Master Shapes and Puzzles by Making Your Own Tangram!

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If you’ve played with a tangram before, you know that the possibilities are truly endless with what you can make and, more importantly, what you can learn!

This experiment guides you through making a tangram and how to introduce the shapes to your child, while building problem-solving skills and spatial awareness.

Let’s walk through this ancient Chinese puzzle together to build some seriously cool shapes!

mastering geometry and puzzles by making your own tangram

How to make the Master Shapes and Puzzles Tangram math experiment

Supplies you will need

For this experiment, you will need the following:

One piece of construction paper
Glue stick
Scissors
Cardboard

If you want to supplement with a fun book, here’s a good one that includes trapezoids!

Before you start

This experiment is a great way to introduce your child to a lot of shapes at once. We’ll cover them in the steps below, but if you want to supplement, check out this book to talk through a few of the shapes.

Instructions

Here is how to do this experiment with your child:

Step 1: Fold and cut the first pieces of the tangram

Place the piece of construction paper down with the longer, vertical sides to the left and right and the shorter, horizontal sides near and far to you.

Take the top right corner of the paper and have it meet the left vertical side of the paper, folding it down once you match up the sides.

You should have a right triangle with a rectangle below it.

Take top right corner and fold down to meet the left long side of the paper

Cut the rectangular piece from the bottom of the right triangle.

Once you have cut out the rectangle from the bottom of the triangle, place it aside since we will not be folding and cutting the rectangle piece anymore.

Cut out the rectangle below the triangle

This is what you will have when you finish the first step (place the rectangle aside)

Step 2: Fold and cut out triangles

In this step, we will be folding and cutting from the first triangle we folded in step 1 which opened into a square.

First, cut the square in half by cutting along the fold we created in step 1.

For the younger ones, we have just created two triangles from the square.
For the older kids, we have created two isosceles triangles from the square. Isosceles triangles have two sides that are the same length with one side longer.

Cut along the line where we folded in the first step. This is what you’ll have when you cut it.

Next, fold your two isosceles triangles down the middle. Only cut one of those triangles where you folded; leave the other original triangle alone for this step.

Place the two smaller triangles that you just cut aside with the rectangle; we are done with those shapes.

We are left with three isosceles triangles and one rectangle.

Cut one of the two triangles along the fold and place it aside with the rectangle from step 1

Step 3: Make next round of folds and cuts

Now, take the larger triangle and place it down with the longest side closest to you.

Fold the top corner down to meet the long side close to you. Cut along the fold you just created (not the vertical fold, but the horizontal fold you just completed in this step).

Take top corner of triangle and fold down to meet the bottom of the triangle

Cut along the fold and place the small triangle to the side

Now that you’ve made that cut, show your child the shapes that we have!

We are left with:

One small isosceles triangle
One isosceles trapezoid

Place your small isosceles triangle to the side since we will no longer need to cut that shape. Now, we’re working with our trapezoid.

Place the isosceles trapezoid with the longest side closest to you. Take the bottom left corner and fold it to meet the fold in the middle of the trapezoid to create a right triangle.

Cut along the fold you just created to make another isosceles triangle.

Next, cut the square from the last fold.

What’s left is called a right trapezoid, with a right angle on the left side of the trapezoid.

Be sure to talk through these shapes with your child! It’s a great exercise in learning types of shapes.

Fold the left corner of the trapezoid to meet the fold in the middle of the trapezoid

Cut out the right triangle along the fold as well as the square along the fold

These are the cuts you will have when you have completed step 3

Step 4: Make final cuts on the trapezoid

We’re on the final stretch!

Place the right trapezoid down with the longest side facing you. Fold the top right corner down to meet the bottom left corner.

Cut along that fold to make your final cut.

What’s left is:

One parallelogram
One isosceles triangle

Fold top right corner of trapezoid to meet the bottom left corner. This is the fold you’ll get. Cut along fold.

All of the cuts you will make, displayed

Step 5: Cut cardboard and glue shapes

Onto the final step before you can start making tangram designs: gluing the paper you just cut onto the cardboard pieces.

Outline each of your paper shapes on the cardboard and cut them out. Add some glue to the cardboard and press each shape onto the cardboard cut-outs.

Use your shapes to trace outline on the cardboard

Use the gluestick to add glue to the cardboard

Line up and press the paper to the cardboard

Step 6: Make fun tangram shapes!

The math behind the Master Shapes and Puzzles Tangram experiment

This experiment teaches:

Spatial awareness
Geometry concepts
Problem-solving skills

How it works

A tangram is a traditional Chinese puzzle consisting of seven geometric shapes: a square, a parallelogram, and five triangles. These pieces, called “tans,” can be arranged to form a large square.

The challenge lies in using these tans to create various shapes, animals, and objects by rearranging them without any overlaps. Ideally, tangrams always use all seven pieces, but for the sake of introducing it to kids, it’s not necessary.

Tangrams encourage creativity and critical thinking while teaching concepts like geometry, symmetry, and congruence.

Spatial awareness

Tangrams help children develop an understanding of how shapes fit together in a two-dimensional space. This improves their spatial perception and visualization skills.

Geometry concepts

Tangrams introduce children to basic geometry concepts such as angles, shapes, symmetry, and congruence.

In this experiment, we create the following shapes:

One parallelogram
One square
Five isosceles triangles

This is a great opportunity to talk through any shapes your child is not familiar with, as well as how we can make shapes from other shapes (like two triangles from the square!).

Problem-solving skills

Figuring out how to arrange the tans to create specific shapes or pictures requires logical thinking and problem-solving abilities.

It may be difficult for your child to start creating shapes right out of the gate, so be sure to work alongside your child. You should also feel free to start by using just a few shapes to create something (like the sailboat I made earlier) so they can start to get the hang of it.