How Well Can You Measure?: IM 7.3.1
[url=https://im.kendallhunt.com/MS/teachers/2/3/1/preparation.html]“How Well Can You Measure?”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.3.1
- IM 7.3.1 Lesson: How Well Can You Measure?
- Practice 7.3.1
- IM 7.3.1 Practice: How Well Can You Measure?
IM 7.3.1 Lesson: How Well Can You Measure?
A student got 16 out of 21 questions correct on a quiz. Use mental estimation to answer these questions.
Did the student answer less than or more than 80% of the questions correctly?
Did the student answer less than or more than 75% of the questions correctly?
Your teacher will assign your group 3 squares to examine. For each of your assigned squares, measure the length of the diagonal and the perimeter of the square in centimeters. After you come to an agreement, record your measurements in the table.
Plot the diagonal and perimeter values from the table above on the coordinate plane.
What do you notice about the points on the graph? Record measurements of the other squares to complete your table.[br]
In the table, record the length of the diagonal for each of your assigned squares from the previous activity. Next, calculate the area of each of your squares. Then pause here so your teacher can review your work. Be prepared to share your values with the
Plot the diagonal and area values from the table above on the coordinate plane.
Examine the graph of these values. What do you notice?
How is the relationship between the diagonal and area of a square the same as the relationship between the diagonal and perimeter of a square from the previous activity? How is it different?
Here is a rough map of a neighborhood.
There are 4 mail routes during the week.[br][list][*]On Monday, the mail truck follows the route A-B-E-F-G-H-A, which is 14 miles long.[/*][*]On Tuesday, the mail truck follows the route B-C-D-E-F-G-B, which is 22 miles long.[/*][*]On Wednesday, the truck follows the route A-B-C-D-E-F-G-H-A, which is 24 miles long.[/*][*]On Thursday, the mail truck follows the route B-E-F-G-B.[/*][/list][br]How long is the route on Thursdays? [br]
IM 7.3.1 Practice: How Well Can You Measure?
Estimate the side length of a square that has a 9 cm long diagonal.
Select [b]all [/b]quantities that are proportional to the diagonal length of a square.
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.
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.