# Tangrams

Canonical: https://manipulatives.org/manipulatives/tangrams/

A seven-piece dissection puzzle for composing shapes, comparing area, and reasoning about position.

![Seven tangram pieces arranged as a square](https://manipulatives.org/_astro/tangrams.BR3XSNNF.svg)

Published: 2026-10-09
Reviewed: 2026-10-10

Topics: geometry, fractions

## What they teach

### Shape composition

Combine familiar polygons to make new outlines.

### Spatial reasoning

Rotate and flip pieces to test whether they fit a position.

### Area relationships

Compare how smaller pieces cover the same area as larger pieces.

## How to use them

1. **Explore the seven pieces.** Sort the triangles, square, and parallelogram. Compare sizes and angles.

2. **Cover an outline.** Choose a silhouette and arrange all seven pieces without overlaps.

3. **Describe your decisions.** Explain which edge, corner, or area relationship helped you place a difficult piece.

## Try an activity: Make the square in stages

Start with the two smallest triangles. Find ways they can combine into a square, a triangle, and a parallelogram. Then use all seven pieces to rebuild the large square.

## A piece can look different when it moves

Turn the small square so it stands on a corner and ask whether it is still a square. The orientation has changed, but its side lengths and angles have not. Tangrams make this distinction easy to discuss while solving a puzzle.

The standard set has two large triangles, one medium triangle, two small triangles, a square, and a parallelogram. With the assembled large square as the whole, each small triangle has one sixteenth of the total area. Compare pieces by covering or composing areas instead of judging their longest sides alone.

When a puzzle becomes frustrating, reveal the position of one piece or use an outline with some internal boundaries. This changes the amount of spatial information available while preserving the central task of finding how shapes fit.

## Choose your toolkit

Check that each set includes the standard seven pieces and appropriately scaled outlines if those are supplied. Loose pieces allow flipping; some inset boards restrict it.

- [Learning Resources 4-Color Tangrams (30 Sets)](https://www.amazon.com/dp/B000VUJO1A) — Thirty complete seven-piece tangram sets in four colors suit whole-class puzzles and small-group comparisons. A plastic storage bucket and activity guide are included.

- [3 Otters Wooden Tangram Puzzles (4 Sets)](https://www.amazon.com/dp/B07BXJM6QN) — Four complete seven-piece wooden tangram sets provide 28 pieces for building silhouettes and comparing solutions. An explanation card is included.

## Related tools

- [Pattern Blocks](https://manipulatives.org/manipulatives/pattern-blocks/)
- [Geoboards](https://manipulatives.org/manipulatives/geoboards/)
- [Geometric Shapes](https://manipulatives.org/manipulatives/geometric-shapes/)