Day 1 Exploration

After each student creates a set of tangrams, the teacher should lead the following exploration. For more information on how to create a set of tangrams or this lesson go to:

http://forum.swarthmore.edu/trscavo/tangrams/contents.html

Trace the small square. Let's suppose this square has area one square unit.

The two small congruent triangles make a square congruent to the first one, which has area one square unit.

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

Since the small square has area one square unit, each of the triangles must have area one-half square unit.

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

This is the medium size triangle. Each of the triangles has area one-half square unit, so the medium-size triangle must have area one square unit.

Trace one of the large triangles. 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.

This is a large triangle. Since the small square has area one square unit and each of the small triangles has area one-half square unit, the large triangle must have area two square units.

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

Since each large triangle has area two square units, the large square must have area four square units.

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