Tangrams in Math  – Definition, Uses, Examples, Facts, FAQs

Tangram is an old Chinese geometrical operation puzzle. It uses seven geometrical shapes (called tans) that can be arranged or assembled in different ways to form many shapes like animals, people, birds, etc. 

This puzzle offers the challenge of creating a geometric shape(s) by arranging and utilizing only seven pieces. It is a very interesting puzzle game in which the competitor is asked to replicate some shape within the given time frame. Playing with tangrams will help kids learn about geometric shapes.

Tangram Pieces or Tans

The seven shapes used in tangrams are: two big triangles, one medium triangle, two small triangles, one square, and one parallelogram.

The tangram triangles are isosceles right  triangles, and thus similar. Their interior angles measure 45°, 45°, and 90°, and the corresponding sides are in proportion. 

We can form a variety of designs using these seven shapes. 

Tangram: Definition

Tangram is an ancient operation puzzle originated in China, consisting of seven flat shapes: two big triangles, one medium triangle, two small triangles, one square, and one parallelogram. The objective of the puzzle is to form a specific shape (given only an outline or silhouette), which may not overlap.

Tangram sets usually come in four colors—red, green, blue, and yellow. 

The puzzle was created by cutting a square into seven geometric shapes. Thus, the seven parts fit perfectly together to form a square!

Here’s a tangram square with 7 pieces:

Can you identify the seven shapes in this square?

1 and 2: Big triangles 

3 and 5: Small triangles

7: Medium triangle

4: Square

6: Parallelogram

How Do You Make Your Own Tangram?

You can create your own tangram from scratch using simple household items.

Requirements:

1. A cardboard paper
2. Pencil 
3. Ruler
4. Scissor
5. Colors

Step 1: Using a ruler and pencil, draw a square with side 8’’ (or a convenient measurement). Mark lines in light color after 2’’ as shown in the figure.

Step 2: Draw lines as shown in the figure below.

Step 3: Cut the cardboard into seven pieces along the dotted lines as shown in the diagram below.

Step 4: We can label it as 1, 2, 3, 4, 5, 6, and 7 as shown below. this labeling can be randomly done. Labeling is done only for convenience while instructing to make some shapes.

The tangram is ready! We can also add colors to make it more attractive.

How to Create Different Tangram Shapes

You can create a wide variety of shapes using a tangram. Let’s understand some basic rules first.

• All the seven tangram pieces (or tans) must be used.
• All the pieces must lay flat on a plane surface.
• All these pieces must touch but should not overlap.

You can form animals, birds, people, day-to-day objects, number shapes. Let’s see some examples.

First, label your tangram so that understanding the instructions is convenient. Mark the pieces as shown below. 

Tangram Birds

It is easier to form a shape once you have the outline ready in mind. Understand the position of each piece and arrange the shapes as indicated below.

You can create a large set of bird shapes using tangrams. Many shapes of birds can be made using tangrams. Can you do this without the help of the number markings? Try your hand at this flying sparrow bird shape!

Tangram Animals

Let’s create a tangram dog! Arrange the pieces as indicated below.

We can also make a large set of animal shapes using tangrams. Try creating a tangram cat shown below just using your knowledge of shapes! 

Figure: Tangram cat

Tangram House

Let’s build a tangram house! 

Tangram Shapes

Tangrams can be used to make different kinds of day-to-day shapes.

Here are examples of shapes formed by tangrams.

• Tangram number 1

• Tangram man

Tangram Puzzles

A tangram is used as a puzzle game. 

Try making the following shapes!

1. Swan
2. Cat
3. Dog
4. Elephant
5. Fish
6. Kangaroo
7. Rabbit
8. Whale
9. Women
10. Man
11. Snake
12. Camera
13. Rhino
14. Rocket
15. Triangle
16. Tangram triangle with 5 pieces
17. Tangram square with 5 pieces
18. Tangram triangle with 7 pieces

When Do We Use Tangrams?

We use tangrams to develop the imagination of geometrical figures, learn the properties of different geometrical shapes. It develops problem-solving ability and reasoning. Tangrams can also be used to introduce concepts like perimeter and area. Tangram in mathematics can be used as an aid in teaching geometry. 

Facts about Tangrams

Conclusion

Tangram is a challenging puzzle game that is used to boost the mental ability of the geometrical figure. It’s ideal for children at a young age. Tangrams are also used in mathematical calculation, i.e., for calculating the perimeter and area. In this article, we learned the technique to make some shapes using tangrams.

Solved Examples on Tangrams

1. Make the shape of a fish using a tangram.

Solution: To form a fish using tangram pieces, we can arrange them in the following fashion. Two small triangles and a square are used to make a tail. Two large triangles form the mouth. The middle portion is created using the parallelogram and the remaining triangle.

2. Make a zero using the tangram.

Solution: Arrange the shapes as shown in the image below to create a tangram zero. The big triangles can be used to create the top and bottom.

3. Make a tangram T-shirt.

Solution:  

We can make many day-to-day items using tangram pieces. You can form a shape of a T-shirt using the structure given below.

Practice Problems on Tangrams

Frequently Asked Questions about Tangrams