Areas of Tangram Pieces

Objectives

a basic understanding of area without formulas
a familiarity with the names of certain polygons
(e.g., square, triangle, and parallelogram)
the meaning of the term congruent
to develop geometric intuition

Materials

a package of tangrams (seven pieces) for each student
(if tangrams are not available, students may
construct their own)
a student notebook (to record observations)
a sharp pencil (for tracing geometric figures)
a ruler
an overhead projector (to illustrate geometric constructions)

Warm-up activities

Have each student inventory his or her package of tangrams. Ask the question "What's in your package of tangrams?" Every student should have seven tangram pieces, including

a small square
two small congruent triangles
two large congruent triangles
a medium-size triangle
a parallelogram

Primary activities

The goal of these activities is to determine the area of each tangram piece. These areas will be used to compute the areas of other polygons in the next lesson.

1. Trace the small square in your notebook. Let's suppose this square has area one square unit. Write "one square unit" next to the small square.

2. Make a square with the two small congruent triangles. What is the area of this square? How do you know?

3. Trace one of the small triangles in your notebook. What is the area of this triangle? How do you know? Write the area next to the small triangle.

4. Trace the parallelogram in your notebook.

5. Make a (non-square) parallelogram with the two small congruent triangles. What is the area of this parallelogram? How do you know? Write the area next to the parallelogram.

6. Trace the medium-size right triangle in your notebook.

7. Make a triangle with the two small congruent triangles. What is the area of this triangle? How do you know? Write the area next to the medium-size triangle.

8. Trace one of the large triangles in your notebook.

9. Make a triangle with the small square and the two small congruent triangles. What is the area of this triangle? How do you know? Write the area next to the large triangle.

10. Make a square with the two large congruent triangles. What is the area of this square? How do you know?

Homework

Repeat the primary activities assuming the small square has area two square units.