Question

Jason has 75 feet of wallpaper border. He wants to put up a wallpaper border around his rectangular bedroom that measures 12 feet by 14 feet. He multiplies 12 x 14 = 168 to get an exact answer of how much border he needs. He concludes that he does not have enough border for the whole job.

7) Tell how you can critique Jason’s reasoning.



8) Critique Jason’s reasoning.



9) Jason uses an overestimate to decide how many rolls of wallpaper he needs for another room. Explain why his reasoning to use an overestimate does or does not make sense.

Answer 1

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Answer:

7) compare what Jason needed to do with what he did

8) Jason used an incorrect formula to estimate his need

9) an overestimate ensures Jason can finish the job

Explanation:

7) A critique is a comparison of what you have with what you expect. We can critique Jason's reasoning by comparing what he did with what we expected him to do. (We don't actually know his reasoning; we only know his action.)

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8) Jason multiplied the dimensions of his room, an action appropriate to finding its area. We expected that Jason would use a formula for the perimeter of the room. We conclude that Jason chose the wrong formula for computing the length of border needed. We also note that Jason did not make any use of dimensional analysis. Had he done so, he would have known that his result was in square feet, not linear feet, so was not applicable to the question of whether he had enough border.

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9) If Jason's goal is to finish his wallpaper job without making another trip to the store, he would want to make sure that he does not run short of wallpaper before the task is done. To ensure that he has enough, it makes sense that he would make an estimate that would give him more than enough.