Lesson 1
How Well Can You Measure?
Problem 1
Estimate the side length of a square that has a 9 cm long diagonal.
Solution
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Problem 2
Select all quantities that are proportional to the diagonal length of a square.
Area of the square
Perimeter of the square
Side length of the square
Solution
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Problem 3
Diego made a graph of two quantities that he measured and said, “The points all lie on a line except one, which is a little bit above the line. This means that the quantities can’t be proportional.” Do you agree with Diego? Explain.
Solution
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Problem 4
The graph shows that while it was being filled, the amount of water in gallons in a swimming pool was approximately proportional to the time that has passed in minutes.
- About how much water was in the pool after 25 minutes?
- Approximately when were there 500 gallons of water in the pool?
- Estimate the constant of proportionality for the gallons of water per minute going into the pool.
![Plotted points of amount of water in gallons as time passes.](https://cms-im.s3.amazonaws.com/8UmseYNP5pZHRmAZyocbTfuB?response-content-disposition=inline%3B%20filename%3D%227-7.3.PP.New.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%277-7.3.PP.New.Image.07.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240907%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240907T234746Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b2b2bbd70df07d798db95cab7b936cb903d76db19e49621cf5e7a651713428bb)
Solution
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