What Is a Tangram?
A tangram is a square cut into seven pieces, called tans: two large triangles, one medium triangle, two small triangles, one square and one parallelogram. The rules are simple. Every puzzle uses all seven pieces, the pieces lie flat, and no piece may overlap another. With just those seven shapes you can make thousands of pictures: animals, people, boats, letters, numbers and geometric shapes.
In Chinese the puzzle is called 七巧板 (qīqiǎobǎn), which means “seven clever boards”. The earliest known tangram books were printed in China in the early 1800s, and the puzzle soon became a craze in Europe and America, where books of tangram silhouettes were sold by the hundred. You may read stories about how the tangram was invented, for example by someone who dropped a tile and tried to put the pieces back together; these are fun legends, not history.
The Seven Pieces and Their Areas
Because the pieces all come from one square, their sizes are linked in a neat way. Take the small triangle as one unit of area:
- Each small triangle is 1 unit.
- The medium triangle, the square and the parallelogram are 2 units each: each can be made from two small triangles.
- Each large triangle is 4 units, the same as two small triangles and a square, or a medium triangle and two small triangles.
Altogether that is 1 + 1 + 2 + 2 + 2 + 4 + 4 = 16 units. So every tangram picture, however different it looks, has exactly the same area. A thin swan and a chunky square cover the same amount of table. This is a lovely way to show children that area is about how much surface a shape covers, not how long or wide it looks.
Tips for Solving Tangram Puzzles
- Start with the two large triangles. They cover half the shape, and there are usually only one or two places where they fit.
- Look at the corners of the outline. A sharp corner almost always needs the pointed end of a triangle; a square corner may be the square, the right-angle corner of a triangle, or two pieces meeting.
- Follow the long straight edges. A long side of the outline is often the long side of a large triangle.
- Keep the small triangles for last. They are the gap fillers.
- Flip the parallelogram if it seems to fit but leans the wrong way. It is the only piece that changes when you flip it.
The Maths Inside a Tangram
Tangram play is full of mathematics that children meet in primary school. They name and sort shapes (triangles, a square, a parallelogram) and notice that two pieces can be the same shape and size, the idea mathematicians call congruence. They turn pieces through 45° and 90° and see that every corner of every piece is 45°, 90° or 135°. They discover that a piece can be turned or flipped, and that flipping only matters for the parallelogram. And they build an understanding of area by seeing that the medium triangle, the square and the parallelogram all cover the same space although they look different. The tangram maths quiz on this page asks exactly these questions.
How to Use This Page
- Choose a puzzle from the picture list. Easy shapes come first.
- Choose a level. Easy shows the lines between the pieces inside the outline. Medium shows only the outline. Hard shows a small picture in the corner, and you build the shape anywhere on the board.
- Drag the pieces onto the shape. Tap a piece to choose it, then turn it with the buttons or by double-tapping. Pieces snap into place when their corners are close.
- Stuck? A hint shows where one piece goes. Show solution puts every piece in place, but the puzzle then earns no stars.
- Free play lets children invent their own shapes, save them as a picture, and print them as a puzzle for someone else.
- Print a cut-out tangram to make real pieces, and puzzle cards with an answer page for table time.
Tips for Parents and Teachers
- Make a real set. Print the cut-out tangram on card, colour the pieces and cut them out. Hands-on pieces are the best way in for young children.
- Talk while you play. Ask “Which piece fits this pointy corner?” or “How could you turn it?” Naming turns and flips builds the language of position and movement.
- Let them struggle a little. A puzzle that takes a few tries is more satisfying than one solved at once. Offer a hint before the full solution.
- Invent and swap. Children love making a shape in Free play, printing it, and challenging a friend or a parent to solve it.
- Count the area. Older children can check that every shape is 16 small triangles, or work out the area of each piece in square centimetres from a printed set.
Nothing to Install, Nothing Uploaded
The tangram runs entirely in your browser on any phone, tablet or computer, with no account and no download. The stars you earn and the level you chose are remembered on this device only; nothing is sent to us, and saved pictures go straight to your own device.
Frequently Asked Questions
A tangram is a puzzle made by cutting a square into seven pieces, called tans: two large triangles, one medium triangle, two small triangles, a square and a parallelogram. The challenge is to use all seven pieces, without overlapping, to make a given shape. In Chinese it is called 七巧板, the seven clever boards.
If a small triangle has an area of 1 unit, the medium triangle, the square and the parallelogram each have an area of 2 units, and each large triangle has an area of 4 units. All seven pieces together make 16 units, so every tangram shape has the same area.
Place the two large triangles first, because they fill half of the shape and fit in only a few places. Look for sharp corners in the outline, which usually need a triangle, and straight edges, which need a long side. Save the small triangles for last: they fill the gaps.
Yes. There is no account, no download and no limit. Progress is kept only in your own browser, and the cut-out tangram and puzzle cards print with an answer page.