Activity 2: Tangrams and Fractions (Grades 6-8)

The Abacus | Tangrams and Fractions | Take A Trip | Career Connections | More Math Concepts


  • Students will learn to construct a tangram puzzle and determine the fractional parts of the tangram.
  • Students will compare the value of fractions and determine the larger fraction.

Standard 1: Number and Operation

  • Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
  • Understand meanings of operations and how they relate to one another
  • Compute fluently and make reasonable estimates
Standard 3: Geometry and Spatial Sense
  • Analyze characteristics and properties of two-three-dimensional geometric shapes and develop mathematical arguments about geometric relationships
  • Specify locations and describe spatial relationships using coordinate geometry and other representational systems
  • Apply transformations and use symmetry to analyze mathematical situations
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.

adobe acrobat Student Activity (PDF File)
Answers (PDF File)
Student Worksheet #1: Fractions on the Tangram (PDF File)
Student Worksheet #1 Solutions: Fractions and Tangrams (PDF File)

Make Your Own Tangram

Materials Needed:

  • One piece of square construction paper per student 6 in. (15 cm) x 6 in. (15cm)
  • One pair of scissors per student.
Read the following directions aloud:
1. Fold the large square in half diagonally. Cut on the fold. You should have two large congruent triangles.

2. Take one of the triangles. Fold the triangle in half diagonally (see Figure 1) to form two triangles. Save these two pieces.

Tangram Directions

3. Take the other large triangle (from step #1). Take Triangle ABC and fold point B to the midpoint of AC. Cut off the triangle formed (see Figure 2). Save this triangular piece.

Tangram Directions

4. The remaining shape from triangle ABC is a trapezoid (see Figure 3). Fold this figure in half. The remaining figure looks like Figure 4.

Tangram DirectionsTangram Directions
5. Unfold, and fold C to F (see Figure 5).

Tangram Directions

6. Unfold and fold X down to F (see Figure 6).

Tangram Directions

Figure 6.

7. The shape now has three folds in it (see Figure 7). Cut on the folds and save the four shapes. The pieces formed are two triangles, one square, and one parallelogram.

Tangram Directions


  1. Name the seven shapes that have been formed. Use geometric terms to describe each shape.
  2. Are any of the shapes congruent?
Put the tangram pieces together to form the same square piece you started with (see Figure 8).

Tangram Directions
Fraction your Tangram: 1. Find the fractional value of each of the tangram pieces. Assume that the value of the original square is 1.

Tangram Directions

                                 Figure 9

2. Use Student Worksheet #1 - Fractions on the Tangram to introduce the comparison of fractions.