Exploring Tangrams

Curriculum Goal

Compose and decompose two-dimensional shapes, and show that the area of a shape remains constant regardless of how its parts are rearranged.

Teacher-led discussion followed by individual or pair-based work at desks or on the carpet.

Paper Tangram set instructions (Appendix A)
Plastic Tangram sets
Tangram puzzles (Mathigon has a variety of Tangram puzzles you can use with your students)
Pieces of card stock
Scissors

Ask students to share what they know about Tangrams.
- Have you ever heard of Tangrams? Where have you seen or used them before?
Lead students through a visual and auditory history of the Tangram. Watch the video for an overview of Tangram history; ask students what they notice about its history. Guiding questions:
- Why makes the Tangram an appealing/useful math manipulative? Why might this have been relevant when it was first invented, as well as over time? 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)?
Have students create their own Tangram set from card stock, following written instructions (Appendix A). Encourage students to put the set back together into a square shape.
Invite students to recreate the Tangram puzzles using their paper Tangrams.
Discuss the strategies used to solve the puzzles.

How do students identify where each Tangram piece should be placed? Do students instantly recognize the correct position? Do they visualize whether the piece is correct before placing it in its position?
What kind of positional language are students using with one another?

This activity explores composing and decomposing 2D shapes. Students use multiple 2D shapes to construct different images.