Lesson 7

Building Polygons (Part 2)

Lesson Narrative

In this lesson, students experiment with constructing triangles given 2 or 3 side lengths. They start by working with cardboard strips and metal fasteners, as in the previous lesson. They discover that there are some combinations of lengths that do not make a triangle. Then students move toward using a ruler and compass, seeing that it recreates the functionality of the cardboard strips and metal fasteners more efficiently. The purpose of this transition is to help students move toward a mental understanding that does not depend on physical objects, helping them work toward the understanding that in a triangle the sum of any two sides must be greater than the other side.

When students use repeated reasoning with specific cases to formulate a general rule about which side lengths are possible for triangles, they engage in MP8.

Learning Goals

Teacher Facing

• Explain (in writing) how to use circles to locate the point where the sides of a triangle with known side lengths should meet.
• Use manipulatives to justify when it is not possible to make a triangle with three given side lengths.
• Use manipulatives to show that there is a minimum and maximum length the third side of a triangle could be, given the other two side lengths.

Student Facing

Let’s build more triangles.

Required Preparation

Print the Swinging the Sides Around blackline master. Prepare 1 copy for every 2 students.

Students will also need the cardboard strips and metal paper fasteners from the previous lesson, as well as access to geometry toolkits and compasses.

Note: If using the digital version of every activity, these supplies will not be needed.

Student Facing

• I can reason about a figure with an unknown angle.
• I can show whether or not 3 side lengths will make a triangle.