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    NCTM Illuminations

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In this math lesson, learners create parallelograms from square sheets of paper and connect them to form octagons. During the construction, learners consider angle measures, segment lengths, and areas in terms of the original square. At the end of the lesson, the octagon is transformed into a pinwheel, and learners discover a surprising result (the area of the octagon is equal to the area of the original square). This lesson guide includes questions for learners, assessment options, extensions, and reflection questions.

Quick Guide

Preparation Time:
5 to 10 minutes

Learning Time:
1 to 2 hours

Estimated Materials Cost:
1 cent - $1 per student

Age Range:
Ages 11 - 18

Resource Types:
Activity, Lesson/Lesson Plan


Materials List (per student)


  • Mathematics
    • Algebra
    • Geometry
      • Plane Geometry
    • Measurement
      • Polygons
    • Number and Operations
    • Problem Solving
    • Reasoning and Proof

Informal Categories

  • Arts and Crafts
  • Toys


To use this activity, learners need to:

  • see
  • see color
  • read
  • touch

Learning styles supported:

  • Links STEM to other topics of interest such as arts and humanities
  • Involves hands-on or lab activities


Includes alignment to state and/or national standards

Common Core State Standards for Mathematics:

Includes assesments for student learning

Access Rights:

  • Free access


  • Warloe, Kris A.


  • All Rights Reserved, National Council of Teachers of Mathematics, ©2008

Funding Source:

  • Thinkfinity/Verizon Foundation


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