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.
1. Tell how you can critique Jason’s reasoning.

2. Critique Jason’s reasoning

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

Answer 1

Let's summarize the facts:

the tape is 75 feet long

the bedroom is 12 feet by 14 feet. 

1. Tell how you can critique Jason’s reasoning.

If you want to Critique Jason's reasoning, you could a) ask yourself the same questions that Jason did and see if you would come with the same answers and used the same analysis or b) analyse Jason's answer to see if he did a mistake or missed an important detail and made a thought mistake


2. Critique Jason’s reasoning

 I will use the option b from above:  
? 
Jason first multiplied 12 x 14 = 168. This multiplication is correct, but what did he get? He needed to get the perimeter of the bedroom  because it was only the wallpaper border, not the wallpaper itself - so getting the perimeter was needed, but this we get by the formula ( 2* *(length+width), not length* width - as Jason did.
So Jason made a mistake here! his actual answer should be 2*(12+14)=2*26=52, so the tape of 75 feet would have been enough!

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

Using an overestimate is often a good idea- in case some of the tape gets damaged, he will have some left. However, since his calculations are wrong by a lot (he multiplies rather than adds and multiplies by 2), his overestimate will be a lot higher than would be practical - he would be left with a lot of leftovers and spend too much money. So his reasoning does not make sense