Unit 1, Lesson 15
Building Polygons
Accelerated 7
Preparation
Lesson Narrative
The goal of the lesson is for students to make sense of the different shapes that are possible under given constraints about side lengths, including whether only one shape is possible or no shape is possible (MP1). In this lesson, students experiment with constructing triangles given 2 or 3 side lengths. They start by working with cardboard strips and metal fasteners to 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 doing so recreates the function 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.
Students use repeated reasoning with specific cases to formulate a general rule about which side lengths are possible for triangles (MP8).
- Generalize (orally) that four side lengths do not determine a unique quadrilateral, but that three side lengths can determine a unique triangle.
- Use manipulatives to show that there is a minimum and maximum length that the third side of a triangle could be, given the other two side lengths.
Let's build shapes.
Required Materials
Activity 1
Activity 2
Required Preparation
For some activities in this lesson, you will need slips cut from copies of the "What Can You Build?" blackline master. Prepare 1 copy for every 2 students. These slips can be reused from one class to the next. To make the slips sturdier, it is recommended to copy them onto card stock. If card stock is not available, consider gluing each copy to light cardboard, such as a cereal box. Also if possible, copy each set of slips on a different color of paper, so that a stray strip can quickly be put back.
After the slips are cut, punch holes into the endpoints of each segment. A standard hole punch makes holes that are a little larger than needed for the metal paper fasteners, causing the cardboard strips to wiggle around. If possible, find a way to punch holes that are slightly smaller than the size of a standard hole punch.
Put each set of strips in an envelope. Prepare to distribute at least 12 metal paper fasteners (i.e., brass brads) to each group.
Note: If using the digital version of every activity, the strips and fasteners will not be needed.
For the digital version of the activity, acquire devices that can run the applet.
Each group needs 2 sets of strips and fasteners from an earlier lesson. If needed, prepare additional sets of strips and fasteners, including punching holes in the strips.
For the digital version of the activity, acquire devices that can run the applet.