Authentic Lessons for 21st Century Learning

Department of the Interior Angles

Polygons and the Interior Angle Sum Theorem

K20 Center, Daniel Schwarz, Alexandra Parsons | Published: July 18th, 2022 by K20 Center

  • Grade Level Grade Level 9th, 10th
  • Subject Subject Mathematics
  • Course Course Geometry
  • Time Frame Time Frame 60 minutes
  • Duration More 1-2 class period(s)

Summary

This lesson introduces and enforces the polygon interior angle sum theorem and the corresponding formula. This lesson does not include a proof related to the theorem, but it does have students critique a claim using the theorem as the reasoning foundation.

Essential Question(s)

How creatively can a math theorem be interpreted and applied?

Snapshot

Engage

Students watch a TikTok video that makes a claim about the U.S. states.

Explore

Students use a Geogebra activity to collect data about angles in different polygons.

Explain

Students draw conclusions based on their data from the Explore activity.

Extend

Students use their data to verify the formula for calculating the sum of polygon interior angles.

Evaluate

Students use their knowledge to confirm or refute the TikTok video’s claim.

Lesson Format

This lesson is built for flexibility and promoting quick yet deep student understanding of interior angles. It is supported by a self-contained handout without a lot of frills. The intent is to give students an opportunity to gather information and draw conclusions on their own with as little dependence on you as possible.

Students can work at their own pace either independently or in small groups. Even though this lesson is student-driven, don’t think of it as a slow cooker where you can set it and forget it! Frequent check-ins and in-the-moment formative assessments will help you keep students on track and help them build confidence in their independence.

Materials

  • Polygon Interior Angles Exploration handout (attached; one per student)

  • Student devices with internet access

Engage

5 Minute(s)

Make sure each student gets a copy of the Polygon Interior Angles Exploration handout and has access to a Chromebook or other internet-connected device.

Inform students they are never safe from learning things, no matter the social media platform. TikTok is not an exception! (The specific video used in this lesson is not on TikTok anymore, but the downloaded video is attached to the lesson.) Open the Interior Angles TikTok attachment and have the video ready to play for the class.

Draw students’ attention to Step 1 on the handout. Before you play the video, tell students to look for evidence of the creator’s logic; they'll use this evidence later.

Play the TikTok video. The video ranks the states based on the creator's estimation of the sum of the interior angles of each state.

After watching the video, students will visit the Polygon interior angle sum patterns page in on the GeoGebra website and formulate a preliminary definition of interior angles and how the number of sides relates to the number of interior angles.

Explore

15 Minute(s)

Students will use the same GeoGebra page to complete Step 2 on the handout. They will move the vertices of the three polygons around and document the angle measurements and the sums of those angles. Remind students that they are making three versions of each polygon, not a mix of random angles.

Explain

10 Minute(s)

Students will complete Step 3 on the handout. Students should look back over the data they collected in the Explore section and make inferences and determine patterns based upon their results.

Extend

15 Minute(s)

To extend their learning, students will complete Step 4 on the handout. They are presented with three options for the formula for calculating the sum of interior angles. They must use their data from the Explore activity to identify which of the three is the correct formula.

Once they’ve made a selection, students will use their chosen formula to calculate the sum of interior angles for various polygons.

Evaluate

5 Minute(s)

Students will complete Step 5 on the handout as an evaluation to wrap up the lesson.

They will watch the TikTok video from the Engage section again, using what they just learned to decide whether they agree or disagree with the creator's claim and logic.

Resources