Lesson 1: How Well Can You Measure?
About this lesson
The purpose of this lesson is for students to apply what they have learned about proportional relationships to describing geometric figures. The work in this lesson focuses on squares. In the first activity, students see that there is a proportional relationship between the length of the diagonal and the perimeter for squares of different sizes. They use a graph and a table to estimate the constant of proportionality and recognize that measurement error means they can only find an approximate value. This prepares students for future lessons when they will explore the relationship between diameter and circumference of circles.
In the second activity, students see that even taking measurement error into account, the relationship between the length of the diagonal and the area of a square is not a proportional relationship, in preparation for investigating area of circles in future lessons.
Lesson overview
 1.1 Warmup: Estimating a Percentage (5 minutes)

1.2 Activity: Perimeter of a Square (15 minutes)
 There is a digital applet in this activity.

1.3 Activity: Area of a Square (15 minutes)
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 1.4 Cooldown: Examining Relationships (5 minutes)
Learning goals:
 Create and describe (in writing) graphs that show measurements of squares.
 Justify (orally and in writing) whether the relationship shown on a graph is close enough to a straight line through the origin that it might be a proportional relationship with some measurement error.
 Recognize that when we measure the quantities in a proportional relationship, measurement error can cause the graph to be not perfectly straight and the quotients to be not exactly constant.
Learning goals (student facing):
 Let’s see how accurately we can measure.
Learning targets (student facing):
 I understand that it can be difficult to measure the quantities in a proportional relationship accurately.
 I can examine quotients and use a graph to decide whether two associated quantities are in a proportional relationship.
Required materials:
 copies of blackline master
 fourfunction calculators
 rulers marked with centimeters
Required preparation:
 Make enough copies of the Perimeter of a Square blackline master for each group of 3 students to get one copy.
 Note: Due to differences in printers and copiers, the measurements students obtain on the Blackline Master may differ from the student responses provided in this lesson. It is suggested that teachers print and measure in advance to inform the measurements students will likely get on their versions.
 Prepare to distribute rulers.
Glossary:
 Access the complete Grade 7 glossary.
Standards
 This lesson builds on the standard:CCSS.6.RP.A.3.cMS.6.RP.3cMO.6.RP.A.3c
 This lesson builds towards the standards:CCSS.7.G.B.4MS.7.G.4MO.7.GM.A.4b CCSS.7.RP.A.3MS.7.RP.3MO.7.RP.A.3
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.