Lesson 1

How Well Can You Measure?

Lesson Narrative

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.

Learning Goals

Teacher Facing

  • 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.

Student Facing

Let’s see how accurately we can measure.

Required Preparation

Make enough copies of the Perimeter of a Square blackline master for each group of 3 students to get one copy. Prepare to distribute rulers.

Learning Targets

Student Facing

  • I can examine quotients and use a graph to decide whether two associated quantities are in a proportional relationship.
  • I understand that it can be difficult to measure the quantities in a proportional relationship accurately.

CCSS Standards

Building On


Building Towards