Tangrams
2026-02-28 13:31 Diff
https://brightchamps.com/en-us/math/numbers/tangrams

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Last updated on December 2, 2025

A tangram is a collection of seven geometric shapes consisting of two large triangles, one medium triangle, two small triangles, a square, and a parallelogram. The seven pieces of the ancient Chinese puzzle are known as tans. In this topic, we will take a closer look at tangrams and their properties.

What are Tangrams?

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We love bringing things to life with the power of our imagination and creativity. We often create animals, houses, boats, and birds using paper and simple geometric shapes. Tangram pieces can be used to form a wide variety of shapes. A square can be formed by arranging all seven pieces of a tangram. A tangram is a puzzle created by cutting a square into seven specific geometric shapes.

History of tangrams:

The tangram was invented in China. It uses seven shapes known as tans. More than 6000 shapes can be made using the tangrams. They gained popularity when they were introduced in European countries. Tangrams were made of wood and glass in ancient times. Later, we used paper, and now we can even access these puzzles online, virtually, or digitally. They are available online for everyone to access as tangram games, featuring interactive tangram visuals that let us arrange and organize them however we want. We have even made some magnetic tangrams for children to play with.

How to Create Tangrams?

Now, let us create a tangram using simple household materials. All we need is:

  • Cardboard or thick paper 
     
  • Pencil
     
  • Ruler 
     
  • Scissors 
     
  • Colors 
     

To create a tangram easily, we need to follow certain steps. Let us go through each step in detail. 

Step 1: Draw a square with an 8-inch side length using a ruler and pencil. Mark lines for every 2 inches.

Step 2: Divide the square into seven geometric shapes by drawing the necessary lines. 

Step 3: Separate the seven tans by cutting along the marked lines on the cardboard. 

Step 4: Label the tans 1 to 7, and this can be done randomly.  

The tangram is assembled, and you can now color the tans. Usually, tangrams come in four colors: red, blue, green, and yellow. 

How to Create Different Tangram Shapes?

Tangrams are used for making birds, houses, animals, and other items. When we create different tangram shapes, keep in mind that:
 

  • We must use all 7 tangram pieces or tans.
     
  • Every piece of tangram must lay flat on a plane surface. 
     
  • Each piece must be in contact with another, but they should not overlap.  
     

Let us see how to create a bird using tangram shapes.
 

  • When creating a tangram bird, start with the head. Place the medium-sized triangle to form the head. 
     
  • Next, place the largest triangle as the main body part and the other largest triangle as the wing. 
     
  • Place one small triangle at the lower body, and the other should properly align with the large triangle to extend the wing. 
     
  • The square is positioned near the small triangle supporting the body part, and a parallelogram is used to form the tail of the bird. 

Similarly, we can create many other shapes by arranging them in specific ways. Let us learn how to make different tangrams using the seven shapes. For that, let us arrange and name the shapes as shown in the image below. 

Now, we can create a dog using the tans. Arrange the numbered pieces as shown in the image below.

Tangram house

Let us now build a tangram house. Arrange the numbered tans as shown in the image below. 

Tangram shapes

We can also make different shapes for day-to-day use. For example, we can make the tangram number 1 by arranging the tans as shown in the image below.

We can also make a lotus from the numbered tans by arranging them as shown in the image below.

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Why Do We Use Tangrams?

Like building blocks, tangrams help children develop their problem-solving, logical thinking, perceptual reasoning, visual–spatial, and creativity skills, as well as many mathematical concepts such as congruence, symmetry, area, geometry, and perimeter. They also support children in learning geometric shapes, which will improve their performance on basic arithmetic tests. With a tangram set, kids can explore and create more than 6000 different shapes and figures.

Tips and Tricks to Master Tangrams

Tangrams are a powerful tool for learning spatial reasoning, geometry, and creativity. Here are some tips and tricks to help you master the concept of tangrams. 
 

  • Parents should let their children explore freely with the tans. Let them touch and move the seven pieces to create whatever shapes they want. Let them learn the combinations on their own. Please do not ask them to make shapes in the beginning. 
     
  • Teachers should help the children identify each tan. Talk with children about the shapes, sides, and angles. It develops their basic geometric vocabulary. 
     
  • Parents and teachers can encourage their children to look for straight edges and match large pieces to large outline areas, and small triangles for narrow corners. This would help them in developing their logical placement strategies. 
     
  • Students should focus on creating their own patterns and on rebuilding them. Trace around the tans by placing them on paper. 
     
  • Learners can make use of some Tangram apps for extra practice. They offer instant feedback, progressive puzzles, and interactive tangrams.
     
  • Create a new design for a day. Learners should practice it daily. Pick a shape to create or solve a new design.

Common Mistakes and How to Avoid Them in Tangrams

Tangrams are ancient Chinese puzzles that can be assembled in various ways to form a wide variety of shapes. However, small mistakes can lead to improper conclusions and designs. Here are some common mistakes and ways to avoid them.

Real-Life Applications of Tangrams

Tangrams are an essential tool for enhancing problem-solving skills and creativity. They are not just fun puzzles; they also have countless applications in various fields. 

  • Students who focus on mathematics, geometry, symmetry, and spatial reasoning can use tangrams. They enhance their understanding of various mathematical aspects such as area, perimeter, and angles. 
  • Tangrams enhance students' logical thinking and critical analysis skills by challenging them to strategically arrange shapes to form a specific figure.  
  • In psychology and therapy, medical professionals use tangrams as a recovery method to help patients coordinate their physical activities and engage in stress relief activities. 
  • Tangrams help strengthen memory, improve cognitive abilities, and enhance concentration in students. Teachers and parents use them to improve the reasoning skills of their children.

Problem 1

Create a big triangle using all the tangram pieces.

Okay, lets begin

NA

Explanation

To form a big triangle using all 7 tangram pieces, we have to place each piece as: 

Step 1: Place two large triangles at the bottom edges.

Step 2: Place the square at the top center to form the peak of the triangle.

Step 3: Place the two small triangles next to the large two triangles. 

Step 4: Use the parallelogram and place it beside one large triangle. 

Step 5: Insert the medium-sized triangle between the parallelogram and the small triangle, ensuring they fit together to maintain the triangular shape.  

Well explained 👍

Problem 2

Arrange the tangram pieces to form a house.

Okay, lets begin

NA

Explanation

We can create a house using the tangram pieces by following the below-mentioned steps: 

Step 1: Begin by placing a large triangle on the roof of the house. 

Step 2: Use the square to form a chimney by placing it at the top edge of the large triangle roof.

Step 3: Place another large triangle to form the main body of the house. 

Step 4: Position the parallelogram near the roof, which can represent a room or a garage. 

Step 5: Use the medium-sized triangle and two small triangles at the bottom to create the remaining walls of the house.

Well explained 👍

Problem 3

Create a cat using the 7 tangram pieces.

Okay, lets begin

NA

Explanation

To form a cat, place the 7 tangram pieces as follows:

Step 1: Place the square at the top to form the cat head.

Step 2: Use both the small triangles to shape the ears.

Step 3: Next, arrange one large triangle below the head to form the front body.

Step 4: The second large triangle should be placed diagonally at the bottom to form the cat’s lower body.

Step 5: Use the parallelogram to form the curved tail.

Step 6: Finally place the medium triangle to form the neck of the cat.

Well explained 👍

Problem 4

Arrange the tangram pieces to form a fish.

Okay, lets begin

NA

Explanation

We can create a fish by correctly placing all the 7 shapes as follows:

Step 1: At first, place the large triangle horizontally to form the main body part of the fish.

Step 2: Use the second large triangle to create a V-shaped tail. It should be placed next to the first large triangle. 

Step 3: Position a small triangle at the front of the body to form the head.

Step 4: Use the parallelogram to form a fin and place it near the middle of the body.

Step 5: To give a more defined shape, place the square near the tail. 

Step 6: Finally, use the other small triangle and medium-sized triangle to complete the details of the fish’s body and fins.

Well explained 👍

Problem 5

Create a swan using all 7 tangram pieces.

Okay, lets begin

NA

Explanation

To create a swan, we can use specific geometric shapes:

Two large triangles, two small triangles, a square, a parallelogram, and a medium-sized triangle.

Step 1: First, we can place the large triangle for the body part of the swan.

Step 2: To form the curved neck, place the parallelogram. 

Step 3: Take the other large triangle and place it above the body to form the wing. 

Step 4: Place a small triangle on the top edge of the parallelogram to form the head. Ensure that one side of the triangle aligns with one side of the parallelogram. 

Step 5: Use the square to connect the neck and body of the swan. 

Step 6: Place the medium-sized triangle to refine the shape of the back. 

Step 7: To form the tail of the swan, place the last small triangle.

Well explained 👍

FAQs on Tangrams

1.Define tangrams.

Tangrams are geometric puzzles used to form various shapes and figures by using the 7 flat tangram pieces (tans). 

2.What are the basic rules of tangram?

The basic rules of tangram are:

  • We must use all 7 tangram pieces or tans.
  • Every piece of tangram must lay flat on a plane surface. 
  • Each piece must touch another, but they should not overlap.  

3.Is it possible to remove a piece from the tangram?

No, a tangram puzzle must use all 7 pieces to form various shapes and figures. If we remove any piece, the final result becomes incomplete and looks different. 

4.List the 7 shapes in a tangram.

The seven flat shapes of a tangram consist of:

  • Two large triangles 
     
  • One medium triangle
     
  • Two small triangles
     
  • A square
     
  • A parallelogram

Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.