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
a student notebook (to record observations)
a sharp pencil (for tracing geometric figures)
a ruler
an overhead projector (to illustrate geometric constructions)
Warmup 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 mediumsize 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.
 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.
 Make a square with the two small congruent triangles. What is the area of this square? How do you know?
 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.
 Trace the parallelogram in your notebook.
 Make a (nonsquare) 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.
 Trace the mediumsize right triangle in your notebook.
 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 mediumsize triangle.
 Trace one of the large triangles in your notebook.
 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.
 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.
