Adding It All Up

"In this lesson, students draw various polygons and investigate their interior angles. The investigation is done using both an interactive tool and paper and pencil to foster an understanding of how different patterns can lead to the same solution. After comparing results with a partner, students develop a formula showing the relationship between the number of sides of a polygon and the sum of the interior angles." Along with the Angle Sum tool provided, this lesson demonstrates the relationship between a polygon's number of sides and the polygon's sum of interior (180(n-2)) angles using triangulation and prompts for students to conceive and validate the pattern through experimentation.

Weblink address (URL): 
Adding It All Up

Standards & Objectives

Learning objectives: 

Learning Objectives:

Students will:

  • Investigate the pattern between the number of sides of a polygon and the sum of the interior angles using in two different methods.
  • Determine that the interior angle sum is always the same for polygons with the same number of sides.
  • Create a formula to find the interior angle sum given the number of sides.
  • Explore interior angles in regular polygons.
Essential and guiding questions: 

Questions for Students:

  • Are all the angle measures always the same for a single polygon
  • As the number of sides increases, what happens to the sum of the angle measures? 
  • Does the formula work for both regular and non-regular polygons? What about shapes like scalene triangles or trapezoids?

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • Have students explore exterior angles. The sum of the exterior angles for any polygon is 360°, and therefore the measure of one exterior angle in a regular polygon is 360/n 
  • In the bottom right-hand corner of the Angle Sum Tool, there is an animation for the triangle and square showing how the sum of the interior angles relates to tiling. Have students watch the animations and write a journal entry on what they demonstrate.

 

Helpful Hints

Materials:

  • Computers with internet access
  • Adding It All Up Activity Sheet 
  • Adding It All Up Answer Key 
  • Unlined paper
  • Rulers
  • Colored pencils or markers (optional)
  • Computers with Internet access

 

References

Contributors: 
Jeffrey Hill
Originator: 
Ayers Institute for Learning & Innovation