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

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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.

Shapes made using tangrams block

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.

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

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:

Tangram square

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.

Cardboard square for creating a tangram

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

Making a tangram from scratch

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

Constructing Tangram Step Three

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.

Constructing Tangram Step Four

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

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.

Tangram bird

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 of a flying sparrow

Tangram Animals

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

Tangram dog

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! 

Tangram cat

Figure: Tangram cat

Tangram House

Let’s build a tangram house! 

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 of the number 1
  • Tangram man
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

  • The tangram has its origins in China.
  • It uses seven different shapes, called tans.
  • Using tangrams, we can make more than 6000 shapes.
  • Tangram History: As mentioned earlier, the tangram was first invented in China thousands of years ago. It gained more popularity when it got introduced in European countries. In ancient times, tangrams were made from wood, glass. Today, we can access this puzzle even online!

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.

Tangram fish

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.

Tangram zero

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.

Tangram T-shirt

Practice Problems on Tangrams

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

Attend this quiz & Test your knowledge.

1

Tangram is an operation puzzle that uses _____ geometrical shapes.

6
7
8
5
CorrectIncorrect
Correct answer is: 7
A tangram uses 7 geometrical shapes.
2

The triangles used in a tangram are _____.

congruent
equilateral
scalene
right isosceles
CorrectIncorrect
Correct answer is: right isosceles
The triangles used in a tangram are right isosceles triangles.
3

Which of the following shapes is not used in a tangram?

Square
Triangle
Rectangle
Parallelogram
CorrectIncorrect
Correct answer is: Rectangle
A rectangle is not one of the seven tangram shapes.

Frequently Asked Questions about Tangrams

The rules for playing tangrams are as follows:

  • All the tans must be used.
  • No pieces should overlap.
  • They must be placed on a flat surface.
  • The pieces must all be connected.
  • The tans may also be rotated or flipped to form a shape.

A tangram has 5 different sizes of triangles, 1 square, and 1 parallelogram.

Solving tangrams helps develop the understanding of 2D shapes, spatial reasoning, problem-solving, visual perception, and geometry skills.

Tangram can be played by all age groups except minors. The optimal age for playing tangram is for children in the age group of 5 to 13 years of age.

Yes. Making shapes using the tangram puzzle is an excellent STEM activity. STEM activities refer to projects, games or experiments that can be used to teach different scientific principles and concepts in an interesting manner.