How to Solve Tangram Puzzles: Step-by-Step Examples
The concept of tangram in maths is essential in mathematics and helps in solving real-world and exam-level problems efficiently. Tangram puzzles are widely used in geometry learning, shape recognition, and creative problem-solving, making them a valuable tool in both classrooms and exams.
Understanding Tangram in Maths
A tangram in maths is a classic geometric dissection puzzle that consists of seven flat shapes—called “tans”—which can be arranged to form a square or various other figures. This concept is widely used in geometry, logical reasoning, and creative pattern recognition. The traditional 7-piece tangram set includes 5 triangles (2 large, 1 medium, 2 small), 1 square, and 1 parallelogram. All pieces must touch without overlapping to create new shapes. Tangram puzzles promote visualization, spatial awareness, and understanding of congruence and symmetry.
Origin and History of Tangram
The tangram originated in China centuries ago, where it was known as the “seven boards of skill.” It gained global popularity in the 19th and 20th centuries, spreading to Europe and America as both an educational and recreational tool. Its simple rules yet endless creative outputs have made it a favourite for students, teachers, and puzzle enthusiasts alike. The puzzle set often formed the basis for teaching symmetry, angles, and geometric reasoning.
How to Make and Use a Tangram: Step-by-Step Guide
Creating your own tangram in maths is easy and fun. Follow these steps to make the classic 7-piece tangram from a square:
1. Start with a perfect square piece of paper or cardboard.2. Draw one diagonal to form two triangles.
3. Cut along the diagonal — this makes two right triangles.
4. Take one of the triangles, divide it again to get two smaller triangles.
5. From the remaining triangle, mark and cut to form a medium triangle and a small square.
6. From the square, measure appropriately to form a parallelogram and another triangle.
7. Ensure you have seven pieces in total: 5 triangles, 1 square, and 1 parallelogram.
Once cut, you can use the pieces to make countless shapes such as animals, houses, boats, letters, and more. All seven pieces must be flat, touch edge-to-edge, and cannot overlap while forming a figure.
Tangram Pieces and Types
A standard tangram puzzle has these seven pieces:
| Piece Type | Count | Description |
|---|---|---|
| Large Right Triangle | 2 | Biggest pieces |
| Medium Right Triangle | 1 | Single medium-sized piece |
| Small Right Triangle | 2 | Smallest triangles |
| Square | 1 | Simple square |
| Parallelogram | 1 | Unique slanted piece |
Some variations use 5-piece tangrams for simpler shapes, but the 7-piece set is the most common and versatile for maths activities.
Tangram in Maths: Geometry Concepts
Tangram in maths helps students understand important geometry concepts like angles, symmetry, area, and perimeter. Each tangram piece has specific angle measures and side lengths. By rearranging pieces to form different shapes, students learn about congruence, the properties of basic shapes, and how area is conserved when shapes are transformed. Using tangram puzzles also reinforces spatial reasoning and logical problem-solving—skills vital for maths Olympiads and board exams.
Worked Example – Making a Tangram Animal
Let’s solve a typical problem: Form a tangram “swan” using all 7 pieces from a square tangram set.
1. Lay out all seven tans in front of you.2. Start by using one large triangle as the body of the swan.
3. Place a medium triangle for the neck, connecting it to the body at an angle.
4. Use a small triangle at the top to make the swan’s head.
5. Arrange the parallelogram near the base as part of the lower body.
6. Fit the two remaining small triangles and the square to fill out the tail and back.
7. Check that all pieces are touching—none should overlap or be left out.
Your swan is complete! All steps use logic and trial, reinforcing geometric skills.
Tangram Practice Problems
- Create a tangram rabbit using all 7 pieces.
- Identify the symmetry in a tangram house figure.
- Form a parallelogram using exactly two tangram pieces. List which ones you used.
- If a tangram square has side 14 cm, what’s the area of the largest triangle?
- List all four-sided shapes the tangram set can make.
Common Mistakes to Avoid
- Overlapping pieces—each tangram solution must have pieces touch, but none should cover another.
- Leaving out pieces—every tangram figure (unless the puzzle says otherwise) must use all 7 tans.
- Confusing parallelogram with a square or rectangle due to its slant.
- Not checking for symmetry or alignment while forming shapes.
Real-World Applications and Further Learning
The concept of tangram in maths appears in classroom pattern puzzles, design tasks, coding, and architecture. It helps children understand how bigger objects are made from simple shapes. Teachers use tangram sets to make geometry classes interactive, while competitive exams sometimes include tangram-based questions on symmetry and rotation. Vedantu helps students connect tangram puzzles to real-life shapes, logical reasoning, and develop a stronger maths foundation.
Downloadable Resources & Online Practice
Students can find printable tangram PDFs for extra puzzles and online tangram games to test pattern skills. Tangram puzzles may also be part of your CBSE or ICSE exams—practicing these boosts confidence in symmetry and reflection symmetry concepts.
Summary
We explored the idea of tangram in maths, its origin, practical uses, types of pieces, and importance in geometry. Step-by-step examples and hands-on puzzles show how tangrams make maths fun and easy to understand. Practice more with Vedantu to build confidence in these creative and logical maths concepts.
Related Topics for Deeper Understanding
- Reflection Symmetry
- Understanding Elementary Shapes
- What Are Solid Shapes
- Types of Quadrilaterals
- Figures with Symmetry
- Perimeter and Area of Plane Figures
- Patterns
- Polygon Curve Angle
- Congruence of Plane Figures
- Lines and Angles
FAQs on Tangram in Maths: Definition, Shapes, and Practical Uses
1. What is a tangram in maths?
A tangram in maths is a classic geometric puzzle consisting of seven flat shapes called tans. These pieces include five triangles, one square, and one parallelogram that together form a square. Tangrams help improve spatial reasoning, shape recognition, and problem-solving skills for students.
2. Is tangram originated in China?
Yes, the tangram is believed to have originated in China during the Song Dynasty. It became widely popular worldwide after being introduced to Europe and America in the 18th century. Its Chinese puzzle roots are an important part of its history and cultural significance.
3. What are the 7 pieces of a tangram called?
The seven pieces of a tangram are collectively called tans. They comprise:
- 2 large triangles
- 1 medium triangle
- 2 small triangles
- 1 square
- 1 parallelogram
These shapes can be rearranged to form numerous figures without overlapping.
4. What is a 5 piece tangram?
A 5 piece tangram is a simplified version of the classic tangram consisting of only five geometric shapes. While the traditional tangram has seven pieces, this variant typically uses fewer triangles and other polygons to form shapes. It is sometimes used for easier or beginner-level puzzles.
5. How do you cut a 7 piece tangram from a square?
To cut a 7 piece tangram from a square, follow these steps:
1. Start with a perfect square sheet.
2. Cut it into 2 large right-angle triangles.
3. Cut one large triangle into 1 medium-sized triangle and 2 small triangles.
4. Cut the central area into a square and a parallelogram.
5. Ensure all pieces are flat and can fit together without overlapping.
This method produces the classic set of five triangles, one square, and one parallelogram.
6. Where can I find tangram puzzles online or as PDF?
You can find downloadable tangram PDFs and interactive online tangram puzzles on educational platforms such as Vedantu Maths, BYJU’S, and other learning websites. These resources provide printable templates and interactive tools to practice tangram puzzles effectively.
7. Why do students confuse tangram shapes with other geometric puzzles?
Students sometimes confuse tangram shapes with other geometric puzzles because many puzzles share similar flat polygons and assembly rules. Lack of clarity about the specific seven-piece composition (five triangles, one square, one parallelogram) and rules like no overlapping often causes this confusion. Clear definitions and practice help eliminate this misunderstanding.
8. Can tangram pieces cover all possible animal or object shapes?
While tangram pieces can be arranged to form a wide variety of animal and object shapes, they cannot represent every possible figure perfectly. The puzzle’s limitation to seven specific shapes means some complex or curved shapes cannot be recreated exactly, but creative approximations are common in tangram exercises.
9. Why is working with tangrams useful for understanding symmetry and area?
Working with tangrams enhances understanding of symmetry and area because:
- Students observe how pieces reflect and rotate to form symmetric designs.
- The fixed total area of tans allows learning area addition and comparison by rearrangement.
- It concretely demonstrates geometric concepts like congruence, angle relationships, and shape composition.
10. How do tangram puzzles appear in school board exams?
Tangram puzzles commonly appear in school board exams as questions on:
- Identifying component shapes
- Constructing given figures from the tans
- Finding the area or perimeter of tangram compositions
- Understanding symmetry and congruence through tangram arrangements.
These questions assess spatial reasoning and application of geometry concepts aligned with the syllabus.
11. What mistakes are common when assembling a tangram for the first time?
Common mistakes when first assembling a tangram include:
- Overlapping pieces instead of just touching.
- Missing one or more tans.
- Misidentifying the parallelogram and confusing its orientation.
- Incorrectly orienting pieces causing gaps or overlaps.
Careful attention to the shapes and following rules helps avoid these errors.
