Exploring Tangrams

Created by Tia Chambers, Kei Muto, and Jennifer Richardson
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Curriculum – Measurement and Geometry and Spatial Sense

Measurement, Measurement Relationships: determine through investigation and strategies, the relationship between the area of a rectangle and the areas of parallelograms and triangles by decomposing and composing

Geometry and Spatial Sense, Geometric Properties: construct properties using a variety of tools

Goal

To help students understand that, throughout history, civilizations have been interested in creating and solving various forms of dissection puzzles and to engage students in a hands-on exploration of the tangram and its underlying mathematical principles.

Materials

Lesson
Introduction

  • Students will create their own tangram set from card stock using written instructions (Appendix A) and the teacher as a guide. Students will then be encouraged to put the set back together into a square shape, from which it originally was cut.
  • Students will be led through a visual and auditory history of the tangram using a teacher-created timeline (Appendix B).
  • Students will be asked to share what they know about the tangram, and what they notice about the history. Guiding Questions:
  • Before the history: Have you ever heard of tangrams? Where have you seen or used them before? What do you know about tangrams?
  • After the history: What do you notice about the history that we have shared with you? Why do you think the tangram became so popular? Why do you think it is called “seven ingenious plans” or “seven boards of skill” in Chinese? Why do you think an American might have named it “tangram” (a made-up English word)?

Activity

  • Using ready made plastic or paper tangram sets, students will solve pre-made puzzles with various shapes traced on paper (Appendix C).

Closure

  • Have a discussion about the strategies students used when solving the tangram puzzles.

Possible Extensions

  • Use tangrams to contrast area of various polygons
  • Use tangrams to explore fractions
  • Tangrams can provide visual support when studying Pythagorean Theorem

*Download the lesson to see all appendices.