Activity 2: Tangrams and Fractions (Grades 6-8)
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- 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
Standard 3: Geometry and Spatial Sense
- 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
- 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.
Make Your Own Tangram
Read the following directions aloud:
- One piece of square construction paper per student 6 in. (15 cm) x 6 in. (15cm)
- One pair of scissors per student.
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.
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.
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.
5. Unfold, and fold C to F (see Figure 5).
6. Unfold and fold X down to F (see 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.
Put the tangram pieces together to form the same square piece you started with (see Figure 8).
- Name the seven shapes that have been formed. Use geometric terms to describe each shape.
- Are any of the shapes congruent?
Fraction your Tangram:
1. Find the fractional value of each of the tangram pieces. Assume that the value of the
original square is 1.
2. Use Student Worksheet #1 - Fractions on the Tangram to introduce the comparison of fractions.