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, provide students with the link to the GeoGebra activity: geogebra.org/m/qqx4vtKs. Here students will 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 activity 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
@jakespankenheimer. (n.d.). Ranking all 50 states by the sum of their interior angles Pt. 4 [Video]. TikTok. https://www.tiktok.com/@jakespankenheimer
K20 Center. (n.d.). GeoGebra. Tech Tools. https://learn.k20center.ou.edu/tech-tool/2352
Mueller, M. (n.d.). Polygon interior angle sum patterns. GeoGebra. https://www.geogebra.org/m/qqx4vtKs