Tangram geometry story
Turn the ancient puzzle of seven pieces into lessons on shape, rotation, area and creativity.
Quick answer
A Tangram is an ancient Chinese puzzle made of seven flat shapes that can be arranged to form many different pictures and designs. You can learn about shapes, area, rotation, and creativity by playing with these pieces.
Learning outcome
By the end of this page, you will understand how to use tangram pieces to make new shapes and learn about area, rotation, and symmetry by creating your own designs.
- I can identify the seven tangram pieces and their names
- I can make new shapes by combining tangram pieces
- I can describe how shapes can be turned and moved to fit together
- I can compare the sizes of different tangram shapes
Why this matters
Learning with tangrams helps you understand how shapes fit together, how to think creatively, and how to solve problems. These skills are useful in many areas of life, from building with LEGO to designing a room, or even helping you with puzzles and games. Tangrams also connect to real-world maths like area, rotation, and symmetry.
How it works
Imagine you have a square piece of paper. If you cut it into seven different shapes, you can make many different pictures. These seven shapes are called tangram pieces. Each piece is a different shape and size, but they all come from one original square.
- Take a square piece of paper
- Draw lines to divide it into seven pieces
- Each piece is a different shape: two large triangles, one medium triangle, two small triangles, one square, and one parallelogram
- Use these pieces to make new designs
- Rotate or flip pieces to fit them together
Examples you can see
Let’s look at the seven tangram pieces and how they work together:
| Shape | Description | How it fits |
|---|---|---|
| Large Triangle | Half of the square | Can be used as a base or corner |
| Medium Triangle | Quarter of the square | Good for filling gaps |
| Small Triangle | One-eighth of the square | Can be used for details |
| Small Square | One-eighth of the square | Good for filling small areas |
| Parallelogram | One-eighth of the square | Can be turned to fit in different spaces |
Imagine you are making a bird with your tangrams. You might use:
- Two large triangles for the wings
- One medium triangle for the body
- One small triangle for the beak
- One small square for the eye
- One parallelogram for the tail
Try it as a mini adventure
Let’s go on a tangram adventure! You are a detective trying to solve a mystery. The clues are in the shape of tangram pieces. You need to find the right pieces to make a picture of a house, a cat, and a tree.
Adventure steps:
- First time: Find the large triangles and make a simple roof
- Second time: Add the medium triangle to make a house body
- Third time: Use small triangles to make a door
- Fourth time: Place the small square for a window
- Fifth time: Use the parallelogram to make a chimney
- Sixth time: Try making a cat using only triangles
- Seventh time: Create a tree using all seven pieces
Common mistakes
- Mistake: Thinking that all pieces are the same size.
- Why it happens: It’s easy to confuse shapes that look similar.
- Fix: Count how many small triangles make up each piece to see the sizes.
- Mistake: Not rotating or flipping pieces to fit them together.
- Why it happens: Children might think pieces must stay in one position.
- Fix: Try turning pieces to see if they fit better.
- Mistake: Not checking if pieces fit exactly.
- Why it happens: Children might rush and not pay attention to details.
- Fix: Take time to check that pieces fit perfectly without gaps.
Parent and carer guide
Playing with tangrams is a fun way to help your child understand shapes and space. Here’s how to help:
- Ask your child to name each piece and compare their sizes
- Encourage them to try making different animals or objects
- Ask questions like, "How did you fit that piece there?"
- Let them create their own designs and tell you what they made
- Point out how shapes can be turned or flipped to fit together
- Don’t worry if they don’t get it right the first time – that’s how learning happens!
Practice questions
- How many pieces are in a tangram set?
- Which pieces are the same size?
- Can you make a square using only two triangles?
- How many small triangles make up a large triangle?
- Can you make a triangle using all seven pieces?
Answers:
- Seven pieces
- The two small triangles and the square
- Yes, if you use two large triangles
- Four small triangles
- Yes, you can make a large triangle
FAQ
What is the history of tangrams?
Tangrams were invented in China during the Song Dynasty (960–1279 AD). They were originally called "Tsi Chiao T'u" or "Seven Boards of Wisdom." They were used for entertainment and education, helping people learn about shapes and spatial reasoning.
Can tangrams be used for learning other subjects?
Yes! Tangrams help with geometry, problem-solving, creativity, and even storytelling. You can make pictures of animals, people, or objects and tell stories about them.
Are there online tangram games?
Yes, there are many online games and apps that let you play with tangrams on a screen. These can be great for practicing, but real hands-on tangrams are better for learning.
Can I make my own tangrams?
Absolutely! You can cut out a square and follow instructions to make the seven pieces. It's a fun activity that helps you understand how they work.
What shapes are in a tangram set?
A tangram set includes two large triangles, one medium triangle, two small triangles, one square, and one parallelogram.