How to make a tangram

A thinking mathematically targeted teaching opportunity focussed on creating tangram pieces from a piece of paper


Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023


  • MAO-WM-01
  • MAE-GM-03
  • MAE-2DS-01
  • MAO-WM-01
  • MA1-GM-03
  • MA1-2DS-01
  • MAO-WM-01 
  • MA2-GM-02 
  • MA2-2DS-01 
  • MA2-2DS-02 
  • MAO-WM-01 
  • MA3-2DS-01 

Note: There must be an adult helping you with this project.

Collect resources

You will need:


Watch How to make a tangram video (4:13).

Fold and cut square paper to create tangram pieces.

[Screen shows a pair of scissors, a coloured, square sheet of paper and 2 adults. Screen reads: You will need… a pair of scissors, a square sheet of paper and you also need an adult.]


Cut the square into 2 triangles. Cut the triangle into 2 smaller triangles.

[Screen shows the presenter waving before picking up the paper and scissors. She folds the paper corner to corner to create a triangle shape, unfolds the paper and cuts along the crease. There are now two triangles. The presenter folds each triangle in half again, unfolds them and cuts along the crease once more to create two smaller triangles.]


Watch this part carefully. Just mark the centre there. Now cut the triangle into a trapezium and a triangle. And cut the trapezium into 2 smaller trapeziums.

[Screen shows presenter making a small crease on the longest side of the triangle. She folds the top corner of the triangle down towards the mark and creates a crease. The presenter unfolds the shape and cuts along the crease to create a trapezium and a triangle. She folds the trapezium shape in half, unfolds it and cuts along the crease.]


Cut the trapezium into a square and triangle. Cut the trapezium into a parallelogram and a triangle.

[Screen shows presenter taking one of the smaller trapeziums and folding the corners together. She unfolds them and cuts along the crease to create a square and a triangle. The presenter takes the other trapezium and folds the bottom edge upwards to create a crease, unfolds it and cuts along it to create a parallelogram and a triangle.]


Look at all the shapes we have now. We have 5 triangles, 2 big ones a medium one and 2 small ones. A parallelogram and a square.

[Screen shows the presenter spreading the shapes out. It shows the different shapes made including the 5 triangles of different sizes, the parallelogram and the square.]


Now let's try to rearrange it back into our original square sheet of paper. Can you remember how it went?

[Screen shows presenter rearranging shapes back into a square.]


There we go, a tangram. Good job.

[Screen reads: So, what's some of the mathematics here?

When we involve children in making mathematical tools, we help them make meaning from them.

By making a tangram, we can build spatial skills and focus attention on important ideas like, how bigger shapes can be decomposed or broken up into smaller shapes.

Providing hands-on activities like this one allows children to manipulate geometric shapes, which helps build understanding of geometry and spatial sense.]

Over to you now mathematicians. Have fun making.

[End of transcript]

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