information in the table to support the clerk’s conclusion.
5. Write a statement comparing the number of people who preferred Cereals A and C that can be supported using the information in the table.
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North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. A grocery store worker said that twice as many people preferred Cereal A than Cereal B. Use the information in the table to refute the clerk’s conclusion.
NAME
2H
DATE
PERIOD
Homework Practice
6.S.3.4
Interpret Data TRAVEL The graph below shows the cumulative distance traveled by
the Gonzalez family during the family vacation.
Cumulative Distance
Gonzalez Family Vacation 1,100 1,000 900 800 700 600 500 400 300 200 100 0
1,050 700 700 670 370 220 100 1 2 3 4 5 6 7 8
Day
1. Mr. Gonzalez said that the family traveled the farthest on Day 4. Use the information in the graph to refute his conclusion.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Mrs. Gonzalez said that there was one day that the family did not travel. Use the information in the graph to support her conclusion.
3. Write a statement about the Gonzalez family vacation that can be supported using the information in the graph.
SPORTS The scores for ten games during the Fort Hayes basketball
season are shown in the table.
opponent Fort Hayes
Fort Hayes Basketball Scores 1 2 3 4 5 6 7 40 35 29 53 38 24 36 43 39 33 39 45 46 32
8 35 40
9 28 31
10 34 37
4. At the team banquet, one of the players said that the team won all but one game. Use information from the table to refute the player’s claim. 5. Coach Singh said that the Fort Hayes team outscored its opponents. Use information from the table to support the coach’s claim. 6. Write a statement about the Fort Hayes basketball season that can be refuted using the information in the table.
Chapter 2
North Carolina, Grade 6
47
NAME
2H
DATE
PERIOD
Problem-Solving Practice
6.S.3.4
Interpret Data MOVIES The tables show the ages of people viewing matinee screenings of two
movies. Use the information in the tables for Exercises 1–4. Ages of People Viewing Movie A 10 40 8 11 9 7 34 10 9 12 19 37 29 8 10 11 38 9 7 9 1. Use the information in the tables to support the following statement.
Ages of People Viewing Movie B 72 60 58 46 79 47 55 64 69 49 63 72 68 51 64 75 60 2. Use the information in the tables to refute the following statement.
The Movie A audience is younger than The Movie B audience.
The range of the ages of people viewing Movie B is greater than the ages of people viewing Movie A.
3. Write a statement about the matinee audiences that can be supported using the information in the tables.
4. Write a statement about the matinee audiences that can be refuted using the information in the tables.
The shelter had more dogs available for adoption than cats.
26
30
Number
5. Use the information in the graph to support the following statement.
Animals Available for Adoption 25 20 15 10
21
18 14
12 13
14
10
5 0
June
July
August September
Month Dogs
Cats
6. Write a statement about the number of dogs and cats available for adoption that can be refuted using the information in the graph.
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North Carolina, Grade 6
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
PETS The graph shows the number of dogs and cats available for adoption at a shelter over a four-month time period. Use the information in the graph for Exercises 5 and 6.
NAME
2I
DATE
PERIOD
Explore Through Reading
6.N.3.1
Integers and Graphing Get Ready for the Lesson Read the introduction at the top of page 121 in your textbook. Write your answers below. 1. What number represents owing 5 dollars? What number represents having 8 dollars left? 2. Who has the most money left? Who owes the most?
Read the Lesson 3. Write an example of a situation that a positive number could represent.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Write an example of a situation that a negative number could represent.
5. In the number lines shown in this lesson, how is “continues without end” indicated?
6. How do values change as you move from left to right on a number line?
Remember What You Learned 7. Antonyms are two words that have opposite meanings, such as cold and hot. Integers can be described by the antonyms negative or positive or as being above zero or below zero. Make a table of antonyms that describe situations involving negative and positive integers. Negative Integer loss
Chapter 2
Positive Integer gain
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NAME
2I
DATE
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Study Guide
6.N.3.1
Integers and Graphing Negative numbers represent data that are less than 0. A negative number is written with a - sign. Positive numbers represent data that are greater than 0. Positive numbers are written with a + sign or no sign at all. Opposites are numbers that are the same distance from zero on a number line, but in opposite directions. The set of positive whole numbers, their opposites, and zero are called integers.
Example 1 Write an integer to show 3 degrees below zero. Then graph the integer on a number line. Numbers below zero are negative numbers. The integer is -3. Draw a number line. Then draw a dot at the location that represents -3. 26 25 24 23 22 21 0
Example 2
1
2
3
4
5
6
Make a line plot of the data represented in the table.
Draw a number line. Put an × above the number that represents each score in the table. Rachel’s Summer Golf Scores 3 3 3 3 3 3 3 3 3 3 3 3 1
2
3
4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
25 24 23 22 21 0
Rachel’s Summer Golf Scores 0 +3 -4 -2 0 +1 +3 -4 +1 -5 -2 +1
5
Exercises Write an integer to represent each piece of data. Then graph the integer on the number line. 2. a gain of 2 points
1. 4 degrees below zero 26 25 24 23 22 21 0
1
2
3
4
5
6
3. BOOKS The table shows the change in the ranking from the previous week of the top ten best-selling novels. Make a line plot of the data. Novel Change in Ranking
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North Carolina, Grade 6
A +3
B -2
C 0
D +1
E -2
F 0
G H I +2 - 4 +1
J -2
Chapter 2
NAME
2I
DATE
PERIOD
Homework Practice
6.N.3.1
Integers and Graphing Write an integer to represent each situation. 1. Bill drove 25 miles toward Tampa.
2. Susan lost $4.
3. Joe walked down 6 flights of stairs.
4. The baby gained 8 pounds.
Draw a number line from -10 to 10. Then graph each integer on the number line. 5. 2 9. -7
6. 6 10. -4
7. 10 11. -9
8. 8 12. -3
15. -2 19. +10
16. +9 20. -7
Write the opposite of each integer. 13. +8 17. -11
14. -5 18. +21
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
21. SCIENCE The average daytime surface temperature on the Moon is 260°F. Represent this temperature as an integer. 22. GEOGRAPHY The Salton Sea is a lake at 227 feet below sea level. Represent this altitude as an integer. 23. WEATHER The table below shows the extreme low temperatures for select cities. Make a line plot of the data. Then explain how the line plot can be used to determine whether more cities had extremes lower than zero degrees or greater than zero degrees. Extreme Low Temperatures by City City Temp. °F City Mobile, AL 3 Boston, MA Wilmington, DE Jackson, MS -14 Jacksonville, FL 7 Raleigh, NC Savannah, GA 3 Portland, OR New Orleans, LA 11 Philadelphia, PA Baltimore, MD Charleston, SC -7
Temp. °F -12 2 -9 -3 -7 6
Source: The World Almanac
Chapter 2
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NAME
2I
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Problem-Solving Practice
6.N.3.1
Integers and Graphing 2. GEOGRAPHY Mt. Whitney in California is 14,494 feet above sea level. Write this number as an integer.
3. GEOGRAPHY Badwater in Death Valley is 282 feet below sea level. Write this number as an integer.
4. SCHOOL Dick forgot to put his name on his homework. His teacher deducts 5 points for papers turned in without names on them. So, Dick lost 5 points from his score. Write this number as an integer.
5. GEOGRAPHY Multnomah Falls in Oregon drops 620 feet from the top to the bottom. Suppose a log is carried by the water from the top to the bottom of the falls. Write the integer to describe the location of the log now.
6. TRAVEL The train left the station and traveled ahead on the tracks for 30 miles. Write an integer to describe the new location of the train from the station.
7. WEATHER The table shows the average normal January temperature of three cities in Alaska. Graph the temperatures on a number line.
8. GAMES The table below shows the number of points Chantal scored on each hand of a card game. Make a line plot of the data.
City Anchorage Barrow Fairbanks
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North Carolina, Grade 6
Temperature (°F) 15 -13 -10
+20 -5 +5
Points Scored 0 +5 -10 +5 +10 +10
Chapter 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. MONEY Katryn owes her father $25. Write this number as an integer.
NAME
3
DATE
PERIOD
Anticipation Guide Adding and Subtracting Decimals
STEP 1
Before you begin Chapter 3
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. The decimal 0.42 represents 42 hundredths. 2. 0.70 is greater than 0.7 because 70 is greater than 7. 3. On a number line, numbers to the right of zero are positive and numbers to the left of zero are negative. 4. To round a decimal to the hundredths place, look at the digit in the thousandths place. 5. The decimal 2.628 can be rounded to 2.63 or 2.6.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. To estimate the sum of two decimals, always round both decimals to the tenths place. 7. Only decimals to the same place value can be added or subtracted. 8. When solving math problems, estimation can be used when an exact answer is not necessary. 9. To multiply a decimal by a whole number, you must first rewrite the whole number as a decimal. 10. The solution to 3.5 × 4.62 will have three decimal places. 11. Before dividing by a decimal, change the divisor to a whole number. STEP 2
After you complete Chapter 3
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
Chapter 3
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NAME
3
DATE
PERIOD
Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Amber weighed three bags all containing different things. If Amber puts all three bags into a previously empty box, how much will the contents of the box weigh altogether?
2. The following illustration shows the town of Big Pony, Montana. If Eddie rides his bike from French Street to English Avenue, how much farther does he ride than his sister, who rides her bike from French Street to Spanish Circle? 4.1 miles 1.25 miles
Bag A 5.78 kg
Bag B 6.2 kg
Bag C 12.12 kg
French Street
Spanish Circle
English Avenue
A 3.85 miles
A 24.1 kg
B 2.85 miles
B 18.52 kg
C 1.85 miles
C 24.11 kg
D 3.15 miles
D 23.92 kg
Solution
Solution 1. Hint: Remember to line up the decimals points when you add and subtract decimals! 1 1
5.78 6.20 + 12.12 ____ 24.10
← Insert a zero to help you add
3 1010
24.10 kg is equivalent to 24.1 kg.
The answer is A.
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North Carolina, Grade 6
2. Hint: Remember to add zeros to the minuend (the number being subtracted from) if necessary to complete the subtraction problem. Also remember to borrow from the next greater place value when subtracting a larger number from a smaller number.
4.10 -1.25 ___ 2.85
← Insert a zero to help you subtract
The answer is B. Chapter 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fold here.
NAME
3A
DATE
PERIOD
Explore Through Reading
6.N.3.1
Comparing and Ordering Decimals Get Ready for the Lesson Read the introduction at the top of page 142 in your textbook. Write your answers below. 1. Which city has the longest subway system? Explain.
Read the Lesson For Exercises 2–4, refer to the paragraph above Example 2 on page 143. 2. What are equivalent decimals?
3. What does it mean to annex a zero in a decimal? What happens to the value of the decimal?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. List three decimals that are equivalent to 0.8.
5. Look at Example 2 on page 143. Why is annexing zeros used in ordering decimals?
6. What does the expression 7.6 < 7.8 mean?
7. What symbol would you use to compare 7.6 and 7.3? Explain.
Remember What You Learned 8. Explain how using a number line to compare decimals is similar to using a number line to compare whole numbers.
Chapter 3
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Study Guide
6.N.3.1
Comparing and Ordering Decimals Example 1
Use > or < to compare 68.563 and 68.5603. Then, starting at the left, find the first place the digits differ.
First, line up the decimal points.
Compare the digits.
Since 3 . 0,
3.0
68.563 . 68.5603
68.563 68.5603 So, 68.563 is greater than 68.5603. Example 2
Order 4.073, 4.73, 4.0073, and 4 from least to greatest.
First, line up the decimal points.
Annex zeros so that each has the same number of decimal places.
Use place value to compare
4.0730 4.7300 4.0073 4.0000
4.0000 4.0073 4.0730 4.7300
4.073 4.73 4.0073 4
and order the decimals.
Exercises Use >, <, or = to compare each pair of decimals. 1. 4.08
4. 50.031
4.080
50.030
2. 0.001
5. 7
0.01
7.0001
3. 23.659
6. 18.01
22.659
18.010
Order each set of decimals from least to greatest. 7. 0.006, 0.6, 0.060, 6
8. 456.73, 465.32, 456.37, 456.23
Order each set of decimals from greatest to least. 9. 3.01, 3.009, 3.09, 3.0001
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North Carolina, Grade 6
10. 45.303, 45.333, 45.03, 45.0003, 45.003
Chapter 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
The order from least to greatest is 4, 4.0073, 4.073, and 4.73.
NAME
3A
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Homework Practice
6.N.3.1
Comparing and Ordering Decimals Use >, <, or = to compare each pair of decimals. 1. 8.8 4. 5.10
8.80 5.01
2. 0.3
3.0
5. 4.42
3. 0.06
4.24
7. 0.305
0.315
8. 7.006
10. 91.77
91.770
11. 7.2953
7.060 7.2593
0.6
6. 0.009
0.9
9. 8.408
8.044
12. 0.0826
0.0286
Order each set of decimals from least to greatest. 13. 33.6, 34.01, 33.44, 34
14. 78.203, 78.34, 78.023, 78.23
Order each set of decimals from greatest to least.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
15. 8.7, 8.77, 8.07, 8.777
16. 26.0999, 26.199, 25.99, 26.1909
17. LIBRARY Books in the library are placed on shelves in order according to their Dewey Decimal numbers. Arrange these numbers in order from least to greatest.
Book Number 943.678 943.6 943.67
18. ANALYZE TABLES The following table shows the amount of money Sonia spent on lunch each day this week. Order the amounts from least to greatest and then find the median amount she spent on lunch. Day Amount Spent ($)
Chapter 3
Mon. 4.45
Tues. 4.39
Wed. 4.23
Thu. 4.53
Fri. 4.38
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6.N.3.1
(Use with Lesson 3A)
Comparing and Ordering Decimals Shade a hundred grid to show each decimal. Which decimal is greater? 1. 0.78
0.87
2. 0.65
is greater.
3. 0.3
0.41
is greater.
4. 0.98
0.47
is greater.
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0.9
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
is greater.
5. 0.5
0.49
is greater.
6. 0.09
0.63
is greater.
Chapter 3
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Explore Through Reading
6.N.2.1
Adding and Subtracting Decimals Get Ready for the Lesson Read the introduction at the top of page 156 in your textbook. Write your answers below. 1. Estimate the sum of the top two countries. 2. Add the digits in the same place-value position for the top two countries. 3. Compare the estimate with the actual sum. Place the decimal point in the sum. 4. Make a conjecture about how to add decimals.
Read the Lesson For Exercises 5–7 look at the paragraph just above Example 1 on page 156 in your textbook.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Before you add or subtract decimals, what do you need to do?
6. Then, starting on the right, what do you do next?
7. Why do you think the first sentence of that paragraph says “in the same place-value position”? Give an example.
8. In Examples 1–5 on pages 156–158 in your textbook, the first step is to estimate the sum or difference. How does the estimate help?
Remember What You Learned 9. Tell what steps you would use to evaluate the algebraic expression x + y if x = 3.4 and y = 5.68.
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Study Guide
6.N.2.1
Adding and Subtracting Decimals To add or subtract decimals, line up the decimal points then add or subtract digits in the same placevalue position. Estimate first so you know if your answer is reasonable.
Example 1
Find the sum of 61.32 + 8.26.
First, estimate the sum using front-end estimation. 61.32 + 8.26 → 61 + 8 = 69
61.32 + 8.26 69.58 Since the estimate is close, the answer is reasonable. Example 2
Find 2.65 - 0.2.
Estimate: 2.65 - 0.2 → 3 - 0 = 3
2.65 - 0.20 2.45
Annex a zero.
Since the estimate is close, the answer is reasonable. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Find each sum or difference. 1.
2.3 + 4.1
2.
$13.67 - 7.19
3.
0.0123 - 0.0028
4.
132.346 + 0.486
5.
113.7999 + 6.2001
6.
0.0058 - 0.0026
7.
$5.63 + 4.10
8.
5.00921 -4.00013
9. 0.2 + 5.64 + 9.005
11. 216.8 – 34.055
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10. 12.36 - 4.081
12. 4.62 + 3.415 + 2.4
Chapter 3
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Homework Practice
6.N.2.1
Adding and Subtracting Decimals Find each sum. 1. 5.4 + 6.5
2. 6.0 + 3.8
3. 3.65 + 4
4. 52.47 + 13.21
5. 91.64 + 19.5
6. 0.675 + 28
8. 69 - 12.88
9. 17.46 - 6.79
Find each difference. 7. 7.8 - 4.5
10. 74 - 59.29
11. 87.31 - 25.09
12. 19.75 - 12.98
ALGEBRA Evaluate each expression if a = 219.6 and b = 12.024.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. a - b
14. b + a
15. a - 13.45 - b
Find the value of each expression. 16. 4.3 + 6 × 7
17. 32 - 2.55
19. BIKE RIDING The table shows the distances the members of two teams rode their bicycles for charity. a. How many total miles did Lori’s team ride?
18. 19.7 - 42
Distance Ridden for Charity Lori’s Team Tati’s Team Lori 13.8 mi Tati 13.6 mi Marcus 11.8 mi
Luis
15.1 mi
Hassan 15.4 mi
b. How many more miles did Lori’s team ride than Tati’s team?
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PERIOD
6.N.2.1
Adding and Subtracting Decimals 2. MUSIC A piano solo on a CD is 5.33 minutes long. A guitar solo is 9.67 minutes long. How much longer is the guitar solo than the piano solo? First estimate the difference. Then find the actual difference.
3. WHALES The average length of a humpback whale is 13.7 meters. The average length of a killer whale is 6.85 meters. How much longer is the humpback whale than the killer whale?
4. GARDENING Alan is connecting three garden hoses to make one longer hose. The green hose is 6.25 feet long, the orange hose is 5.755 feet long, and the black hose is 6.5 feet long. First, estimate the total length. Then find the actual total length.
5. ASTRONOMY Distance in space can be measured in astronomical units, or AU. Jupiter is 5.2 AU from the Sun. Pluto is 39.223 AU from the Sun. How much closer to the Sun is Jupiter than Pluto?
6. ALGEBRA It is x miles from James City to Huntley and y miles from Huntley to Grover. How many miles is it from James City to Grover? To find out, evaluate x + y if x = 4.23 and y = 16.876.
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1. MICE The average length of the head and body of a western harvest mouse is 2.9 inches. The average length of the tail is 2.8 inches. First, estimate the total length of the mouse. Then find the actual total length.
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Explore Through Reading
6.N.1.1
Multiplying Decimals by Whole Numbers Get Ready for the Lesson Read the introduction at the top of page 163 in your textbook. Write your answers below. 1. Use the addition problem and the estimate to find 2 × $4.92. 2. Write an addition problem, an estimate, and a multiplication problem to find the total over 3 days, 4 days, and 5 days.
3. MAKE A CONJECTURE about how to find 5.35 × 4.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read the Lesson 4. When multiplying a whole number and a decimal, it is very important that the decimal point in the product is in the right place. What are two methods for determining the placement of the decimal point in the product?
5. If you place the decimal point in the product of a whole number and a decimal by counting decimal places, how is this done?
6. What does it mean to annex zeros in the product? Why is it sometimes necessary to do this?
Remember What You Learned 7. Work with a partner. Explain the difference between standard form and scientific notation, and give examples of each.
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Study Guide
6.N.1.1
Multiplying Decimals by Whole Numbers When you multiply a decimal by a whole number, you multiply the numbers as if you were multiplying all whole numbers. Then you use estimation or you count the number of decimal places to decide where to place the decimal point. If there are not enough decimal places in the product, annex zeros to the left.
Example 1
Find 6.25 × 5.
Method 1 Use estimation.
Method 2
Round 6.25 to 6.
6.25 × 5 ___ 31.25
6.25 × 5 → 6 × 5 or 30 12
6.25 × 5 ___ 31.25
Since the estimate is 30 place the decimal point after 31.
Example 2
Find 3 × 0.0047.
Count decimal places. There are two places to the right of the decimal point.
Count the same number of decimal places from right to left.
2
0.0047 × 3 ____ 0.0141
There are four decimal places.
Example 3
Find 6.3 × 1,000.
Method 1 Use paper and pencil.
Method 2
Use mental math.
1,000 × 6.3 3000 6000 6300.0
Move the decimal point to the right the same number of zeros that are in 1,000 or 3 places. 6.3 × 1,000 = 6,300
Exercises Multiply.
64
1. 8.03 × 3
2. 6 × 12.6
3. 2 × 0.012
4. 0.0008 × 9
5. 2.32 × 10
6. 6.8 × 100
7. 5.2 × 1000
8. 1.412 × 100
North Carolina, Grade 6
Chapter 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Annex a zero on the left of 141 to make four decimal places.
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Homework Practice
6.N.1.1
Multiplying Decimals by Whole Numbers Multiply. 1. 0.8 × 6
2. 0.7 × 4
3. 1.9 × 5
4. 3.4 × 9
5. 6 × 3.4
6. 5.2 × 9
7. 0.6 × 6
8. 4 × 0.8
9. 5 × 0.05
10. 3 × 0.029
11. 0.0027 × 15
12. 0.0186 × 92
ALGEBRA Evaluate each expression.
13. 5.02h if h = 36
14. 72.33j if j = 3
15. 21k if k = 24.09
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Multiply. 16. 4.23 × 100
17. 3.7 × 1,000
18. 2.6 × 10
19. 4.2 × 1,000
20. 1.23 × 100
21. 5.14 × 1,000
22. 6.7 × 10
23. 7.89 × 1,000
24. SHOPPING Basketballs sell for $27.99 each at the Super D and for $21.59 each at the Bargain Spot. If the coach buys a dozen basketballs, how much can he save by buying them at the Bargain Spot? Justify your answer.
25. SCHOOL Jaimie purchases 10 pencils at the school bookstore. They cost $0.30 each. How much did she spend on pencils?
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6.N.1.1
Multiplying Decimals by Whole Numbers 2. TIME Amanda works on a farm out in the hills. It takes her 2.25 hours to drive to town and back. She usually goes to town twice a week to get supplies. How much time does Amanda spend driving if she takes 8 trips to town each month?
3. EXERCISE The local health club is advertising a special for new members: no initiation fee to join and only $34.50 per month for the first year. If Andy joins the health club for one year, how much will he spend on membership?
4. BIKING In order to train for a crossstate biking trip, Julie rides her bike 34.75 miles five times a week. How many total miles does she ride each week?
5. MONEY David wants to buy 16 bolts from a bin at the hardware store. Each bolt costs $0.03. How much will David pay for the bolts?
6. INSECTS One wing of a Royal Moth is 0.75 inch across. How wide is the moth’s wingspan when both wings are open?
7. COSTUMES KJ is making costumes for this year’s samba parade. The pattern she is using calls for 2.125 yards of fabric for each costume. How many yards of fabric will she need to make 34 costumes?
8. POOL PASSES The girl scouts are going to the pool. It will cost them $2.50 per person to go and there are 10 people going. What will the total cost be?
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1. COOKING Norberto uses three 14.7 oz cans of chicken broth when he makes his delicious tortilla soup. How many total ounces of chicken broth does he use?
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Explore Through Reading
6.N.1.1
Multiplying Decimals Get Ready for the Lesson Read the introduction at the top of page 169 in your textbook. Write your answers below. 1. The average weight of each block is 2.5 tons. The expression 2.3 × 2.5 can be used to find the total weight, in millions of tons, of the blocks in the pyramid’s base. Estimate the product of 2.3 and 2.5. 2. Multiply 23 by 25. 3. MAKE A CONJECTURE about how you can use your answers in Exercises 2 and 3 to find the product of 2.3 and 2.5? 4. What is the total weight of the blocks in the pyramid’s base?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Use your conjecture in Exercise 3 to find 1.7 × 5.4. Explain each step.
Read the Lesson 6. When multiplying decimals, what is the relationship between the number of decimal places in each factor and the number of decimal places in the product?
7. Look at Exercises 1 and 2 above and the answers for these exercises. a. How is 25 related to 2.5 tons? b. How is 23 related to 2.3? c. What is the actual weight if 2.3 is multiplied by 2.5? d. How is 575 related to the actual weight of the blocks?
Remember What You Learned 8. In situations where you are multiplying decimals by whole numbers it is easy to think of the calculation as adding the same value multiple times. What does it mean to multiply decimals? Describe some situations where you would need to multiply decimals.
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Study Guide
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6.N.1.1
Multiplying Decimals When you multiply a decimal by a decimal, multiply the numbers as if you were multiplying all whole numbers. To decide where to place the decimal point, find the sum of the number of decimal places in each factor. The product has the same number of decimal places.
Example 1
Find 5.2 × 6.13.
Estimate: 5 × 6 or 30 5.2 × 6.13 ____ 156 52 312 ____ 31.876
one decimal place two decimal places
three decimal places
The product is 31.876. Compared to the estimate, the product is reasonable. Example 2
Evaluate 0.023t if t = 2.3.
0.023t = 0.023 × 2.3
three decimal places one decimal place
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.023 × 2.3 ___ ____ 69 46 0.0529
Replace t with 2.3.
Annex a zero to make four decimal places.
Exercises Multiply. 1. 7.2 × 2.1
2. 4.3 × 8.5
3. 2.64 × 1.4
4. 14.23 × 8.21
5. 5.01 × 11.6
6. 9.001 × 4.2
ALGEBRA Evaluate each expression if x = 5.07, y = 1.5, and z = 0.403.
7. 3.2x + y
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8. yz + x
9. z × 7.06 - y
Chapter 3
NAME
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DATE
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Homework Practice
6.N.1.1
Multiplying Decimals Multiply. 1. 0.3 × 0.9
2. 2.6 × 1.7
3. 1.09 × 5.4
4. 17.2 × 12.86
5. 0.56 × 0.03
6. 4.9 × 0.02
7. 2.07 × 2.008
8. 26.02 × 2.006
ALGEBRA Evaluate each expression if r = 0.034, s = 4.05, and t = 2.6.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. 5.027 + 4.68r
10. 2.9s - 3.7t
11. 4.13s + r
12. rst
13. MINING A mine produces 42.5 tons of coal per hour. How much coal will the mine produce in 9.5 hours?
14. SHOPPING Ms. Morgan bought 3.5 pounds of bananas at $0.51 a pound and 4.5 pounds of pineapple at $1.19 a pound. How much did she pay for the bananas and pineapple?
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6.N.1.1
Multiplying Decimals 2. GROCERY Iona’s favorite peaches are $2.50 per pound at the local farmers’ market. She bought 3.5 pounds of the peaches. How much did she spend?
3. SHOPPING Jennifer is buying new school clothes. The items she wants to buy add up to $132.50 before sales tax. Sales tax is calculated by multiplying the total amount by 0.08. What is the amount of sales tax for the items?
4. DRIVING Ana bought a van that holds 20.75 gallons of gas and gets an average of 15.5 miles per gallon. How many miles can she expect to go on a full tank?
5. INCOME Ishi makes $8.50 an hour rolling sushi at Kyoto Japanese Restaurant. His paycheck shows that he worked 20.88 hours over the past two weeks. How much did Ishi make before taxes?
6. TRAVEL Manny is on vacation in France. He rented a car to drive 233.3 kilometers from Paris to Brussels and wants to figure out the distance in miles. To convert from kilometers to miles, he needs to multiply the total kilometers by 0.62. How many miles will Manny drive?
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1. GIFTS Colin is filling 4.5 ounce bottles with lavender bubble bath that he made for gifts. He was able to fill 7.5 bottles. How many ounces of bubble bath did he make?
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Explore Through Reading
6.N.1.1
Dividing Decimals by Whole Numbers Get Ready for the Lesson Complete the Mini Lab at the top of page 173 in your textbook. Write your answers below. Use base-ten blocks to show each quotient. 1. 3.4 ÷ 2
2. 4.2 ÷ 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. 5.6 ÷ 4
Find each whole number quotient. 4. 34 ÷ 2
5. 42 ÷ 3
6. 56 ÷ 4
7. Compare and contrast the quotients in Exercises 1–3 with the quotients in Exercises 4–6.
8. MAKE A CONJECTURE Write a rule for dividing a decimal by a whole number.
Read the Lesson 9. In the equation 4.8 ÷ 8 = 0.6, how can you check to see if the division sentence is true? 10. Where do you place the decimal point in the quotient when dividing by a whole number?
Remember What You Learned 11. Work with a partner. Pretend your partner missed the class that covered this lesson. Explain to your partner the method for knowing where to place the decimal point when you are dividing with decimals. Chapter 3
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Study Guide
6.N.1.1
Dividing Decimals by Whole Numbers When you divide a decimal by a whole number, place the decimal point in the quotient above the decimal point in the dividend. Then divide as you do with whole numbers.
Example 1
Find 8.73 ÷ 9.
Estimate: 9 ÷ 9 = 1 0.97 9 8.73 -0 __ 87 -8 1 ___ 63 -63 ____ 0
Place the decimal point directly above the decimal point in the quotient.
Divide as with whole numbers.
8.73 ÷ 9 = 0.97 Compared to the estimate, the quotient is reasonable. Example 2
Find 8.58 ÷ 12.
Estimate: 10 ÷ 10 = 1 Place the decimal point. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.715 12 8.580 -8 4 ____ 18 -12 ____ 60 -60 _____ 0
Annex a zero to continue dividing.
8.58 ÷ 12 = 0.715 Compared to the estimate, the quotient is reasonable.
Exercises Divide.
72
1. 9.2 ÷ 4
2. 4.5 ÷ 5
3. 8.6 ÷ 2
4. 2.89 ÷ 4
5. 3.2 ÷ 4
6. 7.2 ÷ 3
7. 7.5 ÷ 5
8. 3.25 ÷ 5
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Homework Practice
6.N.1.1
Dividing Decimals by Whole Numbers Divide. Round to the nearest tenth if necessary. 1. 25.2 ÷ 4
2. 147.2 ÷ 8
3. 5.69 ÷ 7
4. 13.28 ÷ 3
5. 22.5 ÷ 15
6. 65.28 ÷ 12
7. 243.83 ÷ 32
8. 654.29 ÷ 19
9. WEATHER What is the average January precipitation in Arches National Park? Round to the nearest hundredth if necessary.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
January Precipitation in Arches National Park Year 1997 1998 1999 2000 2001 2002 2003 Precipitation (in.) 1.09 0.013 0.54 0.80 0.89 0.24 0.11
2004 0.16
Source: National Park Service
10. SHOPPING A 3-pack of boxes of juice costs $1.09. A 12-pack of boxes costs $4.39. A case of 24 boxes costs $8.79. Which is the best buy? Explain your reasoning.
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Problem-Solving Practice
6.N.1.1
Dividing Decimals by Whole Numbers 2. FOOD There are 25 servings in a 12.5 ounce bottle of olive oil. How many ounces are in a serving?
3. RUNNING Isabella has found that she stays the most fit by running various distances and terrains throughout the week. On Mondays she runs 2.5 miles, on Tuesdays 4.6 miles, on Thursdays 6.75 miles, and on Saturdays 4.8 miles. What is the average distance Isabella runs on each of the days that she runs? Round to the nearest hundredth of a mile.
4. BUSINESS Katherine spends $1,089.72 each month for rent and supplies to run her hair salon. If she charges $18 for a haircut, how many haircuts must Katherine do to cover her monthly expenses? Round to the nearest whole number.
5. CONSTRUCTION It took Steve and his construction crew 8 months to build a house. After expenses, he was left with $24,872.67 for himself. On average, how much did Steve make per month? Round to the nearest dollar.
6. GRADES Shane wants to figure out what grade he is getting in math. His test scores were 85.6, 78.5, 92.5, 67, and 83.7. What was his average test score? What grade will he receive? Grade A B C D F
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Average Score 90 – 100 80 – 89 70 – 79 60 – 69 50 – 59
Chapter 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. ENTERTAINMENT Frank, Gina, Judy, and Connie are splitting their dinner bill. After tip, the total is $30.08. How much does each owe if they split the bill four ways?
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Explore Through Reading
6.N.1.1
Dividing by Decimals Get Ready for the Lesson Complete the Mini Lab at the top of page 179 in your textbook. Write your answers below. Use a calculator to find each quotient. 1. Describe a pattern among the division problems and their quotients for each set.
2. Use the pattern in Set A to find 36 ÷ 0.0009 without a calculator. 3. Use the pattern in Set B to find 0.0036 ÷ 9 without a calculator. 4. Use the pattern in Set C to find 0.0036 ÷ 0.0009 without a calculator.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. How could you find 0.042 ÷ 0.07 without a calculator?
Read the Lesson 6. When dividing decimals, what happens to the decimal point in the divisor and the dividend when you multiply both by the same power of 10?
7. Without doing any dividing, describe what you must do to start dividing 0.07 by 1.5.
Remember What You Learned 8. Write a short song or come up with a clever saying that will help you remember that whatever change you make to the decimal point of the divisor you must also make to the decimal point of the dividend.
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Study Guide
6.N.1.1
Dividing by Decimals When you divide a decimal by a decimal, multiply both the divisor and the dividend by the same power of ten. Then divide as with whole numbers.
Example 1
Find 10.14 ÷ 5.2.
Estimate: 10 ÷ 5 = 2 Multiply by 10 to make a whole number.
1.95 52 101.40 - 52 494 - 468 260 - 260 0
5.2 10.14 Multiply by the same number, 10.
10.14 divided by 5.2 is 1.95. Check: 1.95 × 5.2 = 10.14 Example 2
Place the decimal point. Divide as with whole numbers.
Annex a zero to continue.
Compare to the estimate.
Find 4.09 ÷ 0.02.
Multiply each by 100.
204.5 2 409.0 -4 __ 00 -0 09 -8 10 - 10 0
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.02 4.00
Place the decimal point. Divide.
Write a zero in the dividend and continue to divide.
4.09 ÷ 0.02 is 204.5. Check: 204.5 × 0.02 = 4.09 Exercises Divide.
76
1. 9.8 ÷ 1.4
2. 4.41 ÷ 2.1
3. 16.848 ÷ 0.72
4. 8.652 ÷ 1.2
5. 0.5 ÷ 0.001
6. 9.594 ÷ 0.06
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6.N.1.1
Dividing the Decimals
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Divide. 1. 12.92 ÷ 3.4
2. 22.47 ÷ 0.7
3. 0.025 ÷ 0.5
4. 7.224 ÷ 0.08
5. 0.855 ÷ 9.5
6. 0.9 ÷ 0.12
7. 3.0084 ÷ 0.046
8. 0.0868 ÷ 0.007
9. WHALES After its first day of life, a baby blue whale started growing. It grew 47.075 inches. If the average baby blue whale grows at a rate of 1.5 inches a day, for how many days did the baby whale grow, to the nearest tenth of a day?
10. LIZARDS The two largest lizards in the United States are the Gila Monster and the Chuckwalla. The average Gila Monster is 0.608 meter long. The average Chuckwalla is 0.395 meters long. How many times longer is the Gila Monster than the Chuckwalla to the nearest hundredth?
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6.N.1.1
Dividing by Decimals MARATHON For Exercises 1 and 2, use the table that shows course
records for the Boston Marathon. Course Records for the Boston Marathon Division Record-holder Year Time (hours) Men’s Open Cosmas Ndeti 1994 2.121 Women’s Open Margaret Okayo 2002 2.345 Men’s Wheelchair Ernst Van Dyk 2004 1.305 Women’s Jean Driscoll 1994 1.523 Wheelchair
2. To the nearest hundredth, how many times greater was the men’s open time than the women’s wheelchair time?
3. DRIVING The Martinez family drove 48.7 miles to the river. It took them 1.2 hours to get there. How fast did they drive? Round to the nearest whole number.
4. SHOPPING Nikki is buying some refrigerator magnets for her friends. Her total bill is $16.80. If magnets are $0.80 each, how many magnets is she buying?
5. SCALE MODEL Matt is making a scale model of a building. The model is 3.4 feet tall. The actual building is 41.48 feet tall. How many times smaller is the model than the actual building?
6. COOKING Yori has 14.25 cups of cupcake batter. If each cupcake uses 0.75 cup of batter, how many cupcakes can Yori make?
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1. The Boston Marathon is 26.2 miles. Use the times shown in the table to calculate the miles per hour for each division winner. Round to the nearest thousandth.
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Anticipation Guide Fractions and Decimals
STEP 1
Before you begin Chapter 4
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. The greatest common factor of two numbers can be found by listing all factors of both numbers. 2. The greatest common factor of two numbers is always less than both numbers. 3. Two fractions are equivalent only if their numerators are the same and their denominators are the same. 4. A fraction is in simplest form only when the greatest common factor of the numerator and denominator is 1. 7 5. _ is an example of a mixed number.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
6. Improper fractions can be rewritten as mixed numbers. 7. A multiple of a number is always divisible by the number. 8. When comparing two fractions, the greater fraction is always the fraction with the greater denominator. 9. To write a fraction as a decimal, divide the denominator into the numerator. 10. To write the decimal 0.32 as a fraction, first write 32 over one thousand, then simplify. 11. Since 8 does not divide evenly into 7, it is not possible to 7 write _ as a decimal. 8
12. On the coordinate plane, the x-axis is horizontal and the y-axis is vertical. STEP 2
After you complete Chapter 4
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible. Chapter 4
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Which of the following choices is the lowest common multiple that can be used to add fractions with denominators of 16, 6, and 8? 3 5 1 _ +_ +_ 16
6
2. When changed to a decimal, which of the following fractions is written as 0.75? 1 A _ 2
3 B _
8
5
A 16
6 C _
B 32
8
1 D _
C 96
4
D 48
Solution
Solution
1. Hint: To find the least common multiple, list the multiples of each number until you find a common multiple.
2. Hint: In order to change a fraction to a decimal, you divide the numerator (top of the fraction) by the denominator (bottom of the fraction).
16: 16, 32, 48 A 1 ÷ 2 = 0.5 6: 6, 12, 18, 24, 30, 36, 42, 48
B 3 ÷ 5 = 0.6 C 6 ÷ 8 = 0.75
8: 8, 16, 24, 32, 40, 48
D 1 ÷ 4 = 0.25
48 is the least common multiple listed.
The answer is D.
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North Carolina, Grade 6
The answer is C. Chapter 4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fold here.
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4A
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PERIOD
Study Guide
6.S.2.2
Problem-Solving Investigation: Make an Organized List When solving problems, one strategy that is helpful is to make an organized list. A list of all the possible combinations based on the information in the problem will help you solve the problem. You can use the make an organized list strategy, along with the following four-step problem solving plan to solve a problem. 1 Understand – Read and get a general understanding of the problem. 2 Plan – Make a plan to solve the problem and estimate the solution. 3 Solve – Use your plan to solve the problem. 4 Check – Check the reasonableness of your solution.
Example 1 ELECTIONS Tyler, McKayla, and Kareem are running for student council office. The three positions they could be elected for are president, treasurer, and secretary. How many possible ways could the three of them be elected? Understand You know that there are three positions and three students to fill the positions. You need to know the number of possible arrangements for them to be elected. Plan
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Solve
Check
Make a list of all the different possible arrangements. Use T for Tyler, M for McKayla, and K for Kareem. President Treasurer Secretary
T M K
T K M
K M T
K T M
M T K
M K T
Check the answer by seeing if each student is accounted for in each situation.
Exercises SHOPPING Khuan has to stop by the photo store, the gas station, the grocery
store, and his grandmother’s house. How many different ways can Khuan make the stops?
Chapter 4
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Skills Practice
PERIOD
6.S.2.2
Problem-Solving Investigation: Make an Organized List Solve. Use the make an organized list strategy. 1. BACKPACKS A department store sells three different styles of backpacks. Each style comes in navy, black, or red. How many different backpacks are available?
2. MUSIC A popular band has two of their concerts each available on tape, CD, DVD, and VHS. How many different items do they have available for these two concerts?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. MANUFACTURING A candle factory makes 8 different candle scents available in a votive candle, pillar candle, or jar candle. How many combinations of scent and type of candle are possible?
4. AWARD CEREMONY For an awards ceremony, the school principal, vice principal, athletic director, and student council president are all sitting on the stage. How many arrangements are there for all of them to sit on the stage?
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Chapter 4
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Homework Practice
6.S.2.2
Problem-Solving Investigation: Make an Organized List Mixed Problem Solving Use the make an organized list strategy to solve Exercises 1 and 2.
5. FOOD Is $6 enough money to buy a head of lettuce for $0.99, two pounds of tomatoes for $2.38, and two pounds of avocados for $2.78?
1. FLAGS Randy wants to place the flag of each of 3 countries in a row on the wall for an international fair. How many arrangements are possible?
2. KITES A store sells animal kites, box kites, and diamond kites in four different colors. How many combinations of kite type and color are possible?
6. MONEY Nikki earns $45 a week pet sitting. How much does she earn each year?
Use any strategy to solve Exercises 3–7. Some strategies are shown below. Problem-Solving Strategies Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
• Make a table. • Guess and check.
3. SHIRTS A mail-order company sells 4 styles of shirts in 6 different colors. How many combinations of style and color are possible?
4. PATTERNS If the pattern continues, how many small squares are in the fifth figure of this pattern?
Chapter 4
7. WRITING The number of magazine articles Nora sold in her first four years is shown. At this rate, how many articles will she sell in the fifth year?
Year 1 2 3 4 5
Number Sold 2 4 7 11 ?
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Problem-Solving Practice
6.S.2.2
Problem-Solving Investigation: Make an Organized List 1. GEOMETRY Find the difference in the areas of the square and rectangle.
3 ft 6 ft
Ice Cream Prices $1.05 One scoop Two scoops
$2.05
Ice cream sandwich
$0.99
Ice cream sundae
$2.79
3. FUND-RAISER The school band is selling cookie dough for a fund-raiser. A tub of cookie dough sells for $12, a pack of dry cookie mix sells for $5, and drop cookie dough sells for $15 a pack. If the school band sells 24 tubs, 15 dry mixes, and 30 packs of drop cookie dough, how much money will they collect?
4. SHOPPING At a sports store, Curtis bought some baseball card packs and some T-shirts. The baseball card packs cost $3 each and the T-shirts cost $8 each. If Curtis spent $30, how many baseball card packs and how many T-shirts did he buy?
5. LANGUAGE ARTS On Monday, 86 science fiction books were sold at a book sale. This is 8 more than twice the amount sold on Thursday. How many science fiction books were sold on Thursday?
6. PATTERNS What number is missing in the pattern . . . , 234, 345, ? , 567, . . . ?
North Carolina, Grade 6
Chapter 4
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84
8 ft
2. ICE CREAM Meagan is taking the kids she is babysitting to the local ice cream parlor. If she has $7, does she have enough money for two ice cream sandwiches, one sundae, and one scoop of ice cream?
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Explore Through Reading
6.N.3.1
Comparing and Ordering Fractions Get Ready for the Lesson Complete the Mini Lab at the top of page 220 in your textbook. Write your answers below. 1. Which fraction is greater? Use a model to determine which fraction is greater. 3 1 or _ 2. _ 2
7
2 1 3. _ or _ 6
9
3 4 4. _ or _ 8
7
Read the Lesson For Exercises 4–6, look at the key concept box on page 220. 4. How is LCM related to LCD?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. How can you find the least common denominator?
6. For the second step, it says to write an equivalent fraction for each fraction using the LCD. What are equivalent fractions?
7. When comparing numbers, you can use the signs <, >, and =. What does each sign mean
Remember What You Learned 8. Explain how to order fractions having different denominators from least to greatest.
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Study Guide
6.N.3.1
Comparing and Ordering Fractions To compare two fractions, • Find the least common denominator (LCD) of the fractions; that is, find the least common multiple of the denominators. • Write an equivalent fraction for each fraction using the LCD. • Compare the numerators.
Example 1
_ _5 true.
with <, >, or = to make 1
Replace
3
12
• The LCM of 3 and 12 is 12. So, the LCD is 12. • Rewrite each fraction with a denominator of 12. ×4 4 _1 = _, so _1 = - _ . 3
3
12
5 5 _ =_ 12
12
12
×4 5 5 4 1 • Now, compare. Since 4 < 5, _ <_ . So _ <_ . 12
__ _
12
3
_
12
Order 1 , 2 , 1 , and 3 from least to greatest.
Example 2
6
3
4
8
The LCD of the fractions is 24. So, rewrite each fraction with a denominator of 24. ×4 ×8 4 _1 = _, so _1 = _ . 6
24
16 . _2 = _, so _2 = _
24
3
24
×4
×8
×6
×3
24
4
24
9 . _3 = _, so _2 = _
6 _1 = _, so _1 = _ . 4
3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6
8
24
24
3
24
×3
×6
3 _ 1 _ , 1, _ , 2. The order of the fractions from least to greatest is _ 6 4 8 3
Exercises Replace each 5 1. _ 12
with <, >, or = to make a true sentence.
_3 8
6 2. _ 8
_3
2 3. _
4
7
_1 6
Order the fractions from least to greatest. 3 _ 1 _ , 3, _ , 1 4. _ 4 8 2 4
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5 _ 2 _ 5. _ , 1, _ , 7 3 6
18 9
5 _ 1 _ 6. _ , 5, _ , 5 2 6 8 12
Chapter 4
NAME
4B
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Homework Practice
6.N.3.1
Comparing and Ordering Fractions Replace each
with <, >, or = to make a true statement.
11 1. _
_2
2 4. 6 _
12 6_
3 5. 5 _
8 5_
2 6. _
18 7. _
2 1_
11 8. _
1 2_
34 9. _
21
3
14
1 2. _
3
2
15
4
7
12
9 _
3 3. 2 _
18
8
12
3
3
18
8 2_ 24
10 _ 18 5 1_ 6
Order the fractions from least to greatest. 3 _ 1 _ , 1, _ , 2 10. _
7 _ 5 _ 11. _ , 13 , _ , 2
5 4 2 5
9 18 6 3
3 _ 5 3 12. 6 _ , 61 , 6_ , 6_ 5
2
6
3 2 _ 4 13. 2 _ , 2 6 , 2_ , 2_
8
3
15
5
9
14. MUSIC Ramundus is making a xylophone. So far, he has bars that are
3 7 2 1_ feet, 1 _ feet, and 1 _ feet long. What is the length of the longest bar?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
12
3
19 11 15. DANCE Alana practiced dancing for _ hours on Monday, _ hours on 4
8
3 Wednesday, and 2 _ hours on Friday. On which day did she practice the 5
closest to 2 hours? Explain your reasoning.
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Problem-Solving Practice
6.N.3.1
Comparing and Ordering Fractions 1. SHOES Toya is looking in her closet. If
_
_
1 of her shoes are black and 2 are 3 5
brown, does she have more black shoes or more brown shoes? Explain.
3. WOODWORKING Isi drilled a hole that
_ _
is 5 inch wide. She has a screw that 9 is 5 inch wide. Is the hole wide enough 6 to fit the screw? Explain.
3 2. BUDGET Daniel spends _ of his money 7 4 of his money on food. on rent and _ 9
Does he spend more money on food or rent? Explain.
2 4. FOOD In a recent survey, _ of the 5 people surveyed said their favorite food 1 was pizza, _ said it was hot dogs, and
4 3 _ said it was popcorn. Which food was 10
favored by the greatest number of people? Explain.
_ _ _
1 inch wide. A silver paper clip is 6 3 inch wide, and a red paper clip is 8 1 inch wide. What color paper clip has 3
the smallest width? Explain.
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North Carolina, Grade 6
5 6. GUMBALLS A red gumball is _ inch 8
5 across. A green gumball is _ inch 6
7 across, and a blue gumball is _ inch 9
across. List the gumballs in order from smallest to largest.
Chapter 4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. OFFICE SUPPLIES A blue paper clip is
NAME
4C
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PERIOD
Explore Through Reading
6.N.3.2
Writing Decimals as Fractions Get Ready for the Lesson Read the introduction at the top of page 225 in your textbook. Write your answers below. 1. Write the word form of the decimal that represents the part of those surveyed who play a stringed instrument.
2. Write this decimal as a fraction.
3. Repeat Exercises 1 and 2 with each of the other decimals.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Exercises 4–6, look at Example 1 on page 225. 4. Why is the denominator of the fraction 10?
5. How does the example tell you to simplify the fraction?
6. What do the letters GCF stand for?
7. Look at Example 3 on page 226. What is the place value of the last decimal place? What does that mean when you go to write the corresponding fraction?
Remember What You Learned 8. Work with a partner. Each of you write several decimals with varying numbers of digits. Next, exchange papers and write the decimals as fractions. Then, exchange the papers again and check one another’s work.
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Study Guide
6.N.3.2
Writing Decimals as Fractions Decimals like 0.58, 0.12, and 0.08 can be written as fractions. To write a decimal as a fraction, you can follow these steps. 1. Identify the place value of the last decimal place. 2. Write the decimal as a fraction using the place value as the denominator.
Example 1 0.5
Write 0.5 as a fraction in simplest form. 5 =_
0.5 means five tenths.
10
_1 10 _
5 =_
Simplify. Divide the numerator and denominator by the GCF, 5.
2
_
1 So, in simplest form, 0.5 is _ .
= 1 2 Example 2 0.35
2
Write 0.35 as a fraction in simplest form. 35 =_
0.35 means 35 hundredths.
100
7 _ 100 _
35 =_
Simplify. Divide the numerator and denominator by the GCF, 5.
20
7 =_
Example 3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7 So, in simplest form, 0.35 is _ .
20
20
Write 4.375 as a mixed number in simplest form.
375 4.375 = 4 _
0.375 means 375 thousandths.
1,000 3 _
=
375 4_
_
3 = 4_
1,000 8
Simplify. Divide by the GCF, 125.
8
Exercises Write each decimal as a fraction or mixed number in simplest form. 1. 0.9
2. 0.8
3. 0.27
4. 0.75
5. 0.34
6. 0.125
7. 0.035
8. 0.008
9. 1.4 13. 12.05
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10. 3.6
11. 6.28
12. 2.65
14. 4.004
15. 23.205
16. 51.724 Chapter 4
NAME
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Homework Practice
6.N.3.2
Writing Decimals as Fractions Write each decimal as a fraction in simplest form. 1. 0.5
2. 0.8
3. 0.9
4. 0.75
5. 0.48
6. 0.72
7. 0.625
8. 0.065
9. 0.002
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each decimal as a mixed number in simplest form. 10. 3.6
11. 10.4
12. 2.11
13. 29.15
14. 7.202
15. 23.535
16. DISTANCE The library is 0.96 mile away from Theo’s home. Write this distance as a fraction in simplest form.
17. INSECTS A Japanese beetle has a length between 0.3 and 0.5 inch. Find two lengths that are within the given span. Write them as fractions in simplest form.
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Problem-Solving Practice
6.N.3.2
Writing Decimals as Fractions 2. EARTH Eighty percent of all life on Earth is below the ocean’s surface. Write 0.80 as a fraction in simplest form.
3. VENUS The planet Venus is 67.24 million miles away from the Sun. Write the decimal as a mixed number in simplest form.
4. SATURN If you weighed 138 pounds on Earth, you would weigh 128.34 pounds on Saturn. Write the weight on Saturn as a mixed number in simplest form.
5. MERCURY If you were 10 years old on Earth, you would be 41.494 years old on Mercury. Write the age on Mercury as a mixed number in simplest form.
6. INTERNET According to recent figures, 4.65 million people in the Middle East are online. Write the decimal as a mixed number in simplest form.
North Carolina, Grade 6
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92
1. FIELD TRIP About 0.4 of a biology class will be going on a field trip. Write the decimal as a fraction in simplest form.
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4D
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Explore Through Reading
6.N.3.2
Writing Fractions as Decimals Get Ready for the Lesson Read the introduction at the top of page 229 in your textbook. Write your answers below. 3 1. Write the decimal for _ . 10
1 2. Write the fraction equivalent to _ with a denominator of 10. 2
3. Write the decimal for the fraction you found in Exercise 2.
Read the Lesson 4. Look at Exercise 2 at the top of page 229. What do you need to do to the fraction in order to write the decimal?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Look at Example 1 on page 229. Why do you multiply both the numerator and denominator by 2?
6. Look at Example 3 on page 230. Why do you annex zeros in method 1?
7. Explain what the word annex means.
Remember What You Learned 8. Write the following fractions as decimals. First, use the paper and pencil method. Then, use a calculator and compare your answers. 3 _ 1 _ _ , 3 ,_ , 5 12 20 5 8
Chapter 4
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Study Guide
6.N.3.2
Writing Fractions as Decimals Fractions whose denominators are factors of 10, 100, or 1,000 can be written as decimals using equivalent fractions. Any fraction can also be written as a decimal by dividing the numerator by the denominator.
_
Write 3 as a decimal.
Example 1
5
Since 5 is a factor of 10, write an equivalent fraction with a denominator of 10. ×2 6 _3 = _ 5
10
×2 = 0.6 3 = 0.6. Therefore, _ 5
_
Write 3 as a decimal.
Example 2
8
Divide.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0.375 8 3.000 -2 4 ____ 60 -56 ____ 40 -40 ___ 0 3 = 0.375. Therefore, _ 8
Exercises Write each fraction or mixed number as a decimal. 3 1. _
3 2. _
1 3. _
3 4. _
1 5. _
1 6. 2 _
6 7. _
9 8. _
5 11. 3 _
9 12. 4 _
10
8
3 9. 1 _ 8
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4
4
5 10. 1 _ 8
4
20
16
5
25
20
Chapter 4
NAME
4D
DATE
PERIOD
Homework Practice
6.N.3.2
Writing Fractions as Decimals Write each fraction or mixed number as a decimal. 4 1. _
7 2. _
13 3. _
7 4. _
3 5. _
11 6. _
29 7. 9 _
29 8. 7 _
11 9. 4 _
5
20
8
16
40
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
32
80
Replace each 1 10. _
250
32
with <, >, or = to make a true sentence. 13 11. _
0.2
20
0.63
_3
12. 0.5
5
4 13. DISTANCE River Road is 11 _ miles long. Prairie Road is 14.9 miles long. 5 How much longer is Prairie Road than River Road?
14. ANIMALS The table shows lengths of different pond insects. Using decimals, name the insect having the smallest length and the insect having the greatest length.
Insect Length (in.)
Deer Fly
Pond Insects Spongilla Fly
Springtail
Water Treader
_2
3 _
3 _
_1
5
10
20
2
Source: Golden Nature Guide to Pond Life
Chapter 4
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Problem-Solving Practice
6.N.3.2
Writing Fractions as Decimals 1. PLANETS The planet Mercury is roughly
_2 the size of Earth. Write the fraction 5
5 3. HOMEWORK Miko has finished _ of 16
her homework. Write the fraction as a decimal.
8
3 hours. Write the mixed number as 3_ 4
a decimal.
3 7. HEIGHT Winona is 2 _ the height of 12
her little brother. Write the mixed number as a decimal.
7 4. EXERCISE Tate has been dancing for _ 10 of an hour. Write this fraction as a decimal.
3 6. COOKING A recipe calls for 2 _ cups of 4
milk. Write the mixed number as a decimal.
8. RECESS Jennifer has been spinning in 3 minutes. Write the circles for 4 _ 16
mixed number as a decimal.
Chapter 4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. SPORTS Charlie played tennis for
North Carolina, Grade 6
_5 inch wide. Write the marble’s width
as a decimal.
as a decimal.
96
2. MARBLES Lin has a marble that is
NAME
5
DATE
PERIOD
Anticipation Guide Operations with Fractions
STEP 1
Before you begin Chapter 5
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. If the numerator of a fraction is about half of the 1 denominator, the fraction can be rounded to _ .
2.
2
_1 can be rounded to 0 or _1 . 4
2
3. When adding two fractions, first add the numerators and then add the denominators.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Finding the least common denominator of two fractions is the same as finding the least common multiple of the denominators. 5. Before adding or subtracting mixed numbers, the numbers must be rewritten as improper fractions. 2 6. 3 _ can not be subtracted from 5 since 5 does not have a 3 fractional part. 1 7. 3 is a good estimate for _ × 19. 6
8. To multiply two mixed numbers, multiply the whole numbers, and then multiply the fractions. 5 7 4 2 9. To divide _ by _ , multiply _ by _ . 5
7
4
2
10. Before dividing two mixed numbers, rewrite both as improper fractions. STEP 2
After you complete Chapter 5
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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NAME
5
DATE
PERIOD
Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1 1. On Sunday, Billy ate _ of a pizza. On 6
2 of the pizza. Monday, he ate another _ 3
How much of the pizza remained for Tuesday?
2. Dennis is mixing together the ingredients for a recipe that calls for
1 1 4_ cups of flour and 1 _ cup of sugar. 2
4
How much more flour goes into the recipe than sugar? 1 A 3_ 2
3 B 2_ 4
2 C 5_ 6
1 D 3_
1 A _
4
6
1 B _ 3
6 C _ 9 6
Fold here. Solution
Solution
1. Hint: To find the sum of these fractions, you need to find the least common denominator. The amount of pizza Billy ate is
_1 + _2 = _1 + _4 or _5 . The amount left 6 3 6 6 6 6 over is a whole pizza ( _ ) minus the
amount eaten.
6
6
In order to subtract, the denominators in the fractions should be the same. 1 1 2 1 1 4_ - 1_ = 4_ - 1_ = 3_
_6 - _5 = _1 6
2. Hint: The denominators of the fractions should be the same in order to subtract the fraction. You can also change the mixed number to an improper fraction to make subtraction easier.
2
4
4
4
4
6
You can also used mixed numbers: 18 5 13 1 _9 - _5 = _ -_ =_ = 3_ 2
The answer is A.
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North Carolina, Grade 6
4
4
4
4
4
The answer is D. Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5 D _
NAME
5A
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PERIOD
Explore Through Reading
6.N.2.1
Adding and Subtracting Fractions with Like Denominators Get Ready for the Lesson Complete the Mini Lab at the top of page 256 in your textbook. Write your answers below. Find each sum using grid paper. 3 4 +_ 1. _ 12
12
1 1 2. _ +_ 6
6
3 5 3. _ +_ 10
10
4. What patterns do you notice with the numerators?
5. What patterns do you notice with the denominators? 3 1 6. Explain how you could find the sum of _ +_ without using grid paper.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8
8
Read the Lesson Look at the paragraph below the Mini Lab on page 256 in your textbook. 7. Write a definition for like fractions.
8. What meaning does your textbook give for denominator?
9. The units being added are twelfths. Write a fraction that indicates one twelfth.
Remember What You Learned 10. In your own words, explain how to add like fractions. Then explain how to subtract like fractions.
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Study Guide
6.N.2.1
Adding and Subtracting Fractions with Like Denominators Fractions with the same denominator are called like fractions. • To add like fractions, add the numerators. Use the same denominator in the sum. • To subtract like fractions, subtract the numerators. Use the same denominator in the difference. 3 3 Find the sum of _ and _ .
Example 1
5
1 1 Estimate _ +_ =1 2
3 5
5
3 5
+
2
3+3 _3 + _3 = _ 5 5 5 6 _ = 5 1 = 1_
Add the numerators.
1 15
Simplify. Write the improper fraction as a mixed number.
5
Compared to the estimate, the answer is reasonable.
_
_
4
4
Find the difference of 3 and 1 .
Example 2
Estimate 1 - 0 = 1
4
2
Subtract the numerators. Simplify.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3-1 _3 - _1 = _ 4 4 4 2 1 _ = or _
Compared to the estimate, the answer is reasonable. Exercises Add or subtract. Write in simplest form. 1 4 +_ 1. _
9 7 2. _ -_
9 5 3. _ +_
9 11 4. _ -_
5 4 5. _ +_
4 1 6. _ -_
7 5 7. _ +_
6 4 8. _ -_
3 3 9. _ +_
4 1 10. _ -_
5 1 11. _ +_
9
7
4
100
9
7
4
North Carolina, Grade 6
11
9
5
11
9
5
10
8
6
10
8
6
12
7
12
7
7 1 12. _ -_ 10
10
Chapter 5
NAME
5A
DATE
PERIOD
Homework Practice
6.N.2.1
Adding and Subtracting Fractions with Like Denominators Add or subtract. Write in simplest form. 3 6 +_ 1. _
2 4 2. _ +_
3 3 3. _ +_
2 2 4. _ +_
5 7 5. _ +_
7 11 6. _ +_
7 3 7. _ -_
3 1 8. _ -_
7
8
7
5
8
16
6 11 9. _ -_ 15
7
4
16
8
7 4 10. _ -_
15
9
5 6 1 13. _ +_ +_ 7
5
7
4
3
8
10
9 6 11. _ -_
9
11
9 9 3 14. _ +_ -_ 10
10
10
3
10
17 5 12. _ -_
11
18
18
7 5 11 15. _ -_ +_ 12
12
12
Write an addition or subtraction expression for each model. Then add or subtract.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16.
17.
18. WEATHER In January through March, Death Valley gets a total of about
6 21 _ inch of precipitation. In April through June, it gets a total of about _ 25
25
inch. How much more precipitation occurs in January through March?
19. ANALYZE GRAPHS What part of the school population likes basketball, baseball, or football? How much larger is this than the part of the student population that prefers soccer?
Brown Middle School's Favorite Sports
Football 3 12
Basketball 4 12
Soccer 3 12
Chapter 5
Baseball 2 12
North Carolina, Grade 6
101
NAME
DATE
Mini-Project
PERIOD
6.N.2.1
(Use with Lesson 5A)
Adding and Subtracting Fractions Shade each figure to model each fraction. Use the models to find the sum. 1.
5 _
4 _
+
16
=
16
1
2.
_3
5
_1
-
4
=
4
5
2
11 _ 20
3 _
-
=
20
2
4.
5
9 _
+
16
1
102
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3.
North Carolina, Grade 6
13 _ 16
=
5
Chapter 5
NAME
5B
DATE
PERIOD
Explore Through Reading
6.N.2.1
Adding and Subtracting Fractions with Unlike Denominators Get Ready for the Lesson Read the introduction at the top of page 263 in your textbook. Write your answers below. 1. Write each fraction in simplest form. 2. What fraction of one hour is equal to the sum of 15 minutes and 20 minutes? Write in simplest form. 1 1 1 3. Explain why _ hour + _ hour = _ hour. 6
3
2
7 1 1 4. Explain why _ hour + _ hour = _ hour. 12
2
12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read the Lesson 5. Look at the Key Concept box on page 263 in your textbook. What does it mean to rename a fraction? 6. What do the letters LCD stand for?
1 1 7. What is the LCD of _ and _ ? 6
4
Remember What You Learned 8. Work with a partner. Pretend you are a teacher. You are teaching your partner how to add and subtract fractions with unlike denominators.
3 1 Simplify _ +_ , showing and explaining the steps to your partner. Then 2 4 1 2 have your partner simplify _ -_ , showing and explaining each step. 2
Chapter 5
5
North Carolina, Grade 6
103
NAME
5B
DATE
PERIOD
Study Guide
6.N.2.1
Adding and Subtracting Fractions with Unlike Denominators To find the sum or difference of two fractions with unlike denominators, rename the fractions using the least common denominator (LCD). Then add or subtract and simplify.
Example 1
_ _
Find 1 + 5 . 3
6
5 1 and _ is 6. The LCD of _ 3
Write the problem.
6
Rename using the LCD, 6.
_1 3 _ +5
Add the fractions.
_2 6 5 +_ 6 __ _7 or 1 _1
1×2 2 _ =_ 3×2 6 5×1 _ _ + =5
6 __
6×1
6
6
Example 2
6
_ _
Find 2 - 1 . 3
4
2 1 and _ is 12. The LCD of _ 3
Write the problem.
4
Rename using the LCD, 12.
8 2×4 _ =_ 3×4 12 1×3 3 -_ =_
4 __
4×3
8 _ 12 3 -_ 12 ___ 5 _
12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
_2 3 _ -1
Subtract the fractions.
12
Example 3
_
_
2
5
Evaluate x - y if x = 1 and y = 2 .
1 2 -_ x-y=_
2 5 1×5 = - 2×2 2×5 5×2 5 4 = 10 10 1 = 10
_ _ _ _ _
1 2 Replace x with _ and y with _ . 2
5
1 2 Rename _ and _ using the LCD, 10. 2
5
Simplify. Subtract the numerators.
Exercises Add or subtract. Write in simplest form. 1 1 1. _ +_
2 1 2. _ -_
7 1 3. _ +_
9 3 4. _ -_
2 1 5. _ +_
5 1 6. _ -_
7 1 7. _ +_
4 1 8. _ -_
6
4
2
2
3
6
4
2
10
12
1 1 9. Evaluate x + y if x = _ and y = _ . 12
104
North Carolina, Grade 6
6
8
2
10
9
5
3
3 1 10. Evaluate a + b if a = _ and b = _ . 2
4
Chapter 5
NAME
5B
DATE
PERIOD
Homework Practice
6.N.2.1
Adding and Subtracting Fractions with Unlike Denominators Add or subtract. Write in simplest form. 1.
_3 4 _ +1
2.
_1 6 3 _ +
6.
6 1 9. _ +_
_3 4 _ +1
7.
10
7 _ 10 1 -_
4.
2 __
_3 5 _ -1
_6 7 _ -3
8.
4 __
9 3 10. _ +_
3
11 _ 12 2 -_
3 __
6 __
10 ___
7
3.
3 __
8 __
5.
_1 2 _ +1
5
4 __
3 11 11. _ -_ 12
7 1 12. _ -_
4
11
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ALGEBRA Evaluate each expression. 3 5 and b = _ 13. a + b if a = _ 5
9 5 14. c - d if c = _ and d = _
8
10
6
9 15. ANIMALS A newborn panda at the San Diego zoo grew about _ pound 16
5 pound the second week. How much more did the first week and about _ 8
the panda grow the second week? Justify your answer.
3 16. EXERCISES Every day Kim does leg muscle exercises for _ of an hour 7 2 and foot muscle exercises for _ of an hour. Which exercises does she 3
spend the most time doing and by how much?
Chapter 5
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105
NAME
5B
DATE
PERIOD
Problem-Solving Practice
6.N.2.1
Adding and Subtracting Fractions with Unlike Denominators BUSINESS For Exercises 1–4, use the table below. It lists the fractions of United States car sales held by several companies in a recent year.
Leading Car Sales in U.S. Company Fraction of Sales Company A
_1
Company B
4 _
Company C
_2
Company D
3 _
25 5 20
2. How much greater was the fraction of the market of Company A than of Company D?
3. How much more than Company A’s fraction of the market did Company C have?
4. Find the total fraction of the market that Company D and Company B hold together.
5. TRAVEL Gabriella’s travel shampoo
6. EXERCISE Bill and Andy were racing to see who could run the farthest in
2
leaving on vacation, she filled the bottle
5 5-minutes. Bill ran _ of a mile, and
1 cup of shampoo. How to the top with _
8 3 of a mile. How much Andy ran _
much shampoo was already in the bottle?
farther did Andy run than Bill?
8
North Carolina, Grade 6
4
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. What fraction of the U.S. sales did Company C and Company B hold together?
1 cup of shampoo. Before bottle holds _
106
5
NAME
5C
DATE
PERIOD
Explore Through Reading
6.N.2.1
Adding and Subtracting Mixed Numbers Get Ready for the Lesson Complete the Mini Lab at the top of page 270 in your textbook. Write your answers below. 1. How many whole paper plates can you make?
2. What fraction is represented by the leftover pieces?
Use paper plate models to find each sum or difference. 3 1 + 2_ 3. 1 _ 4
2
3 1 4. 2 _ - 1_ 4
4
2 1 5. 1 _ + 2_ 3
6
Read the Lesson Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. What is a mixed number? Give an example.
7. In Example 2 on page 271 in your textbook, the letters LCD are used. What does LCD stand for?
Remember What You Learned 8. In your own words, summarize how to add or subtract mixed numbers.
Chapter 5
North Carolina, Grade 6
107
NAME
5C
DATE
PERIOD
Study Guide
6.N.2.1
Adding and Subtracting Mixed Numbers To add or subtract mixed numbers: 1. Add or subtract the fractions. 2. Then add or subtract the whole numbers. 3. Rename and simplify if necessary.
_
_
3
4
Find 2 1 + 4 1 .
Example 1
1 1 The LCD of _ and _ is 12. 3
4
Write the problem.
1 2_
add the whole numbers.
_ _
4 2_
24 12 3×4 1×3 +4 = +43 12 4×3 ___ _____
_
3
Add the fractions. Then
using the LCD, 12.
1×4 2_ =
3 + 41 4 ___ 1 So, 2 _
Rename the fractions
_
12
3 + 4_ 12 ___ 7 6_ 12
7 + 4 _14 = 6 _ . 12
_
_
2
3
Find 6 1 - 2 1 .
Example 2
1 1 The LCD of _ and _ is 6. 2
3
_ _
Rename the fractions
Subtract the fractions. Then
using the LCD, 6.
subtract the whole numbers.
_ _
_ _
3 6_
63 61 × 3 = 6 2×3 1×2 -2 = - 22 6 3 × 2 _____ ___
61 2 - 21 3 ___
6
2 - 2_ 6 ___ _ 41 6
1 So, 6 _ - 2 _1 = 4 _1 . 2
3
6
Exercises Add or subtract. Write in simplest form. 1.
2 3_
2.
3 - 21 3 ___
_
108
3.
4 + 13 4 ___
2
North Carolina, Grade 6
1 5_
4.
2 + 41 3 ___
_
_
2 1 5. 3 _ - 1_ 3
_
43
2 1 6. 4 _ + 2_ 3
4
7 6_
8 - 31 2 ___
_
1 1 7. 5 _ - 2_ 3
4
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write the problem.
NAME
5C
DATE
PERIOD
Homework Practice
6.N.2.1
Adding and Subtracting Mixed Numbers Add or subtract. Write in simplest form. 1.
5.
5
2.
4 - 3_ 7 ___
3 9_
6.
4 - 23 8 ___
3.
3 - 2_ 8 ___
9 1 9. 5 _ + 3_ 2
2 6_
7.
3 - 11 6 ___
7 ___
1 8_
_
2 10 _
8.
4 + 24 5 ___
6
7
3 - 4_
3
7 + 8_
10 ___
5 1 11. 8 _ - 3_
8
5 8_
4
8 - 33 8 ___
_
5 5 10. 3 _ + 10 _ 6
7 7_
_
_
_
10
8
6 5 12. 9 _ - 2_
3
7
_
14
_
5 2 1 ALGEBRA. Evaluate each expression if a = 3 , b = 2 , and c = 1 . 6 3 4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. a + b
14. a + c
15. b - c
16. a - c
1 2 17. COOKING A punch recipe calls for 4 _ cups pineapple juice, 2 _ cups 4
3
1 cups cranberry juice. How much juice is needed to orange juice, and 3 _ 2
make the punch?
18. ANALYZE TABLES The wingspans of two butterflies and a moth are shown. How much greater is the longest wingspan than the shortest wingspan? Justify your answer.
Butterfly or Moth Wingspans Butterfly or Moth Width (in.) 3 American Snout 1_ 8 butterfly Garden Tiger Moth
13 1_ 16
Milbert’s Tortoiseshell butterfly
Chapter 5
3 1_ 4
North Carolina, Grade 6
109
NAME
5C
DATE
PERIOD
Problem-Solving Practice
6.N.2.1
Adding and Subtracting Mixed Numbers Solve. Write answers in simplest form. 2 1. SCHOOL Liwanu spent 2 _ hours on his 5
3 math homework and 1 _ hours on his 5
science homework. How much time did he spend doing math and science homework?
3 3. TRAVEL It usually takes Amalie 1 _ 4
hours to get to her aunt’s house. Due to Thanksgiving traffic, this year it took 1 3_ hours. How much longer did it take 3
this year?
8
much more wheat did he plant than corn?
4. COOKING Gina wants to make muffins. The recipe for blueberry muffins calls 3 for 2 _ cups of flour. The recipe for 4
1 cornmeal muffins calls for 1 _ cups of 3
3 cups of Paris powder. If José uses 5 _ 5
for a sculpture, how much plaster will he have left?
7. ANIMALS The average length of a
1 Rufous hummingbird is 3 _ inches. The 2
average length of a Broad-tailed
1 hummingbird is 4 _ inches. How much 2
shorter is the Rufous hummingbird?
5 6. BOOKS Kyle read 3 _ books and Jan 6
1 read 2 _ books. How many more books 3
did Kyle read than Jan?
8. RECYCLING The class collected 5 pounds of glass bottles and 9_ 7
1 pounds of aluminum cans. How 6_ 2
many pounds of glass and aluminum did the class collect in all?
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2
North Carolina, Grade 6
8
5 of wheat and 1 _ acres of corn. How
flour. How many more cups of flour would Gina need for blueberry muffins than corn muffins?
1 5. SCULPTURE José has 8 _ cups of Plaster
110
7 2. FARMING Mr. Garcia planted 4 _ acres
NAME
5D
DATE
PERIOD
Explore Through Reading
6.N.1.2
Multiplying Fractions Get Ready for the Lesson Complete the activity at the top of page 282 in your textbook. Write your answers below. 1 2 1. Refer to the model. What fraction represents _ ×_ ? 2
3
2. What is the relationship between the numerators and denominators of the factors and the numerator and denominator of the product?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
For Exercises 3 and 4, look at Example 3 and the sentence before it on page 283 in your textbook. 3. What must the numerator and denominator have in order to simplify before you multiply? 4. Why is it helpful to simplify before you multiply?
Remember What You Learned 5. Work with a partner. Look at each example on pages 282 and 283 in your textbook. Use a piece of paper to cover up the words that are beside the equations. Explain to your partner in your own words what is happening in each step. Then uncover the words and check.
Chapter 5
North Carolina, Grade 6
111
NAME
5D
DATE
PERIOD
Study Guide
6.N.1.2
Multiplying Fractions Type of Product
What to do
Example 8 2×4 _2 × _4 = _ =_
Multiply the numerators. Then multiply the denominators.
two fractions
3
Rename the whole number as an improper fraction. Multiply the fraction and a whole number numerators. Then multiply the denominators.
_ _
Find 2 × 3 .
Example 1
5
4
2×3 _2 × _3 = _ 5
4
6 3 =_ or _
_
9
11
1
11
11
1 × = _ 1 Estimate: _ 1 2
2
8 Write 8 as _ .
1
1
4×8 = _
Multiply.
9×1
Simplify. Compare to the estimate.
9
_ _
Find 2 × 3 . 5
8
1 × _ 1 = _ 1 Estimate: _ 2
2
4
1
2 ×3 _2 × _3 = __ 5
8
Divide both the numerator and denominator by the common factor, 2.
5×8 4 3 = 20
_
Simplify. Compare to the estimate.
Exercises Multiply. 5 1 ×_ 1. _
3 3 2. _ ×_
1 3. 4 × _
5 4. _ ×2
3 5. _ × 10
3 2 6. _ ×_
1 1 7. _ ×_
2 1 8. _ ×_
4
6
5
112
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7
3
4
8
5
7
7
12
9
2
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
32 5 =_ or 3 _
Example 3
11
2
9
9
3 3 6 18 7 _ ×6=_ ×_ =_ = 1_
1 × = Estimate: _ 8 4
Find 4 × 8.
_4 × 8 = _4 × _8 9
15
Simplify. Compare to the estimate.
10
Example 2
3×5
Multiply the numerators. Multiply the denominators.
5×4
20
5
NAME
5D
DATE
PERIOD
Homework Practice
6.N.1.2
Multiplying Fractions Multiply. 3 1 ×_ 1. _
7 1 2. _ ×_
3 1 3. _ ×_
2 2 4. _ ×_
1 5. _ × 11
1 6. _ × 12
5 7. _ × 21
3 8. _ × 10
1 4 9. _ ×_
7 4 11. _ ×_
3 5 12. _ ×_
4
3
5
8
9
8
10
1 1 1 13. _ ×_ ×_
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
5
21
8
ALGEBRA Evaluate each expression if a =
16. bc
4
5
3 3 2 14. _ ×_ ×_ 4
17. abc
4
2
4
3 4 10. _ ×_
3
2
3
6
9
3
5
12
2 12 1 15. _ ×_ ×_
3
3
17
4
_4 , b = _1 , and c = _2 . 5
2
7
3 18. ab + _ 5
19. PRESIDENTS By 2005, 42 different men had been President of the United 2 States. Of these men, _ had no children. How many presidents had no 21 children?
Chapter 5
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113
NAME
5D
DATE
PERIOD
Problem-Solving Practice
6.N.1.2
Multiplying Fractions COOKING For Exercises 1 and 2, use the recipe for chocolate frosting.
Chocolate Frosting Recipe ______________
_1 cup butter 3
2 ounces melted unsweetened chocolate 2 cups powdered sugar
_1 teaspoon vanilla 2
2 tablespoons milk
1. Georgia wants to cut the recipe for chocolate frosting in half for a small cake that she’s making. How much of each ingredient will she need?
5. ANIMALS Catherine walks her dog
_3 mile every day. How far does she walk 4
each week?
4. EXERCISE A paper published in a medical journal reported that about 11 _ of girls ages 16 to 17 do not exercise 25
at all. The entire study consisted of about 2,500 girls. About how many did not exercise?
6. MUSIC If you practice a musical
2 instrument each day for _ of an hour, 3
how many hours of practice would you get in each week?
114
North Carolina, Grade 6
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1 3. COMPUTERS _ of today’s college 5 students began using computers between the ages of 5 and 8. If a college has 3,500 students, how many of the students began using computers between the ages of 5 and 8?
2. Suppose Georgia wanted to double the recipe; what would the measurements be for each ingredient?
NAME
5E
DATE
PERIOD
Explore Through Reading
6.N.1.2
Multiplying Mixed Numbers Get Ready for the Lesson Complete the activity at the top of page 287 in your textbook. Write your answers below. 1. Write a multiplication expression that shows the size of the Atlantic Giant Squid’s eyeball. 1 1 2. Use repeated addition to find 12 × 1 _ . (Hint: 12 × 1 _ means there are 12 groups of 4
1 1_ .)
4
4
3. Write the multiplication expression from Exercise 1 using improper fractions.
4. Multiply the improper fractions from Exercise 3. How large is the Atlantic Giant Squid’s eyeball? Use a number line and improper fractions to find each product. 1 5. 2 × 1 _
1 6. 2 × 2 _
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
4
0
1
2
3
0
1
2
3
4
5
3 7. 3 × 1 _ 4
0
1
2
3
4
5
6
Read the Lesson 8. What is an improper fraction?
9. What is a mixed number? 10. Why is it helpful to write a mixed number as an improper fraction?
Remember What You Learned 11. Example 2 on page 288 shows how to multiply mixed numbers. Describe a general process you would use to check if your answer is correct. Trade your description with a partner and follow your partner’s process to check the answer for Example 3. Answer any questions your partner may have about your process. Chapter 5
North Carolina, Grade 6
115
NAME
5E
DATE
PERIOD
Study Guide
6.N.1.2
Multiplying Mixed Numbers To multiply mixed numbers, write the mixed numbers as improper fractions, and then multiply as with fractions.
9 5 1 2 2_ × 1_ =_ ×_ 4
3
4
_3
15 3 =_ or 3 _ 4
1 1 × 2_ ab = 1 _ 4
4
1
3
3
4
1
1
9 4 =_ ×_
1
Simplify. Compare to the estimate.
4
_
_
3
4
1 1 Replace a with 1 _ and b with 2 _ . 3
4
Write mixed numbers as improper fractions.
Divide the numerator and denominator by their common factors, 3 and 4.
Simplify.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3 =_ or 3
Estimate: 2 × 2 = 4.
If a = 1 1 and b = 2 1 , what is the value of ab?
Example 2
3
3
Divide the numerator and denominator by their common factor, 3.
3 4×_ 1
9 4 =_ ×_
_
4
Write mixed numbers as improper fractions.
3
×5 9 = __
3
_
Find 2 1 × 1 2 .
Example 1
Exercises Multiply. Write in simplest form. 1 1 1. _ × 1_
3 1 2. 1 _ ×_
3 3. 3 × 1 _
1 5. 9 × 1 _
4 4 6. 2 _ ×_
1 1 7. 2 _ × 1_
3
3
5
6
9
1 9. 8 × 1 _
4
11
3 1 10. _ × 2_
4
8
2
2 1 4. _ × 3_
5
2
3
3
1 11. 4 × 1 _ 8
2
3 1 8. 1 _ ×_ 4
5
1 12. 1 _ ×3 9
2 13. ALGEBRA Evaluate 5x if x = 1 _ . 3
3 14. ALGEBRA If t = 2 _ , what is 4t? 8
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Chapter 5
NAME
5E
DATE
PERIOD
Homework Practice
6.N.1.2
Multiplying Mixed Numbers Multiply. Write in simplest form. 4 1 × 3_ 1. _
9 1 2. _ × 3_
3 3 3. 1 _ ×_
5 2 4. 2 _ ×_
2 1 5. _ × 3_
3 2 6. 3 _ × 2_
1 2 7. 1 _ × 2_
1 1 8. 5 _ × 2_
1 1 9. 2 _ × 1_
5
8
8
3
4
3
1 1 10. 5 _ × 4_ 2
3
10
3
3
4
3
4
4
1 1 1 12. 1 _ × 2_ × 1_
4
2
6
5
_6 , g = 1 _3 , and h = 2 _2 . 7
4
3
3 14. _ h
13. fg
3
5
3 2 1 11. _ ×_ × 2_ 9
5
4
4
ALGEBRA Evaluate each expression if f =
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
15. gh
8
3 16. LUMBER A lumber yard has a scrap sheet of plywood that is 23 _ inches 4
1 by 41 _ inches. What is the area of the plywood? 5
2 1 17. LANDSCAPING A planter box in the city plaza measures 3 _ feet by 4 _ feet 1 by 2 _ feet. Find the volume of the planter box.
3
8
2
Chapter 5
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117
NAME
5E
DATE
PERIOD
Problem-Solving Practice
6.N.1.2
Multiplying Mixed Numbers FOOD For Exercises 1–3, use the table. The table shows Keith’s food
options for a 7-day outdoor survival course. Food Options for 7-day Outdoor Survival Course peanut butter
3 1 plastic jar = 4 _ cups 5
2 14 _ cups
dried noodles/rice
3
_
6 1 cups 6
dried fruit/nuts concentrated juice boxes
1 8 boxes = 16 _ cups 4
1 3_ cups
beef jerky
3
powdered milk dehydrated soup canned tuna/meat
5
2 5 packages = 15 _ cups 3
3 4 cans = 5 _ cups 5
2. Keith would like to bring enough concentrated juice in order to have
1 2_ cups available per day. How much 4
consuming each day?
juice does he need and is 8 boxes of concentrated juice enough?
3. Six other students have been advised to bring the same menu on the course. How many cups of dried fruits and nuts will the students be bringing all together?
_
5. PAINTING Pam is mixing 3 1 batches of 5 paint. If one batch calls for 3 2_ tablespoons of detergent to add to 4
the tempera powder, how many tablespoons of detergent will Pam
4. MEASUREMENT Bill wants to put a large mural on a wall that is
1 1 9_ feet long and 8 _ feet wide. Find 3
8
the area of the wall. If the mural is 100 square feet, will it fit on the wall?
6. COOKING To make a batch of fruit
2 punch, Steve needs 2 _ cups blackberry 3
3 juice. If he wants to make 2 _ batches 4
of punch, how many cups of blackberry juice will he need?
need?
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Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. Keith wants to divide his tuna over the seven-day course. How many cups of tuna meat can Keith plan on
4 1 box = 8 _ cups
NAME
5F
DATE
PERIOD
Explore Through Reading
6.N.2.1
Dividing Fractions Get Ready for the Lesson Complete the Mini Lab at the top of page 293 in your textbook. Write your answers below. 1 1. How many _ -sandwich servings are there? 2
1 1 2. The model shows 3 ÷ _ . What is 3 ÷ _ ? 2
2
Draw a model to find each quotient. 1 3. 3 ÷ _ 4
1 4. 2 ÷ _ 6
1 5. 4 ÷ _ 2
Read the Lesson Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. What is the definition of reciprocals? 1 7. Show that _ × 3 = 1. 3
8. How do you find the reciprocal of a whole number? How do you find the reciprocal of a fraction?
Remember What You Learned 9. Work with a partner. Study Example 3 at the top of page 294. Explain 3 1 1 how you can use a model to show that _ is _ of _ . 8
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Study Guide
6.N.2.1
Dividing Fractions When the product of two numbers is 1, the numbers are called reciprocals.
Example 1
Find the reciprocal of 8.
1 1 , the reciprocal of 8 is _ . Since 8 × _ 8
8
_
Find the reciprocal of 5 .
Example 2
9
5 9 5 9 ×_ = 1, the reciprocal of _ is _ . Since _ 9
5
9
5
You can use reciprocals to divide fractions. To divide by a fraction, multiply by its reciprocal.
_ _
Find 2 ÷ 4 .
Example 3
3
_2 ÷ _4 = _2 × _5 3
5
3
4
5
5 Multiply by the reciprocal, _ . 4
1
2 ×5 = __ 3×4
Divide 2 and 4 by the GCF, 2.
2
6
Multiply numerators and denominators.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5 =_
Exercises Find the reciprocal of each number. 1 2. _
1. 2
4 3. _
6
3 4. _
11
5
Divide. Write in simplest form. 1 2 ÷_ 5. _
1 1 6. _ ÷_
2 1 7. _ ÷_
4 9. _ ÷2
4 1 10. _ ÷_
5 5 11. _ ÷_
9 12. _ ÷3
3 7 13. _ ÷_
9 14. _ ÷9
5 2 15. _ ÷_
7 16. 4 ÷ _
3
5
5
4
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5
10
2
10
3
12
3
3 1 8. _ ÷_
4
2
6
8
4
10
9
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Homework Practice
6.N.2.1
Dividing Fractions Find the reciprocal of each number. 2 1. _
1 2. _
7
3 3. _
9
8
4. 2
5. 12
Divide. Write in simplest form. 2 1 6. _ ÷_
1 2 7. _ ÷_
2 1 8. _ ÷_
1 10. 2 ÷ _
2 11. 8 ÷ _
4 12. 3 ÷ _
5 13. 2 ÷ _
3 14. _ ÷3
4 15. _ ÷ 10
7 16. _ ÷ 14
5 17. _ ÷4
3
6
3 1 9. _ ÷_ 4
10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5
5
2
5
4
4
5
3
7
9
ALGEBRA Find the value of each expression if h =
18. h ÷ k
3
7
_3 , j = _1 , and k = _1 . 8
19. k ÷ j – h
3
4
20. h ÷ j + k
3 1 21. INSECTS An average ant is _ inch long. An average aphid is 3 _ inch long. How many 4
2
times longer is an average ant than an average aphid?
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Problem-Solving Practice
6.N.2.1
Dividing Fractions 9 1. PIZZA Norberto has _ of a pizza. The 10 pizza will be divided equally among 6 people. How much will each person get?
2. CARPENTRY Laura wants to cut a board into three equal pieces. The board is
_5 feet long. How long will each piece 8
be?
1 3. PETS Errol uses _ can of wet dog food
1 4. ICE CREAM Julia ate _ pint of mint
for his dog, Muddy, each day. How many servings will he get from 5 cans of dog food?
chocolate chip ice cream. Mark ate
3
1 garden. If she has _ pound of rosemary, 2
how much will each bundle weigh?
1 7. FOOD Joe has _ of a cake he would like 2
to split among 3 people. What part of the cake will each person get?
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_3 pint of malt ice cream. How many 4
times more ice cream did Mark eat?
3 6. SCHOOL Kirsten has _ hour left to 4 finish 5 math problems on the test. How much time does she have to spend on each problem?
3 8. INTERNET _ of college students use the 4 9 Internet more than the library. _
100
use the library more. How many times more students use the Internet?
Chapter 5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. GARDENING Talia wants to give away 6 bundles of rosemary from her herb
2
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Explore Through Reading
6.N.1.2
Dividing Mixed Numbers Get Ready for the Lesson Complete the activity at the top of page 298 in your textbook. Write your answers below. 1. Write a division expression to find how many times as tall is Mt. Everest than the depth of the average ocean. 2. Write a division expression to find how many times as deep is the Mariana Trench than the average ocean on Earth.
Read the Lesson 3. Describe how to write a mixed number as an improper fraction.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Describe what is happening at each step below. If you need help, use Examples 1 and 2 on pages 298 and 299 as a guide.
_
_
8
4
Find the value of a ÷ b if a = 5 5 and b = 2 1 . a÷b
5 1 ÷ 2_ =5_ 4
8
45 9 =_ ÷_ 8
4
8
9
2
1
45 4 =_ ×_ 5 _ _1 45 4 _ _ = _8 × _9
5 1 =_ or 2 _ 2
2
Remember What You Learned 1 1 5. As an experiment, try to find 4 _ ÷ 2_ in a different way from the way 4
2
you learned in this lesson. First, divide the whole numbers. Next divide the fractions. Then, put together the whole number you found and the 1 1 fraction you found to make a mixed number. Now find 4 _ ÷ 2_ in the 4
2
way the lesson shows how to divide mixed numbers. What two important steps must you do in order when dividing mixed numbers?
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Study Guide
6.N.1.2
Dividing Mixed Numbers To divide mixed numbers, express each mixed number as an improper fraction. Then divide as with fractions.
Example 1 2 1 2_ ÷ 1_ 3
8 6 =_ ÷_
5
_
_
3
5
Find 2 2 ÷ 1 1 .
Write mixed numbers as improper fractions.
3 5 8 = × 5 3 6
_
Estimate: 3 ÷ 1 = 3
_
5 Multiply by the reciprocal, _ . 6
4
8×5 = _
Divide 8 and 6 by the GCF, 2.
3×6 3
20 2 =_ or 2 _ 9
Example 2 3
_
3
4
3 2 Replace s with 1 _ and t with _ .
4
5 3 =_ ÷_ 3 4 5 4 _ _ = × 3 3 20 2 _ = or 2 _ 9
3
4
2 Write 1 _ as an improper fraction. 3
4 Multiply by the reciprocal, _ . 3
Simplify. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9
_
Find the value of s ÷ t if s = 1 2 and t = 3 .
3 2 = 1_ ÷_
s÷t
Simplify. Compare to the estimate.
9
Exercises Divide. Write in simplest form. 1 4 1. 2 _ ÷_
2 1 2. 1 _ ÷1 _
3 3. 5 ÷ 1 _
7 1 4. 2 _ ÷_
9 2 5. 5 _ ÷_
1 2 6. 7 _ ÷1 _
5 7. 3 _ ÷2
1 2 8. 2 _ ÷_
8 11. 1 _ ÷5
3 1 12. _ ÷ 2_
2
5
3
5
2
10
1 9. 9 ÷ 1 _
4
7
3
6
6 4 10. _ ÷ 2_
9
5
7
9
3
4
8
9
7
4
1 13. ALGEBRA If x = 1 _ and y = 3, what is x ÷ y? 4
9 . 14. ALGEBRA Evaluate 18 ÷ t if t = _ 11
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Homework Practice
6.N.1.2
Dividing Mixed Numbers Divide. Write in simplest form. 2 1. 3 _ ÷2
1 1 5. 7 _ ÷ 1_ 2
1 2. 10 ÷ 1 _
3 7 3. 4 _ ÷_
3 1 6. 3 _ ÷ 2_
1 1 7. 2 _ ÷ 1_
4
3
4
8
4
4
10
_
15 7 4. 1 _ ÷_
8
16
8
7 1 8. 4 _ ÷ 2_
5
2
_
10
_
3 4 2 ALGEBRA Evaluate the expression if r = 2 , s = 1 , and t = . 5 4 3
10. s ÷ t
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9. t ÷ 10
11. r ÷ s
12. r ÷ (st)
3 1 13. PIPES How many _ -foot lengths of pipe can be cut from a 6 _ -foot pipe? 4
3
3 14. TRUCKING A truck driver drove 300 miles in 6 _ hours. How many miles 4
per hour did the driver drive?
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Problem-Solving Practice
6.N.1.2
Dividing Mixed Numbers 1. VIDEOTAPES Lyle is putting his videotapes on a shelf. The shelf is 12 inches long. If each videotape is 1 1_ inches wide, how any ideotapes
1 2. FOOD DeLila has 4 _ pies to divide 2
equally among 9 people. How much will each person get?
2
can he put side-by-side on the shelf?
3. GARDENING Maurice mows lawns on 1 Saturday. Last week it took him 5 _ 2
hours to finish. This week it took only 5 hours. How many times longer did it
4. COOKING Chris is cutting a roll of cookie dough into pieces that are
_1 inch thick. If the roll is 10 _1 inches 2
2
long, how many pieces can he make?
take last week than this week?
1 She dove 525 feet in 3 _ minutes. 2
How many feet per minute did she dive?
3 6. GARDENING Catherine got 9 _ pounds 8
of cherries from her tree this year.
_
Last year she only got 6 1 pounds. How 4
many times more pounds did she get this year than last year?
3 7. SEWING Jeanne has 3 _ yards of fabric. 5
2
4 She needs 1 _ yards to make a pair of
1 in 2 _ hours. How many miles per hour
pants. How many pairs of pants can she make?
can he run?
5
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1 8. EXERCISE Del Ray can run 20 _ miles
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Chapter 5
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5. SPORTS Tanya Streeter holds the world record for free-diving in the ocean.
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Anticipation Guide Ratio, Proportion, and Functions
STEP 1
Before you begin Chapter 6
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. A ratio is a comparison of two numbers by division. 2. A ratio can be simplified in the same way as a fraction. 3. A rate is a ratio of two measurements with the same kind of units. 132 miles 4. An example of a unit rate is __ . 2 hours
5.
12 _3 = _ is an example of a proportion. 5
20
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. Cross products can be used to determine if two ratios form a proportion. 7. Looking for patterns in a problem can lead to a solution. 8. A sequence is a list of numbers in order from least to greatest. 9. Each number in a sequence is called a factor of that sequence. 10. The equation y = 5x could represent a sequence in which each output is equal to 5 times the input. STEP 2
After you complete Chapter 6
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 2. Kara is practicing her free throw shot. She is averaging 7 shots made out of every 11 attempted. How many shots would you expect her to make if she attempted 55?
1.
A 21 B 35 C 51 D 42 What is the ratio of stars to balloons? A 3:4 B 4:7 C 4:3 D 7:4
Solution
Solution 1. Hint: Ratios are listed in the specified order, for example the ratio of A to B is A:B, not B:A. There are 4 stars and 3 balloons. The problem asks for the ratio of stars to balloons, so the number of stars will be first in the ratio, or 4 : 3.
2. Hint: She is attempting 5 times as many shots as the total in the provided ratio. If she attempted 55 shots, it would be 5 times as many as 11, and since we expect her to make 7 out of 11, we can expect her to make 7 × 5, or 35 out of 55. You can also use a ratio. 7 ? _ =_ 11
55
The denominator is multiplied by 5, so the same will be true of the numerator.
The answer is C.
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The answer is B. Chapter 6
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Fold here.
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Explore Through Reading
6.N.4.2
Ratios and Rates Get Ready for the Lesson Complete the Mini Lab at the top of page 314 in your textbook. Write your answers below. 1. Compare the number of blue paper clips to the number of red paper clips using the word more and then using the word times.
2. Compare the number of red paper clips to the number of blue paper clips using the word less and then using a fraction.
Read the Lesson 3. A ratio compares amounts of two different things by division. Tell what different things are compared in the examples in your textbook.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 1 Example 2 4. Write the ratio of 2 pens out of a total of 3 pens 3 different ways.
5. What is the denominator in a unit rate?
Remember What You Learned 6. Go to your local grocery store and make a list of unit rates that are used to price items in the store. Also, compare prices for different brands of a certain product. How can you find out which brand provides the best value? Does the store help you to make the comparison? If so, how?
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Study Guide
6.N.4.2
Ratios and Rates A ratio is a comparison of two numbers by division. A common way to express a ratio is as a fraction 2 can be written as in simplest form. Ratios can also be written in other ways. For example, the ratio _ 3 2 to 3, 2 out of 3, or 2:3.
Examples
Refer to the diagram at the right.
Write the ratio in simplest form that compares the number of circles to the number of triangles.
_4
circles triangles
The GCF of 4 and 5 is 1.
5
4 So, the ratio of circles to triangles is _ , 4 to 5, or 4:5. 5
For every 4 circles, there are 5 triangles. Write the ratio in simplest form that compares the number of circles to the total number of figures. ÷2
circles total figures
4 2 _ =_ 10
5
The GCF of 4 and 10 is 2.
÷2
2 The ratio of circles to the total number of figures is _ , 2 to 5, or 2:5. 5 For every two circles, there are five total figures.
Example 3
Write the ratio 20 students to 5 computers as a unit rate.
÷5
20 students 4 students ___ = __ 5 computers
1 computer
÷5
Divide the numerator and the denominator by 5 to get a denominator of 1.
The ratio written as a unit rate is 4 students to 1 computer. Exercises Write each ratio as a fraction in simplest form. 1. 2 guppies out of 6 fish
2. 12 puppies to 15 kittens
3. 5 boys out of 10 students
Write each rate as a unit rate. 4. 6 eggs for 3 people
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5. $12 for 4 pounds
6. 40 pages in 8 days
Chapter 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A rate is a ratio of two measurements having different kinds of units. When a rate is simplified so that it has a denominator of 1, it is called a unit rate.
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Homework Practice
6.N.4.2
Ratios and Rates 1. FRUITS Find the ratio of bananas to oranges in the graphic at the right. Write the ratio as a fraction in simplest form. Then explain its meaning.
2. MODEL TRAINS Hiroshi has 4 engines and 18 box cars. Find the ratio of engines to box cars. Write the ratio as a fraction in simplest form. Then explain its meaning.
3. ZOOS A petting zoo has 5 lambs, 11 rabbits, 4 goats, and 4 piglets. Find the ratio of goats to the total number of animals. Then explain its meaning.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. FOOD At the potluck, there were 6 pecan pies, 7 lemon pies, 13 cherry pies, and 8 apple pies. Find the ratio of apple pies to the total number of pies. Then explain its meaning.
Write each rate as a unit rate. 5. 3 inches of snow in 6 hours
6. $46 for 5 toys
7. TRAINS The Nozomi train in Japan can travel 558 miles in 3 hours. At this rate, how far can the train travel per hour? ANALYZE TABLES For Exercises 8 and 9, refer
to the table showing tide pool animals. 8. Find the ratio of limpets to snails. Then explain its meaning.
Animals Found in a Tide Pool Animal Number Anemones 11 Limpets 14 Snails 18 Starfish 9
9. Find the ratio of snails to the total number of animals. Then explain its meaning.
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Problem-Solving Practice
6.N.4.2
Ratios and Rates 2. GARDENING Rod has 10 rosebushes, 2 of which produce yellow roses. Write the ratio 2 yellow rosebushes out of 10 rosebushes in simplest form.
3. TENNIS Nancy and Lisa played 20 sets of tennis. Nancy won 12 of them. Write the ratio of Nancy’s wins to the total number of sets in simplest form.
4. AGES Oscar is 16 years old and his sister Julia is 12 years old. What will be the ratio of Oscar’s age to Julia’s age in 2 years? Write as a fraction in simplest form.
5. MOVIES Four friends paid a total of $32 for movie tickets. What is the ratio $32 for 4 people written as a unit rate?
6. WORKING At a warehouse, the employees can unload 18 trucks in 6 hours. What is the unit rate for unloading trucks?
7. ANIMALS A reindeer can run 96 miles in 3 hours. At this rate, how far can a reindeer run in 1 hour? Explain.
8. SHOPPING Jenny wants to buy cereal that comes in large and small boxes. The 32-ounce box costs $4.16, and the 14-ounce box costs $2.38. Which box is less expensive per ounce? Explain.
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132
1. FOOTBALL In a recent the NFL season, the Miami Dolphins won 4 games and the Oakland Raiders won 5 games. What is the ratio of wins for the Dolphins to wins for the Raiders?
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Explore Through Reading
6.N.4.1
Ratio Tables Get Ready for the Lesson Read the introduction at the top of page 322 in your textbook. Write your answers below.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. How many cans of juice and how many cans of water would you need to make 2 batches that have the same taste? 3 batches? Draw a picture to support your answers.
2. Find the ratio in simplest form of juice to water needed for 1, 2, and 3 batches of juice. What do you notice?
Read the Lesson 3. In a ratio table, what relationship exists between the columns?
4. Explain how you can check your answers when using a ratio table to solve a problem.
Remember What You Learned 5. Think of a real-world situation in which you would need to find equivalent ratios. Make a ratio table for this situation. Would you need to scale back or scale forward in this situation to find equivalent ratios? Explain.
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Study Guide
6.N.4.1
Ratio Tables A ratio table organizes data into columns that are filled with pairs of numbers that have the same ratio, or are equivalent. Equivalent ratios express the same relationship between two quantities.
Example 1 BAKING You need 1 cup of rolled oats to make 24 oatmeal cookies. Use the ratio table at the right to find how many oatmeal cookies you can make with 5 cups of rolled oats. Cups of Oats Oatmeal Cookies
1 24
5
Find a pattern and extend it. +1
Cups of Oats Oatmeal Cookies
1 24
+1
2 48 + 24
+1
3 72 + 24
+1
4 96 + 24
5 120 + 24
So, 120 oatmeal cookies can be made with 5 cups of rolled oats. Multiplying or dividing two related quantities by the same number is called scaling. You may sometimes need to scale back and then scale forward or vice versa to find an equivalent ratio.
There is no whole number by which you can multiply 4 to get 6. Instead, scale back to 2 and then forward to 6.
4 10
Pairs of Socks Cost in Dollars
6
×3 ÷2
Pairs of Socks Cost in Dollars
2 5
So, the cost of 6 pairs of socks would be $15.
4 10
6 15
÷2 ×3
Exercises 1. EXERCISE Keewan bikes 6 miles in 30 minutes. At this rate, how long would it take him to bike 18 miles? 2. HOBBIES Christine is making fleece blankets. 6 yards of fleece will make 2 blankets. How many blankets can she make with 9 yards of fleece?
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Distance Biked (mi) Time (min)
Yards of Fleece Number of Blankets
6 30
18
6 2
9
Chapter 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2 SHOPPING A department store has socks on sale for 4 pairs for $10. Use the ratio table at the right to find the cost of 6 pairs of socks.
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Homework Practice
6.N.4.1
Ratio Tables For Exercises 1–3, use the ratio tables given to solve each problem. 1. CAMPING To disinfect 1 quart of stream water to make it drinkable, you need to add 2 tablets of iodine. How many tablets do you need to disinfect 4 quarts? 2. BOOKS A book store bought 160 copies of a book from the publisher for $4,000. If the store gives away 2 books, how much money will it lose? 3. BIRDS An ostrich can run at a rate of 50 miles in 60 minutes. At this rate, how long would it take an ostrich to run 18 miles?
2 1
Number of Tablets Number of Quarts
4
Number of Copies Cost in Dollars
160 4,000
2
Distance Run (mi) Time (min)
50 60
18
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. DISTANCE If 10 miles is about 16 kilometers and the distance between two towns is 45 miles, use a ratio table to find the distance between the towns in kilometers. Explain your reasoning.
5. SALARY Luz earns $400 for 40 hours of work. Use a ratio table to determine how much she earns for 6 hours of work. RECIPES For Exercises 6–8, use the following information.
A soup that serves 16 people calls for 2 cans of chopped clams, 4 cups of chicken broth, 6 cups of milk, and 4 cups of cubed potatoes. 6. Create a ratio table to represent this situation. 7. How much of each ingredient would you need to make an identical recipe that serves 8 people? 32 people?
8. How much of each ingredient would you need to make an identical recipe that serves 24 people? Explain your reasoning.
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Problem-Solving Practice
6.N.4.1
Ratio Tables For Exercises 1–4, use the ratio tables below. Table 1
Table 2
1 30
Number of Books Cost in Dollars
Cups of Flour Number of Cookies
1. BAKING In Table 1, how many cookies could you make with 4 cups of flour?
2. BAKING In Table 1, how many cups of flour would you need to make 90 cookies?
3. BOOKS In Table 2, at this rate how many books can you buy with $5?
4. BOOKS In Table 2, at this rate, how much would it cost to buy 9 books?
5. FRUIT Patrick buys 12 bunches of bananas for $9 for the after school program. Use a ratio table to determine how much Patrick will pay for 8 bunches of bananas.
6. HIKING On a hiking trip, LaShana notes that she hikes about 12 kilometers every 4 hours. If she continues at this rate, use a ratio table to determine about how many kilometers she could hike in 6 hours.
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6 10
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Explore Through Reading
6.N.4.2
Proportions Get Ready for the Lesson Read the introduction at the top of page 329 in your textbook. Write your answers below. 1. Express the relationship between the total cost and number of prints he made for each situation as a rate in fraction form.
2. Compare the relationship between the numerators of each rate you wrote in Exercise 1. Compare the relationship between the denominators of these rates.
3. Are the rates you wrote in Exercise 1 equivalent? Explain.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read the Lesson 4. Look at the Key Concept box on page 329. How can you tell that the two examples given are proportions?
5. Explain one method you can use to determine if a relationship among quantities is proportional.
Remember What You Learned 6. Work with a partner. Each of you should write about two different relationships, one which is proportional, and one that is not. Exchange what you wrote with your partner. Then determine which relationship is proportional and which one is not proportional.
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PERIOD
6.N.4.2
Proportions Two quantities are said to be proportional if they have a constant ratio. A proportion is an equation stating that two ratios are equivalent.
Example 1 Determine if the quantities in each pair of rates are proportional. Explain your reasoning and express each proportional relationship as a proportion. $35 for 7 balls of yarn; $24 for 4 balls of yarn. Write each ratio as a fraction. Then find its unit rate. ÷7
÷4
___ ___
___ ___
$35 $5 = 7 balls of yarn 1 ball of yarn
$24 $6 = 4 balls of yarn 1 ball of yarn
÷7
÷4
Since the ratios do not share the same unit rate, the cost is not proportional to the number of balls of yarn purchased. Example 2 Determine if the quantities in each pair of rates are proportional. Explain your reasoning and express each proportional relationship as a proportion. 8 boys out of 24 students; 4 boys out of 12 students Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Write each ratio as a fraction. ÷2
__
4 boys __
8 boys 24 students
12 students
The numerator and the denominator are divided by the same number.
÷2
Since the fractions are equivalent, the number of boys is proportional to the number of students. Exercises Determine if the quantities in each pair of rates are proportional. Explain your reasoning and express each proportional relationship as a proportion. 1. $12 saved after 2 weeks; $36 saved after 6 weeks
2. $9 for 3 magazines; $20 for 5 magazines 3. 135 miles driven in 3 hours; 225 miles driven in 5 hours
4. 24 computers for 30 students; 48 computers for 70 students
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Homework Practice
6.N.4.2
Proportions Determine if the quantities in each pair of ratios are proportional. Explain your reasoning and express each proportional relationship as a proportion. 1. 18 vocabulary words learned in 2 hours; 27 vocabulary words learned in 3 hours
2. $15 for 5 pairs of socks; $25 for 10 pairs of socks
3. 20 out of 45 students attended the concert; 12 out of 25 students attended the concert
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4. 78 correct answers out of 100 test questions; 39 correct answers out of 50 test questions
5. 15 minutes to drive 21 miles; 25 minutes to drive 35 miles
ANIMALS For Exercises 6–8, refer
to the table on lengths of some animals with long tails. Determine if each pair of animals has the same body length to tail length proportions. Explain your reasoning. 6. brown rat and opossum
Animal Lengths (mm) Animal Head & Body Tail Brown Rat 240 180 Hamster 250 50 Lemming 125 25 Opossum 480 360 Prairie Dog 280 40
7. hamster and lemming
8. opossum and prairie dog
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Problem-Solving Practice
6.N.4.2
Proportions 2. BAKING A cookie recipe that yields 48 cookies calls for 2 cups of flour. A different cookie recipe that yields 60 cookies calls for 3 cups of flour. Are these rates proportional? Explain your reasoning.
3. MUSIC A music store is having a sale where you can buy 2 new-release CDs for $22 or you can buy 4 new-release CDs for $40. Are these rates proportional? Explain your reasoning.
4. TRAVEL On the Mertler’s vacation to Florida, they drove 180 miles in 3 hours before stopping for lunch. After lunch they drove 120 miles in 2 hours before stopping for gas. Are these rates proportional? Explain your reasoning.
5. BOOKS At the school book sale, Michael bought 3 books for $6. Darnell bought 5 books for $10. Are these rates proportional? Explain your reasoning.
6. SURVEY One school survey showed that 3 out of 5 students own a pet. Another survey showed that 6 out of 11 students own a pet. Are these results proportional? Explain your reasoning.
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1. FITNESS Jessica can do 60 jumpingjacks in 2 minutes. Juanita can do 150 jumping-jacks in 5 minutes. Are these rates proportional? Explain your reasoning.
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Explore Through Reading
6.N.4.2
Algebra: Solving Proportions Get Ready for the Lesson Read the introduction at the top of page 334 in your textbook. Write your answers below. 1. How many pairs of flip flops can you buy with $20? $25?
2. Write a proportion to express the relationship between the cost of 3 pairs of flip flops and the cost c of 7 pairs of flip flops.
3. How much will it cost to buy 6 pairs of flip flops?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. In Example 1, explain why you multiply by 5 to solve the proportion.
5. Look at the final sentence in Example 4 on page 335—“So, about 400 out of 500 people can be expected to prefer eating at a restaurant.” Why is it important to use can be expected in this answer?
Remember What You Learned 6. Work with a partner. Study Examples 1–3 on pages 334 and 335. Write a proportion that needs to be solved for an unknown value. Exchange proportions and solve for the unknown value. Explain how you arrived at your solution.
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Study Guide
6.N.4.2
Algebra: Solving Proportions To solve a proportion means to find the unknown value in the proportion. By examining how the numerators or denominators of the proportion are related, you can perform an operation on one fraction to create an equivalent fraction.
_ _
Solve 3 = b .
Example 1
4
12
Find a value for b that would make the fractions equivalent. ×3
b _3 = _ 4
Since 4 × 3 = 12, multiply the numerator and denominator by 3.
12
×3
b = 3 × 3 or 9 Example 2 NUTRITION Three servings of broccoli contain 150 calories. How many servings of broccoli contain 250 calories? Set up the proportion. Let a represent the number of servings that contain 250 calories. 150 calories 250 calories ___ = ___ 3 servings
a servings
Find the unit rate. ÷3
150 calories 50 calories ___ = __ 3 servings
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1 serving
÷3
Rewrite the proportion using the unit rate and solve using equivalent fractions. ×5
50 calories 250 calories __ = ___ 1 serving
5 servings
×5
So, 5 servings of broccoli contain 250 calories. Exercises Solve each proportion. 8 2 =_ 1. _ n 3
y 2 2. _ =_
3 b 3. _ =_
16 4 4. _ =_ w 5
d 3 5. _ =_
2 _6 6. _ y =
4
16
8
8
5
15
9
7. MUSIC Jeremy spent $33 on 3 CDs. At this rate, how much would 5 CDs cost?
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NAME
6D
DATE
PERIOD
Homework Practice
6.N.4.2
Algebra: Solving Proportions Solve each proportion. n 2 =_ 1. _
16 2 _ 2. _ x =
80 b 3. _ =_
m 75 4. _ =_
6 42 5. _ =_ a 5
3 21 6. _ =_
f 4 7. _ =_
h 70 8. _ =_
3 27 9. _ =_ p 5
3
2
3
21
50
45
26 r 10. _ =_ 21
63
40
12
120
17 102 _ 11. _ y = 222
100
d
5
56
7 c 12. _ =_ 10
25
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13. MAMMALS A pronghorn antelope can travel 105 miles in 3 hours. If it continued traveling at the same speed, how far could a pronghorn travel in 11 hours?
14. BIKES Out of 32 students in a class, 5 said they ride their bikes to school. Based on these results, predict how many of the 800 students in the school ride their bikes to school.
15. MEAT Hamburger sells for 3 pounds for $6. If Alicia buys 10 pounds of hamburger, how much will she pay?
16. FOOD If 24 extra large cans of soup will serve 96 people, how many cans should Ann buy to serve 28 people?
17. BIRDS The ruby throated hummingbird has a wing beat of about 200 beats per second. About how many wing beats would a hummingbird have in 3 minutes?
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Problem-Solving Practice
6.N.4.2
Algebra: Solving Proportions 2. FACTORIES A factory produces 6 motorcycles in 9 hours. Write a proportion and solve it to find how many hours it takes to produce 16 motorcycles.
3. READING James read 4 pages in a book in 6 minutes. How long would you expect him to take to read 6 pages?
4. COOKING A recipe that will make 3 pies calls for 7 cups of flour. Write a proportion and solve it to find how many pies can be made with 28 cups of flour.
5. TYPING Sara can type 90 words in 4 minutes. About how many words would you expect her to type in 10 minutes?
6. BASKETBALL The Lakewood Wildcats won 5 of their first 7 games this year. There are 28 games in the season. About how many games would you expect the Wildcats to win this season? Explain your reasoning.
7. FOOD Two slices of Dan’s Famous Pizza have 230 Calories. How many Calories would you expect to be in 5 slices of the same pizza?
8. SHOPPING Andy paid $12 for 4 baseball card packs. Write a proportion and solve it to find how many baseball card packs he can purchase for $21.
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144
1. SCHOOL The ratio of boys to girls in history class is 4 to 5. How many girls are in the class if there are 12 boys in the class? Explain.
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Explore Through Reading
6.A.2.1, 6.A.2.2, 6.A.2.3
Sequences and Expressions Get Ready for the Lesson Read the introduction at the top of page 343 in your textbook. Write your answers below. 1. Find the rate of slices to the number of pizzas for each row in the table.
2. Is the number of pizzas proportional to the number of slices? Explain your reasoning.
3. Make an ordered list of the number of slices and describe the pattern between consecutive numbers in this list.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. What relationship appears to exist between the pattern found in Exercise 3 and the rates found in Exercise 1?
Read the Lesson 5. If you have a list of numbers, how can you tell if they are an arithmetic sequence?
6. In extending a sequence, how can you use an algebraic expression to find the tenth term?
Remember What You Learned 7. Work with a partner. Make up a sequence of numbers that follow a certain pattern. Exchange lists with your partner. For the list you receive from your partner, describe the pattern, write a function describing the pattern, and then find the tenth term in the pattern.
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Study Guide
6.A.2.1, 6.A.2.2, 6.A.2.3
Sequences and Expressions A sequence is a list of numbers in a specific order. Each number in the sequence is called a term. An arithmetic sequence is a sequence in which each term is found by adding the same number to the previous term.
Example Use words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence. 1 4
Position Value of Term
2 8
3 12
Position 1 2 3 4 n
Study the relationship between each position and the value of its term. Notice that the value of each term is 4 times its position number. So the value of the term in position n is 4n. To find the value of the tenth term, replace n with 10 in the algebraic expression 4n. Since 4 × 10 = 40, the value of the tenth term in the sequence is 40.
4 16
×4 ×4 ×4 ×4 ×4
n ?
= = = = =
Value of Term 4 8 12 16 4n
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Use words and symbols to describe the value of each term as a function of its position. Then find the value of the tenth term in the sequence.
146
1. Position Value of Term
3 1
4 2
5 3
6 4
n ?
2. Position Value of Term
1 5
2 10
3 15
4 20
n ?
3. Position Value of Term
4 11
5 12
6 13
7 14
n ?
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Homework Practice
PERIOD
6.A.2.1, 6.A.2.2, 6.A.2.3
Sequences and Expressions Use words and symbols to describe the value of each term as a function of its position. Then find the value of the sixteenth term in the sequence. 1. Position Value of Term
2 8
3 12
4 16
5 20
n
2. Position Value of Term
8 14
9 15
10 16
11 17
n
3. Position Value of Term
11 4
12 5
13 6
14 7
n
4. Position Value of Term
21 12
22 13
23 14
24 15
n
Determine how the next term in each sequence can be found. Then find the next two terms in the sequence.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. 3, 16, 29, 42, …
6. 29, 25, 21, 17, …
7. 1.2, 3.5, 5.8, 8.1, …
Find the missing number in each sequence. 1 ,… 8. 5, , 10, 12 _ 2
9. 11.5, 9.4, , 5.2
1 10. 40, , 37 _ , 36, … 3
11. MEASUREMENT There are 52 weeks in 1 year. In the space at the right, make a table and write an algebraic expression relating the number of weeks to the number of years. Then find Hana’s age in weeks if she is 11 years old.
12. COMPUTERS There are about 8 bits of digital information in 1 byte. In the space at the right, make a table and write an algebraic expression relating the number of bits to the number of bytes. Then find the number of bits there are in one kilobyte if there are 1,024 bytes in one kilobyte.
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Problem-Solving Practice
PERIOD
6.A.2.1, 6.A.2.2, 6.A.2.3
Sequences and Expressions 2. MEASUREMENT There are 12 inches in 1 foot. The height of Rachel’s door is 7 feet. Find the height in inches. Make a table then write an algebraic expression relating the number of feet to inches.
3. RUNNING There are 60 seconds in 1 minute. Pete can run all the way around the track in 180 seconds. Find how long it takes Pete to run around the track in minutes. Make a table then write an algebraic expression relating the number of seconds to the number of minutes.
4. FRUIT There are 16 ounces in 1 pound. Chanda picked 9 pounds of cherries from her tree this year. Find the number of ounces of cherries Chanda picked. Make a table then write an algebraic expression relating the number of ounces to the number of pounds.
5. SPORTS There are 3 feet in 1 yard. Tanya Streeter holds the world record for free-diving in the ocean. She dove
6. COOKING There are 8 fluid ounces in 1 cup. A beef stew recipe calls for 3 cups of vegetable juice. Find the number of fluid ounces of vegetable juice needed for the recipe. Make a table then write an algebraic expression relating the number of fluid ounces to the number of cups.
1 525 feet in 3 _ minutes. Find the 2
number of yards she dove. Make a table then write an algebraic expression relating the number of feet to the number of yards.
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1. AGE There are 12 months in 1 year. If Juan is 11 years old, how many months old is he? Make a table then write an algebraic expression relating the number of months to the number of years.
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Anticipation Guide Percent and Probability
STEP 1
Before you begin Chapter 7
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. Percent means hundredths. 1 2. To write a fraction as a percent, multiply the fraction by _ . 100
3. In a circle graph the percents add up to 360%. 4. By comparing the size of the sections in a circle graph you can compare the data represented by those sections.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Moving the decimal point in a number two places to the left is the same as dividing that number by 100. 6. To write a decimal as a percent, first write the decimal as a fraction with a denominator of 100. 7. The probability that an event will occur is always a number from 0 to 100. 8. A tree diagram can be used to find the number of possible outcomes of an event. 9. To have an accurate survey of a group of people, all people in the group must be surveyed. 10. 85 is a good estimate of 48% of 150. STEP 2
After you complete Chapter 7
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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NAME
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Devon reaches into a bag containing six yellow tiles and 8 green tiles. What is the probability that he will pull out a green tile?
2. A survey was conducted at a local middle school. One hundred students were asked to name their favorite color. Here are the results. Favorite Colors at Blues Middle School Black
Red Yellow
Blue Green
8 A _
About what percentage of the students said green is their favorite color?
16
C
14
A 20%
6 _
B 25%
14
C 33%
6 D _
D 50%
8
Fold here. Solution
Solution
1. Hint: The probability of a specific event occurring is the number of times it would be possible for the specific event to occur over the total number of events. The bag contains 8 green tiles and 6 yellow tiles, or a total of 14 tiles. The probability of choosing a green one is the number of green tiles (8) over the total number of tiles (14), which can be 8 . represented as _ 14
2. Green represents one-fourth of the circle shown in the graph, which
1 of the students chose means that _ 4
green as their favorite color. One-fourth, or one quarter of the circle is 25%. You can also calculate the percentage from the fraction by either dividing the numerator by the denominator and multiplying by 100% or setting up a ratio for the percentage, in this case: ? _1 = _ 4
The answer is B.
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100
The answer is B. Chapter 7
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8 B _
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Explore Through Reading
6.N.3.2
Percents and Fractions Get Ready for the Lesson Read the introduction at the top of page 365 in your textbook. Write your answers below. 1. What ratio compares the number of students who prefer grape fruit bars to the total number of students? 2. Draw a decimal model to represent this ratio.
3. What fraction represents this ratio?
Read the Lesson 4. Write the two steps to use to write a percent as a fraction.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Look at the graph at the top of page 365. What is the sum of the number of students? Look at Example 3. Based on the information given, what percentage of cell phone owners said that they do not use the text messaging feature? How do you know?
6. Look at Example 2 on page 366. Why is 125% written as a mixed number?
Remember What You Learned 7. Write a fraction as a percent using the steps shown in Examples 4 and 5 on pages 366 and 367. Choose any fraction you like different from those in the Examples. Step Set up a proportion. Write the cross products. Multiply. Divide. Conclusion. Chapter 7
Equation(s)
So, ___________ is equivalent to ____________. North Carolina, Grade 6
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Study Guide
6.N.3.2
Percents and Fractions To write a percent as a fraction, write it as a fraction with a denominator of 100. Then simplify.
Example 1
Write 15% as a fraction in simplest form.
15% means 15 out of 100. 15 15% = _
Definition of percent.
100 3 _
3 15 =_ or _ 100 _
Simplify. Divide the numerator and
20
denominator by the GCF, 5.
20
Example 2
Write 180% as a fraction in simplest form.
180% means 180 out of 100. 180 180% = _
Definition of percent.
100
9 _ 100 _
180 4 =_ or 1 _
Simplify.
5
5
You can also write fractions as percents. To write a fraction as a percent, write a proportion and solve.
n _2 = _ 5
100
_
Write 2 as a percent. 5
Example 4
5
100
× 20
_
4
n _7 = _
Set up a proportion.
4
Set up a proportion.
100
× 25
× 20
40 _2 = _
_
Write 7 as a percent.
Since 5
175 _7 = _
× 20 = 100,
4
multiply 2 by 20 to find n.
_
× 25 = 100,
multiply 7 by 25 to find n.
× 25
_
So, 2 = 40 or 40% 5 100
Since 4
100
_
So, 7 = 175 or 175% 4 100
Exercises Write each percent as a fraction in simplest form. 1. 20%
2. 35%
3. 70%
4. 60%
5. 150%
6. 225%
Write each fraction as a percent. 3 7. _ 10
1 10. _ 5
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8.
2 _ 100
12 11. _ 5
8 9. _ 5
13 12. _ 100
Chapter 7
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Example 3
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7A
DATE
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Homework Practice
6.N.3.2
Percents and Fractions Write each percent as a fraction in simplest form. 1. 60%
2. 18%
3. 4%
4. 35%
5. 10%
6. 1%
7. 175%
8. 258%
9. 325%
10. ENERGY The United States uses 24% of the world’s supply of energy. What fraction of the world’s energy is this? Write each fraction as a percent. 6 11. _
2 12. _
6 14. _
15.
10
9 13. _
5
4
5
7 _
16.
100
4 _ 100
Write a percent to represent the shaded portion of each model. 18.
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17.
19.
20.
22.
21.
23. ANALYZE TABLES The table shows what fraction of a vegetable garden contains each kind of vegetable. What percent of the garden contains other kinds of vegetables? Plant Fraction
Chapter 7
Beans
Corn
Tomatoes
_1
_1
_1
5
2
4
Other
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Problem-Solving Practice
6.N.3.2
Percents and Fractions 2. MUSIC There are 4 trombones out of 25 instruments in the Landers town band. What percent of the instruments are trombones?
3. SHOPPING Alicia’s favorite clothing store is having a 30% off sale. What fraction represents the 30% off sale?
4. FOOD At Ben’s Burger Palace, 45% of the customers order large soft drinks. What fraction of the customers order large soft drinks?
5. BASKETBALL In a recent NBA season, Shaquille O’Neal of the Los Angeles Lakers made 60% of his field goals. What fraction of his field goals did Shaquille make?
6. SCHOOL In Janie’s class, 7 out of 25 students have blue eyes. What percent of the class has blue eyes?
17 7. TESTS Michael answered _ questions
8. RESTAURANTS On Saturday afternoon,
20
correctly on his test. What percent of the questions did Michael answer correctly?
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41 _ telephone calls taken at The 50
Overlook restaurant were for dinner reservations. What percent of the telephone calls were for dinner reservations?
Chapter 7
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. TOYS The Titanic Toy Company has a 4% return rate on its products. Write this percent as a fraction in simplest form.
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DATE
PERIOD
Explore Through Reading
6.N.3.2
Percents and Decimals Get Ready for the Lesson Read the introduction at the top of page 377 in your textbook. Write your answers below. 1. What percent does the entire circle graph represent? 2. What fraction represents the section of the graph labeled math?
3. Write the fraction from Exercise 2 as a decimal.
Read the Lesson Complete each of the following sentences.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. To rewrite a fraction with a denominator of 100 as a decimal, move the decimal point of the numerator __________ places to the __________.
5. To rewrite a fraction with a denominator of __________ as a decimal, move the decimal point of the numerator 3 places to the left. 6. Look at Example 6 on page 378. Why do you multiply the numerator and denominator by 10?
Remember What You Learned 7. Look at Example 5 on page 378. Explain why you first write the decimal as mixed number. Then explain what happens at the next step.
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PERIOD
6.N.3.2
Percents and Decimals To write a percent as a decimal, first rewrite the percent as a fraction with a denominator of 100. Then write the fraction as a decimal.
Example 1 23 23% = _ 100
= 0.23 Example 2 127 127% = _ 100
= 1.27
Write 23% as a decimal. Rewrite the percent as a fraction with a denominator of 100. Write the fraction as a decimal.
Write 127% as a decimal. Rewrite the percent as a fraction with a denominator of 100. Write the fraction as a decimal.
To write a decimal as a percent, first write the decimal as a fraction with a denominator of 100. Then write the fraction as a percent.
Example 3 44 0.44 = _ 100
= 44%
Write the decimal as a fraction. Write the fraction as a percent.
Write 2.65 as a percent.
265 2.65 = _
Write 2 and 65 hundredths as a mixed number.
_
Write the mixed number as an improper fraction.
100 = 265 100
= 265%
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 4
Write 0.44 as a percent.
Write the fraction as a percent.
Exercises Write each percent as a decimal. 1. 39%
2. 57%
3. 82%
4. 135%
5. 112%
6. 0.4%
Write each decimal as a percent. 7. 0.86 10. 0.2
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8. 0.36
9. 0.65
11. 1.48
12. 2.17
Chapter 7
NAME
7B
DATE
PERIOD
Homework Practice
6.N.3.2
Percents and Decimals Express each percent as a decimal. 1. 29%
2. 63%
3. 4%
4. 9%
5. 148%
6. 106%
7. 10%
8. 32%
9. ENERGY The United States gets about 39% of its energy from petroleum. Write 39% as a decimal. 10. SCIENCE About 8% of the earth’s crust is made up of aluminum. Write 8% as a decimal. Express each decimal as a percent. 11. 0.45
12. 0.12
13. 1.68
14. 2.73
15. 0.2
16. 0.7
17. 0.95
18. 0.46
19. POPULATION In 2000, the number of people 65 years and older in Arizona was 0.13 of the total population. Write 0.13 as a percent.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
20. GEOGRAPHY About 0.41 of Hawaii’s total area is water. What percent is equivalent to 0.41? Replace each 21. 26%
0.3
with <, >, or = to make a true sentence. 22. 0.9
9%
23. 4.7
47%
24. ANALYZE TABLES A batting average is the ratio of hits to at bats. Batting averages are expressed as a decimal rounded to the nearest thousandth. Show two different ways of finding how much greater Derek Jeter’s batting average was than Jason Giambi’s batting average. Express as a percent. New York Yankees, 2005 Batting Statistics Player Batting Average Jason Giambi 0.286 Derek Jeter 0.307 Hideki Matsui 0.297 Jorge Posada 0.257 Source: ESPN
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Problem-Solving Practice
PERIOD
6.N.3.2
Percents and Decimals 2. BASEBALL A player’s batting average was 0.29 rounded to the nearest hundredth. Write 0.29 as a percent.
3. ELECTIONS In a recent U.S. midterm elections, 39% of eligible adults voted. What is 39% written as a decimal?
4. BASKETBALL In a recent season, Jason Kidd of the New Jersey Nets had a field goal average of 0.40 rounded to the nearest hundredth. What is 0.40 written as a percent?
5. SPORTS When asked to choose their favorite sport, 27% of U.S. adults who follow sports selected professional football. What decimal is equivalent to 27%?
6. AGE Lawrence is 18 years old and his brother Luther is 12 years old. This means that Lawrence is 1.5 times older than Luther. What percent is equivalent to 1.5?
7. WATER About 5% of the surface area of the U.S. is water. What decimal represents the amount of the U.S. surface area taken up by water?
8. POPULATION China accounts for 0.21 of the world’s population. What percent of the world’s population lives in China?
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Chapter 7
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158
1. COMMUTING According to the U.S. census, 76% of U.S. workers commute to work by driving alone. Write 76% as a decimal.
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Explore Through Reading
6.S.1.1, 6.S.1.2
Probability Experiments Experimental probability is found using frequencies obtained in an experiment or game. Theoretical probability is the expected probability of an event occurring.
P(3) =
number of times 3 occurs _____
25
Number of Rolls
The graph shows the results of an experiment in which a number cube was rolled 100 times. Find the experimental probability of rolling a 3 for this experiment.
Example 1
14
13
1
2
15
21 17
16
10 5 0
number of possible outcomes 16 = or 4 100 25
_
20
19
_
3
4
5
6
Number Showing
4 , which is close to its theoretical The experimental probability of rolling a 3 is _ 25
1 . probability of _ 6
Example 2
In a telephone poll, 225 people were asked for whom they planned to vote in the race for mayor. What is the experimental probability of Juarez getting a vote from a person selected at random?
Candidates Juarez Davis Abramson
Number of People 75 67 83
75 1 or _ . So, the experimental probability is _ 225
Example 3
3
Suppose 5,700 people vote in the election. How many can be expected to vote for Juarez?
_1 · 5,700 = 1,900 3
About 1,900 will vote for Juarez.
Exercises 1. PETS Use the graph of a survey of 150 students asked whether they prefer cats or dogs. a. What is the probability of a student preferring dogs? b. Suppose 100 students were surveyed. How many can be expected to prefer dogs?
120 100 80 60 40
Chapter 7
18
20 0
c. Suppose 300 students were surveyed. How many can be expected to prefer cats?
132
140
Number of Students
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Of the 225 people polled, 75 planned to vote for Juarez.
Cats
Dogs
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6.S.1.1, 6.S.1.2
Probability Experiments 1. A number cube is rolled 50 times and the results are shown in the graph below. 14
Number of Rolls
12
12 10
10
9
8
8
6
5
6 4 2 0 1
2
3
4
5
6
a. Find the experimental probability of rolling a 2. b. What is the theoretical probability of rolling a 2? c. Find the experimental probability of not rolling a 2. d. What is the theoretical probability of not rolling a 2? e. Find the experimental probability of rolling a 1.
a. What is the probability that a person’s favorite season is fall? Write the probability as a fraction.
What is your favorite season of the year? Spring Summer
39%
Fall Winter
b. Out of 300 people, how many would you expect to say that fall is their favorite season?
13%
None, I like them all
25% 13% 10%
c. Out of 20 people, how many would you expect to say that they like all the seasons? d. Out of 650 people, how many more would you expect to say that they like summer more than they like winter?
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2. SEASONS Use the results of the survey at the right.
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Homework Practice
6.S.1.1, 6.S.1.2
Probability Experiments 1. A number cube is rolled 24 times and lands on 2 four times and on 6 three times. a. Find the experimental probability of landing on a 2. b. Find the experimental probability of not landing on a 6. c. Compare the experimental probability you found in part a to its theoretical probability.
d. Compare the experimental probability you found in part b to its theoretical probability.
2. ENTERTAINMENT Use the results of the survey in the table shown.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
a. What is the probability that someone in the survey considered reading books or surfing the Internet as the best entertainment value? Write the probability as a fraction.
b. Out of 500 people surveyed, how many would you expect considered reading books or surfing the Internet as the best entertainment value?
Best Entertainment Value Type of Entertainment Percent Playing Interactive Games 48 Reading Books 22 Renting Movies 10 Going to Movie Theaters 10 Surfing the Internet 9 Watching Television 1
c. Out of 300 people surveyed, is it reasonable to expect that 30 considered watching television as the best entertainment value? Why or why not? 3. A spinner marked with four sections blue, green, yellow, and red was spun 100 times. The results are shown in the table. a. Find the experimental probability of landing on green.
Section Blue
b. Find the experimental probability
Green Yellow Red
of landing on red. c. If the spinner is spun 50 more times, how many of these times would you expect the pointer to land on blue?
Chapter 7
Frequency 14 10 8 68
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Problem-Solving Practice
6.S.1.1, 6.S.1.2
Probability Experiments HOBBIES For Exercises 1–3, use the
graph of a survey of 24 seventh-grade students asked to name their favorite hobby. What is your favorite hobby? Singing
What is your favorite winter activity?
1
Hanging with friends
Building a snowman
3
Building things
14
Snowboarding/skiing
1
Bike riding
WINTER ACTIVITIES For Exercises 5 and 6, use the graph of a survey with 104 responses in which respondents were asked about their favorite winter activities.
Sledding
2
T.V.
3 3 3
Computer Roller skating
69 21 0 10 20 30 40 50 60 70
Respondents
Sports
8 0
2
4
6
8 10 12 14
Number of Students
2. Suppose 200 seventh-grade students were surveyed. How many can be expected to say that roller skating is their favorite hobby?
3. Suppose 60 seventh-grade students were surveyed. How many can be expected to say that bike riding is their favorite hobby?
4. A bag contains 5 blue, 4 red, 9 white, and 6 green marbles. If a marble is drawn at random and replaced 100 times, how many times would you expect to draw a green marble?
5. What is the probability that someone’s favorite winter activity is building a snowman? Write the probability as a fraction.
6. If 500 people had responded, how many would have been expected to list sledding as their favorite winter activity? Round to the nearest whole person.
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1. What is the probability that a student’s favorite hobby is roller skating?
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Explore Through Reading
6.S.2.1
Constructing Sample Spaces Get Ready for the Lesson Read the introduction at the top of page 389 in your textbook. Write your answers below. 1. List the possible ways to choose a soft drink, a popcorn, and a candy.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. How do you know you have accounted for all possible combinations?
Read the Lesson 3. In Example 1 on page 389, what is the sample space? What method was used to find the sample space?
4. In the tree diagram in Example 2 on page 390, which part of the diagram shows the sample space?
5. Using the Fundamental Counting Principle in Example 3 on page 390, how do you determine the number of possible outcomes? How many possible outcomes are there?
Remember What You Learned 6. Work with a partner. Think up a situation and use the Fundamental Counting Principle to determine the number of possible outcomes. Then make an organized list, or draw a tree diagram, to determine the sample space. Chapter 7
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Study Guide
6.S.2.1
Constructing Sample Spaces The Fundamental Counting Principle is another way to find the number of possible outcomes. This principle states that if there are m outcomes for a first choice and n outcomes for a second choice, then the total number of possible outcomes can be found by finding m × n.
Example 1 How many sandwiches are possible from a choice of turkey or ham with jack cheese or Swiss cheese? Draw a tree diagram. Sandwich
Outcome
Cheese jack (J)
TJ
Swiss (S)
TS
jack (J)
HJ
Swiss (S)
HS
turkey (T)
ham (H)
There are four possible sandwiches.
There are twelve possible sandwiches. To determine the number of possible outcomes, multiply the number of first choices, 3, by the number of second choices, 4, to determine that 1 , or 0.083, or 8.3%. there are 12 possible outcomes. So, P(ham, jack) = _ 12
Exercises First use the Fundamental Counting Principle to determine the number of possible outcomes. Then, check your result and find the sample space by drawing a tree diagram. Finally, find the probability. 1. buy a can or a bottle of grape or orange soda Find P(bottle, grape).
2. toss a coin and roll a number cube Find P(4, tails).
3. wear jeans or shorts with a blue, white, black, or red T-shirt. Find P(jeans, white T-shirt).
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Example 2 Using the Fundamental Counting Principle, how many sandwiches are possible from a choice of roast beef, turkey, or ham, with a choice of jack, cheddar, American, or Swiss cheese? Find the probability of chossing a ham with jack cheese sandwich.
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Homework Practice
6.S.2.1
Constructing Sample Spaces 1. SCULPTURE Diego is lining up driftwood sculptures in front of his woodshop. He has a dolphin, gull, seal, and a whale. In how many different ways can he line up his sculptures? Make an organized list to show the sample space.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. CYCLES A cycle shop sells bicycles, tricycles, and unicycles in a single color of red, blue, green, or white. Draw a tree diagram to find how many different combinations of cycle types and colors are possible.
For Exercises 3–5, a coin is tossed, and the spinners shown are spun. 3. Using the Fundamental Counting Principle, how many outcomes are possible?
Spinner 1
Spinner 2
B
A
C D
G E
4. What is P(heads, C, G)? 5. Find P(tails, D, a vowel).
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PERIOD
6.S.2.1
Constructing Sample Spaces 2. PETS Terence is going to get a parrot. He can choose among a yellow, green, or multi-colored female or male parrot. Draw a tree diagram showing all the ways Terence can choose. What is the probability he will choose a yellow female?
3. CAKE Julia is ordering a birthday cake. She can have a circular or rectangular chocolate or vanilla cake with chocolate, vanilla, or maple frosting. Draw a tree diagram showing all the possible ways Julia can order her cake. How many options does she have?
4. GAMES Todd plays a game in which you toss a coin and roll a number cube. Use the Fundamental Counting Principle to determine the number of possible outcomes. What is P(heads, odd number)?
5. SCHOOL Melissa can choose two classes. Her choices are wood shop, painting, chorus, and auto shop. List all the ways two classes can be chosen.
6. SHOPPING Kaya has enough allowance to purchase two new baseball caps from the five he likes. How many ways can he choose?
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1. OUTINGS Olivia and Candace are deciding between Italian or Chinese food and then whether to go to a movie, walk in the park, or go for a bike ride. Using the Fundamental Counting Principle, how many choices do they have?
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Explore Through Reading
6.S.2.1
Making Predictions Get Ready for the Lesson Complete the Mini Lab at the top of page 394 in your textbook. Write your answers below. 1. When working in a group, how did your group predict the number of students in your school with green eyes?
2. Compare your group’s prediction with the class prediction. Which do you think is more accurate and why?
Read the Lesson 3. Write the three characteristics of a good sample.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Using the characteristics listed above, do you think that a classroom is a good sample of an entire school? Explain.
5. If the question of the survey is, “What is your favorite television program?” would you change the sample in any way? If so, how would you change it?
6. In Examples 1 and 2 on page 395, how is the prediction used?
Remember What You Learned 7. Work with a partner. Find the results of a survey that is of interest to you. For example, to find surveys on favorite TV programs, go to a search engine on the Internet and enter “survey TV programs.” Choose one survey. Do you think the survey is a good survey? If so, why? If not, why not and how would you change it? Chapter 7
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Study Guide
6.S.2.1
Making Predictions A survey is a method of collecting information. The group being surveyed is the population. To save time and money, part of the group, called a sample, is surveyed. A good sample is: • selected at random, or without preference, • representative of the population, and • large enough to provide accurate data.
Example 1 Every sixth student who walked into the school was asked how he or she got to school. What is the probability that a student at the school rode a bike to school?
School Transportation Method Students walk 10 ride bike 10 ride bus 15 get ride 05
of students that rode a bike _______ P(ride bike) = number number of students surveyed
10 1 =_ or _ 40
4
1 So, P(ride bike) = _ , 0.25, or 25%. 4
There are 360 students at the school. Predict how many bike to school. 10 s _ =_ 40
360
You can solve the proportion to find that of the 360 students, 90 will ride a bike to school.
Example 2 SCHOOL Use the following information and the table
shown. Every tenth student entering the school was asked which one of the four subjects was his or her favorite. 1. Find the probability that any student attending school prefers science.
Favorite Subject Subject Students Language Arts 10 Math 10 Science 15 Social Studies 05
2. There are 400 students at the school. Predict how many students would prefer science.
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Write a proportion. Let s = number of students who will ride a bike.
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Homework Practice
6.S.2.1
Making Predictions QUIZ SHOW For Exercises 1 and 2, use the following information.
On a quiz show, a contestant correctly answered 9 of the last 12 questions. 1. Find the probability of the contestant correctly answering the next question.
2. Suppose the contestant continues on the show and tries to correctly answer 24 questions. About how many questions would you predict the contestant to correctly answer? Least Favorite Chore Number of CHORES For Exercises 3–6, use the Chore Students table to predict the number of students out of 528 that would say Clean my room 7 each of the following was their least Take out the garbage 4 favorite chore. Wash dishes 5 3. clean my room 4. wash dishes Walk the dog 3 Vacuum or dust 5
6. take out the garbage
7. SCIENCE Refer to the bar graph below. A science museum manager asked some of the visitors at random during a typical day which exhibit they preferred. If there are 630 visitors on a typical day, predict the number of visitors who prefer the magnets exhibit. Compare this to the number of visitors who prefer the weather exhibit.
16 12 8
12
11 8
7
7
W
ea
th
er
ts
d un
ag ne M
ro
sc
tri
ic M
So
op
e
ty
4 0 ci
Number of Visitors
Visitor Preferences
El ec
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5. walk the dog
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Problem-Solving Practice
6.S.2.1
Making Predictions MOVIES For Exercises 1–3, use
SLEEP For Exercises 4–7, use the table
the table of results of Jeremy’s survey of favorite kinds of movies.
of results of the Better Sleep Council’s survey of Americans to find the most important factors for good sleep.
Favorite Movie Type Type People Drama 12 03 Foreign Comedy 20 Action 15
1. MOVIES How many people did Jeremy use for his sample?
2. If Jeremy were to ask any person to name his or her favorite type of movie, what is the probability that it would be comedy?
3. If Jeremy were to survey 250 people, how many would you predict would name comedy?
4. SLEEP Predict how many people out of 400 would say that a good mattress is the most important factor.
5. What is the probability that any person chosen at random would not say that a healthy diet is the most important factor?
6. Suppose 250 people were chosen at random. Predict the number of people that would say good pillows are the most important factor.
7. What is the probability that any person chosen at random would say that daily exercise is the most important factor for a good night sleep?
8. ICE CREAM Claudia went to an ice cream shop to conduct a survey. She asked every tenth person who entered the shop to name his or her favorite dessert. Did Claudia select a good sample? Explain.
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170
Most Important Factors for Good Sleep Type People Good Mattress 32 Daily Exercise 20 08 Good Pillows Healthy Diet 11 Other Factors 29
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Explore Through Reading
6.N.3.2
Estimating with Percents Get Ready for the Lesson Complete the Mini Lab at the top of page 401 in your textbook. Write your answers below. Use grid paper to find the fractional portion of each number. 1 of 10 1. _
1 2. _ of 10
2
2 3. _ of 20
5
5
5 4. _ of 36 6
5. MAKE A CONJECTURE How can you find a fractional part of a number without drawing a model on grid paper?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. Write the fraction for each percent. 20% =
40% =
60% =
80% =
25% =
50% =
75% =
100% =
1 33 _ %=
2 66 _ %=
3
3
7. Complete the sentence. When you estimate with percents, you round to numbers that are _______________.
Remember What You Learned 8. Work with a partner. Using the fractions and percents in the table you completed for Exercise 6, take turns saying either a fraction or percent. If you say a fraction, your partner writes the corresponding percent. If you say a percent, your partner writes the corresponding fraction. Make sure your partner cannot see the table above. Continue with your practice until you can remember all the fractions and percents.
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Study Guide
6.N.3.2
Estimating with Percents The table below shows some commonly used percents and their fraction equivalents.
Percent-Fraction Equivalent 1 20% = _ 5 _ 30% = 3 10 _ 40% = 2 5
Examples
_ 2 _ 60% = 3 5 _ 70% = 7
_ 5 _ 90% = 9
50% = 1
10
_
80% = 4
25% = 1 4 3 75% = 4
_
10
_ 3 _ 662/3% = 2 331/3% = 1 3
100% = 1
Estimate each percent.
20% of 58
76% of 21
1 20% is _ .
3 76% is close to 75% or _ .
Round 58 to 60 since it is divisible by 5.
Round 21 to 20 since it is divisible by 4.
_1 of 60¬is 12.
_1 of 24¬is 5.
5
4
4
5
3 So _ of 20 is 3 × 5 or 15
¬
4
So, 20% of 58 is about 12.
So, 76% of 21 is about 15.
1 25% is _ . Round 218 to 200. 4
_1 of 200 is 50. 4
So, Isabel should read about 50 pages by Friday.
Exercises Estimate each percent. 1. 49% of 8
2. 24% of 27
3. 19% of 46
4. 62% of 20
5. 40% of 51
6. 81% of 32
7. TIPS Jodha wants to tip the pizza delivery person about 20%. If the cost of the pizzas is $15.99, what would be a reasonable amount to tip?
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Example 3 Isabel is reading a book that has 218 pages. She wants to complete 25% of the book by Friday. About how many pages should she read by Friday?
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Homework Practice
6.N.3.2
Estimating with Percents Estimate each percent. 1. 51% of 62
2. 39% of 42
3. 78% of 148
4. 34% of 99
5. 74% of 238
6. 70% of 103
7. 22% of 152
8. 91% of 102
9. 26% of 322
10. 65% of 181
11. 98% of 60
12. 11% of 10
13. Estimate twenty-nine percent of forty-eight.
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14. Estimate sixty-two percent of one hundred twenty-four.
Estimate the percent that is shaded in each figure. 15.
16.
17.
18. WORK Karl made $365 last month doing odd jobs after school. If 75% of the money he made was from doing yard work, about how much did Karl make doing yard work?
19. HOMEWORK Jin spent 32 hours on math and language arts homework last month. She spent 11 hours on math. About what percent of her homework hours were spent on language arts? Explain.
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Problem-Solving Practice
PERIOD
6.N.3.2
Estimating with Percents 2. BASKETBALL In a recent regular season the WNBA Houston Comets won 54.76% of their games. They had 42 games in their regular season. About how many games did they win?
3. SALES TAX The sales tax rate in Lacon is 9%. About how much tax would you pay on an item that costs $61?
4. SPORTS The concession stand at a football game served 178 customers. Of those, about 52% bought a hot dog. About how many customers bought a hot dog?
5. SLEEP A recent study shows that people spend about 31% of their time asleep. About how much time will a person spend asleep during an average 78 year lifetime?
6. BIOLOGY The human body is 72% water, on average. About how much water will be in a person that weighs 138 pounds?
7. MONEY A video game that originally costs $25.99 is on sale for 50% off. If you have $14, would you have enough money to buy the video game?
8. SHOPPING A store is having a 20% sale. That means the customer pays 80% of the regular price. If you have $33, will you have enough money to buy an item that regularly sells for $44.99? Explain.
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1. SCHOOL At Westside High School, 24% of the 215 sixth grade students walk to school. About how many of the sixth grade students walk to school?
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Anticipation Guide Systems of Measurement
STEP 1
Before you begin Chapter 8
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. Inch, meter, yard, and kilometer are all measures of length in the customary system. 2. There are 3 feet in 1 yard. 3. Cup, pint, and quart are all measures of capacity in the customary system. 4. Since a quart is more than a pint, division would be used to convert a measure from quarts to pints. 5. There are 8 ounces in 1 pound.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. In the metric system, the basic unit of length is the meter. 7. One yard is a little longer than 1 meter. 8. One kilogram is about the same as 2 pounds. 9. 100 millimeters = 1 centimeter 10. To change a measure from liters to milliliters you would multiply by 1000. 11. Since there are 60 minutes in 1 hour, 140 minutes is the same as 1 hour 20 minutes. 12. Fahrenheit and Celsius are both measures of temperature. STEP 2
After you complete Chapter 8
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Four boards are measured in metric units. They are 24.1cm, 2.41 m, 240.8 mm, and 0.45 km. Put the lengths of these boards in order from least to greatest.
2. Michael’s mom sent him to the grocery store to buy a bag of sugar to use in cookies for the Student Council bake sale.What is a reasonable unit of measure for amount of sugar he bought?
A 24.1 cm, 2.41 m, 240.8 mm, 0.45 km B 2.41 m, 240.8 mm, 0.45 km, 24.1 cm
A milligrams
C 0.45 km, 2.41 m, 24.1 cm, 240.8 mm
B gallons
D 240.8 mm, 24.1 cm, 2.41 m, 0.45 km
C pounds D tons
Solution
Solution 1. Hint: Convert all of the various units to the same unit. In this case, changing to meters is a reasonable choice because there are units smaller and bigger than the meter listed. 1 cm = 0.01 m; so 2.41 cm = 0.241 m 1 mm = 0.001 m; so 240.8 mm = 0.2408 m 1 km = 1,000 m; so 0.45 km = 450 m
2. Measures of volume are typically used for liquids, so gallons can be eliminated as an option. Milligrams are used to measure very small objects and tons are used for the weight of very large objects, eliminating both of those options. Sugar is usually sold in 5 and 10 pound bags, so option C is reasonable.
Put all meter measures in order and write their equivalents. 0.2408 m → 240.8 mm 0.241 m → 24.1 cm 2.41 m → 2.41 m 450 m → 0.45 km The answer is D.
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The answer is C. Chapter 8
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Fold here.
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Study Guide
6.M.1.1
Converting Between Metric and Customary Units Relating Customary and Metric Units Both customary and metric measurements are used in the United States. Therefore, it is a good idea to develop some sense of the relationships between the two systems. The tables show the approximate equivalents between customary and metric units. Units of Capacity Units of Length Metric Metric Customary Metric Metric Customary Customary Customary 1 qt ≈ 0.9 L 1 L ≈ 1.1 qt 1 in. ≈ 2.5 cm 1 cm ≈ 0.4 in. 1 pt ≈ 0.5 L 1 L ≈ 2.1 pt 1 yd ≈ 0.9 m 1 m ≈ 1.1 yd 1 mi ≈ 1.6 km 1 km ≈ 0.6 mi Example 1 Complete each sentence. a.
42 in. ≈ cm There are approximately 2.5 cm in an inch. 42 in. × 2.5 = 105 cm
b.
6m≈ yd There are approximately 1.1 yards in a meter. 6 m × 1.1 = 6.6 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2 Amber is using a recipe to make soup. The recipe calls for 3 quarts of chicken broth. How many liters of chicken broth will Amber need? There is approximately 0.9 liter in a quart. 3 qt × 0.9 = 2.7 L The table below shows the approximate equivalents between customary and metric units of weights and mass. Units of Weight/Mass Metric Metric Customary Customary 1 oz ≈ 28.3 g 1 g ≈ 0.04 oz 1 lb ≈ 0.5 kg 1 kg ≈ 2.2 lb Example 3 Complete: 500 oz =
kg
There are approximately 28.3 grams in an ounce. First find the number of grams in 500 ounces. 500 oz × 28.3 = 14,150 g Then change grams to kilograms. There are 1,000 grams in a kilogram. 14,150 g ÷ 1,000 = 14.15 kg Exercises Complete each sentence. 1. 17 oz ≈ 4. 1.5 mi ≈ Chapter 8
g m
2. 90 km ≈ 5. 67 kg ≈
mi lb
3. 7 L ≈ 6. 12 pt ≈
pt L
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Skills Practice
6.M.1.1
Converting Between Metric and Customary Units Recall what you know about metric and customary equivalents. Tell whether each statement is true or false. 1. A length of 4 meters is longer than 4 yards.
2. A weight of 10 pounds is more than 5 kilograms.
3. A capacity of 1 gallon is more than 4 liters.
4. A length of 1 foot is about the same as 30 centimeters.
5. A kilometer is more than half a mile.
6. A pound is a little more than half a kilogram.
8. Sean has a recipe that calls for 0.25 L of milk. He has a one-cup container of milk in the refrigerator. Is this enough milk for the recipe?
9. The posted load limit for a bridge is 10. Leah is pouring paint from a 5-gallon 5 tons. The mass of Darryl’s truck is can into some jars. She has twelve jars 1,500 kilograms and it is holding cargo that each hold 1 liter and six jars that that weighs a half ton. Can Darryl drive each hold 1.25 liters. Does she have his truck across the bridge? enough jars for all the paint?
Choose the better estimate for each measure. 11. the height of a palmetto tree: 10 yards or 10 kilometers
12. the amount of water in a cooler: 8 pints or 8 liters
13. the weight of a bag of sugar: 4 pounds or 4 kilograms
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7. On a road in Canada, the posted speed limit is 45 kilometers per hour. Aimee is driving at a speed of 40 miles per hour. Is this above or below the speed limit?
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Homework Practice
6.M.1.1
Converting Between Metric and Customary Units Complete each conversion. Round to the nearest hundredth if necessary. 1. 10 cm ≈
in
2. 300 gal ≈
3. 250 g ≈
oz
4. 5.5 kg ≈
5. 145 m ≈
mi m
9. 23 pt ≈
L
10. 12 g ≈
yd
12. 504 L ≈
11. 44 m ≈ 13. 118 oz ≈
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15. 4 mi ≈
lb
6. 9.5 L ≈
7. 13 yd ≈
L
pt
8. 1.095 mi ≈
g
km
oz qt
14. 3,000 cm ≈
m
16. 7 km ≈
in.
yd
Convert each rate using dimensional analysis. Round to the nearest hundredth if necessary. 17. 88 mi/h ≈
km/min
18. 10 ft/min ≈
19. 165 L/h ≈
qt/min
20. 26 yd/s ≈
21. 474 gal/day ≈
L/week
22. 33.6 m/s ≈
23. 22 fl oz/min ≈
mL/s
24. 229 km/h ≈
m/h km/h ft/min mi/min
25. TRAVEL Lisa is traveling to Europe. The information from the airlines said that she is only allowed to check 25 kilograms worth of baggage. How many pounds is this?
26. SPACE SHUTTLE The space shuttle travels at an orbital speed of about 17,240 miles per hour. How many meters per minute is this?
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PERIOD
Problem-Solving Practice
6.M.1.1
Converting Between Metric and Customary Units 1. COOKING Ty enters a chili cook-off. If he uses 2 pounds of ground beef in his recipe, how many kilograms of ground beef does he use?
2. GIFTS Jayda brought 27 bottles of flavored water to give her class. If each bottle holds 1 pint of water, how many liters of water did Jayda bring?
3. BUILDING Davis built a shelf that holds a maximum of 30 kilograms. If Davis has a set of books that each
4. DECORATING Maya is cutting streamers for the school dance. Each streamer she cuts is 1 meter long. If the roll of streamers is 81 inches, how many 1 meter streamers can Maya get from each roll?
1 weigh _ pound, how many books can 2
Davis put on his shelf? Explain.
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6. COOKING Bri needs 1 quart of halfand-half for each batch of homemade ice cream she makes. If Bri has 10 liters of half-and-half, how many batches of ice cream can she make? Explain.
Chapter 8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. PETS Andrew has a 20-pound bag of dry dog food. Each day he feeds his dog 150 grams of dry dog food. For approximately how many days will the bag of dog food be enough to feed his dog? Explain.
NAME
10
DATE
PERIOD
Anticipation Guide Measurement: Perimeter, Area, and Volume
STEP 1
Before you begin Chapter 10
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. The area of a rectangle will double if the length and width are both doubled. 2. The perimeter of a rectangle can be found by adding two times the length and two times the width. 3. The circumference of a circle is the distance around the circle. 4. The radius of a circle is two times the diameter.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. To find the area of a parallelogram, multiply the length of the longer side by the length of the shorter side. 1 6. In the formula for the area of a triangle, A = _ bh, b is the 2
length of the base and h is the height of the triangle. 7. Volume is measured in cubic units. 8. A rectangular prism with a volume of 42 must have dimensions of 2, 3, and 7. 9. To find the surface area of a rectangular prism, multiply the area of the base by 6 (the number of faces of the prism). 10. A possible unit for the surface area of a rectangular prism is square inches. STEP 2
After you complete Chapter 10
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
Chapter 10
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NAME
10
DATE
PERIOD
Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Emilio knows that his car tire has a diameter of 0.5 m. He wants to know how far the wheel will go in three complete spins. How can he find this?
2. Find the volume of the following rectangular prism.
0.2 m
0.5 m
8 cm
A He can multiply the diameter by π and then by 3.
10 cm
B He can divide the diameter by π and then multiply by 3.
A V = 1,600 cm 2
C He can multiply the diameter by 3.
C V = 16 cm 2
D He cannot determine how far the wheel will go in 3 turns.
D V = 16 cm 3
B V = 1,600 cm 3
Solution
Solution
1. Hint: The circumference of a circle is the distance around the circle. The formula for circumference is πd or 2πr. Each point around the circle will touch the ground once in a complete spin, so the circumference of the circle is the distance the tire will go in one spin. The circumference can be found by multiplying the diameter by pi (π), so for each spin, the tire will travel πd meters. For three spins, the circumference should be multiplied by three, or 3πd. The option that describes this process is Option A, or the diameter multiplied by pi (π) and then multiplied by 3.
The answer is A.
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2. Hint: Before you calculate the volume, make sure that all of the dimensions are converted to the same units. The height should be converted to centimeters so that the units are consistent. There are 100 cm in a meter, so 0.2 m is equivalent to 20 cm. The volume of a rectangular prism can be calculated using this formula: V = × w × h. In this case the volume is: V = 8 cm × 10 cm × 20 cm = 1600 cm 3 Notice that the units are cubed, because you are multiplying cm × cm × cm = cm 3. The units for volume will always be cubic. The answer is B. Chapter 10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fold here.
NAME
10A
DATE
PERIOD
Explore Through Reading
6.M.2.1
Perimeter Get Ready for the Lesson Complete the Mini Lab at the top of page 522 in your textbook. Write your answers below. distance around in simplest form for squares A through D. 1. Write the ratio ___ side length
What do you notice about these ratios?
2. MAKE A CONJECTURE Write an expresson for the distance around a square that has a side length of x centimeters.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. The formula for the perimeter of a square is P = 4s. What does that tell you about the sides of a square?
4. The perimeter of a rectangle is equal to 2 + 2w. What does the formula tell you about the lengths and widths of a rectangle?
5. Can you use the formula for the perimeter of a rectangle to find the perimeter of a square? Why or why not?
Remember What You Learned 6. Think of a way to remember the formula for the perimeter of a rectangle, P = 2 + 2w. For example, use the letters of the variables as the first letters of words in a sentence.
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North Caroline, Grade 6
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10A
DATE
PERIOD
Study Guide
6.M.2.1
Perimeter The distance around any closed figure is called its perimeter. To find the perimeter, add the measures of all the sides of the figure. Finding Perimeter Figure
Words
Symbols
Square
The perimeter P of a square is four times the measure of any of its sides s.
P = 4s
Rectangle
The perimeter P of a rectangle is the sum of the lengths and widths. It is also two times the length plus two times the width w.
P=++w+w P = 2 + 2w
Example 1 P = 4s P = 4(6) P = 24
Find the perimeter of the square. Write the formula.
6 in.
Replace s with 6. Multiply.
The perimeter of the square is 24 inches. Example 2
Find the perimeter of the rectangle.
3 ft
Estimate: 5 + 5 + 5 + 5 = 20 = = = =
2 + 2w 2(5) + 2(3) 10 + 6 16
Write the formula. Replace ℓ with 5 and w with 3.
5 ft
5 ft
Multiply. Add.
The perimeter of the rectangle is 16 feet. Compared to the estimate, the answer is reasonable.
3 ft
Exercises Find the perimeter of each square or rectangle. 1. 1 in.
3 yd
2.
4 in. 1 in. 4 in.
1
3.
1
10 2 yd
5 ft
10 2 yd
5 ft 3 yd
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
P P P P
NAME
10A
DATE
PERIOD
Homework Practice
6.M.2.1
Perimeter Find the perimeter of each figure. 17 m
1.
2.
17 m
21 in. 8 ft
17 m
21 in.
17 m
78 cm
4.
8 ft
18 ft
21 in.
1
5.
6.
49 2 yd
4.1 m
3
3
29.3 m
16 4 yd
16 4 yd 92 cm
18 ft
3. 21 in.
92 cm 1
49 2 yd
29.3 m 4.1 m
78 cm
12 mm
8.
4 mm
5m
11 ft 9 mm
9 mm 6 mm
5m
6 mm
5m
5m 5 mm
5m
11 ft 3 mm
5m
5m
5m
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
11 ft
5m
11 ft
5m
9.
5m
11 ft
7.
5m
How many segments x units long are needed for the perimeter of each figure? 11.
10. x
x x
x
x
x
x
x
12. POOLS A 4-foot wide walkway surrounds a 10-foot square wading pool. What is the perimeter of the walkway?
10 ft 4 ft
13. RUGS Jan wants to sew a fringe border on all sides of a rectangular rug for her bedroom. The rug is 3.4 feet wide and 5.5 feet long. How many feet of fringe does she need?
Chapter 10
North Caroline, Grade 6
185
NAME
10A
DATE
Problem-Solving Practice
PERIOD
6.M.2.1
Perimeter 2. FRAMING How many inches of matting are needed to frame an 8 inch by 11 inch print?
3. GARDENING Jessica wants to put a fence around her 10.8 foot by 13 foot rectangular garden. How many feet of fencing will she need?
4. SEWING Amy is making pillows to decorate her bed. She is going to make three square pillows that are each 2 feet by 2 feet. She wants to use the same trim around each pillow. How many feet of trim will she need for all three pillows?
5. JOGGING Before soccer practice, Jovan warms up by jogging around a soccer field that is 100 yards by 130 yards. How many yards does he jog if he goes around the field four times?
6. POSTER Ted is making a stop sign poster for a talk on safety to a first grade class. He will put a strip of black paper around the perimeter of the stop sign. Each of the stop sign’s eight sides is 16 inches. How long a strip of paper will he need?
7. FLAG Jo is making a triangular banner. 2 Each of the three sides is 14 _ inches 3 long. If she puts a braided trim around the banner, how much trim will she need?
8. PYRAMIDS The Great Pyramid at Giza, Egypt, has a square base, with each side measuring 250 yards. If you could walk once all the way around the pyramid at its base, how far could you walk? Explain.
North Caroline, Grade 6
Chapter 10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
186
1. GEOGRAPHY The state of Colorado is nearly rectangular. It is about 589 kilometers by 456 kilometers. What is the approximate perimeter of Colorado?
NAME
10B
DATE
PERIOD
Explore Through Reading
6.M.3.1, 6.M.3.2
Circles and Circumference Get Ready for the Lesson Read the introduction at the top of page 528 in your textbook. Write your answers below. 1. Describe the relationship between the diameter and radius of each hoop.
2. Describe the relationship between the circumference and diameter of each hoop.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. What is the real value of π? What does it mean that the real value never ends?
4. Why is the symbol ≈ used in the solutions of the circumference problems in the examples?
5. What are the two formulas that you can use to find the circumference of a circle? When would you use each of them?
Remember What You Learned 6. Make a model of a circle and its parts using materials from your home. Label the center, radius, diameter, and circumference.
Chapter 10
North Caroline, Grade 6
187
NAME
10B
DATE
PERIOD
Study Guide
6.M.3.1, 6.M.3.2
Circles and Circumference The circumference is the distance around a circle.
Center
The radius, r, is the distance from the center to any point on a circle.
The diameter, d, is the distance across a circle through its center.
The circumference of a circle is equal to π times its diameter or π times twice its radius.
Example 1 C = πd ≈3×4 ≈ 12
C = πd or C = 2πr
Estimate the circumference of a circle whose diameter is 4 meters. Write the formula. Replace π with 3 and d with 4. Multiply.
The circumference of the circle is about 12 meters. Example 2 Find the circumference of a circle whose radius is 13 inches. Use 3.14 for π. Round to the nearest tenth. Write the formula. Replace r with 13 and π with 3.14. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C = 2πr = 2 × 3.14 × 13 = 81.64
Multiply.
Rounded to the nearest tenth, the circumference is about 81.6 inches.
Exercises Estimate the circumference of each circle. 2.
1.
3. 8 in.
15 ft
5m
4. The radius of a circle measures 16 miles. Find the measure of its circumference to the nearest tenth. Use 3.14 for π. 5. Find the circumference of a circle whose diameter is 12 yards. Use 3.14 for π. Round to the nearest tenth. 6. Find the circumference of a circle with a radius of 7 inches. Use 3.14 for π. Round to the nearest tenth.
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NAME
10B
DATE
PERIOD
Homework Practice
6.M.3.1, 6.M.3.2
Circles and Circumference Find the missing radius or diameter of each circle with the given dimensions. 1. d = 18 in.
2. d = 29 m
3. r = 21 ft
r=
r=
4. r = 13 mm
d=
d=
Estimate the circumference of each circle. 6.
5. 26 m
7. 11 in. 4 yd
8. d = 31 mm
9. r = 29 cm
10. d = 32 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the circumference of each circle. Use 3.14 for π. Round to the nearest tenth. 11.
12.
13. 18 in.
5 mm 14 ft
14. r = 22 cm
15. r = 15 yd
16. d = 31 m
17. PLANTS The world’s largest flower, the Giant Rafflesia, is 91 centimeters in diameter. Use a calculator to find the circumference of a Giant Rafflesia to the nearest tenth.
18. GEOLOGY Ubehebe Crater in Death Valley has a diameter of a little more
1 mile. If Latisha walks around its rim at a rate of 2 miles per hour, than _ 2
about how long will it take her to walk all the way around the crater? Find your answer to the nearest tenth. Use 3.14 for π.
Chapter 10
North Caroline, Grade 6
189
NAME
DATE
Mini-Project
PERIOD
6.M.3.1, 6.M.3.2
(Use with Lesson 10B)
Circumference Place a piece of string around the circumference of each circle. Measure the string to the nearest eighth of an inch. Record the measurement. Then draw the diameter and measure it to the nearest eighth of an inch. Use the formula c = π to calculate π.
_ d
1.
2.
Circumference =
Diameter =
Diameter =
π=
π=
3.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Circumference =
4.
Circumference =
Circumference =
Diameter =
Diameter =
π=
π=
22 5. How do your values for π compare to _ ? 7
How do your values for π compare to 3.14?
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NAME
10C
DATE
PERIOD
Study Guide
6.M.3.2
Area of Circles The area A of a circle equals the product of pi (π) and the square of its radius r. A = πr 2
Example 1 A = πr 2
Find the area of the circle. Area of circle
A ≈ 3.14 · 5
2
Replace
5 cm
π with 3.14 and r with 5.
A ≈ 78.5 The area of the circle is approximately 78.5 square centimeters. Example 2
Find the area of a circle that has a diameter of 9.4 millimeters.
A = πr 2
Area of a circle
A ≈ 3.14 · 4.7 2
Replace
π with 3.14 and r with 9.4 ÷ 2 or 4.7.
A ≈ 69.4 The area of the circle is approximately 69.4 square millimeters.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Find the area of each circle. Use 3.14 for π. Round to the nearest tenth. 2.
1.
3.
7 in. 25 mm 12 ft
4. radius = 2.6 cm
5. radius = 14.3 in.
1 6. diameter = 5 _ yd
3 7. diameter = 4 _ mi
8. diameter = 7.9 mm
1 9. radius = 2 _ ft
4
Chapter 10
2
5
North Caroline, Grade 6
191
NAME
10C
DATE
PERIOD
Skills Practice
6.M.3.2
Area of Circles Find the area of each circle. Use 3.14 for π. Round to the nearest tenth. 2.
1.
4 yd 1 cm
3.
4. 14 in.
35 mm
5.
6. 4.3 ft 8 cm
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7.
8. 4.7 yd 22.5 in.
9.
10. 11.9 ft
2.1 mm
11. radius = 5.7 mm
12. radius = 8.2 ft
1 13. diameter = 3 _ in.
14. diameter = 15.6 cm
15. radius = 1.1 in.
3 16. diameter = 12 _ yd
4
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Chapter 10
NAME
10C
DATE
PERIOD
Homework Practice
6.M.3.2
Area of Circles Find the area of each circle. Use 3.14 for π. Round to the nearest tenth if necessary. 3.
2.
1. 7.1 m
13 km
12 ft
4.
5.
6.
4 in. 10 yd
7. diameter = 9.4 mm 3 10. radius = 4 _ yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
5.6 cm
1 8. diameter = 3 _ ft
1 9. radius = 6 _ in.
1 11. diameter = 15 _ mi
12. radius = 7.9 km
2
4
2
Estimate to find the approximate area of each circle. 13.
14.
15. 6.1 m 14 cm
3.8 yd
16. SPOTLIGHT A spotlight can be adjusted to effectively light a circular area of up to 6 meters in diameter. To the nearest tenth, what is the maximum area that can be effectively lit by the spotlight? 17. ARCHERY The bull’s eye on an archery target has a radius of 3 inches. The entire target has a radius of 9 inches. To the nearest tenth, find the area of the target outside of the bull’s eye.
3 in.
9 in.
Chapter 10
North Caroline, Grade 6
193
NAME
10C
DATE
Problem-Solving Practice
PERIOD
6.M.3.2
Area of Circles 1. POOLS Susan designed a circular pool with a diameter of 25 meters. What is the area of the bottom of the pool? Round to the nearest tenth.
2. MONEY Find the area of the coin to the nearest tenth.
19 mm
3. DRUMS What is the area of the drumhead on the drum shown below? Round to the nearest tenth.
4. PIZZA Estimate the area of the top of a round pizza that has a diameter of 16 inches. Round to the nearest tenth.
14 in.
6. UTILITIES What is the area of the top surface of a circular manhole cover that has a radius of 30 centimeters? Use 3.14 for π.
5.5 yd
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. GARDENING Jane needs to buy mulch for the garden with the dimensions shown in the figure. For how much area does Jane need to buy mulch? Round to the nearest tenth.
NAME
10D
DATE
PERIOD
Explore Through Reading
6.M.2.2
Area of Parallelograms Get Ready for the Lesson Complete the Mini Lab at the top of page 534 in your textbook. Write your answers below. 1. How does a parallelogram relate to a rectangle?
2. What part of the parallelogram corresponds to the length of the rectangle?
3. What part corresponds to the rectangle’s width?
4. MAKE A CONJECTURE What is the formula for the area of a parallelogram?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Look back at Lesson 1-9, Algebra: Area Formulas. Write the definition for the area of a figure.
6. Look at the models in the Mini Lab at the top of page 534 in your textbook. How can you tell from the models that the areas of the rectangle and the parallelogram are the same?
7. Look at Examples 2 and 3 on pages 535 and 536. Explain what the dotted lines in the figures represent.
Remember What You Learned 8. Work with a partner. Using models, demonstrate that the area of a parallelogram equals the product of any base of the parallelogram and its height.
Chapter 10
North Caroline, Grade 6
195
NAME
10D
DATE
PERIOD
Study Guide
6.M.2.2
Area of Parallelograms The area A of a parallelogram is the product of any base b and its height h. Symbols
A = bh
Model height (h ) base (b )
Examples
Find the area of each parallelogram. 5 in.
9 in.
The base is 4 units, and the height is 7 units.
A = bh A=4×7 A = 28 The area is 28 square units or 28 units2.
A = bh A=9×5 A = 45 The area is 45 square inches or 45 in2.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Find the area of each parallelogram. 1.
2.
4.
5.
3.
6. 1 14 2
yd
10.4 m
35 cm 1
16 3 yd
8.8 m
18 cm
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North Caroline, Grade 6
Chapter 10
NAME
10D
DATE
PERIOD
Homework Practice
6.M.2.2
Area of Parallelograms Find the area of each parallelogram. 2.
1.
11 in.
3. 9 in.
4.
1
5.
4 ft
6.
9 2 yd
24.9 m 1
5 3 yd
8 ft
59.3 m
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the area of the shaded region in each figure. 7.
8.
31 mm
13 mm 6 mm
7 in.
18 mm
12 in.
13 in.
21 in.
5 9. Estimate the area of a parallelogram whose base is 6 _ feet and whose 2 feet. height is 5 _
8
5
10. Estimate the area of a parallelogram with base 9.44 yards and height 7.56 yards. 11. FLAGS Estimate the area of the shaded region of the flag of the Republic of the Congo.
6.8 in. 5.2 in.
12. GARDENING Liam is preparing a 78 square foot plot for a garden. The plot will be in the shape of a parallelogram that has a height of 6 feet. What will be the length of the base of the parallelogram? Explain your reasoning.
Chapter 10
2 in. 8 in.
North Caroline, Grade 6
197
NAME
10D
DATE
PERIOD
Problem-Solving Practice
6.M.2.2
Area of Parallelograms 1. SUNFLOWERS Norman is a sunflower farmer. His farm is in the shape of a parallelogram with a height measuring 3.5 kilometers and a base measuring 4.25 kilometers. What is the total land area Norman uses?
2. VOLLEYBALL Ella and Veronica are in charge of making a banner for the volleyball game this Saturday. How much poster paper will they need for a parallelogram-shaped banner with 1 1 feet and base 6 _ feet? height 3 _ 2
3. FLAGS Joseph is painting the flag of Brunei (a country in Southeast Asia) for a geography project at school. How many square inches will he cover with white paint?
4
4. FLAGS Use the flag from Exercise 3. How many square inches will Joseph cover with black paint?
White Black
8 in.
72 in.
5. QUILTING The pattern shows the dimensions of a quilting square that Sydney will use to make a quilt. How much blue fabric will she need? Explain how you found your answer.
6. QUILTING Use the quilting pattern from Exercise 5. How much pink fabric will Sydney need?
6 in. red
red pink 3 in.
blue 8 in.
green 12 in.
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7 in.
Yellow
NAME
10E
DATE
PERIOD
Explore Through Reading
6.M.2.2
Area of Triangles Get Ready for the Lesson Read the introduction at the top of page 540 in your textbook. Write your answers below. 1. Compare the two triangles.
2. What figure is formed by the two triangles?
3. MAKE A CONJECTURE Describe the relationship that exists between the area of one triangle and the area of the entire figure.
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. Look at the figure at the right. Explain how the height can be a, b, or d. a
c d b
5. Using models, demonstrate that congruent triangles have the same area.
6. Look at the illustrations of h on page 540. What is the symbol found where h and b meet? How does that affect the length of h?
Remember What You Learned 7. Work with a partner. Using models, demonstrate that the area of a triangle is one-half the product of the base b and the height h of the triangle.
Chapter 10
North Caroline, Grade 6
199
NAME
10E
DATE
PERIOD
Study Guide
6.M.2.2
Area of Triangles The area A of a triangle is one half the product of any base b and its height h. bh Symbols A = _
Model
2
height (h ) base (b )
Examples
Find the area of each triangle.
6m 14 m height
bh A=_
The measure of the base is 5 units, and the height is 8 units.
base
Area of a triangle
2 14 × 6 A= 2
__
Replace b with 14 and h with 6.
84 A=_
Simplify the numerator.
2
bh A=_
2 5×8 A= 2
_
Area of a triangle
A = 42
Replace b with 5 and h with 8.
The area of the triangle is 42 square meters.
Simplify the numerator.
A = 20
Divide.
2
The area of the triangle is 20 square units. Exercises Find the area of each triangle. 1.
2.
3. 5 ft
2 ft
4.
5.
6.
2.6 cm
3
12 4 in.
6.8 cm 30 yd 1
14 2 in.
10 yd
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North Caroline, Grade 6
Chapter 10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
40 A=_
Divide.
NAME
10E
DATE
PERIOD
Homework Practice
6.M.2.2
Area of Triangles Find the area of each triangle. 1.
2.
12 mm
3.
10 mm
4.
5.
6.
14 in.
1
9 2 yd
4.9 m 23.7 m
34 in. 1
19 4 yd
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7. height: 15 ft base: 38 ft
8. height: 22 cm base: 17 cm
9. height: 12 in. base: 21 in.
12 cm
10. COMPLEX FIGURES Find the area of the figure at the right.
4 cm 16 cm
11. MURALS Raul is painting a mural of an ocean scene. The triangular sail on a sailboat has a base of 4 feet and a height of 6 feet. Raul will paint the sail using a special white paint. A can of this paint covers 10 square feet. How many cans of white paint will Raul need? 12. FLAGS What is the area of the triangle on the flag of Bosnia and Herzegovina?
9 cm
7 cm
18 cm
34 cm
Chapter 10
North Caroline, Grade 6
201
NAME
DATE
Mini-Project
PERIOD
6.M.2.2
(Use with Lesson 10E)
Areas of Triangles Use a metric ruler to measure the base and height of each triangle. If the height is not shown, sketch it. Label these segments with their measurements to the nearest millimeter. Use your measurements to calculate the area to the nearest square millimeter. 1.
2.
Area =
4.
Area =
5.
Area =
6.
Area =
202
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3.
Area =
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Area =
Chapter 10
NAME
11
DATE
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Anticipation Guide Integers and Transformations
STEP 1
Before you begin Chapter 11
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. An integer is any positive or negative whole number, or 0. 2. A positive integer plus a negative integer will always equal a negative integer. 3. To subtract -5 from 9, add 9 and 5. 4. The product of two integers with the same sign is always positive.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. The quotient of any integer divided by a negative integer is negative. 6. In the ordered pair (-4, 9), -4 is the x-coordinate and 9 is the y-coordinate. 7. To locate the ordered pair (3, -5) on the coordinate plane, move 3 units up and 5 units to the left. 8. When a figure is translated, the size and shape stays the same. 9. When a figure is reflected, the size and shape stays the same. 10. Translating a figure is the same as reflecting it over two parallel lines. STEP 2
After you complete Chapter 11
• Reread each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Identify points A, B, and C on the number line below. " -10
#
2. Use the number line below to help you find the sum of this problem:
$
-5
-8 + (-4) = 0 -13-12-11-10 -9 -8 -7 -6 -5 -4 -3
A -6, -4, -1 B -7, -4, -1
A -4
C -5, -3, -1
B -12
D -7, -3, -1
C -11 D This problem cannot be solved.
Solution
Solution
1. Hint: Use the numbers provided to determine the location of the points. Counting from -5, point A is two spaces to the left, which is -7. Point B is one space to the right of -5, so it corresponds with -4. Point C is the same for all of the answer options, and is located one space to the left of 0, or -1. Point A is located at -7. Point B is located at -4. Point-C is located at -1.
The answer is B.
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2. Hint: When you add a negative number, it is the same as subtracting the number. Starting at the point -8, we are adding -4, which is the same as subtracting 4, so the answer should be smaller, or more negative, than -8. In order to subtract, move to the left on the number line 4 spaces. The result is -12. -8 + -4 = -8 - 4 = -12
The answer is B. Chapter 11
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Fold here.
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Explore Through Reading
6.N.3.1
Ordering Integers Get Ready for the Lesson Read the introduction at the top of page 572 in your textbook. Write your answers below. 1. Write an integer to represent the amount of money that each person has in his or her account at the Snack Emporium.
2. Order the integers from least to greatest.
3. Who has the least money in his or her Snack Emporium account?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Read the Lesson 4. What symbol is used to show greater than? Write a mathematical statement using this symbol.
5. What symbol is used to show less than? Write a mathematical statement using this symbol.
6. How is a number line helpful when ordering integers from least to greatest?
Remember What You Learned 7. Describe a real-world situation in which you would have to order integers from least to greatest or greatest to least. Create integers for this situation. Then order them from least to greatest and greatest to least.
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Study Guide
6.N.3.1
Ordering Integers The inequality symbol ‘>’ means is greater than. The inequality symbol ‘<’ means is less than.
Example 1
Replace
with < or > to make the statement 4
-5 true.
Graph 4 and -5 on a number line. Then compare. -5 -4 -3 -2 -1 0 1 2 3 4 5
Since 4 is to the right of -5, 4 > -5 is a true statement. Example 2
Order the integers 1, -2, and 3 from least to greatest.
Graph each integer on a number line. Then compare. -5 -4 -3 -2 -1 0 1 2 3 4 5
The order from least to greatest is -2, 1, and 3. Exercises Replace each
with < or > to make a true statement.
0
2. 3
-3
3. -9
8
4. -8
-3
5. 11
3
6. -2
10
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1. -2
Order each set of integers from least to greatest. 7. -2, 3, 0, -1, 1
9. 5, -7, -2, 1, 9
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8. 3, -3, -2, 1, -1
10. -2, 1, 5, -5, 0
Chapter 11
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Homework Practice
6.N.3.1
Ordering Integers Replace each 1. 18 5. 6
23 -3
with < or > to make a true sentence. 2. -9 6. 0
-1 8
3. -3 7. 6
-5 -7
4. 8
-2
8. -23
-16
Order each set of integers from least to greatest. 9. 10, -5, 3 16, -1, 0, and 1
10. -2.5, 4, 23, -1, 5, -3, and 0.66
11. 1, -2.5, 0.75, 3, and -0.75
12. 63, -34, 36, -27, -13, and 12
Order each set of integers from greatest to least. 13. 8, 43, -25, 12, -14, and 3
14. -8, 32, 55, -32, -19, and -3
15. -100, -89, -124, -69, and -52
16. 6, 17, -20, 15, -19, and 26
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
ROLLER COASTERS The table shows how
several roller coasters compare to the Mantis. Refer to the table to answer Exercises 17–20. 17. Which roller coaster has the greatest lift height?
18. What is the median lift height for the roller coasters listed? Round to the nearest tenth.
Lift Vertical Heights (ft) Drop (ft) Gemini -20 -19 Magnum XL-200 60 58 Top Thrill Dragster 275 263 Mantis 0 0 Millenium Force 165 163 Mean Streak 16 18 Raptor -8 -18 Roller Coaster
Source: Cedar Point
19. Arrange the given roller coasters from least to greatest lift height.
20. What is the median of the data for vertical drop?
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Problem-Solving Practice
6.N.3.1
Ordering Integers 1. BUSES Melanie, Byron, and Chin are all waiting at the bus stop. Melanie’s bus leaves at 10 minutes after noon. Byron’s bus leaves at 15 minutes before noon. Chin’s bus leaves at 5 after noon. Arrange the three according to who will leave the bus stop first.
2. INTERNET Darnell pays for 500 minutes of Internet use a month. The table indicates his Internet usage over the past 4 months. Positive values indicate the number of minutes he went over his allotted time and negative values indicate the number of minutes he was under. Arrange the months from least to most minutes used. Month June July August September
4. WEATHER The table shows the average normal January temperature of four cities in Alaska. Compare the temperatures of Barrow and Fairbanks, using < or >. City Temperature (°F) Anchorage 15 Barrow -13 Fairbanks -10 Juneau 24
5. WEATHER Use the table in Exercise 4. Compare the temperatures of Anchorage and Fairbanks using < or >.
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6. WEATHER Use the table from Exercise 4. Write the temperatures of the four cities in order from highest to lowest temperature.
Chapter 11
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. GOLF In a golf match, Jesse scored 5 over par, Neil scored 3 under par, Felipo scored 2 over par, and Dawson scored an even par. Order the players from least to greatest score.
Time -20 65 -50 20
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Explore Through Reading
6.G.1.1
The Coordinate Plane Get Ready for the Lesson Complete the activity at the top of page 599 in your textbook. Write your answers below. 1. Describe the location of the barber shop in relation to the town hall.
2. What building is located 7 miles east and 5 miles north of the town hall?
3. Violeta is at the library. Describe how many blocks and in what direction she should travel to get to the supermarket.
4. Let north and east directions be represented by positive integers. Let west and south directions be represented by negative integers. Describe the location of the high school as an ordered pair using integers.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. Describe the location of the bank as an ordered pair using integers.
Read the Lesson 6. Describe how to locate the point (-5, -3) on a coordinate grid.
7. In which quadrant is the point (-5, -3)?
Remember What You Learned 8. Work with a partner. Draw a coordinate system that can be used to locate objects in your classroom. Have one person say the ordered pair of a location and the other say what object is located at that point.
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Study Guide
6.G.1.1
The Coordinate Plane The x-axis and y-axis separate the coordinate system into four regions called quadrants.
Example 1
Identify the ordered pair that names point A.
Quadrant II
A
Step 1 Move left on the x-axis to find the x-coordinate of point A, which is -3. Step 2 Move up the y-axis to find the y-coordinate, which is 4.
-4 -3 -2
O
Quadrant I
B
1 2 3 4x
-2 -3 -4
Point A is named by (-3, 4). Example 2
y 4 3 2 1
Quadrant III
Graph point B at (5, 4).
Quadrant IV
Use the coordinate plane shown above. Start at 0. The x-coordinate is 5, so move 5 units to the right. Since the y-coordinate is 4, move 4 units up. Draw a dot. Label the dot B. See grid at the top of the page.
Exercises
1. C 3. E
2. D
-4 -3 -2
O
J
4. F F
5. G
6. H
7. I
8. J
Graph and label each point using the coordinate plane at the right. 9. A(-5, 5)
10. M(2, 4)
11. G(0, -5)
12. D(3, 0)
13. N(-4, -3)
14. I(2, -3)
C
-2 -3 -4
North Carolina, Grade 6
H
I
1 2 3 4x
D E
y
O
210
B
x
Chapter 11
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
G
y 4 3 2 1
A
Use the coordinate plane at the right. Write the ordered pair that names each point.
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Homework Practice
6.G.1.1
The Coordinate Plane Use the coordinate plane at the right for Exercises 1–6. Identify the point for each ordered pair. 1. (-3, 4)
y
2. (-4, -3)
( $
3. (-2, -2)
%
, )
-
O
4. (3, -1)
&
*
x
#
5. (0, 1)
'
6. (-1, -4)
+
"
For Exercises 7–12, use the coordinate plane above. Write the ordered pair that names each point. Then identify the quadrant where each point is located. 7. C
8. L
9. D
10. A
11. G
12. I y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph and label each point on the coordinate plane at the right. 13. L(-2, 0)
14. M(5, 2)
15. N(-4, -3)
16. P(1, -1)
17. Q(0, -4)
18. R(3, -3)
x
O
y
Use the map of the Alger Underwater Preserve in Lake Superior to answer the following questions. 19. In which quadrant is the Stephen M. Selvick located?
Lake Superior
Williams Island
Grand Island
Superior Stephen M. Selvick George x
20. What is the ordered pair that represents the location of the Bermuda? the Superior?
21. Which quadrant contains Williams Island?
Shipwrecks
Herman H. Hettler Manhattan Smith Moore
Bermuda
Munising
22. Which shipwreck is closest to the origin?
Chapter 11
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Mini-Project
6.G.1.1
(Use with Lesson 11B) The Coordinate System a. Graph and label each point. b. Connect the points in order, including the last and the first points. c. Name the figure. 1. A(-3, 3), B(1, 3), C(1, -1), D(-3, -1)
2. J(-5, 2), K(3, 2), L(3, -3), M(-5, -3)
y
y
5
4 3 2 1 -5 -4 -3 -2 -1
5
4 3 2 1
O 1
-1 -2 -3
2 3
4 5x
-5 -4 -3 -2 -1
1 2 3
-1
4 5x
-2 -3
-4
-4 -5
3. P(-3, 3), Q(2, 3), R(5, -2), S(-5, -2)
4. E(-3, 4), F(4, 2), G(4, -2), H(-3, 0)
y
y
4 3 2 1 -5 -4 -3 -2 -1
5
4 3 2 1
O 1 2 3 4 5x
-1
-5 -4 -3 -2 -1
-2 -3
-1 -2 -3
-4 -5
-4 -5
5. S(-4, 5), T(0, 5), U(0, -2), V(-4, -2)
y
5
-5 -4 -3 -2 -1
-1
1 2 3 4 5x
6. P(-2, 4), Q(1, 4), R(3, 1), S(3, -1), T(1, -4), U(-2, -4), V(-4, -1), W(-4, 1)
y
4 3 2 1
O
5
4 3 2 1
O 1 2 3
-2 -3 -4 -5
North Carolina, Grade 6
4 5x
-5 -4 -3 -2 -1
-1
O 1 2 3
4 5x
-2 -3 -4 -5
Chapter 11
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
-5
5
212
O
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Study Guide
6.G.1.2
Intersections of Geometric Figures An intersection is a point that two or more geometric figures have in common. Suppose two figures lie in the same plane. There are several possibilities of how many points they may have in common.
Example A line and a square lie are on a coordinate grid. How many points of intersection are there in each figure below? a.
9 8 7 6 5 4 3 2 1
y
b.
1 2 3 4 5 6 7 8 9x
O
y
c.
1 2 3 4 5 6 7 8 9x
O
The square and line do not intersect. There are no points of intersection.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9 8 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1
y
1 2 3 4 5 6 7 8 9x
O
The line intersects the square at two points, (3, 4), and (6, 7).
The line intersects the square along one of its sides. The intersection is a segment and a segment contains an infinite number of points.
Exercises Describe the points of intersection shown in each figure. 1.
9 8 7 6 5 4 3 2 1 O
y
2.
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1 O
y
3.
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1 O
y
1 2 3 4 5 6 7 8 9x
4. Draw figures to show all possible numbers of intersections of a line and a circle. Tell how many intersections there are in each figure.
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Skills Practice
6.G.1.2
Intersections of Geometric Figures Describe the points of intersection shown in each figure. 1.
9 8 7 6 5 4 3 2 1
y
1 2 3 4 5 6 7 8 9x
O
4.
y
7.
9 8 7 6 5 4 3 2 1 O
214
5.
y
North Carolina, Grade 6
9 8 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1 O
3.
1 2 3 4 5 6 7 8 9x
y
6.
y
y
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1
y
1 2 3 4 5 6 7 8 9x
O
9.
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1 O
1 2 3 4 5 6 7 8 9x
O
8.
1 2 3 4 5 6 7 8 9x
y
O
1 2 3 4 5 6 7 8 9x
O
9 8 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1 O
y
1 2 3 4 5 6 7 8 9x
Chapter 11
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9 8 7 6 5 4 3 2 1
2.
NAME
11C
DATE
PERIOD
Homework Practice
6.G.1.2
Intersections of Geometric Figures Describe the points of intersection shown in each figure. 1.
9 8 7 6 5 4 3 2 1
y
1 2 3 4 5 6 7 8 9x
O
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4.
9 8 7 6 5 4 3 2 1 O
2.
y
y
9 8 7 6 5 4 3 2 1 O
3.
1 2 3 4 5 6 7 8 9x
O
5.
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1
y
y
1 2 3 4 5 6 7 8 9x
O
6.
1 2 3 4 5 6 7 8 9x
9 8 7 6 5 4 3 2 1
9 8 7 6 5 4 3 2 1 O
y
1 2 3 4 5 6 7 8 9x
7. Draw figures to show all possible numbers of intersections of a line and a right triangle. Describe the intersections in each figure.
8. A circle and a triangle intersect on a plane. What is the maximum number of points of intersection possible? Make a drawing to explain your answer.
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NAME
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Problem-Solving Practice
PERIOD
6.G.1.2
Intersections of Geometric Figures 1. AMUSEMENT PARK RIDES The parents group at the middle school sponsored a carnival. The sketch below represents the framework of the small Ferris Wheel ride they had. From this picture, which point represents the point that is the intersection of all triangles in the picture?
2. ART Juanita has an assignment for art class in which she must arrange a rectangle or square, an isosceles triangle and a circle into a frame so that all three figures intersect each other. Draw a sketch of what her art piece might look like in the picture frame below.
#
"
$
)
,
%
( '
&
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. CLOTHING Argyle is a pattern composed of intersecting polygons. This pattern is often used in sweaters and socks. a. Select one triangle in the pattern. How many times does a single white line intersect that triangle? b. Part of the pattern is made of squares. How many points of intersection exist between two gray squares? c. Find a gray square and a black square. How many points of intersection exist between these two squares?
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Explore Through Reading
6.G.1.3
Translations Get Ready for the Lesson Read the problem at the top of page 604. Write your answers below. 1. On Jose’s second turn, he spins a 4. Describe where his piece will be after moving.
2. Did the size or shape of the came piece change after moving?
Read the Lesson 3. Example 1 shows the translation of a square. What is used to indicate the new vertices?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. In Example 2, a triangle is translated. What shape is the resulting figure?
5. In Example 3, what would be the ordered pair of A’ if the original figure was translated 5 units right and 4 units down? 6. A point at ordered pair (2, 4) is translated 3 units right and 2 units up and then translated again 2 units left and 3 units up. What is the ordered pair of the final point? How would you write this as one translation?
Remember What You Learned 7. If a figure with vertices X(2, 3), Y(-1, 5), and Z(3, -6) is translated 3 units left and 4 units up, find the vertices of the translated figure.
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Study Guide
6.G.1.3
Translations • A transformation is a movement of a geometric figure. • The resulting figure is called the image. • A translation is the sliding of a figure without turning it. • A translation does not change the size or shape of a figure. Example 1
Translate triangle ABC 5 units to the right.
Step 1 Move each vertex of the triangle 5 units right. Label the new vertices A’, B’, C’. Step 2 Connect the new vertices to draw the triangle. The coordinates of the vertices of the new triangle are A’(2, 4), B’(2, 2), and C’(5, 0). Example 2
A B
y 4 3 2 1
24232221 O
A B C
1 2 3 4x
y 4 3 2 1
24232221O
22 23 24
A B C
C
1 2 3 4x
22 23 24
A placemat on a table has vertices at (0, 0), (3, 0), (3, 4), and (0, 4). Find the vertices of the placemat after a translation of 4 units right and 2 units up. (x + (0 + (3 + (3 + (0 +
4, y 4, 0 4, 0 4, 4 4, 4
+ 2) + 2) + 2) + 2) + 2)
New vertex (4, 2) (7, 2) (7, 6) (4, 6)
Exercises Find the coordinates of the image of (2, 4), (1, 5), (1, -3), and (3, -4) under each transformation.
218
1. 2 units right
2. 4 units down
3. 3 units left and 4 units down
4. 5 units right and 3 units up
North Carolina, Grade 6
Chapter 11
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Vertex (0, 0) (3, 0) (3, 4) (0, 4)
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Homework Practice
6.G.1.3
Translations 1. Translate LMN 5 units down. Graph triangle L’M’N’.
N
y 8 7 6 5 4 3 2 1
2827262524232221O
2. Translate TRI 2 units left and 3 units up. Graph T’R’I’.
M
I L
1 2 3 4 5 6 7 8x
y 8 7 6 5 4 3 2 1
2827262524232221O
22 23 24 25 26 27 28
22 23 24 25 26 27 28
T
1 2 3 4 5 6 7 8x
R
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A table has vertices of (0, 3), (6, 2), (0, 8), and (-2, 5) on a floor. Find the vertices of the table after each translation. 3. 4 units right
4. 2 units left
5. 6 units up
6. 9 units down
7. 1 unit left and 5 units up
8. 7 units right and 8 units up
9. 4 units left and 6 units down
11. 1 unit left and 9 units up
10. 9 units right and 3 units down
12. 5 units right and 7 units down
13. One of the vertices of a square is (3, 5). What is the ordered pair of the image after a translation of 3 units up, 5 units left and then 4 units down? What translation will give the same result?
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Problem-Solving Practice
PERIOD
6.G.1.3
Translations 2. CAMPING The Larsons’ tent corners have the coordinates (0, 5), (5, 5), (5, 0), (0, 0). They want to move it 5 units right and 2 units up. What are the new coordinates of the tent corners?
3. FLOWER BEDS Jeanne’s flower bed has the following coordinates for its corners: (-1, 2), (-1, -2), (2, -2), (2, 2). She wants to move it 3 units left and 2 units up. What are the coordinates of the corners of the new flower bed?
4. BASEBALL The corners of home plate are now at (0, 0), (1, 0), (1, 1), and (0, 1). It was moved 2 units right and 3 units down from its previous position. What are the original coordinates of home plate?
5. LOGOS A company is designing a logo that uses a triangle. The triangle’s corners has coordinates (3, 4), (-2, -2) and (5, -1). They decide to move the triangle left 2 units and up 4 units. What are the new coordinates of the corners of the translated triangle?
6. T-SHIRTS The final position of a T-shirt design has corners at (2, 3), (-5, 1) and (4, 0). This is a translation of 4 units left and 3 units down from the original position. What were the coordinates of the original corners?
North Carolina, Grade 6
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220
1. PICNIC TABLE After moving a picnic table at a shelter, the coordinates of its corners are (3, 4), (-2, 4), (3, 2) and (-2, 2). If the picnic table was moved 3 units left and 4 units up, what were the original coordinates of the picnic table?
NAME
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Explore Through Reading
6.G.1.4
Reflections Get Ready for the Lesson Read the problem at the top of page 610. Write your answers below. 1. What do you notice about each wing of the butterfly?
2. If the butterfly were to fold its wings together, would the markings on the butterfly's wings line up? Explain.
Read the Lesson 3. Example 1 shows the reflection of a figure over the x-axis. Which coordinate changes when reflecting over the x-axis? Explain.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. In Example 2, a figure is reflected over the y-axis. Which coordinate changes when reflecting over the y-axis? Explain.
5. Describe a way to help you remember which coordinate changes?
6. What is the line of reflection?
Remember What You Learned 7. If a figure with vertices X(2, 3), Y(-1, 5), and Z(3, -6) is reflected over the x-axis, find the vertices of the translated figure.
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Study Guide
6.G.1.4
Reflections • A reflection is the mirror image that is created when a figure is flipped over a line. • A reflection is a type of geometric transformation. • When reflecting over the x-axis, the y-coordinate changes to its opposite. • When reflecting over the y-axis, the x-coordinate changes to its opposite. Example 1
Reflect triangle ABC over the x-axis. A
Step 1 Graph triangle ABC on a coordinate plane. Then count the number of units between each vertex and the x-axis.
B
y 4 3 2 1
24232221 O
A is 4 units from the axis. B is 2 units from the axis. C is 0 units from the axis.
C
1 2 3 4x
22 23 24
Step 2 Make a point for each vertex the same distance away from the x-axis on the opposite side of the x-axis and connect the new points to form the image of the triangle. The new points are A’(-3, -4), B’(-3, -2), and C’(0, 0).
A B
y 4 3 2 1
24232221O
C
1 2 3 4x
22 23 24
Exercises
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Find the coordinates of the image of (2, 4), (1, 5), (1, -3) and (3, -4) under each transformation. 1. a reflection over the x-axis
2. a reflection over the y-axis
Find the coordinates of the image of (-1, 1), (3, -2) and (0, 5) under each transformation. 3. a reflection over the x-axis
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4. a reflection over the y-axis
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Homework Practice
6.G.1.4
Reflections 1. Reflect PQR over the x-axis. Graph P’Q’R’. y 8 7 6 5 4 3 2 1
R
2. Reflect PQR over the y-axis. Graph P’Q’R’. y 8 7 6 5 4 3 2 1
P
2827262524232221O
Q R 1 2 3 4 5 6 7 8x
2827262524232221O
22 23 24 25 26 27 28
3. Reflect DEF over the x-axis. Graph D’E’F’.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
D
y 4 3 2 1
24232221O 22 23 24
1 2 3 4 5 6 7 8x
4. Reflect DEF over the y-axis. Graph D’E’F’. D
F
Q
22 23 24 25 26 27 28
E
1 2 3 4x
P
y 4 3 2 1
24232221O 22 23 24
E
1 2 3 4x
F
A table has vertices of (0, 3), (6, 2), (0, 8), and (-2, 5) on a floor. Find the vertices of the table after each transformation. 5. a reflection over the x-axis
6. a reflection over the y-axis
A piece of artwork has vertices of (2, 5), (-1, 6) and (0, -7) on a wall. Find the vertices of the table after each transformation. 7. a reflection over the x-axis
Chapter 11
8. a reflection over the y-axis
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Problem-Solving Practice
6.G.1.4
Reflections 2. CHALK Chrissy is drawing a chalk design on the sidewalk. The corners have coordinates (3, 5), (-1, 2), and (0, -5). She wants to reflect it over the y-axis. What are the new coordinates on the artwork corners?
3. ARTWORK Ling’s artwork uses reflections. The right half of her artwork is shown. Copy the design and draw the entire artwork after it has been reflected over a vertical line.
4. BUTTERFLIES Half of a butterfly is shown. The other half can be drawn by reflecting it over a vertical line. Copy the butterfly and draw the entire butterfly after it has been reflected over a vertical line.
5. BOWLING SHIRTS The design for the school’s bowling team shirts is shown. Describe the transformation that was used to create the design.
6. TILING A floor tile design is shown below. Describe the transformation that was used to create the design.
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1. FURNITURE After moving a couch, the coordinates of its corners are (2, 5), (5, 5), (5, -3) and (2, -3). If the couch was reflected over the x-axis, what were the original coordinates of the couch?
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Anticipation Guide Algebra: Properties and Equations
STEP 1
Before you begin Chapter 12
• Read each statement. • Decide whether you Agree (A) or Disagree (D) with the statement. • Write A or D in the first column OR if you are not sure whether you agree or disagree, write NS (Not Sure). STEP 1 A, D, or NS
STEP 2 A or D
Statement 1. By using the Distributive Property, the 3 would be multiplied with both the x and the 2 in the expression 3(x + 2). 2. 3 and 3x are like terms because they both contain the number 3. 3. 7 + x + 1 can be simplified to 8 + x by using the Commutative Property. 4. (y + 8) + 15 = y + (8 + 15) shows how the Associative Property can be used.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. To solve the equation 4 + b = -32, add 4 to both sides. 6. “Five less than a number” can be written as 5 + n. 7. Inequalities can be solved using the same form of inverse operations as equations. 8. Multiplication and division are inverse operations. 9. If you add the same number to both sides of an equation, the equation will remain equal. 10. To solve the equation 7x = 42, multiply both sides by 7. STEP 2
After you complete Chapter 12
• Review each statement and complete the last column by entering an A (Agree) or a D (Disagree). • Did any of your opinions about the statements change from the first column? • For those statements that you mark with a D, use a separate sheet of paper to explain why you disagree. Use examples, if possible.
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Family Activity State Test Practice
Fold the page along the dashed line. Work each problem on another piece of paper. Then unfold the page to check your work. 1. Find the solution to the equation written below:
2. Simplify the following algebraic expression: (5 + x) = 3
x - 7 = -11 A x = 18
A x+8
B x = -18
B 15x
C x = -4
C 15 + 3x
D x=4
D 8x
Solution
Solution
1. Hint: Do the opposite operation to the one shown in the equation. Because the opposite operation of subtraction is addition, add 7 to both sides of the equal sign. Since -7 + 7 = 0, only x is left on the left side. Now, add 7 to -11. Since they have opposite signs, subtract and get 4, but since -11 has the greater absolute value, the answer becomes -4. -4 - 7 = -11 The answer is C.
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2. Hint: Put together numbers and letters which look alike. Using properties helps to make this problem easier. See the steps below: (5 + x) + 3 = (x + 5) + 3 Commutative Property = x + (5 + 3) Associative Property =x+8 Add. (5 + x) + 3 = x + 8 The answer is A. Chapter 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Fold here.
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12A
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Explore Through Reading
6.N.2.2
Simplifying Algebraic Expressions Get Ready for the Lesson Complete the activity at the top of page 636 in your textbook. Write your answers below. 1. Evaluate the expression (40 + 30) + 50. 2. Evaluate the expression 40 + (30 + 50). 3. Evaluate the expression 40 + (50 + 30). 4. What do you notice about your answers in Exercises 1–3?
5. What can you conclude about the order in which you add any three numbers?
Read the Lesson
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
6. How are the Commutative and Associative properties different?
7. Which property is being modeled in the following problem: 7 + (3 + 4) = (7 + 3) + 4? 8. Which of the following are like terms: 3x, 4, xy, 7b, x, 2y, 9x?
9. Simplify the following expression: 5y + 4 + 2y + 8.
Remember What You Learned 10. Using the Commutative and Associative properties as well as combining like terms, simplify the expression 7 + (3 + 4x) + 12 + 6x. Show all your steps and justify your reasoning.
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Study Guide
6.N.2.2
Simplifying Algebraic Expressions • Commutative Property: The order which numbers are added or multiplied does not change the sum or the product. • a + b = b + a or a · b = b · a. • Associative Property: The way in which numbers are grouped does not change the sum or the product. • (a + b) + c = a + (b + c) or (a · b) · c = a · (b · c) • Like terms contain the same variables. Ex: 2y, y, and 7y are all like terms, but 4x is not.
Example 1
Simplify the expression 16 + (v + 4).
16 + (v + 4) = 16 + (4 + v) Commutative Property = (16 + 4) + v Associative Property = 20 + v Add. So, 16 + (v + 4) in simplified form is 20 + v. Example 2
Simplify the expression 3x + (6 + 2x).
3x + (6 + 2x) = 3x + (2x + 6) Commutative Property = (3x + 2x) + 6 Associative Property = 5x + 6 Combine like terms. So, 3x + (6 + 2x) in simplified form is 5x + 6. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exercises Simplify each expression. Justify each step.
228
1. 5 + x + 3
2. 6 + (x + 4)
3. (b + 10) + 15
4. 8x + 5 + 2x
5. (12 + 2u) + 3
6. 11p + 8 + 7p
7. 9x + (4 + 3x)
8. (8 + 12x) + (2 + 7x)
9. 5y + 4 + 7y
North Carolina, Grade 6
Chapter 12
NAME
12A
DATE
PERIOD
Homework Practice
6.N.2.2
Simplifying Algebraic Expressions
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Simplify each expression. Justify each step. 1. (7 + x) + 7x
2. 5 · (4 · x)
3. 15 + (x + 9)
4. (6x + 21) + 14
5. 3x + 2 + 11x
6. (x + 13) + 8
7. (12 + 2x) + 4
8. 8 · (x · 4)
9. 3(5x)
10. 3x + (7x + 10)
11. 5x + (2 + x)
12. 4 · x · 10
13. (x · 12) · 3
14. 14x + 9 + 6x
15. 5x + (24 + 14x)
ALGEBRA For Exercises 16 through 21, translate each verbal expression
into an algebraic expression. Then, simplify the expression. 16. The sum of three and a number is added to twenty-four. 17. The product of six and a number is multiplied by nine. 18. The sum of 10 times a number and fifteen is added to eleven times the same number. 19. Two sets of the sum of a number and eight are added to five times the same number. 20. Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen. 21. Five friends went to a baseball game. Three of the friends each bought a ticket for x dollars and a soda for $6.00. The other two friends each bought only tickets. Write and simplify an expression that represents the amount of money spent.
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Problem-Solving Practice
PERIOD
6.N.2.2
Simplifying Algebraic Expressions 1. AMUSEMENT PARKS Four friends went to a local amusement park. Three of the friends bought ride tickets for x dollars, plus a game pass for $10. The other friend bought just a ride ticket. Write and simplify an expression showing the amount of total money spent.
2. ALGEBRA Translate and simplify the expression: the sum of fifteen and a number plus twelve. Justify your steps.
3. AGE Julianna is x years old. Her sister is 2 years older than her. Her mother is 3 times as old as her sister. Her Uncle Rich is 5 years older than her mother. Write and simplify an expression representing Rich’s age.
4. REASONING In the expression 30 + 40 + 70, Jillian added 30 and 40 and then 70, while Samuel added 30 and 70 and then 40. Who is correct? Explain your reasoning.
ICE CREAM For Exercises 5 through
Toppings Ice Cream (Scoop) Sprinkles Hot Fudge Whipped Cream Nuts
Cost x dollars $0.25 $0.75 $0.50 $0.35
5. Ten kids each order a scoop of ice cream. Five of the kids add sprinkles, 3 add nuts, and 2 add nothing extra. Write and simplify an expression that represents the total cost.
7. Three friends went for ice cream. Two ordered a scoop with whipped cream, and the other one ordered a scoop with everything. Write and simplify an expression that represents the total cost.
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8. Two people order ice cream. The first one orders two scoops plus sprinkles, and the second one orders three scoops. Write and simplify an expression showing the total cost.
Chapter 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8, use the following information provided in the table.
6. Write and simplify an expression that represents the total cost of ordering nuts on a scoop of ice cream and then adding hot fudge.
NAME
12B
DATE
PERIOD
Explore Through Reading
6.A.1.1, 6.A.1.2
Solving Addition Equations Get Ready for the Lesson Read the introduction at the top of page 644 in your textbook. Write your answers below. 1. Write an expression to represent the gain of 4 yards.
2. Write an addition equation you could use to find the yards needed before gaining 4 yards.
3. You could solve the addition equation by counting back on the number line. What operation does counting back suggest?
Read the Lesson For Exercises 4–7, look at Example 2 at the top of page 645.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. What is the inverse operation and why is it used?
5. How is the Subtraction Property of Equality used in the solution?
6. What is the additive identity (Identity Property of Addition) and how is it used in the solution?
7. What does the checkmark at the end of the example indicate?
Remember What You Learned 8. In your own words, describe what inverse means. Discuss your idea with a partner. How does the concept of inverse operations compare to your understanding of inverse?
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Study Guide
PERIOD
6.A.1.1, 6.A.1.2
Solving Addition Equations Subtraction Property of Equality If you subtract the same number from each side of an equation, the two sides remain equal. 5= 5 -3 = -3 ____ 2= 2
Example 1
Solve x + 2 = 7 using models. 1 1
5
1 1 1 1 1 1 1
x12
5
7
1 1 x1222
1 1 1
5
1 1 1 1
5
Remove 2 counters from each side of the mat.
722 1
5
1 1 1 1
5
5
The counters remaining on the right side of the mat represent the solution or value of x.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
x
Model the equation.
The solution is 5. 5 + 2 = 7 5 substituted in the original equation is correct. Example 2
Solve b + 3 = 2.
b + 3 = 2 Write the equation. - 3 = -3 Subtract 3 from each side to undo the addition of 3 on the left. ______ b + 0 = -1 Simplify. b = -1 The solution is -1. Check
b+3=2 Write the original equation. -1 + 3 2 Replace b with -1. 2 = 2 This sentence is true.
Exercises Solve each equation. Use models if necessary. Check your solution.
232
1. a + 1 = 7
2. 3 + b = 8
3. c + 7 = 4
4. 9 = x + 4
5. g + 8 = -2
6. d + 6 = -5
North Carolina, Grade 6
Chapter 12
NAME
12B
DATE
PERIOD
Homework Practice
6.A.1.1, 6.A.1.2
Solving Addition Equations Solve each equation. Use models if necessary. Check your solution. 1. 9 + d = -5
2. b + 2 = 6
3. x + (-4) = 1
4. -2 + j = -9
5. m + (-4) = 9
6. 1 = f + (-7)
7. 6 + c = 3
8. 8 + y = -9
9. 3 + h = -6
10. p + (-6) = -4
3 1 11. _ +a=_ 4
4
3 2 12. - _ +g=_ 8
8
13. ALGEBRA What is the value of n if 7 + n = 5?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
THOROUGHBREDS The table shows the
earnings of some of the leading horses at Northlands Park. Use the table to answer Exercises 14 and 15. 14. Sparhawk has earned $8,329 more than Silver Sky. Write and solve an equation to find Silver Sky’s earnings.
Horse Earnings at Northlands Park Horse Earnings Sparhawk $52,800 Griffin’s Web $43,757 Kaylee’s Magic $121,113 Eternal Secrecy $57,532 Silver Sky Huntley’s Creek
15. Write and solve an equation to find Huntley’s Creek’s earnings if the total earnings for all the horses is $354,386.
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Mini-Project
6.A.1.1, 6.A.1.2
(Use with Lesson 12B)
Solving Addition Equations Write the equation that is represented by each model. 2.
1. + + + +
+ + + + + +
3.
– – –
+ + + + + + + + +
– – –
+ + + +
4. + +
+ + + + + +
Solve each equation using cups and counters. Sketch the arrangement in the boxes. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
5. x + 2 = 6
6. x + (-2) = -7
7. x + 1 = -3
8. Solve x + 4 = -3 without using models.
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x= Chapter 12
NAME
12C
DATE
PERIOD
Explore Through Reading
6.A.1.1, 6.A.1.2
Solving Subtraction Equations Get Ready for the Lesson Read the introduction at the top of page 651 in your textbook. Write your answers below. 1. Let s represent Charmaine’s Score. Write an equation for 36 points less than Charmaine’s Score is equal to 109.
2. Find Charmaine’s height by counting forward. What operation does counting forward suggest?
Read the Lesson 3. In modeling a subtraction equation, how and why are zero pairs used?
For Exercises 4 and 5, look at Example 2 on page 652. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. What is the inverse operation and why is it used?
5. How is the Addition Property of Equality used in the solution?
6. In the equation y - 4 = -10, how could you get the variable alone on one side of the equation?
Remember What You Learned 7. Work with a partner. Pretend your partner missed this lesson on subtraction equations. Make up a subtraction equation and solve it for your partner on a piece of paper. Show each step and explain how an inverse operation, the Addition Property of Equality, and the Additive Identity are used.
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Study Guide
PERIOD
6.A.1.1, 6.A.1.2
Solving Subtraction Equations Addition Property of Equality If you add the same number to each side of an equation, the two sides remain equal. 5 = -5 +3 = +3 ____ 8= 8
Example 1
Solve x - 2 = 1 using models. 2 2
5
x22
5
1
2 1 2 1
5
1 1 1
x2212
5
2 1 2 1 x
1
Model the equation.
Add 2 positive counters to each side of the mat.
112
5
1 1 1
5
3
Remove the zero pairs.
Example 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
The solution is 3. Solve b - 3 = -5.
b - 3 = -5 Write the equation. + 3 = +3 Add 3 to each side to undo the subtraction of 3 on the left. ______ b + 0 = -2 Simplify. b = -2 Check
Write the original equation. b - 3 = -5 -2 - 3 -5 Replace b with -2. -5 = -5 This sentence is true.
Exercises Solve each equation. Use models if necessary. Check your solution. 1. a - 2 = 3
2. b - 1 = 7
3. c - 4 = 4
4. -2 = x - 4
5. z - 6 = -3
6. g - 3 = -4
7. -9 + w = 1
8. v - 8 = 5
9. -7 = y - 5
10. u - 3 = -4
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11. -2 = t - 9
12. f - 6 = -3
Chapter 12
NAME
12C
DATE
PERIOD
Homework Practice
6.A.1.1, 6.A.1.2
Solving Subtraction Equations Solve each equation. Use models if necessary. Check your solution. 1. t - 7 = -19
2. x - 2 = -5
3. g - 6 = -2
4. -6 = c - 5
5. h - 5 = 4
6. 8 - j = 5
7. y - (-7) = 7
8. 9 = a - 9
9. p - (-3) = 5
10. d - 5 = -9
3 11 11. m - _ =_ 8
18
3 12. b - _ = -1 15
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
13. PARASAILING A parasailer is attached by a cable to a boat and towed so that the parachute she is wearing catches air and raises her into the air. When the boat slows down to turn back towards the beach the parasailer’s chute catches less air and dips 25 meters. She must descend another 45 meters to return to the boat. Write and solve a subtraction equation to find her original height above the boat before the turn.
14. ALGEBRA What is the value of k if -6 = 9 - k?
15. The Petrified Forest National Park in Arizona recently expanded their boundaries by 93,533 acres. The original acreage was 125,000. Write and solve a subtraction equation to find the new acreage of the park.
16. A mako shark caught by a rod and reel in Massachusetts Bay weighed 1,324 pounds. This was 103 pounds more than the International Game Fish Association (IGFA) record. What is the IGFA record for a mako shark?
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Problem-Solving Practice
PERIOD
6.A.1.1, 6.A.1.2
Solving Subtraction Equations 2. APPLES David brought apples to school one day. After giving one to each of his 5 closest friends, David had 6 apples left. Write and solve an equation to find how many apples David brought to school.
3. BASKETBALL The basketball team is practicing after school. Four students have to leave early. If 12 basketball players remain, write and solve an equation to find how many students are on the basketball team.
4. MARBLES Virginia’s mother gave her marbles for her birthday. Virginia lost 13 of them. If she has 24 marbles left, write and solve an equation to find how many her mother gave her.
5. MONEY Claudio went for a walk. While he was walking, $1.35 fell out of his pocket. When he returned home, he counted his money and had $2.55 left. Write and solve an equation to find how much money was in Claudio’s pocket when he started his walk.
6. HANG GLIDING Aida was hang gliding. After losing 35 feet in altitude, she was gliding at 125 feet. Write and solve an equation to find her height when she started hang gliding.
7. SHARKS The average great hammerhead shark is 11.5 feet long. The average great hammerhead shark is 13.5 feet shorter than the average whale shark. Write and solve an equation to find the length of the average whale shark.
8. JOKES At a party, Tex told 17 fewer knock-knock jokes than he did riddles. If he told 23 knock-knock jokes, write and solve an equation to find how many riddles Tex told at the party.
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
238
1. BIRDS A house cat, Sophie, scared away 5 birds when she arrived on the porch. If 3 birds remain, write and solve an equation to find how many birds were on the porch before Sophie arrived.
NAME
12D
DATE
PERIOD
Explore Through Reading
6.A.1.1, 6.A.1.2
Solving Multiplication Equations Get Ready for the Lesson Read the introduction at the top of page 657 in your textbook. Write your answers below. 1. Let x represent the number of ringtones. Explain how the equation 2x = 10 represents the situation.
Read the Lesson 2. In the equation 2x = 10, what is the coefficient?
3. In the equation 2x = 10, what is the operation? How do you know?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. In Example 1 on page 657, why are both sides of the equation divided by 2?
5. In Example 3 on page 658, why is the equation 3 = 5t?
6. Describe what is happening in each step. -3x -3x _ -3 1x x
= 27 27 =_ -3 = -9 = -9
Remember What You Learned 7. Work with a partner. Explain how you use division to solve a multiplication problem. Describe an example from real life where you would use division in this way.
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Study Guide
PERIOD
6.A.1.1, 6.A.1.2
Solving Multipication Equations In a multiplication equation, the number by which a variable is multiplied is called the coefficient. In the multiplication equation, 2x = 8, the coefficient is 2.
Example 1
Solve 2x = 6 using models.
2x
5
1 1 1 1 1 1
5
6
5
1 1 1 1 1 1
2x 2
5
6 2
x
5
3
Model the equation.
Divide the 6 counters equally into 2 groups. There are 3 in each group.
2x = 6 Write the original equation. 2(3) 6 Replace x with 3. 6 = 6 This sentence is true. The solution is 3. Check
-4b = 12
-4b 12 _ =_ -4
-4
1b = -3 b = -3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Example 2
Solve -4b = 12.
Write the equation. Divide each side by -4 to get a single positive variable by itself. Simplify.
-4b = 12 Write the original equation. -4(-3) 12 Replace b with -3. 12 = 12 This sentence is true. The solution is -3.
Check
Exercises Solve each equation. Use models if necessary. Check your solution. 1. 5a = 25
2. 7c = 49
3. 24 = 6d
4. 2x = -8
5. 18 = -9y
6. -8g = -16
7. 18 = -3z
8. -4w = -36
9. 56 = 7v
10. 24 = -8f
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11. 3u = -27
12. -42 = 6t
Chapter 12
NAME
12D
DATE
PERIOD
Homework Practice
6.A.1.1, 6.A.1.2
Solving Multipication Equations Solve each equation. Use models if necessary. 1. 7a = 63
2. -14k = 0
3. -13w = 39
4. 55 = -11x
5. 3v = -42
6. 96 = 12f
7. -14u = -70
8. -3c = 3
9. 15s = -120
13. 72 = -6r
10. 35q = -5
11. -6 = -2y
12. -13t = -117
14. 0.8b = -1.12
15. -2.3g = 7.13
16. 40 = -1.6m
14. TIME The Russian ice breaker Yamal can move forward through 2.3-meter thick ice at a speed of 5.5 kilometers per hour. Write and solve a multiplication equation to find the number of hours it will take to travel 82.5 kilometers through the ice.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
FUNDRAISING A school is raising
money by selling calendars for $20 each. Mrs. Hawkins promised a party to whichever of her English classes sold the most calendars over the course of four weeks. Use the table to answer Exercises 15–17. 15. Write and solve an equation to show the average number of calendars her 3rd period class sold per week during the four-week challenge.
Mrs. Hawkins’ Funderaising Challege Number of Class Calendars Sold 1st Period 60 2nd Period 123 3rd Period 89 4th Period 126
16. How many calendars did the 1st and 2nd period classes sell on average per week? Write and solve a multiplication equation.
17. What was the average number of calendars sold in a week by all of her classes?
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12D
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Problem-Solving Practice
PERIOD
6.A.1.1, 6.A.1.2
Solving Multipication Equations 2. CATS Steve’s tabby cat eats 5 times as often as his black cat. The tabby cat ate 10 times yesterday. Write and solve an equation to find how many times the black cat ate.
3. FOOTBALL In last night’s football game, the home team earned 3 times as many points as the visiting team. They won the game with 21 points. Write and solve an equation to find how many points the visiting team had.
4. MONEY Paz has 3 times as much money in her wallet as in her pocket. There is $18 in her wallet. Write and solve an equation to find how much money is in her pocket.
5. MORNINGS It takes Jun 3 times as long as it takes Kendra to get ready in the morning. It takes Jun 45 minutes to get ready. Write and solve an equation to find how long it takes Kendra.
6. FISH In his home aquarium, Enli has 12 times as many guppies as he has goldfish. Enli just counted 72 guppies. Write and solve an equation to find how many goldfish he has.
7. MUSIC Ray’s favorite song is 2 times as long as Meli’s favorite song. Write and solve an equation to find the length of Meli’s favorite song if Ray’s lasts 6 minutes.
8. TRAILS The forest trail to Round Lake is 3 times as long as the rocky trail to Round Lake. The forest trail is 15 miles long. Write and solve an equation to find the length of the rocky trail.
North Carolina, Grade 6
Chapter 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
242
1. BAND SOLO Kai’s solo in the next school band performance is 4 times as long as Dena’s solo. Kai’s solo is 12 minutes long. Write and solve an equation to find the length of Dena’s solo.
NAME
12E
DATE
PERIOD
Study Guide
6.A.1.3
Inequalities A mathematical sentence that contains < or > is called an inequality. When used to compare a variable and a number, inequalities can describe a range of values. Some inequalities use the symbols ≤ or ≥. The symbol ≤ is read is less than or equal to.The symbol ≥ is read is greater than or equal to.
Examples
Write an inequality for each sentence.
SHOPPING Shipping is free on orders of more than $100.
Let c = the cost of the order. c > 100 RESTAURANTS The restaurant seats a maximum of 150 guests.
Let g = the number of guests. g ≤ 150 Inequalities can be graphed on a number line. An open or closed circle is used to show where the solutions start, and an arrow pointing either left or right indicates the rest of the solutions. An open circle is used with inequalities having > or <. A closed circle is used with inequalities having ≤ or ≥.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Examples
Graph each inequality on a number line.
d ≤ -2 Place a closed circle at -2. Then draw a line and an arrow to the left. 24 23 22 21 0 1 2 3 4
d > -2 Place an open circle at -2. Then draw a line and an arrow to the right. 24 23 22 21 0 1 2 3 4
Exercises Write an inequality for each sentence. 1. FOOD Our delivery time is guaranteed to be less than 30 minutes. 2. DRIVING Your speed must be at least 45 miles per hour on the highway. Graph each inequality on a number line. 3. r > 7
Chapter 12
4. x ≤ -1
North Carolina, Grade 6
243
NAME
12E
DATE
Skills Practice
PERIOD
6.A.1.3
Inequalities Write an inequality for each sentence. 1. SPORTS You need to score at least 30 points to take the lead. 2. SEASONS There are less than 12 hours of daylight each day in winter. 3. TRAVEL The bus seats at most 60 people. 4. MONEY The coupon is good for any item that costs less than $10. 5. TESTS A score of at least 92 on the test is considered an A. 6. HEALTH The baby weighed more than 7 pounds at birth. 7. DRIVING Victor drives less than 12,000 miles per year. 8. TRAVEL Your waiting time will be 18 minutes or less. 9. SCHOOL TRIPS At least 15 students must sign up for the school trip. For the given value, state whether each inequality is true or false. 11. 12 > u - 1, u = 14
12. p + 5 ≥ -6, p = 1
13. -6 < a - 3, a = -1
14. 4s ≤ 15, s = 4
15. -5 > 1 - d, d = -9
16. -2 - g ≥ -7, g = 5
k 17. _ > 4, k = 12
-10 18. 4 < _ z , z = -2
12 19. _ m ≥ 3, m = 4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
10. y + 2 < 8, y = 3
3
Graph each inequality on a number line. 20. v ≥ 3
21. b > 5
22. n ≤ -3
23. w < 4
24. r > -1
25. h ≥ -7
244
North Carolina, Grade 6
Chapter 12
NAME
12E
DATE
PERIOD
Homework Practice
6.A.1.3
Inequalities Write an inequality for each sentence. 1. JOBS Applicants with less than 5 years of experience must take a test. 2. FOOTBALL The home team needs more than 6 points to win. 3. VOTING The minimum voting age is 18. 4. GAMES You must answer at least 10 questions correctly to stay in the game. 5. DINING A tip of no less than 10% is considered acceptable. 6. MONEY The cost including tax is no more than $75. For the given value, state whether the inequality is true or false. 7. 9 + b < 16, b = 8 10. 51 ≤ 3m, m = 17
8. 14 - f > 8, f = 5 z 11. _ ≤ 7, z = 40 5
9. -5t < 24, t = 5 -28 12. _ > 7, d = -4 d
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Graph each inequality on a number line. 13. y > 5
14. h < 5
15. c ≤ 1
16. t ≥ 2
17. x ≥ 4
18. r < 9
For Exercises 19 and 20, use the table that shows the literacy rate in several countries. 19. In which country or countries is the literacy rate less than 90%?
20. In which country or countries is the literacy rate at least 88%?
Chapter 12
Country Albania Jamaica Panama Senegal
Literacy Rate 87% 88% 93% 40%
North Carolina, Grade 6
245
NAME
12E
DATE
PERIOD
Problem-Solving Practice
6.A.1.3
Inequalities 2. RESTAURANTS Before Valerie and her two friends left Mel’s Diner, there were more than 25 people seated.Write an inequality for the number of people seated at the diner after Valerie and her two friends left.
3. FARM LIFE Reggie has 4 dogs on his farm. One of his dogs, Lark, is about to have puppies. Write an inequality for the number of dogs Reggie will have if Lark has fewer than 4 puppies.
4. MONEY Alicia had $25 when she arrived at the fair. She spent t dollars on ride tickets and she spent $6.50 on games. Write an inequality for the amount of money Alicia had when she left the fair.
5. HEALTH Marcus was in the waiting room for 26 minutes before being called. He waited at least another 5 minutes before the doctor entered the examination room.Write an inequality for the amount of time Marcus waited before seeing the doctor.
6. POPULATION The population of Ellisville was already less than 250 before Bob and Ann Tyler and their three children moved away. Write an inequality for the population of Ellisville after the Tyler family left.
7. HOMEWORK Nova spent one hour on Thursday, one hour on Saturday, and more than 2 hours on Sunday working on her writing assignment. Write an inequality for the amount of time she worked on the assignment.
8. YARD WORK Harold was able to mow 3 of his lawn on Saturday more than _ 4 night. Write an inequality for the fraction of the lawn that Harold will mow on Sunday.
North Carolina, Grade 6
Chapter 12
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
246
1. SPORTS Colin’s time in the 400-meter run was 62 seconds. Alvin was at least 4 seconds ahead of Colin. Write an inequality for Alvin’s time in the 400-meter run.
Name
Date
Diagnostic Test Student Answer Document
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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North Carolina, Grade 6
A1
Name
Date
Diagnostic Test 1. The simplified result of the expression (3 × 27) + 19 is equal to the number of counties in North Carolina. How many counties are there in North Carolina? A 67 B 74 C 81 D 100
4. Diane is a graphic designer. She is 5 working on an ad that is 3__ inches 8 5 __ wide. What is 3 8 in decimal form?
A B C D
3.253 3.53 3.58 3.625
5. Dymond drives an average of 50 miles 2. Which expression can be used to estimate the circumference of the circle shown below?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16
A B C D
22 × 8 (___ 7) 22 × 8 2 × (___ 7) 22 × 16 2 × (___ 7) 22 × 8 (___ 7)
per hour. The width of North Carolina is 150 miles. If she continues at the same speed, how long will it take her to drive across North Carolina? A 1 B 3 C 5 D 10
hour hours hours hours
2
6. What is the prime factorization of 36? A B C D
2×3×7 22 × 3 32 × 4 22 × 32
3. Which of the following patterns follow the rule multiply the previous term by 4 then add 2 to the product? A B C D
1, 6, 26, 106, … 1, 4, 16, 64, … 1, 12, 56, 232, … 1, 6, 16, 36, …
Diagnostic Test
7. Look at the equation below. What value of n makes the equation true? 4n = 12 A 3 B 8
C 16 D 48
North Carolina, Grade 6
A3
8. Which is the solution set for the inequality below?
winner of four races.
x > 18 __ 3
A B C D
x x x x
> > > >
11. The table below lists the age of the 2008 Female Winners Race Spring Blossom Marathon Mountain Valley Marathon Country Road Marathon Summer Garden Marathon
6 15 21 54
Age 24 37 32 35
Which statement is true of the data?
9. In which quadrant is Point A on the grid below? y 4 3 2 1
A -4 -3 -2
O
1
2
3
4 x
A The mean age is greater than the median age. B The median age is greater than the mean age. C The median age and the mean age are the same. D The range of the data is greater than the mean age.
-2 -3 -4
12. The North Carolina flag was adopted quadrant quadrant quadrant quadrant
I II III IV
in 1885.
Y 20th 1775 MA
APR
IL 12TH 17 76
10. Triangle PQR has the coordinates (5, -2), (5, -6), and (10, -6). Triangle PQR has coordinates (-5, 2), (-5, -2), and (0, -2). Which of the following describes the translation of ΔPQR to ΔPQR? A B C D
A4
up 10 units and left 4 units up 10 units and right 4 units right 10 units and down 4 units left 10 units and up 4 units
North Carolina, Grade 6
Enrique is making a North Carolina flag out of poster board. He wants the length of the flag to be 1.9 times the height. If the flag’s height is 3 feet, what is the area of the flag? A 17.1 square feet B 14.7 square feet C 9 square feet D 5.7 square feet
Diagnostic Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
13. Below is a diagram of Neil’s backyard.
15. There are 6 oranges, 5 grapefruits, 2 apples, and 5 lemons in a bag. A fruit is selected without looking. Which fruit is most likely to be chosen?
40 ft
A B C D
8 ft 6 ft
patio 58 ft
Neil plans to plant grass seed everywhere in his backyard except the patio. What is the area of the backyard that is planted with grass? A B C D
2,320 2,272 1,952 1,830
square square square square
feet feet feet feet
orange grapefruit apple lemon
16. A frozen yogurt stand has 3 different types of cones, 4 different flavors of frozen yogurt, and 4 different types of toppings. How many different combinations consisting of 1 type of cone, 1 flavor of frozen yogurt, and 1 topping can be made? A 12 B 36
C 48 D 52
14. Which graph correctly shows the 1 , __ 1 , and 20%? location of 0.7, __ 2 3
17. If the pattern continues, which of the
A Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
0
1 0.7 1 3
1, 4, 5, 9, 14, 23, …
20%
1 2
B 0
1 20% 1 2
C 0
1 1 2
3
0
1 3
Diagnostic Test
1 2
C 149 D 254
18. Which of the following is equivalent to the expression 92 × 34?
20%
D 20% 1
A 57 B 92
0.7
1 3
0.7 1
following would be the 11th term?
0.7
A B C D
3 3 3 3
× × × ×
3 3 3 3
× × × ×
3 3 3 3
× × × ×
3 9 3 9
× × × ×
3×9 9×9 9×9 9
North Carolina, Grade 6
A5
19. Which table of data is represented by
20. The table below shows the number of customers who visited a bicycle shop each hour on a Saturday afternoon.
the graph below?
Number of People
Fair Attendance
Number of Customers
40 30 20 10 0 0–5
6–10 11–15 16–20
Age
Time 2:00 P.M. 3:00 P.M. 4:00 P.M. 5:00 P.M.
Number of Customers 8 10 4 15
What is the range of the data set? A
Fair Attendence Age 0–5 6–10 11–15 16–20
B
Fair Attendence Age 0–5 6–10 11–15 16–20
Number of People 25 30 15 25
Fair Attendence Age 0–5 6–10 11–15 16–20
D
Number of People 20 30 20 25
Fair Attendence Age 0–5 6–10 11–15 16–20
Number of People 20 25 15 25
North Carolina, Grade 6
A 11 B 15
C 19 D 20
21. The ages of students on a dance team are 12, 10, 8, 7, 9, 12, and 12. Suppose that another 9-year-old joins the team. Which two measures of central tendency would decrease? A B C D
mode and range mean and median mean and range mode and median
22. There are 3 yellow marbles, 2 red marbles, 9 blue marbles, and 1 green marble in a bag. Carlos will choose a marble at random from the bag. What is the probability that the marble will be yellow? 1 A ___
1 C __
2 B ___ 15
1 D __
15
5 3
Diagnostic Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
A6
Number of People 20 30 15 25
23. Hailey uses the expression (2 · 3) · 4 to compute the number of sugar cubes arranged in a container as shown.
25. What is the missing number in the ratio table below?
A B C D
8
12
24
120
3
4.5
9
?
10.5 18 45 96
26. The diagram shows the number of Which other expression could she have used? A B C D
4(2 + 3) 2·3+4 2 · (3 · 4) (2 + 3) + 4
= 294 oranges
24. Mai recorded her scores on four social Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
studies quizzes in the table below. Social Studies Scores # Correct 21 8 17 12
Quiz 1 Quiz 2 Quiz 3 Quiz 4
# Possible 25 10 20 16
On which quiz did Mai score the greatest percent correct? A B C D
oranges an average orange tree produces in one season.
Quiz Quiz Quiz Quiz
1 2 3 4
Which expression best describes how many oranges will be produced if an orchard has t trees? A B C D
t × 294 294 - t t + 294 294 ÷ t
27. Catalina has 4 shirts, 2 pairs of shorts, and 3 pairs of socks in her locker for gym class. How many different outfits consisting of 1 shirt, 1 pair of shorts, and 1 pair of socks can she make? A 24 B 16
Diagnostic Test
C 8 D 4
North Carolina, Grade 6
A7
28. Which ordered pair names the location of Point T on the grid below? 7 6 U 5 4 S T 3 2 1 0
A B C D
31. Which function rule describes the relationship in the table below? Input, x
1
3
5
7
Output, y
2
10
18
26
A Add 4 to the input value and then multiply this sum by 2. B Subtract 2 from the input value and then multiply this difference by 4. C Multiply the input value by 4 and then add 2 to this product. D Subtract 2 from the product of 4 and the input value.
V
1 2 3 4 5 6 7
(0, 4) (1, 3) (1, 5) (3, 1)
32. A function machine divides each input 29. What is the perimeter, in feet, of the figure shown below?
value x by 9. Which equation models this relationship? x A y = __ 9
6 ft
B y = 9x
5 ft
3 ft
4 ft
C 12 feet D 8 feet
33. North Carolina’s state insect is a 30. Luiz simplifies the expression below to find the total amount he spent ongroceries this week. Which expression could he also use to get the same result? 20 + 14 + 5 + 6 A B C D
A8
5(6 + 20) + 14 (20 - 14) + (6 - 5) 6(5 + 14 + 20) 20 + 5 + 14 + 6
North Carolina, Grade 6
honeybee. An average worker 1 teaspoon honeybee produces about ___ 12 of honey in her lifetime. About how many milliliters is this? 1 teaspoon ≈ 5 milliliters 1 milliliters A __
6 1 milliliters B __ 4 1 milliliters C __ 2 5 milliliters D ___ 12
Diagnostic Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 24 feet B 18 feet
9 C y = __ x D y=x-9
price of a gallon of gas over a fourweek period. Gas Prices 1 2
Week Price per Gallon
$2.11
$2.15
3
4
$2.30
$2.57
Which graph matches the data in the table? A
GAS PRICES OVER FOUR WEEKS
35. The graph below shows the cost of renting a boat. Boat Rental Prices
Price (in dollars)
34. The table below shows the average
$2.50 $2.40 $2.30 $2.20 $2.10
75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0
1
2
3
4
5
6
4 ee
k
3 k ee
W
2 k W
ee W
W
ee
k
1
Number of Hours
B Gas Prices Over Four Weeks WK 1 $2.11 WK 2 $2.15
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
WK 4 $2.57 WK 3 $2.30
C
Gas Prices Over Four Weeks 2.57 2.30 2.15 2.11 0
1
2
3
4
D Gas Prices Over Four Weeks WK 4 WK 3 WK 2 WK 1 2.11
Diagnostic Test
2.15
2.30
2.57
Based on this graph, which of the following is true? A For each hour you rent a boat, the cost doubles. B The longer you rent a boat, the more it costs per hour. C The longer your rent a boat after the first hour, the less it costs per hour. D The hourly cost is the same no matter how many hours, after the first hour, you rent a boat.
36. Which of the following patterns follow the rule subtract 4? A B C D
32, 36, 40, 44, … 32, 8, 2, 0.5, … 32, 28, 24, 20, … 32, 28, 32, 28, …
North Carolina, Grade 6
A9
37. John is asked to measure the distance around a coffee can and to measure its diameter.
39. The fair spinner below is spun 4 times.
Red Yellow
Coffee
Next, his teacher asks him to divide the distance around the coffee can by its diameter. Which measure is John computing? A B C D
the the the the
area of top of the can circumference of the can volume of the can approximate value of π
38. Rochelle is using a model to find the quotient below. 2 ÷ ___ 1 __ 12 3
Blue
What is the probability that the spinner will land on blue the first time, blue the second time, red the third time, and yellow the fourth time? 1 A ____
2 C __
1 B __ 4
1 D __ 2
128
7
40. The table shows the number of books borrowed from the library this week. Library Books Borrowed M 24
T 30
W 42
TH 18
F 10
Which explains how to use the model to find the quotient? A The figure is divided into twelfths. 2 Count the twelfths that fit within __ 3 of the entire figure. B The figure is divided into twelfths. 2 of the twelfths, and Remove __ 3 count those remaining. C Count the number of thirds in the figure. Multiply this number by 12. D Count the number of rectangles in the entire figure. Divide this number by 3.
A10
North Carolina, Grade 6
A 17.7 B 24.8
C 32 D 42
41. Amy has to read 6 short stories for a class. The list below shows the number of pages in each story. 10, 14, 12, 13, 12, 11, 5 Which measure is the same as the median number of pages? A mode B range
C mean D total sum
Diagnostic Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
What is the mean of the data set?
42. A toy company tallied the number of toys produced each day for 12 days. Which stem-and-leaf plot correctly displays the data below? 57, 42, 61, 64, 59, 33, 22, 61, 33, 66, 59, 61 Toy Production
A Stem 2 3 4 5 6
B
C
x-8>5 A 10 11 12 13 14 15 16
B 10 11 12 13 14 15 16
C 0
1
2
3
4
5
6
0
1
2
3
4
5
6
D 6 | 1 = 61 toys
Leaf 2 3 2 7 9 9 1 1 4 6
45. Hugo’s teacher put 5 lemon, 12 cherry,
6 | 1 = 61 toys
Toy Production Stem 2 3 4 5 6
Leaf 2 3 3 2 7 9 9 1 1 4 6
Stem 2 3 4 5 6
Leaf 2 3 3 2 7 9 9 1 1 1 4 6
6 | 1 = 61 toys
45 30 15 10
Diagnostic Test
21 4 B __ 8 1 C __ 4 4 D ___ 21
46. The average distance from the Sun to 6 | 1 = 61 toys
43. 32 × 5 is the prime factorization of what number?
4 grape, and 8 orange candies in a bag. She has each student pick a candy from the bag without looking. If eight students pick their piece of candy before Hugo and no one picks grape, what is the probability that Hugo will pick a grape candy? 17 A ___
Toy Production
D
A B C D
for the inequality below?
Toy Production Stem 2 3 4 5 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Leaf 2 3 2 7 9 1 4 6
44. Which is a graph of the solution set
Earth is 1.496 × 1011 meters. How is this distance written in standard notation? A 149,600,000 B 1,496,000,000 C 14,960,000,000 D 149,600,000,000
North Carolina, Grade 6 A11
47. Jeremiah is graphing points on the
and time Rob traveled during his last business trip.
number line below. " 1 4
0
51. The table below shows the distance
# 1 2
3 4
Rob’s Business Trip Distance 195 325 ? (in miles) Time 3 5 6 (in hours)
1
Which of the following could be the coordinate at point B?
520 8
If Rob maintained a constant rate throughout the trip, how many miles did he travel in 6 hours?
3 A __ 8
B 0.625 C 65% D 0.71
A B C D
390 330 280 190
miles miles miles miles
48. Reagan spent a total of $6.93 on turkey that was priced at $1.98 per pound. How many pounds did she purchase?
52. Which type of transformation on figure LMNO resulted in LMNO?
A B C D
2.5 3.5 4.5 5.5
pounds pounds pounds pounds
y
L M M N
N O
O x
49. If the pattern continues, what is the 8th term? 2, 7, 12, 17, 22, … A 27 B 32
C 37 D 42
A B C D
reflection rotation translation dilation
50. Which of the following is equivalent to the expression 2 × 4 × 3 × 2 × 3 × 2? A B C D
A12
2×3×4 23 × 32 × 4 22 × 33 × 4 23 × 32
North Carolina, Grade 6
Diagnostic Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
O
L
53. The probability of winning a game is 1 . Laura plays the game 390 times. __ 6
Based on the probability, how many games should she expect to win? A B C D
56. Kendrick travels __23 mile to his
3 friend’s house. He cycles __ of this 4 distance and walks the rest of the way. What fraction of a mile did he cycle?
1 A __
55 60 65 70
4 2 B __ 3 1 C __ 2 3 D __ 4
54. Josh is a member of the Digital Music Store. The graph below represents his monthly subscription fee and the cost for each song purchased. Based on the information in the graph, which statement is true?
57. Keesha needs 3.5 square yards of cotton to make a blanket. Fabric Prices (per square yard) Felt $1.20 Cotton $2.50 Silk $3.75
Monthly Cost (in dollars)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
DIGITAL MUSIC STORE 16 14 12 10
y
According to the chart, how much will the fabric cost?
8 6 4 2
x 1 2 3 4 5 6 7 8
Songs Purchased
A B C D
The The The The
cost of each song is $6. subscription fee is $2. subscription fee is $12. cost of each song is $2.
55. The distance from Raleigh to Charlotte is about 130 miles. About how many kilometers is this? 1 mile ≈ 1.61 kilometers
A $0.71 B $7.55 C $8.75 D $87.50
58. In 2009, the estimated population of North Carolina was 9.38 million. Which of the following shows 9.38 million written in scientific notation? A B C D
9.38 93.8 9.38 93.8
× × × ×
109 106 106 105
A 209 kilometers B 160 kilometers C 130 kilometers D 65 kilometers
Diagnostic Test
North Carolina, Grade 6 A13
59. Student participation in JV and Varsity sports is shown in the double bar graph below.
61. Which grid shows only a reflection of figure ABCDE? y
A
B C
PARTICIPATION IN SPORTS 16
A
Number of Students
14
E D
12
O
A
10 8
E
B
D
C
x
6 4
JV
2 0
Varsity Sixth
Seventh
y
B A
Eighth
Grade
E
B
D
C
How many more seventh-grade students participate in Varsity sports than in JV sports? A 2 B 4 C 6 D 10
O
x
A E
B
D
C
y
C
D
C
E
B A
O
diameter of 8 feet. The swimming pool cover has an overlap of one foot all the way around the pool.
E
B
D
C
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
60. A round swimming pool has a
x
A
y
D
8 ft
A
Which of the following is the best estimate of the area of the swimming pool cover?
O
E
B
D
C
x
A E
B
D
C
A 50.24 square feet B 78.5 square feet C 200.96 square feet D 254.34 square feet
A14
North Carolina, Grade 6
Diagnostic Test
62. Which coordinate pair represents the intersection of the circle and line on the grid below? 9 8 7 6 5 4 3 2 1 -9 -8 -7 -6 -5 -4 -3 -2
O
translation of ΔABC to ΔABC? y
y
A C
A
B
x
O
C
B
1 2 3 4 5 6 7 8 9x
-2 -3 -4 -5 -6 -7 -8 -9
A (3, 4) B (6, 1)
64. Which of the following describes the
A B C D
C (0, 4) D (0, 1)
down 9 units and right 5 units right 9 units and down 5 units left 9 units and down 5 units left 9 units and up 5 units
65. According to the balance scale shown below, how many blocks weigh the same as the coffee mug?
63. Mr. Yao is building a fence around his Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
vegetable garden, as shown below. 16 ft 8 ft 20 ft 16 ft
12 ft 16 ft
A B C D
3 4 5 7
How many feet of fencing will Mr. Yao need to buy? A 88 feet B 176 feet C 203 feet D 218 feet
Diagnostic Test
North Carolina, Grade 6 A15
Name
Date
Practice by Essential Standard 6.N.1 1. Which statement is true about the product 0.48 × 0.09? A The product is greater than either of the factors. B The product is less than either of the factors. C The product is greater than 0.09 and less than 0.48. D The product has three decimal places.
4. Jasmyn runs 3.75 miles daily on the treadmill. By the end of a 7-day week, about how many miles does Jasmyn run? A B C D
more than 20 miles exactly 20 miles less than 20 miles more than 200 miles
5. Rosalina has 6 yards of canvas to 2. It costs Tristan $22.64 to pump 8
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
gallons of gasoline in his car. What is the price for one gallon of gasoline? A B C D
$1.16 $1.62 $2.83 $3.08
3. According to North Carolina state records, the heaviest largemouth bass 7 pounds. Emilio caught weighed 15__ 8 has a recipe for a largemouth bass. 3 pound of Each serving has about __ 8 fish. How many servings can Emilio make if he cooks the winning largemouth bass? A
61 servings 5___
64 3 servings B 22__ 8 3 servings C 32__ 4 1 servings D 42__ 3
Practice by Essential Standard
make tote bags. Each tote bag 3 requires __ yard of canvas. How many 8 tote bags can Rosalina make? A B
1 tote bag ___
16 1 tote bags 2__ 4
C 16 tote bags D 18 tote bags
6. The energy bar Marta is eating has 12.5 grams of fat. One gram of fat gives you 9.4 Calories. How many Calories from fat are in the energy bar? A 1.175 Calories B 11.75 Calories C 117.5 Calories D 1,175 Calories
North Carolina, Grade 6 A17
Name
Date
Practice by Essential Standard 6.N.1 (continued) 7. Ciana has a plank of wood that is 4.8 meters long. She needs to cut the plank into 0.8-meter lengths. 4.8 m
How many pieces can Ciana cut?
9. The total salary for a professional football team is about $100 million. The total salary for a professional baseball team is about half of that, and the total salary for a professional 9 hockey team is about ___ that of the 10 baseball team. About how much is the hockey team’s total salary?
A 3.84 B 6 C 38.4 D 60
Team Salaries Team football
$100,000,000
baseball
1 __ football salary 2 9 ___ baseball salary 10
hockey
8.
8 Lisa has __ pound of pepitas. She 9
9
A $45 B $55 C $90 D $140
million million million million
9
8 ÷ __ 9 × __ 2 = __ 2 = __ 1 A __
9 9 8 9 4 8 ÷ __ 8 × __ 16 2 = __ 2 = ___ B __ 9 9 9 9 81 8 ÷ __ 9 × __ 9 = ___ 81 = 5___ 2 = __ 1 C __ 9 9 8 2 16 16 8 ÷ __ 8 × __ 9=4 2 = __ D __ 9 9 9 2
10. André has a bag that is half full of paperclips. The full bag of paperclips 3 weighs __ pound. What does the half 4 bag of paperclips weigh? A B
3 pound __ 8 3 pound __ 4
C 1 pound 3 pounds D 1__ 4
A18
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
wants to store them in smaller bags 2 pound. Lisa divides that each hold __ 9 to find the number of bags she needs. 8 ÷ __ 2= ? __
Approximate Salary
Name
Date
Practice by Essential Standard 6.N.2 1. What is the value of the following expression? 4 + (7 × 3) - 15 A B C D
10 18 32 40
square miles, can be found by simplifying the following expression. 460 + 459 + 230 · 230 What is the total area of North Carolina?
2. To evaluate the expression 6 + 5 + 9, Donté adds 6 and 5 to get 11. Then, he adds 11 and 9 to get 20. Lia evaluates the expression in a different way. What could Lia do to get the same result?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4. The total area of North Carolina, in
A Multiply 6 and 5 to get 30. Then add 30 and 9. B Multiply 5 and 9 to get 45. Then add 6 and 45. C Add 5 and 9 to get 14. Then add 6 and 14. D Add 5 and 9 to get 14. Then multiply 6 and 14.
A 264,270 square miles B 53,819 square miles C 20,312 square miles D 1,379 square miles
5. Which expression is equivalent to x + (y + 2x2)? A B C D
(x + y)2x2 (x + x) + (y + 2x2) xy + 2x2y x + (2x2 + y)
6. The average weight of an adult male grizzly bear is equal to the expression below. 100 + 5 × 20 × 3 + 100
3. What is the value of the expression?
(5
25 - 3 22 + ___
A B C D
26 25 24 23
Practice by Essential Standard
)
What is the average weight, in pounds, of an adult male grizzly bear? A B C D
100 300 450 500
North Carolina, Grade 6 A19
Name
Date
Practice by Essential Standard 6.N.2 (continued) 7. The table below shows the steps Kin used to evaluate the expression below. (20 × 6 × 3) + 8
9. How can you group the factors in the expression below so that you can multiply mentally? 67 × 4 × 25
Kin’s Evaluation Step 1 2 3
Description Multiply 20 by 6 to get 120. Multiply 120 by 3 to get 360. Add 360 and 8 to get 368.
A B C D
(67 × 4) × 25 67 × (4 × 25) (60 + 7) × 4 × 25 (4 × 67) × 25
What is another way Kin could have evaluated the expression? A Multiply 6 by 3, multiply 18 by 20, and add 360 and 8. B Multiply 8 by 20, 8 by 6, and 8 by 3. Then add 160 and 48 and 24. C Multiply 20 by 6, add 120 and 3, and multiply 123 by 8. D Multiply 6 by 3, add 18 and 20, and multiply 38 by 8.
during a basketball game can be determined by simplifying the following expression. 15 + 9 · 9 + 25 What was the total score? A 816 B 530 C 121 D 58
expression? 2 + (9 - 3) × 4 A B C D
10 18 26 32
11. To evaluate the expression 21 - 6 × 3, Diego multiplied 6 by 3 to get 18. Then he subtracted 18 from 21 to get 3. Which of the following expressions has the same result? A B C D
A20
North Carolina, Grade 6
6 - 3 × 21 (21 - 6) × 3 (21 - 3) × 6 21 - 3 × 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
8. What is the value of the following
10. The total points scored by both teams
Name
Date
Practice by Essential Standard 6.N.3 3. The chart below shows the progress
1. Which number line shows the approximate location of these fractions in order? 5 A __
1 B __
8
4
A
3 C __ 4
"
11 D ___ 16
Marathon Progress
#$% 1 2
0
of five runners in a marathon. The runners report their progress in different forms.
Runner
1
Tamara
B
# 1 2
0
C
#
D
1
%"$ 1 2
0
# 0
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
$%"
1
"%$ 1 2
1
Amount of Course Completed 5 __ 8
Cindi
one-half
Anshu
75%
Anook
11 ___
Jamal
0.6
20
So far, of the five athletes, who is in third place? A B C D
Tamara Jamal Cindi Anook
2. Sonia scored 84% on her math test. 4 of the test Bryan correctly answered __ 5 questions. Isra scored 44 out of 50. Rico completed 0.86 of the questions correctly. Each test question is worth the same amount. Who has the best score?
A B C D
Sonia Bryan Isra Rico
Practice by Essential Standard
4. According to the 2000 census, 49% of the residents of North Carolina are male. What fraction is this? 49 A ___
10 49 B ___ 50 49 C ____ 100 1 D ___ 49
North Carolina, Grade 6 A21
Name
Date
Practice by Essential Standard 6.N.4 1. According to the chart below, whose book collection has the highest ratio of fiction books to nonfiction books? Book Collection Fiction Nonfiction Nora 6 12 Gary 13 24 Latisha 18 36 Juan 7 12
A B C D
Nora Gary Latisha Juan
4. Kayla is ordering T-shirts for the school band. The table below shows the number of T-shirts Kayla orders and the total cost. School Band T-shirts Number of 10 30 40 T-shirts Total Cost $50 $150 $200
50 $250
If the cost per T-shirt stays the same, how much will it cost to order 70 T-shirts? A B C D
$350 $300 $275 $250
2. The distance from Greensboro to
A 1.2 hours B 3 hours C 6.5 hours D 80 hours
3. Tyrell entered a bubblegum blowing contest. He can blow 9 bubbles in 90 seconds. If he continues at this rate, how many bubbles can he blow in 3 minutes? A 9 B 18
A22
5. Olivia drives 81.8 miles from Winston-Salem to Durham. Ana drives 53.8 miles from Winston-Salem to Kannapolis. They both drive at a constant rate of 60 miles per hour during the entire length of their trips. In decimal form, about how many more hours does Olivia drive than Ana? Round to the nearest hundredth of an hour. A B C D
0.46 hours 0.5 hours 0.52 hours 2.26 hours
C 27 D 90
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wilmington is 210 miles. The distance from Greensboro to Goldsboro is 130 miles. Tina starts in Greensboro. About how many more hours would it take her to drive to Wilmington than to Goldsboro, if she drives at a rate of 65 miles per hour?
Name
Date
Practice by Essential Standard 6.N.5 1. Cape Hatteras lighthouse was originally built in 1802. It took 1,250,000 bricks to build the lighthouse. What is 1,250,000 written in scientific notation? A B C D
1.25 × 106 12.5 × 106 125 × 106 0.125 × 106
5. Which symbol will make the statement below true? 52 × 7 3 A B C D
5×7×5×7
= > < ≠
6. Which of the following correctly shows 2. Which of the following is a true statement?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
74 × 112 = 11 × 7 × 11 × 7 × 7 × 7 74 × 112 > 11 × 7 × 11 × 7 × 7 × 7 74 × 112 < 11 × 7 × 11 × 7 × 7 × 7 74 × 112 ≠ 11 × 7 × 11 × 7 × 7 × 7
0.00545 written in scientific notation? A B C D
0.545 × 10-3 5.45 × 10-5 54.5 × 10-3 5.45 × 10-3
7. Which number has a prime 3. What is the prime factorization of 3,825? A B C D
3 × 5 × 13 3 × 5 × 17 3 × 52 × 17 32 × 52 × 17
factorization of 42 × 33 × 24? A 216 B 2,382 C 6,912 D 8,204
8. Which of the following is the prime 4. How is 8.85 × 104 written in standard notation? A 885 B 8,850 C 88,500 D 885,000
Practice by Essential Standard
factorization of 144? A B C D
23 24 23 24
× × × ×
32 32 33 34
North Carolina, Grade 6 A23
Name
Date
Practice by Essential Standard 6.A.1 1. Jan scored 5 more than half of her team’s goals during the season. Let g stand for the number of goals scored by the team. Which expression models the number of goals Jan scored? A B C D
1+g+5 __
4. The graph below represents the solution set of which inequality? 1
A B C D
2
2g + 5 g÷2+5 1g 5 __
(2 )
2. Maria is preparing party favors using the gift bags below.
4
5
6
7
8
9
x - 7 ≤ 28 4 + x ≤ 28 4x ≤ 28 7x ≤ 28
Izzy still has more savings in her account, which is valued at $580. If a represents the original amount in Roy’s savings account, which inequality represents this situation? a a a a
+ + + +
28 28 28 28
≥ ≤ > <
580 580 580 580
6. Anya spends a total of $600 on food to cater an event. She hopes to make a total profit of $240. She uses the equation below to find r, the total revenue from the event.
7 6 5 3
r - 600 = 240 What is the total revenue?
3. What value for y makes this equation true? 6 + y = 21
A24
A 27
C 20
B 21
D 15
North Carolina, Grade 6
A B C D
360 600 840 940
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
3
5. Roy adds $28 to his savings account.
A B C D She plans to distribute 35 trinkets equally among the bags. How many trinkets will be in each bag?
2
Name
Date
Practice by Essential Standard 6.A.1 (continued) 7. Mikael has $50 to spend on gardening supplies. He spends a total of $36 on tools, potting soil, and seeds. Which graph shows how much he can spend on a gardening book for beginners?
10. In North Carolina, when drivers see the speed limit sign below, they may travel a minimum speed of 50 miles per hour.
A 2
4
6
8 10 12 14 16 18
B 8 10 12 14 16 18 20 22 24
C 6 12 18 24 30 36 42 48 54
D 20 25 30 35 40 45 50 55 60
8. What value of m makes the equation true?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
m + 32 = 48 A 16 B 30
C 48 D 80
9. Candace borrowed $600 from her parents to buy a computer. She pays them back at a rate of $20 per month. Which equation can Candace solve to find m, the number of months it will take for her to pay back all the money to her parents? A B C D
600 = 20 ÷ m 600 = 20 × m 600 = m ÷ 20 20 = 600 × m
Practice by Essential Standard
Which equation can be used to find d, the difference between the posted speed limit and the minimum speed limit? A B C D
70 - d = 50 d - 70 = 50 50 - d = 70 50 - 70 = d
11. A light on Ben’s piggy bank comes on when there are 60 quarters in the bank. Ben already has 15 quarters in his bank. His father gives him x quarters to add to the bank. The light does not come on. Which inequality describes this situation? A B C D
x - 15 x + 15 60 - x 60 + x
< < < <
60 60 15 15
North Carolina, Grade 6 A25
Name
Date
Practice by Essential Standard 6.A.1 (continued) 12. After a 40-pound bag of sand is added to Tom’s punching bag, its total weight is at least 250 pounds. Tom uses the inequality below to find w, the original weight. w + 40 ≥ 250 Which inequality can be used to represent the original weight of the punching bag? A B C D
w w w w
≥ ≥ > >
290 210 290 210
14. In North Carolina, there are 30 private colleges and universities. Let s represent the number of public colleges and universities in North Carolina and let p represent the number of private colleges and universities in North Carolina. The equation below shows how s relates to p. p = s + 14 How many public colleges and universities are there in North Carolina?
13. Some food prices at the county fair are
A B C D
44 30 16 14
shown in the table below. Food Prices Price $5 $4 $2
15. Kenyon has been standing in line for 12 minutes at an amusement park. When he first got in line, he was standing right under this sign.
Suppose that you bought s salads, b burgers, and d drinks. Which expression represents the total cost, in dollars? A B C D
5s 5s 5s 5s
+ + ×
4b 4b 4b 4b
+ ×
2d 2d 2d 2d
maximum waiting time from this point: 20 minutes
He uses the inequality 12 + x ≤ 20 to find the possible number of minutes he has yet to wait. What number must Kenyon subtract from both sides? A 20 B 18 C 12 D 8
A26
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Item Salad Burger Drink
Name
Date
Practice by Essential Standard 6.A.2 1. Look at the pattern below. Which of the following is the 10th term? 3, 7, 15, 31, 63, …
3. Which of the following follows the rule divide by 2 then subtract 4? A B C D
A 4,095 B 2,047 C 1,023 D 511
368, 184, 92, 46 368, 182, 89, 43 136, 64, 28, 10 136, 68, 34, 17
4. Which set of instructions is modeled 2. Rafael makes the table below to show
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
the relationship between the number of subjects he studies s, and the total amount of time t, in minutes, it takes for him to study. s
1
2
3
4
5
t
45
60
75
90
?
Which study routine is Rafael following, and what should the missing value be? A Spend 15 minutes on each subject and then review for 30 minutes; 105. B Spend 20 minutes on each subject and then review for 25 minutes; 125. C Spend 25 minutes on each subject and then review for 20 minutes; 145. D Spend 30 minutes on each subject and then review for 15 minutes; 165.
Practice by Essential Standard
by the table below? x
8
12
16
20
y
2
3
4
5
A Use 1 lemon (x) for every 4 cups of water (y). B Use 4 lemons (x) for every cup of water (y). C Use 2 lemons (x) for every 4 cups of water (y). D Use 4 lemons (x) for every 2 cups of water (y).
5. What rule applies to the pattern below? 4, 11, 18, 25, 32, … A B C D
add 6 subtract 6 subtract 7 add 7
North Carolina, Grade 6 A27
Name
Date
Practice by Essential Standard 6.A.2 (continued) 6. Marissa created an arithmetic pattern starting with 5. She followed the rule multiply by 4 then add 3 to continue the pattern. What number is the 5th term? A 95 B 383 C 1,535 D 6,143
9. What is the 7th term of the pattern below? 64, 32, 16, 8, … A B C D
8 4 2 1
10. Which rule describes the pattern 7. Krystal is playing a game in which she scores 4 points for each correct answer. Which pattern shows the number of points earned when 1, 2, 3, and 4 questions are answered correctly? 4, 8, 12, 16 3, 7, 11, 15 2, 6, 10, 14 1, 5, 9, 13
1, 8, 43, 218, … A B C D
Multiply by 3 then add 5. Multiply by 5 then add 3. Divide by 5 then add 3. Divide by 3 then add 5.
11. Jonah has written a pattern that
8. Which equation could have been used
follows the rule multiply the previous two numbers to find the next number. Below are the first 4 terms of his pattern. What is the 8th term?
to create the function table below?
A B C D
A28
y y y y
= = = =
x
y
16
10
14
8
12
6
10
4
1, 2, 2, 4, … A 8,192 B 265 C 32 D 8
x+6 6x x-6 6÷x
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
below?
Name
Date
Practice by Essential Standard 6.A.3 1. In a survey, businesses were asked
3. Look at the graph below.
how many computers they owned. The results are shown below.
y
× 1
2
3
4
5
6
7
8
S
50
× × × × × ×
× ×
T
60
$0.165&3408/&%
40 30
R Q
20
9
10
Which statement is true of the line plot?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A The line plot shows the trend of the data set. B The line plot shows the spread of the data set. C The line plot shows the number of employees. D The line plot shows the number of hours the computers are used.
2. Registered voters for the 2008 North
0
x
Which table matches the data in the graph? A
B
C
Carolina general election are shown in the table below. 2008 North Carolina Voter Registration Republicans 1,651,762 Democrats 2,529,732 Independent 38,837 TOTAL 4,220,331
10 20 30 40 50 60
D
Point x y Point x y Point x y Point x y
Q
R
S
T
10
20
30
60
30
40
50
60
Q
R
S
T
10
20
50
40
30
40
30
60
Q
R
S
T
30
20
30
40
10
40
50
60
Q
R
S
T
10
20
30
40
30
40
50
60
Which of the following is the ratio of Democrats to total registered voters? A B C D
2,529,732 1,651,762 2,529,732 1,651,762
: 1,651,762 : 2,529,732 : 4,220,331 : 4,220,331
Practice by Essential Standard
North Carolina, Grade 6 A29
Name
Date
Practice by Essential Standard 6.A.3 (continued) 4. Which graph shows the slowest plant growth?
Height (cm)
A 30 25 20 15 10 5 0
Plant Growth
1
2
3
4
5. Armando kept track of the increasing temperature of water he was heating on a stove during a 20-minute time interval. Which graph would best display the data? A B C D
bar graph double bar graph line graph pictograph
Week
Height (cm)
B 5 4 3 2 1 0
Plant Growth
6. Which line plot correctly displays the data below? 15, 15, 13, 11, 10, 11, 14, 15, 11, 14, 15
5 10 15 20
A
Songs Downloaded × × ×
Week
Week
25 20 15 10 5 0
B
2
4
6
8
Height (cm)
Height (cm)
D 25 20 15 10 5 0
×
× ×
10
11
2
3
4
North Carolina, Grade 6
12
13
14
15
12
×
×
× × ×
13
14
15
Songs Downloaded
×
× × ×
10
11
D 1
11
Songs Downloaded
C
Plant Growth
Week
A30
10
Plant Growth
× ×
12
×
× ×
× × × ×
13
14
15
Songs Downloaded
×
× × ×
×
×
× ×
× × × ×
10
11
12
13
14
15
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
×
× × × ×
Name
Date
Practice by Essential Standard 6.G.1 1. Which coordinate grid shows only a
2. Look at the grid below.
translation of ABC? y
A
y
A'
A
x
O
L C'
B'
x
O
B
If parallelogram LMNO is reflected over the x-axis, what would be the ordered pair of M?
y
B'
A
A'
A M (-4, -3) B M (-4, 3)
C M (4, 3) D M (4, -3)
x
O
B
N
O
C
B
M
C'
C
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3. Triangle PQR has coordinates (2, 5), (1, 3), and (3, 3). Triangle PQR is created by reflecting PQR across the y-axis. What are the coordinates of PQR?
y
C A
A' x
O
B
C
C'
B'
A B C D
(2, 5), (1, 3), (3, 3) (2, –5), (1, –3), (3, –3) (–2, –5), (–1, –3), (–3, –3) (–2, 5), (–1, 3), (–3, 3)
y
D
4. Figure ABCD has coordinates (-4, 4), C'
A
B' x
O
B
C
A'
(-1, 4), (-1, 1), (-4, 1). Figure ABCD has coordinates (3, -2), (6, -2), (6, -5), (3, -5). Which describes the translation of figure ABCD to figure ABCD? A B C D
Practice by Essential Standard
left 7 units and down 6 units left 7 units and up 6 units right 7 units and up 6 units right 7 units and down 6 units
North Carolina, Grade 6 A31
Name
Date
Practice by Essential Standard 6.G.1 (continued) 5. Figure RSTU is reflected to create
7. Look at the graph below.
figure RSTU. Which of the following is the equation of the line of reflection?
y 8 6
U'
y
4 2
T'
-8 -6 -4 -2 O 2 -2 -4
S' R' O
T
R
x
4
6
8 x
-6 -8
S U
A y=0 B y=1
C x=0 D x=1
6. The graph below shows some locations in a local park.
0
A32
C (3, 2) D (-7, -1)
8. In which quadrant will a point with the coordinates (-6, -8) lie?
Lake
A quadrant I B quadrant II
C quadrant III D quadrant IV
Picnic Area Restrooms
9. Two parallel lines are located 3 units Playground 1 2 3 4 5 6 7 8 9
Which ordered pair represents the location of the playground? A (6, 1) B (6, 5)
A (0, 0) B (-3, -2)
C (4, 7) D (1, 6)
North Carolina, Grade 6
apart. A circle with a diameter of 4 units is drawn in the same plane. What is the maximum number of points of intersection possible between the two parallel lines and the circle? A 1 B 2
C 4 D 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
9 8 7 6 5 4 3 2 1
At which ordered pair do the two lines intersect?
Name
Date
Practice by Essential Standard 6.G.1 (continued) 10. Which of the following shows ABC
11. Look at the graph below.
reflected across the line x = 4?
y
y
A
A
D B x
O
A
B
B' A'
C
C'
Which point lies on the x-axis? A point A B point B
y
B
C
x
O
A
C point C D point D
B B' A' x
O
12. Look at the graph below. y
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C C'
O
y
C
x
C' B' B
A' A
x
O
Which ordered pairs list the points of intersection of the circle and the line?
C
A B C D
y
D
B' A'
A
B x
O
C'
(3, -3), (3, 3) (-3, -3), (3, -3) (-3, 0), (0, 3) (0, -3), (3, 0)
C
Practice by Essential Standard
North Carolina, Grade 6 A33
Name
Date
Practice by Essential Standard 6.G.1 (continued) 13. Point A is located at (-3, 5) on the coordinate grid. What would be the new coordinates if point A was translated left 4 units and up 3 units? A (1, 0) B (0, 1)
16. Which point on the graph below represents the origin? y 6
C (-7, 8) D (8, -7)
C
4 2
below.
A
D
-6 -4 -2 O -2 -4 -6
14. Look at figure ABCDE on the graph
E
2
4
6 x
B
A point A B point B
C point C D point D
y
A
17. Triangle ABC is translated so that C
E
has coordinates (-5, 0).
B
y
D
C
O
x
A
A (-8, 4) B (4, -8)
C (0, 4) D (4, 0)
O
C
What are the coordinates of B? A (0, 3) B (3, 0)
C (-5, 0) D (0, -5)
15. Circle O is centered at (0, 0) and has a radius of 5. Circle P is centered at (0, 0) and has a radius of 6. At how many points do these two circles intersect? A 3 B 2
C 1 D 0
18. Line segment AB is translated 4 units right and 3 units ___ down. If the endpoints of AB are located at (2, 5) and (8, 1), what are ____the coordinates of the endpoints of AB? A B C D
A34
North Carolina, Grade 6
x
(6, 8) (2, 2) (6, 2) (2, 6)
and and and and
(12, 0) (5, -3) (12, -3) (-3, 12)
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
If figure ABCDE is reflected across the y-axis, what would be the new coordinates for point B?
B
Name
Date
Practice by Essential Standard 6.M.1 1. Alicia found that the width of her textbook is 8 inches. She wants to convert this measurement into centimeters. There are about 2.54 centimeters in each inch. About how wide is the textbook in centimeters? A 4 cm B 15 cm
C 20 cm D 30 cm
5. A recipe calls for 30 milliliters of vanilla extract. If 1 tablespoon is equal to about 14.79 milliliters, about how many tablespoons of vanilla extract is needed? A B C D
2 tablespoons 3 tablespoons 1 tablespoon 0.5 tablespoon
2. A shampoo bottle contains 15 fluid ounces. About how many milliliters is this? 1 fl oz ≈ 29.57 mL
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 450 mL B 45 mL
C 4.5 mL D 0.45 mL
6. At about 160 meters, Fontana Dam is the tallest dam in the eastern United States. If 1 meter is about 3.28 feet, about how many feet tall is Fontana dam? A 53 ft B 180 ft
C 300 ft D 480 ft
3. A league is another unit of length. One league is equal to about 4.83 kilometers. About how many kilometers are in 7 leagues? A 2.5 km B 15 km
C 30 km D 35 km
7. North Carolina has the largest statemaintained highway system in the United States. Currently there are 77,400 miles of roads throughout North Carolina. About how many kilometers is this? 1 mile ≈ 1.61 kilometers
4. North Carolina has 1,500 lakes of 10 acres or more in size. About how many square kilometers are in 10 acres? 1 acre ≈ 4,046.87 km2
A 1,200,000 km B 120,000 km C 12,000 km D 1,200 km
A 404,700 km2 B 40,470 km2 C 4,047 km2 D 407 km2
Practice by Essential Standard
North Carolina, Grade 6 A35
Name
Date
Practice by Essential Standard 6.M.2 1. A new apartment complex is building a swimming pool. According to North Carolina regulations, there must be a 4-foot high fence enclosing the pool area. The drawing below shows the planned pool and fence enclosure.
32 ft
bedroom. He made a plan for the rug.
Each square on the grid represents 2 square feet. What will be the approximate area of the rug in square feet?
8 ft 32 ft
3. Liko is making an area rug for his
24 ft
What is the length of the fencing, in feet?
48 32 24 16
ft2 ft2 ft2 ft2
4. A sailboat has a mainsail that is in the shape of a right triangle, as shown below.
2. A rectangle is 3.2 feet by 7.7 feet. Which is the best estimate for the perimeter of the rectangle? A B C D
26 24 22 21
ft ft ft ft
20 ft
15 ft
What is the area of the mainsail? A 35 ft2 B 75 ft2 C 150 ft2 D 300 ft2
A36
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 96 ft B 184 ft C 192 ft D 1,792 ft
A B C D
Name
Date
Practice by Essential Standard 6.M.2 (continued) 5. Triangle LMN has an area of 56 square centimeters. What is the base of this triangle? .
2
3
/
4
5
6
A 28 cm B 14 cm C 7 cm D 3 cm
What is the area of parallelogram QSTU? A 196 square feet B 126 square feet C 95 square feet D 63 square feet
6. The area of the parallelogram below is 42 square centimeters. Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
has a base of 14 feet and a height of 9 feet. 1
8 cm
-
7. In the figure below, rectangle PRTU
8. Jennifer drew the trapezoid below on the chalkboard.
10 cm
2 in. 7 cm 3 in.
What is the perimeter of the parallelogram? A 6 cm B 12 cm C 20 cm D 32 cm
Practice by Essential Standard
4 in.
What is the area of the trapezoid? A 6 square B 9 square C 16 square D 18 square
inches inches inches inches
North Carolina, Grade 6 A37
Name
Date
Practice by Essential Standard 6.M.3 1. A bank manager decides to frame a print of a quarter to hang in the lobby of the bank. The diameter of the quarter in the print is shown below.
4. The dome of a tourist attraction has a diameter of 165 feet at its base. A cross-section of the base of the dome is shown below.
165 ft
16 in.
Which expression can be used to find the area of the quarter in the print? A B C D
π × 16 × 16 π×8×8 16 × π 8×π
find the diameter of a circle with an approximate circumference of 64 inches? A 64 ÷ 3.14 B 64 × 3.14
his circular swimming pool. He also measures the diameter of the pool. Which of the following measures can he find by dividing the circumference by the diameter?
A38
7 1,815 B _____ feet 7 3,630 C _____ feet 7 7,260 D _____ feet 7
5. What is the best estimate of the area of the circle below?
6 cm
C 314 ÷ 64 D 2 × 3.14 × 64
3. Luke measures the circumference of
A area B π
605 feet A ____
A 6 square centimeters B 10 square centimeters C 30 square centimeters D 36 square centimeters
C radius D volume
North Carolina, Grade 6
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2. Which expression can be used to
What is the circumference of the 22 for π. dome’s base? Use ___ 7
Name
Date
Practice by Essential Standard 6.S.1 1. Juan rolled a fair number cube with faces labeled 1 to 6. He rolled the cube 360 times. Based on theoretical probability, how many times should Juan expect to roll a five? A B C D
40 50 60 70
3. Patricia flips a coin 100 times. Based on the theoretical probability, how many times should the coin land showing heads? A 100 B 75 C 50 D 25
4. Four students are playing a game 2. The table below shows the results after rolling a fair number cube 36 times. Face Number 1 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2 3 4 5 6
Number of times the number is rolled 3 8 9 4 6 6
using a number cube. The experimental probability for each student rolling a 4 is shown in the table below. Student
Experimental Probability
Jason
7 ___
Carla
2 ___
Devon
7 ___
My’Isha
9 ___
10 11 15 17
Which of the following is true about the probability of rolling a 2 on the next roll?
Which student has an experimental probability closest to the theoretical probability?
A The theoretical probability is less than the experimental probability. B The theoretical probability is greater than the experimental probability. C The theoretical probability is equal to the experimental probability. D The theoretical and experimental probabilities are greater than 1.
A B C D
Practice by Essential Standard
Jason Carla Devon My’Isha
North Carolina, Grade 6 A39
Name
Date
Practice by Essential Standard 6.S.1 (continued) 5. A bag contains 6 blue marbles and 7 green marbles. Dora selects one marble without looking. She then replaces the marble and selects another marble. Dora continues this process 65 times. Based on the theoretical probability, how many times should Dora expect to select a blue marble? A 60 B 50
C 40 D 30
6. Jung spun the spinner below 50 times. Based on the theoretical probability, how many times should Jung expect to spin a 4? 4
4
C 30 D 35
7. Evan has a bag that contains 8 blocks with stars, 2 blocks with circles, and 13 blank blocks. He selects a block, records the result, and places it back in the bag 115 times. How many times should Evan expect to select a block with a star? C 20 D 10
North Carolina, Grade 6
9. Cody has a deck of 36 cards. The deck contains an equal number of red, blue, green, yellow, orange, and purple cards. Cody selects a card at random, records the result, then replaces the card. He continues this process 180 times selecting an orange card 45 times. Which of the following statements is true? A The experimental and theoretical probabilities are less than zero. B The experimental probability is equal to the theoretical probability. C The experimental probability is less than the theoretical probability. D The experimental probability is greater than the theoretical probability.
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
2 4
A40
A The theoretical probability is less than the experimental probability. B The theoretical probability is greater than the experimental probability. C The theoretical probability is equal to the experimental probability. D The theoretical and experimental probabilities are greater than 1.
4
3
A 40 B 30
cards, 10 blue cards, 5 green cards, and 10 white cards. He randomly selects one card, records the result, then replaces the card. In 200 trials, Bryan selects a blue card 30 times. How does the experimental probability compare with the theoretical probability?
2
2
A 20 B 25
8. Bryan has a box that contains 15 red
Name
Date
Practice by Essential Standard 6.S.2 1. Andrew is playing a game where a 6-sided number cube is rolled and then a coin is flipped. Which tree diagram correctly displays all of the different possible outcomes of each roll of the number cube followed by a flip of the coin? A
H 1 T H 2 T H 3 T H 4 T H 5 T H 6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
T
B
1 2 3 4 5 6
C H
T
D 1 2 3 4 5 6
H T H T H T
2. Cora has a pink shirt, a blue shirt, and a purple shirt. She has a pair of black pants and a pair of brown pants. Which organized list shows all the possible outfits Cora could wear? A pink, black blue, black purple, black B pink, brown blue, brown purple, brown C pink, black pink, brown blue, black blue, brown purple, black purple, brown D pink, blue blue, purple black, brown blue, brown pink, black purple, brown
3. A deli has a combo special for $5.99.
1 2 3 4 5 6 1 2 3 4 5 6
You pick a sandwich, soup, dessert, and drink from the following choices: Sandwich: chicken, ham, tuna, turkey Soup: tomato, vegetable, clam chowder Dessert: cookie, pie Drink: soda, milk, coffee, tea, juice How many different lunch special combinations are there? H H H H H H
Practice by Essential Standard
T T T T T T
A 120 B 100
C 38 D 14
North Carolina, Grade 6 A41
Name
Date
Practice by Essential Standard 6.S.2 (continued) 4. Kristine is playing a game in which she selects 2 different cards one at a time. There is 1 red card, 1 blue card, 1 green card, and 1 yellow card. The tree diagram below shows all of the possible outcomes for selecting the 2 cards. Blue Red
Green Yellow Red
Blue
Green Yellow Red
Green
Blue Green
16 1 B ___ 12 1 C __ 4 1 D __ 3
A
1 __
B
1 __ 6
3
1 C ___
25 1 D ___ 30
6. Pedro is taking a test that has 5 true/false questions. If he answers each question with true or false and leaves none blank, in how many ways can he answer the whole test? A 5 B 10 C 25 D 32
7. A company places a 6-symbol code on each unit of product. The code consists of 5 digits followed by one letter. The first digit is the number 5. How many different codes are possible? A B C D
A42
North Carolina, Grade 6
100,000 130,000 260,000 320,000
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
What is the probability of selecting a red card then selecting a blue card? 1 A ___
1 yellow, 1 pink, and 1 orange marble. Roxie randomly chooses 2 marbles from the bag one right after the other. What is the probability Roxie will select the pink marble as the second marble?
Blue Yellow Red
Yellow
5. A bag contains 1 red, 1 blue, 1 green,
Name
Date
Practice by Essential Standard 6.S.3 1. Jarod’s science quiz scores are listed
4. The ages of customers entering a store are listed below.
below. Score 100 98 97 95
Frequency 1 1 3 2
15, 27, 25, 40, 22, 22, 27, 49, 53, 64, 16, 53, 41, 37, 22, 23, 27, 12, 32 Which of the following stem-and-leaf plots correctly displays the data? A
Which measure will remain the same if Jarod’s next three quiz scores are 96, 93, and 93? A mode B range
Ages of Customers Stem 1 2 3 4 5 6
C mean D median
Leaf 2 5 6 2 2 2 3 5 7 7 7 2 7 0 1 9 3 3 6 | 4 = 64 years old 4
B Ages of Customers
2. In a game, Missy rolls 3, 4, 2, 3, 5, 6, 2,
Stem 1 2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
and 3. What is her mean score? A 2 B 2.5
C 3 D 3.5
3. The scores for this season’s soccer games are shown in the frequency table below. Soccer Games Score 1 2 3
Frequency 5 2 3
What can be concluded from the data? A B C D
The The The The
range is 3. mean is 2. median is 2. mode is 1.
Practice by Essential Standard
C
Leaf 2 5 6 2 3 5 7
3
2 7
4 5 6
0 1 9 3 4
6 | 4 = 64 years old
Ages of Customers Stem 1 2 3 4 5 6
Leaf 2 5 6 2 2 2 3 5 7 7 7 2 7 0 1 9 3 6 | 4 = 64 years old 4
D Ages of Customers Stem 1 2 3 4 5 6
Leaf 2 5 6 2 2 3 5 7 2 7 0 1 9 3 3 6 | 4 = 64 years old 4
North Carolina, Grade 6 A43
Name
Date
Practice by Essential Standard 6.S.3 (continued) 5. The shoe sizes on display are 8, 7.5, 8, 7.5, 8, 7.5, 8, and 8.5. What is the mode of this data? A B C D
1 7.5 7.875 8
6. Vera documented the grams of protein on the nutrition labels of 12 different types of bread. She recorded her results in a table. Grams of Protein in Bread 2 5 4 2 2 4 2 2 2 4 3 2
A The mean of the data is less than the median of the data. B The mode and median of the data are the same. C The mean of the data is slightly lower than the majority of the data values. D The median of the data is greater than the range of the data.
A44
North Carolina, Grade 6
took each of his students to complete two laps around the track. His notebook entry for his first period class is shown below. First Period Class Number of Minutes to Complete Two Laps Addison
4
Little
4
Brooks
6
Meniko
4
Caldez
4
Marshbanks 5
Cooper
5
Roque
3
Lantz
7
Whitner
4
The second period class has the same mean time as the first period class, but the range of the students’ times was 6 minutes. Which of the following best compares the first period class with the second period class? A On average, the students in first period had slower times than the students in second period. B On average, the students in first period has faster times than the students in second period. C The average times of each class are the same, but there is less difference between the fastest and slowest times in first period. D The average time of each class are the same, but there is greater difference between the fastest and slowest times in first period.
Practice by Essential Standard
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Vera plans to write a report to summarize her findings. Which statement can she use in her report?
7. Coach Gustav recorded the time it
Name
Date
Countdown to the EOG 6 Weeks Until the Test Monday y
1. Which point lies in Quadrant II?
A
A B C D
point point point point
A B C D
D x
O
C
Tuesday
2. Notebooks cost $0.65 each. Rosa bought 8 notebooks. How much money did Rosa spend on notebooks?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
$4.80 $5.20 $480 $520
Wednesday
3. Which fraction is equal to 0.75? 10 A ___
15 C ___
10 B ___ 15
16 D ___ 20
16
Thursday
4. Jamal and Terri collect baseball cards. Jamal has 50 more cards than Terri. Together, they have 425 cards in their collections. If t represents the number of cards in Terri’s collection, which equation represents the total number of cards in both collections? A B C D
t t t t
+ + +
50 = 425 50 = 425 t + 50 = 425 t - 50 = 425
20
Friday
5. The dimensions of a playground are given in the drawing. 3 ft 4 ft 8 ft
13 ft
What is the perimeter of the playground? A 28 B 42 C 64 D 1,248
Countdown to the EOG
B
feet feet feet feet
North Carolina, Grade 6 A45
Name
Date
Countdown to the EOG 5 Weeks Until the Test Monday
1. Triangle ABC is reflected over the x-axis.
y
C
What are the coordinates of A ? A B C D
O
Tuesday
2. Amir is cutting bookcase shelves
1 feet long. He from a board that is 6__ 2 1 foot in wants each shelf to measure __ 2 length. How many shelves can Amir cut from the board?
Wednesday
3. Which expression is the prime factorization of 72? A B C D
22 22 23 23
Thursday
4. Which rule represents the sequence given below? 3, 6, 12, 24, 48, 96 A Add two to the previous term. B Add three to the previous term. C Multiply the previous term by two. D Multiply the previous term by three.
North Carolina, Grade 6
x
× × × ×
32 33 32 33
Friday
5. Maria draws a square with sides 3 units long and a circle with a radius of 2 units. The center of the circle is one of the vertices of the square. At how many points do the square and circle intersect? A 0 B 1
C 2 D 3
Countdown to the EOG
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 3.25 shelves B 6 shelves C 7 shelves D 13 shelves
A46
A
B
(1, 3) (1, -3) (-1, 3) (-1, -3)
Name
Date
Countdown to the EOG 4 Weeks Until the Test Monday
1. Which scenario could be represented by the given graph?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Distance
A A car travels at a constant rate. B A car travels at an increasing rate. C A car travels at an increasing rate and then at a constant rate. D A car travels at a constant rate and then at an increasing rate.
Time
Tuesday
Wednesday
2. At the start of the month, Mr. Ichiro
3. Which relationship is shown by the
had $350 in a bank account. During the month, he made a $40 deposit, a $65 withdrawal, a $50 deposit, and a $30 withdrawal. How much money was in Mr. Ichiro’s account at the end of the month? A B C D
$165 $345 $355 $535
given number line?
0
1 50% 3
3 0.9 1 4
3 A 50% is less than __ . 4 3 B __ is less than 50%.
4
3. C 0.9 is less than __ 4
D 0.9 is less than 50%.
Thursday
4. What is the value of 2n + 5 if
Friday
5. About how many centimeters is four
3n = 12?
inches?
A 4 B 8 C 9 D 13
A 100 B 10 C 4 D 1.5
Countdown to the EOG
North Carolina, Grade 6 A47
Name
Date
Countdown to the EOG 3 Weeks Until the Test Monday
1. The scores on a science quiz are given in the stem-and-leaf plot. Which statement can be supported by the data? A B C D
The The The The
lowest score was 60. range of the scores was 30. mean score was 82.5. median score was 82.5.
Quiz Scores Stem Leaf 6 4 4 5 8 7 2 3 6 9 9 8 1 4 7 8 8 9 9 2 3 4 4 6 6|5 = 65%
Tuesday
Wednesday
2. A bag contains 25 marbles: 3 red, 6 blue, 2 yellow, 8 green, and 6 red. What is the probability of choosing a yellow or green marble on the first draw? 8 C ___
2 B __ 5
2 D ___ 25
25
is scientific notation? A B C D
6.31 6.31 6.31 6.31
× × × ×
10-2 10-1 10 102
Thursday
Friday
4. The dimensions of a playground are given in the drawing.
lowest unit rate? 3 ft
4 ft 8 ft
13 ft
What is the area of the playground? A 28 B 42 C 64 D 1,248
A48
square square square square
feet feet feet feet
North Carolina, Grade 6
5. Which of the canned goods has the Vegetable carrots corn green beans lima beans
A B C D
Price $0.75 for 15 ounces $0.99 for 16 ounces $1.40 for 30 ounces $1.55 for 32 ounces
carrots corn green beans lima beans
Countdown to the EOG
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
16 A ____ 625
3. Which expression shows 631 written
Name
Date
Countdown to the EOG 2 Weeks Until the Test Monday
1. Which unit rate is shown in the graph?
Cost of Sandwiches 25
Cost ($)
A $5 per sandwich B $10 per sandwich C $15 per sandwich D $20 per sandwich
20 15 10 5 0
1 2 3 4 5
Number of Sandwiches
Tuesday
2. Ms. Martino packed 4 blouses, 2 pairs of slacks, and 3 scarves for a business trip. How many different outfits could Ms. Martino create from her clothes?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A 8 outfits B 9 outfits
C 12 outfits D 24 outfits
Wednesday
3. What is the 10th term of the given arithmetic sequence? 3, 5, 7, 9, 11, … A 23 B 21
Thursday
4. What is the approximate area of circle O?
Friday
5. The ages of people viewing a movie are shown below. 10 8 17 16 13 15 14 10 10 37 18
5 inches O
A 78.5 square inches B 19.6 square inches C 15.7 square inches D 7.9 square inches
Countdown to the EOG
C 19 D 17
Which measure of center best represents the data? A B C D
mean median mode range
North Carolina, Grade 6 A49
Name
Date
Countdown to the EOG 1 Weeks Until the Test Monday Basketball Game Attendance
1. The graph shows the attendance at the 8
Warrior’s basketball games this season.
A Each interval represents 50 people. B Each interval represents 100 people. C Between 100 and 199 people attended games on two different occasions. D Between 300 and 399 people attended games on two different occasions.
7
Number of Games
Which of the following statements is true?
6 5 4 3 2 1 0 0–99 100– 200– 300– 400– 500– 600– 199 299 399 499 599 601
Number of People
Tuesday
2. Which inequality is equivalent to n < 3? A 5 + n < 10 B n - 5 < 10
C 5n < 15 D n ÷ 5 < 15
Wednesday
3. On triangle RST, S is located at the point (10, 4). If RST is translated 3 units to the left and 4 units up, where will S be located?
Thursday
4. For any circle, which of the following ratios equals π. A B C D
area to radius area to diameter circumference to radius circumference to diameter
C (13, 0) D (13, 8)
Friday
5. Geraldo spins the fair spinner shown twenty times. The spinner lands on red 3 times, on blue 6 times, on green 5 times, and on yellow 6 times. Which of the outcomes is closest to the theoretical probability?
Red
Blue
Green Yellow
A B C D
A50
North Carolina, Grade 6
the the the the
red spins blue spins green spins yellow spins
Countdown to the EOG
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A (7, 0) B (7, 8)
Name
Date
Practice Test Student Answer Document–Calculator Active
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North Carolina, Grade 6 A51
Name
Date
Practice Test Student Answer Document–Calculator Inactive Record your answers by coloring in the appropriate bubble for the best answer to each question. 1 2 3 4 5 6 7 8 9 10
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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A52
North Carolina, Grade 6
Student Answer Document
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Date
Practice Test Calculator Active Calculator use is permitted on this section of the test.
1.
4. The area of the parallelogram below is 24 square inches.
Which situation is represented by the graph below?
?
4 in.
Cups of Water
COFFEEMAKING 12 y 10 8 6 4 2 0
8 in.
What is the height? x 1 2 3 4 5 6 7 8
Number of Scoops
A B C D
Use Use Use Use
2 2 4 2
scoops for one cup of water. cups of water for one scoop. scoops for 2 cups of water. cups of water for 4 scoops.
A B C D
2 3 4 6
inches inches inches inches
5. At what point does the line in the graph cross the y-axis?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
y
2. Which equation is true? A B C D
(a (a (a (a
+ + + +
2b) 2b) 2b) 2b)
+ + + +
c c c c
= = = =
a(2b + c) (a + 2b)c a + (2b + c) (a + 2)b + c
3. Carolina Beach State Park features 5 miles of hiking trails and 10 miles of beach. About how many kilometers of hiking trails and beach are there in all?
O
A (-6, 0) B (-4, 0)
x
C (0, -4) D (0, -6)
1 mile ≈ 1.61 kilometers A 40 kilometers B 24 kilometers C 15 kilometers D 8 kilometers
Practice Test
North Carolina, Grade 6 A53
6. The ages of the players on a neighborhood baseball team are shown in two different frequency tables below.
8. Which number line is labeled correctly? A 0.3 32%
7 20
0.37
0.4
0.3 32%
0.37
7 20
0.4
Table 1: Baseball Team Age 27 25 22 20
Frequency 2 1 4 2
Table 2: Baseball Team Age 26–28 23–25 20–22
Frequency 2 1 6
Which statement is true based on the information given in the tables?
7. Jave notices that the data in the graph below are tightly clustered around the center. NUMBER OF PAGES IN REPORTS BY STUDENTS
0
1
2
3
4
5
6
7
C 0.3
7 20
0.3
0.37
32% 0.37
0.4
D 7 20
0.4
32%
9. Javier rolled a fair six-sided number cube 24 times. He recorded the results in the table below. Number Shown
1
2
3
4
5
6
Times Rolled
How does Javier’s experimental probability and the theoretical probability of rolling a 2 compare? A The experimental probability is greater than the theoretical probability. B The experimental probability is less than the theoretical probability. C The experimental probability is equal to the theoretical probability. D There is not enough information to compare the actual probability and the theoretical probability.
Which measure best describes Jave’s analysis? A B C D
A54
mean average range median
North Carolina, Grade 6
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A The median is 25. B None of the measures of central tendency can be determined by just looking at Table 2. C The mean is less than the median. D There is no mode.
B
10. Which picture shows only a translation of polygon ABCDE? y
A B
B O
D
D
A
A
x
C C E
E
B
y
E E
A 77.75 B 7.75 C 0.775 D 0.0775
B
12. Circle A has diameter d and radius r.
C
"
r
x
O
D
Adanna knows this means that for every dollar, she will have to pay an extra seven and three-quarter cents. How is 7.75% written as a decimal?
D
A B A
11. North Carolina sales tax is 7.75%.
C
d
E
C
What is the result of dividing the circumference by the diameter?
y
E
B
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C A
O
D
A
D
x
A B C D
2r π 2 2π
C E
B
D
13. Which relationship is shown in the
y
C E
B D
B
A A
D
O
C E
Practice Test
x
table below? Tae Kwon Do Classes 90 135 180 Minutes (m) 2 3 4 Classes (c)
A B C D
Each Each Each Each
class class class class
lasts lasts lasts lasts
225 5
45 minutes. 88 minutes. 92 minutes. 180 minutes.
North Carolina, Grade 6 A55
14. What is the solution of the inequality? 3x > 9 __ 8
A B C D
x x x x
> > > >
216 72 24 14
15. For the past two weeks, Akins has been collecting soda can tabs for charity. The table below shows Akins’ log of the number of tabs he collected. Soda Can Tabs Collected Week 1 t Week 2 80 Total Collected 425
17. What is the maximum possible number of points of intersection between a square and a circle in the same plane? A 2 B 4
C 7 D 8
18. What will be the coordinates of point A when the figure is reflected across the y-axis? y
A C
x
O
B
Which equation can be used to find t, the number of tabs he collected during the first week? t + 80 = 425 t - 80 = 425 80 - t = 425 425 + t = 80
A (-1, -3) B (-1, 3)
C (1, -3) D (1, 3)
19. Which is a true statement about the data given below?
16. The heights in inches of the windows in Shelby’s house are listed below. 36, 72, 14, 12, 8 Which statement is true? A B C D
A56
The mean and range are the same. The mode is 14. The median is less than the mean. The median is greater than the range.
North Carolina, Grade 6
Test Scores 88 75 69 95 94 95
A The range is greater than the mode. B The range is equal to the mode. C The mean is equal to the median. D The mean is less than the median.
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
20. Ramon and four friends want to play a game. Only four people may play at a time. How many different combinations of four players are possible? A 20 B 16 C 5 D 4
23. A penny is tossed 3 times. What is the probability that it will land showing tails on all three tosses? 2 A __ 3
B
1 __
C
1 __
2
5 1 D __ 8
24. The sidewalk from the parking lot to 21. Elizabeth’s water tank holds 100 liters of water. One afternoon it started leaking and lost 8 liters of water every 20 minutes. Which table shows the relationship between M, the number of minutes, and L, the amount of water in the tank? A
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
B
C
D
M
0
20
40
60
L
0
8
16
24
M
0
8
16
24
L
0
20
40
60
M
0
20
40
60
L
100
92
84
76
M
100
80
60
40
L
0
8
16
24
the school has the dimensions shown below. 3 ft
8 ft
3 ft 12 ft
What is the perimeter of the sidewalk? A B C D
76 46 40 26
ft ft ft ft
22. A trapezoid has bases that measure 5 units and 9 units with a height of 5 units. What is the area of the trapezoid? A B C D
35 45 70 90
Practice Test
square square square square
units units units units
25. The radius of a circular garden is 13 feet. How much fencing will be needed to go around the outer edge of the garden? Use 3.14 for π. A 40.82 feet B 81.64 feet C 265.33 feet D 530.66 feet
North Carolina, Grade 6 A57
26. In which quadrant does the figure lie?
ratio table below?
y
O
A B C D
quadrant quadrant quadrant quadrant
x
I II III IV
27. Twelve friends met at a party. Each friend shook the hand of each of the other friends exactly once. How many handshakes were there in all? A 144 B 66 C 24 D 12
6.5
18.2
22.1
31.2
2.5
7
?
12
A 8 B 8.5 C 9 D 11.5
30. The clock on Mr. Barton’s desk has a circumference of 37.7 centimeters. What is the diameter of the clock to the nearest centimeter? A 20 centimeters B 18 centimeters C 12 centimeters D 6 centimeters
31. A box contains colored markers. There
County is the highest waterfall east of the Rocky Mountains. It is about 411 feet high. About how many meters high is Whitewater Falls? 1 meter ≈ 3.28 feet A 1,348 meters B 1,250 meters C 165 meters D 125 meters
North Carolina, Grade 6
are 6 red, 7 blue, and 5 green markers. Jake picks a marker without looking and keeps it. His marker is not red. Shawna picks a marker without looking and keeps it. Her marker is not red. Carl picks a marker from the box without looking. What is the probability that Carl’s marker will not be red? 1 A __ 3 5 B __ 8 5 C __ 9 2 D __ 3
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
28. Whitewater Falls in Transylvania
A58
29. What is the missing number in the
32. The dot plot below shows the number of questions answered correctly by students on a social studies test. QUESTIONS ANSWERED CORRECTLY BY STUDENTS
6
7
8
9 10
What is the median of the data set? A B C D
2.5 4 8 8.3
34. Tara has 10 single socks in her drawer. Four of the socks are blue, 2 socks are red, and 4 socks are green. Tara picks her socks out of the drawer without looking and keeps them. First, she picks a blue sock, and then she picks a green sock. What is the probability that Tara will pick a blue sock on her third try? 1 A __ 4 3 B __ 8 2 C __ 5 4 D __ 5
35. What is the perimeter of the figure 33. Gina tossed a fair coin 17 times and
22 for π. shown below? Use ___ 7
recorded her results in the table below. 14 m
Heads
7m
Tails
20 m
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
7m
Based on theoretical probability, which statement is true. A Gina will most likely toss tails on the next toss of the coin. B Gina will most likely toss heads on the next toss of the coin. C The number of tails Gina actually tossed was equal to the number of tails Gina expected to toss. D The number of tails Gina actually tossed was less than the number of tails Gina expected to toss.
Practice Test
A B C D
104 126 169 236
meters meters meters meters
36. Rafael needs to buy some new shirts. A sale lists a variety of shirts for $17.49 each. How much will four shirts cost? A B C D
$69.96 $68.76 $59.96 $48.66
North Carolina, Grade 6 A59
37. Deidra, Byron, Blake, and Shaniqua each tossed a coin four times. The results are listed in the table. Coin Toss Results Name
H
T
Deidra Byron Blake Shaniqua
Which student’s experimental outcome is closest to the expected outcome? A B C D
Deidre Byron Blake Shaniqua
39. Raun has a drink, a cup of yogurt, a bowl of cereal, and a piece of fruit for breakfast every morning. His drink choices are orange juice or milk. He can choose between three different flavors of yogurt. There are three kinds of cereal he may have. The fruit choices are bananas, strawberries, raisins, or cherries. How many different breakfast combination choices does Raun have? A B C D
72 36 24 20
40. Which of the following is a ratio table? A
38. At what points do the circle and the
2
4
6
8
4
16
12
32
line intersect? B y
O
A B C D
(-5, 4) and (-4, 0) (5, 4) and (-3, -2) (5, 4) and (-2, -3) (6, 6) and (-4, -4)
x
D
North Carolina, Grade 6
4
5
10.4
13
3
4
5
6
4.2
5.6
7
8.4
4
6
8
10
2
4
5
9
41. The vertices of rectangle ABCD lie on (2, 6), (8, 6), (8, 2), and (2, 2). If the figure is reflected across the x-axis, in which quadrant will the reflected figure lie? A B C D
A60
3 4.8
quadrant quadrant quadrant quadrant
I II III IV
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
C
2 3.2
42. The speeds in miles per hour of vehicles traveling on a local street are listed below. 35, 37, 42, 37, 30, 37, 32 A police officer wants to report the most frequent speed. Which measure should he use? A B C D
range mode median mean
43. The North Carolina quarter was the 12th state quarter released.
45. Juan rolled a fair six-sided number cube 36 times. He rolled a 3 eleven times. Which statement is true? A Juan rolled a 3 more times than the expected probability. B Juan rolled a 3 an equal number of times as the expected probability. C Juan rolled a 3 less times than the expected probability. D A comparison between the outcome and the expected probability cannot be made.
46. Which table can be generated using the equation 2x - 5 = y? A
12 mm
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
B
The radius of the quarter is about 12 millimeters. Which expression represents the circumference of the coin? A 12π B 24π C 48π D 144π
millimeters millimeters millimeters millimeters
44. On triangle ABC, A is located at the point (3, 6). If ABC is translated 5 units to the left and 8 units down, where will A be located? A B C D
C
D
x
4
6
8
10
y
3
9
15
21
x
4
6
8
10
y
8
12
16
20
x
4
6
8
10
y
3
7
11
15
x
4
6
8
10
y
13
17
21
25
47. Shoji mailed two packages that had the same weight. Together, they weighed 32.4 pounds. Shoji uses the equation 2w = 32.4 to find w, the weight in pounds of each of the two packages. What is the value of w? A 8.1
C 32.4
B 16.2
D 39.3
(8, -2) (3, -6) (-2, -2) (-5, 2)
Practice Test
North Carolina, Grade 6 A61
48. What are the coordinates of trapezoid
50. Which point lies in quadrant IV?
ABCD? y y
A A
B
B
x
O x
O D
D
D
C C
A B C D
(-5, 3), (1, 3), (1, -3), (6, -3) (-5, 3), (-1, -3), (-3, 1), (-3, -7) (5, -3), (2, 3), (-3, 3), (-3, -7) (-5, 3), (-2, 3), (3, -3), (-7, -3)
A B C D
point point point point
A B C D
51. The number of home runs for the 49. Ms. Flores used a dot plot to show the most recent test scores.
Baseball Games
TEST SCORES
85
90
95
Which of the following cannot be found by using the dot plot? A B C D
A62
the the the the
score of an individual student mean of the test scores median test score range of the test scores
North Carolina, Grade 6
Number of Home Runs 3 2 6 4 3 5 5 5 3
Which statement is true of the data? A The mean or median could be used to accurately describe the data. B Only the median describes the data because the data value of 6 offsets the mean. C The mode is the same as the mean. D The range is greater than 5.
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
80
junior baseball league games is shown in the table below.
52. If triangle ABC is translated 5 units left and 2 units down, where will B lie?
54. Scrap copper currently sells for about $3.00 per pound. Which graph shows this relationship?
y
COPPER PRICES
A
A
Cost ($)
B x
O
C
6 5 4 3 2 1
y
x
0
1 2 3 4 5 6
Amount of Copper (lb)
on the x-axis on the y-axis at the origin in the same position
B
COPPER PRICES
Cost ($)
A B C D
53. The dot plot shows the number of students in Mr. Sisk’s class who own a certain number of pets.
COPPER PRICES
C
Cost ($)
2
3
4
1 2 3 4 5 6
Amount of Copper (lb)
5
6 5 4 3 2 1
y
x
0
Which statement is true based on the information given in the dot plot? A The mean, median, and mode are all the same. B The mean is greater than the median. C The median is greater than the range. D The mean is more representative of the data then the median.
Practice Test
1 2 3 4 5 6
Amount of Copper (lb)
D
COPPER PRICES
Cost ($)
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
1
x
0
PETS OWNED BY STUDENTS
0
6 5 4 3 2 1
y
6 5 4 3 2 1 0
y
x 1 2 3 4 5 6
Amount of Copper (lb)
North Carolina, Grade 6 A63
Name
Date
Practice Test Calculator Inactive Calculators are not permitted on this section of the test.
1. The channel bass is the official saltwater fish of North Carolina. If the average weight of a channel bass is 37.8 pounds, which expression represents the average weight of 100 fish? A B C D
3.78 3.78 3.78 3.78
× × × ×
10-2 101 102 103
4. Which is the correct product? 2.57 × 1.1 = A 0.2827 B 2.827 C 28.27 D 282.7
5. Which inequality is represented by the graph below? 8
2. North Carolina’s dairy farmers produce about 135 million gallons of milk per year. Which expression is equal to 135 · 106? 106 106 106 106
· · · ·
52 · 32 52 · 33 5 · 32 5 · 33
3. Abe played in a hockey match for a total of 50 minutes including penalties. He sat out 5 minutes for each penalty, and he had p penalties. If Abe sat out for 35 minutes of the game, which equation can be used to find the number of penalties he had?
A B C D
9x 9x 9x 9x
9
≤ ≤ ≤ ≤
10
11
12
13
14
15
-60 160 90 95
6. Tina’s mom is buying snacks for a weeklong camping trip. The special trail mix at Fresh Market costs $3.40 per pound. How much will it cost to buy 2.5 pounds? A B C D
$1.36 $5.90 $8.50 $8.70
A 5p = 35 B 5p = 50 p C __ = 35 5
D
A64
p __ = 50 5
North Carolina, Grade 6
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A B C D
?
7. The steps Jack used to evaluate the expression (2 × 3 × 5) + 7 are shown in the table below.
9. What is the ratio of non-shaded squares to total number of squares in the model?
Step 1 Multiply 2 by 3 to get 6. Step 2 Multiply 6 by 5 to get 30. Step 3 Add 30 and 7 to get 37.
Which other series of steps could he have followed to evaluate the expression? A
Step 1 Multiply 3 by 7 to get 21. Step 2 Multiply 21 by 5 to get 105. Step 3 Add 105 and 2.
B
Step 1 Multiply 2 by 5 to get 10. Step 2 Multiply 10 by 3 to get 30. Step 3 Add 30 and 7.
C
Step 1 Multiply 3 by 5 to get 15. Step 2 Add 15 and 7 to get 22. Step 3 Multiply 22 by 2.
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
D
10. Malcolm works as an inspector for a furniture company. The table below shows the number of defective furniture pieces he found in a random sample of 250 pieces. Assembly Line Inspection Report
Step 1 Multiply 2 by 5 to get 10. Step 2 Multiply 10 by 7 to get 70.
Total Pieces of Furniture
Step 3 Add 70 and 3.
No Defects
8. According to the chart below, whose coin collection has the highest ratio of gold to silver coins? Coin Collections Alan Renee Sophie Walter
A B C D
A 7 : 12 B 12 : 7 C 5 : 12 D 12 : 5
Alan Renee Sophie Walter
Practice Test
Silver 10 37 12 48
Gold 13 38 25 51
Defects
250 5 245
At this rate, how many defective pieces of furniture should he expect in 1,000 pieces of furniture? A 25 B 20 C 15 D 10
11. What is the value of the expression below? 1 (62 - 6) + 8 __ 2
A 23 B 19
C 10 D 6
North Carolina, Grade 6 A65
12. Which of the following situations can be displayed best by using a double bar graph? A temperature changes during a 24-hour period B price of gasoline over a six-month period C number of boys and number of girls who participate in various clubs D a puppy’s weight during a twoweek period
13. Six points are graphed on the number line. "# $ 0%
%
&
50%
'
72 A ___
B
9 288 ____ 64
C 8 D 28
A66
North Carolina, Grade 6
A $11.14 B $9.35 C $8.75 D $2.39
16. If n is equal to the term number, what would be the values of the third, fourth, and fifth terms in the sequence? n2 + 6 A 7, 10, 15 B 11, 12, 13 C 12, 14, 16 D 15, 22, 31
17. Bryce has a batting average of 0.403. How would you write 0.403 as a fraction? 36 × 8 ______ . 32 × 22
403 A ____
1 403 B ____ 10 403 C ____ 100 403 D _____ 1,000
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
A, B, C B, C, D C, D, E D, E, F
14. Simplify the expression
movies. They each paid for their own ticket. Tia and each of her friends also bought a small bag of popcorn. Each bag of popcorn cost $2.39 (including tax). The total cost of the outing was $44.56. What was Tia’s share of the expenses?
100%
Which letters represent the 9 , and approximate location of 0.7, ___ 16 40% in order from least to greatest? A B C D
15. Tia and three friends went to the
18. Marie works in a landscaping store. She needs to divide 60 saplings, 100 bushes, and 360 flowers into groups so that each group has the same number of each type of plant, and there are no plants left over. What is the greatest number of groups Marie can make under these conditions?
21. Which number line shows the graph of
3 __ ? 2
A -4 -3 -2 -1
0
1
2
3
4
-4 -3 -2 -1
0
1
2
3
4
-4 -3 -2 -1
0
1
2
3
4
-4 -3 -2 -1
0
1
2
3
4
B C D
A 6 B 10 C 20 D 60
22. Paper comes in a variety of thicknesses. A piece of cardboard is 0.009 inches thick. How is 0.009 expressed in scientific notation?
19. The table shows the number of triangles formed by drawing diagonals inside polygons. Number of Sides (n)
3
4
5
6
…
n
Number of Triangles Formed
1
2
3
4
…
?
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Which formula can be used to predict the nth term? A B C D
n n n n
0.9 × 103 9 × 103 0.9 × 10-3 9 × 10-3
23. Chalese’s ranch is __23 mile by __34 mile, as shown below.
+2 -2 ×2 ÷2
20. Which is the prime factorization of 108? A B C D
A B C D
4 × 27 22 × 27 22 × 3 2 22 × 3 3
Practice Test
2 3 mile
3 4 mile
Which expression can she use to calculate the area of the plot in square miles? 3 2 × __ A __
3 4 2 4 B __ × __ 3 3 3 ÷ __ 3 C __ 2 4 3 2 D __ ÷ __ 3 4
North Carolina, Grade 6 A67
24. If the number pattern continues, which rule can be used to find the missing number? 2, 4, 10,
?
27. The equation below can be used to find x, the number of blue jeans that a store sold during a big sale.
, 82
A multiply the two previous numbers, then add 2 B multiply the previous number by 2, then add 2 C multiply the previous number by 3, then subtract 2 D multiply the previous number by 4, then subtract 4
55 - x = 11 Which value of x makes the equation true? A 66 B 44 C 11 D 5
28. This graph shows the daily high specialist at an electronics assembly plant. The table shows how many defective parts she found in a random sample of 100 parts. Quality Control Report Total Parts 100 Defects 3 No Defects 97
A 30 B 60 C 300 D 600
26. Which 4of the following is equivalent 2 3·5 ·7 to ________ 2 3? 6·5 ·7
5 A __
2 25 B ___ 14 1 C __ 2 2 D __ 5
A68
North Carolina, Grade 6
Charlotte Daily Temperatures in April 2010 90 85 80 75 70 65 60 0
1
2
3
4
5
Day
Which of the following statements best describes the data in the graph? A The temperature decreased each day. B The temperature increased each day. C The temperature remained the same each day. D The temperature increased the first four days. On day 5, the temperature decreased.
Practice Test
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
At this rate, how many defective parts should Luisa expect in a production run of 2,000 parts?
temperatures in Charlotte for five days in April 2010.
Temperature (ºF)
25. Luisa works as a quality control
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