# Tangrams For Kids: Discovering Math Through Art

Tangrams for kids are a brilliant way to connect math and art!

There is a ton of math hidden in these colorful shapes, including logic, geometry, spatial awareness, problem solving, fractions, area, and number sense.

Kids who struggle with math often shine when they can make art or build with their hands. Tangram activities can give these kids a chance to thrive in a math context.

Let’s take a look at some of the ways kids in grades K-5 can explore math tangrams.

## What Are Tangrams?

The tangram (Chinese七巧板pinyinqīqiǎobǎn; literally: “seven boards of skill”) is a puzzle consisting of 7 geometric pieces, called tans, which are put together to form shapes.

The challenge is to fill in the outlined shape using all seven pieces.

The seven shapes, or “tans”, include:

• two large right triangles
• one medium right triangle
• two small right triangles
• one parallelogram
• one small square

You can print out a set here.

True tangram shapes follow three simple rules: they must be made using all 7 pieces, they cannot overlap, and they must touch.

## Math Tangrams for Kids Of All Ages

Young children can sometimes be quite skilled with tangrams, intuitively solving puzzles that stump adults.

Here are some great ways to explore tangrams for kids in elementary grades:

### 1. Make a design or picture using all 7 tangrams

The pieces must touch, but they cannot overlap. Ask kids about their pictures: what shapes did they use? Why did they pick those shapes? What was hard about only having 7 shapes?

### 2. Create your own tangram puzzle

Make a picture using the 7 tangrams, then trace around the pieces to make an outline of your shape. Trade outlines and solve each other’s puzzles by filling them in with tangram pieces.

I like to take a photo of kids’ tangram creations to create an answer key before they trade them as puzzles.

### 3. Solve a tangrams puzzle

Tangrams for kids in younger grades often show where each piece goes.

Older kids can try trickier tangram puzzles that show only the outline of the figure.

HINT: The easiest puzzles are ones with “lots of corners sticking out”.

### 4. Make the same shape in different ways.

Can you make a square with 2 pieces? Three pieces? 4? 5? 6? 7 pieces?

(Because it doesn’t require kids to use all 7 shapes, this is not a true tangram activity–but it’s a great math activity!)

Repeat the activity, making triangles and rectangles with different numbers of pieces.

## More Math Tangrams for Kids in Upper Grades

Kids in grades 3-5 can use tangrams to explore higher-level math ideas such as fractions, area, measurement, proportion, and geometry.

Here are some of my favorite tangram math activities for upper elementary:

### 1. Tangram math hunt

Pick a shape from a set of tangrams. What can you say about that shape using mathematical language?

It might help to brainstorm some math ideas before this activity. Some ideas for math talk include shape names, measurement, perimeter, area, fractions, angles, etc.

### 2. Secret tangram picture

Use all 7 shapes to make a secret tangram picture. Describe your picture to a friend who can’t see your design.

The friend creates the picture from your description, without looking at the original.

This activity is great for practicing geometry vocabulary–and it’s challenging! To make it easier, have kids make a picture using fewer pieces.

### 3. What’s the area?

If the area of the small triangle is 1 unit, what is the area of all the other pieces?

Compare the sizes of each piece to find out what each is worth (ex: two small triangles fit in the small square).

Here are more cool math investigations:

• If the area of the large square is 1, what’s the area of each of the other pieces?
• If the medium triangle is 1/4, what is the area of the other pieces?
• If the large square is 1/2, what is the area of the other pieces?

Here is a worksheet I used with 4th and 5th graders doing this activity.

### 4. Make a symmetrical shape

There are 7 tangram shapes–an asymmetrical number–and not all shapes have an exact match. Can you use these seven shapes to make a design whose outline is symmetrical?

Once you’ve created a symmetrical shape, find the lines of symmetry. Does your shape have horizontal symmetry? Vertical symmetry? Rotational symmetry?

Include your shape in a Symmetry Museum display, or trace it and exchange with a friend to solve each other’s symmetrical tangram puzzles.

### 5. Area impossibilities

Here are two pictures. They each use the same 7 tangram shapes, and their body outlines are the almost identical…but in one picture, there is a foot, and in in the other picture the foot is missing.

How can this be?

Here’s another: The Magic Dice Cup tangram paradox, from Sam Loyd’s book The Eighth Book of Tan(1903). Each was made using the same seven shapes, but the first cup is whole while the other two are missing pieces. How is that possible?

These mathematical mysteries can stir up some lively discussions about whether or not area can change if you move the pieces around in different ways!

(Young kids will not be impressed by these paradoxes; they will just assume that’s how area works.)

## Tangram Kids’ Books

The best math books for kids connect math to kids’ imagination and experience. These tangram books are especially cool because kids can illustrate the story with their own tangrams.

## Tangram Resources For Kids

Ready to try out math tangrams for kids? All you need to get started is a set of your own and you’ll be ready to roll.

## One Comment on “Tangrams For Kids: Discovering Math Through Art”

1. So enjoyed this article. Can’t wait to try. Thank you for contributing to engaging students in creative thinking.