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.

Standards & Objectives

Academic standards
CCSS.ELA-Literacy.RI.7.10
By the end of the year, read and comprehend literary nonfiction in the grades 6-8 text complexity band proficiently, with scaffolding as needed at...
CCSS.ELA-Literacy.RL.7.10
By the end of the year, read and comprehend literature, including stories, dramas, and poems, in the grades 6-8 text complexity band proficiently,...
CCSS.ELA-Literacy.W.7.9
Draw evidence from literary or informational texts to support analysis, reflection, and research.
GLE 0606.4.1
Understand and use basic properties of triangles, quadrilaterals, and other polygons.
GLE 0701.5.2
Analyze text for fact-opinion, cause-effect, inferences, evidence, and conclusions.
GLE 0701.8.1
Read and comprehend a variety of works from various forms of literature.
SPI 0701.4.5
Discern irrelevant research material from written text.
TSS.ELA.7.RI.RRTC.10
Read and comprehend a variety of literary nonfiction throughout the grades 6-8 text complexity band proficiently, with a gradual release of scaffolding...
TSS.ELA.7.RL.RRTC.10
Read and comprehend a variety of literature throughout the grades 6-8 text complexity band proficiently, with a gradual release of scaffolding at the...
TSS.ELA.7.W.RBPK.9
Support interpretations, analyses, reflections, or research with evidence found in literature or informational texts, applying grade 7 standards for...
 
Alignment of this item to academic standards is based on recommendations from content creators, resource curators, and visitors to this website. It is the responsibility of each educator to verify that the materials are appropriate for your content area, aligned to current academic standards, and will be beneficial to your specific students.
 
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: