Tangram
What is a Tangram
A tangram is a geometric dissection puzzle that comes from ancient China.
It starts as one square that is cut into seven fixed pieces, called tans.
These seven pieces can be rearranged to form many different shapes.
The Seven Tangram Pieces (Tans)
2 large right-angled isosceles triangles
1 medium right-angled isosceles triangle
2 small right-angled isosceles triangles
1 square
1 parallelogram
All pieces are flat and together make exactly one square.
Geometric Properties
All angles in tangram pieces are 45° or 90°.
The pieces fit together precisely because they follow the same angle rules.
Pieces can be rotated and flipped, but not stretched or resized.
Rules of a Tangram Puzzle
All seven pieces must be used.
Pieces cannot overlap.
Pieces must lie flat and touch edge to edge.
Area Concept in Tangrams
The total area never changes, no matter how the pieces are arranged.
This shows the idea of conservation of area.
A shape may look bigger or smaller, but it covers the same surface area.
Fractions Explained Using Tangrams
Each piece represents a fixed fraction of the whole square.
Larger triangles represent larger fractions; smaller ones represent smaller fractions.
Pieces can be combined to visually show ½, ¼, ⅛, and other fractions without numbers.
Skills Tangrams Develop
Spatial reasoning (mentally rotating and fitting shapes)
Geometric understanding
Problem-solving and logic
Understanding how parts form a whole
Why Tangrams Are Important
They turn abstract math ideas into visible, touchable concepts.
They connect geometry, fractions, and area in one tool.
They are used in education, art, and design to train the mind.
Fun facts:
The name tangram comes from “Tan” (China) and “gram” (drawing or diagram).
Mathematicians have counted over 6,500 different figures that can be made using the seven pieces.
Tangrams were once used as a travel game, because the pieces are flat and easy to carry.
The original square can be taken apart and rebuilt endlessly, but it always returns perfectly.
Some tangram figures are so challenging that they were used as logic tests in the past.