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You Be the Judge

You Be the Judge. The Task (Algebra Companion Number Sense).

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You Be the Judge

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  1. You Be the Judge

  2. The Task (Algebra Companion Number Sense) John, Paulo, and Ghaurv work for Starr Toys as quality control inspection managers. Today their crews will be inspecting a new action figure by the name of Super Hero Math Crusader! John’s crew pulls every 15th figure (starting with the 15th) that comes off the line to inspect for packaging defects. Paulo’s crew pulls every 20th figure (starting with the 20th ) off the line to inspect for manufacturing defects. Ghaurv’s crew pulls every 25th figure (starting with the 25th) off the line to inspect for fire safety defects. • Which is the first figure inspected by all three inspection crews? Explain how you got your answer. • The Starr Toy Factory is able to produce 225 of these toys in an hour. They keep the factory open twelve hours a day. How many Super Hero Math Crusaders will be inspected by all three inspection crews by the end of one workday?

  3. The Task John, Paulo, and Ghaurv work for Starr Toys as quality control inspection managers. Today their crews will be inspecting a new action figure by the name of Super Hero Math Crusader! John’s crew pulls every 15th figure (starting with the 15th) that comes off the line to inspect for packaging defects. Paulo’s crew pulls every 20th figure (starting with the 20th ) off the line to inspect for manufacturing defects. Ghaurv’s crew pulls every 25th figure (starting with the 25th) off the line to inspect for fire safety defects. • 11% of the Super Hero Math Crusaders produced in one day are found to have some type of defect. How many Crusaders without defects from the total production line can Ms. Starr expect will be available for shipping after one day of production?

  4. Pair up with another students to discuss your solutions and compare your solutions. • After you have shared your solutions to this problem I will share a solution to this problem.

  5. Solution • The 300th Crusader will be the first one inspected by all three inspectors because the LCM(15,20,25) =300. • Nine Crusaders will be inspected by all three inspection crews by the end of one work day because 300x=225(12). 225 Crusaders can be produced per hour and the plant is open 12 hours a day.

  6. Let x and y equal the number of defective Crusaders. x=300 defective Crusaders, 2700-300 = 2400 Crusaders without defects or y = 297 defective Crusaders, 2700-297 = 2403 Crusaders without defects. • Ms. Starr can expect to ship 2400-2403 Crusaders because an 11% defective rate means that approximately 1 out of every 9 Crusaders are defective. If 225(12) or 2700 Crusaders are produced by the end of the day, it can be expected that they would be defective at the same rate. Two methods of finding the number of defective Crusaders is shown below:

  7. Read each of the authentic student responses for the question you solved with Starr Toys. • Separate the entries into two sets: The best and the worst • Write why you have placed it in the best set or the worst set. • We will then discuss the six solutions together

  8. Response 1 This is one of the better answers. Although the final step of applying the non-defective rate to the total number of Crusaders is not done, the rest of the response shows a good understanding of common factors, least common multiples, patterns, and percents.

  9. Response 2 This is one of the best answers. Not only does it have all the correct answers but it shows an understanding of all the concepts as well.

  10. Response 3 This is one of the worst responses. It shows no understanding of how to use the least common multiple or apply the non-defective rate to the total amount.

  11. Response 4 This is one of the best responses. It has correct answers to all parts of the problem. It is not as good as response 2 because the explanation of how the numbers are derived is missing.

  12. Response 5 This is one of the weaker responses. It shows an understanding of the pattern and least common multiple, but it miscalculates the total number of toys inspected by all three. The response also does not show any work for the final part of the problem.

  13. Response 6 This is one of the weaker responses. It shows no understanding of the least common multiple, even though it finds the correct shipping amount by using a proportion.

  14. Best - - Worst

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