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178 LearnersLast updated on October 10, 2025
Tangrams
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?
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.
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.
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.
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.
Mistake 1
Forgetting to Use All the 7 Tans
Students should count the pieces of tangram when they assemble various shapes. A tangram consists of 7 tans including triangles, a square, and a parallelogram. If they forget to use even a single piece, the shape will be incorrect.
Mistake 2
Overlapping Tangram Pieces
Sometimes, students may place the pieces on top of each other instead of placing them side by side. Therefore, kids should check if the pieces are flat and touch each other without overlapping.
For example, in a bird tangram, if one triangle overlaps another, then the bird may look incorrect.
Mistake 3
Confusing Parallelogram with Square
Both parallelograms and squares have four sides, which often causes confusion among kids. So they should be vigilant and understand that a parallelogram has slanted sides, while a square has straight edges. When positioning these pieces, kids should ensure that each piece is correctly placed based on its shape.
Mistake 4
Ignoring the Outline
When creating shapes, students should try to follow the guidelines or the outline to get accurate shapes. If students ignore the outline, then they may end up with the wrong shape and arrangement of tans.
For example, kids need to form a cat shape but ended up with a dog-like shape because they did not use an outline.
Mistake 5
Improper Placement of Pieces
Students should place the correct pieces in the appropriate spot, otherwise the shape will be incorrect. So, they should carefully match each piece with its suitable place.
For example, if students mistakenly place a parallelogram on top of a house instead of a triangle, then the shape will look different and incorrect.
Solved Examples of Tangrams
Problem 1
Create a big triangle using all the tangram pieces.
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.
Problem 2
Arrange the tangram pieces to form a house.
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.
Problem 3
Create a cat using the 7 tangram pieces.
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.
Problem 4
Arrange the tangram pieces to form a fish.
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.
Problem 5
Create a swan using all 7 tangram pieces.
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.
FAQs on Tangrams
1.Define tangrams.
2.What are the basic rules of tangram?
3.Is it possible to remove a piece from the tangram?
4.List the 7 shapes in a tangram.
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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.
