Mr. Hill grew up in San Diego, California – home of the legendary San Diego Chargers. On weekends, he and his friends would play football in the neighborhood park. To simplify keeping track of the score, they would only count touchdowns and field goals. One day, they decided to use the following scoring system:
touchdowns = 5 points
field goals = 3 points
After they were done playing football for the day, Mr. Hill and his friends were hanging out wondering what scores were possible with their unique scoring system. After they spent a few minutes talking about it, Bridget said that after a certain number, all scores were possible. This sounded crazy – how could this be true? Bridget said that after this “highest impossible score” every score was possible all the way to infinity. For this anchor problem, answer the following questions and make Bridget proud! 1. On your own, using the hundreds chart (on next page) and using the scoring system of touchdowns worth 5 points and field goals worth 3 points, before crossing out any numbers, a. What do you think the highest impossible score is? Explain.
b. Discuss with your teammates your response to part a. Decide as a group what you think the highest impossible score is. Explain. c. Using this scoring system, determine the highest impossible score. Show your reasoning.
2. Make up ONE other scoring system having a highest impossible score. Discuss with your teammates and decide as a group what you think the highest impossible score is for your scoring systems. Explain how you arrived at your conclusion.
3. Make up one scoring system that does not have a highest impossible score – meaning the impossible scores continue forever. Discuss with your teammates and decide as a group why you think these systems do not have a highest impossible score. Explain how you arrived at your conclusion.
Module 1 Page 1
4. Look for a rule for the scoring systems that have a highest impossible score. The rule should easily calculate the high impossible score using the points associated with a touchdown and a field goal.
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