- Use all seven tangram pieces to make a non-square rectangle.

a) A rectangle has 4 right angles and opposite sides that are congruent. How can you be sure the figure you built has those properties? Write a convincing mathematical explanation.

b) Describe a way to find the area of your rectangle without using a ruler.

- The seven tangram pieces can be arranged to form a square. We’ll call the square the Tangram Square.

Here is the Tangram Square, with part of it shaded in. C is the center of the square and N, M, P are the midpoints of their sides.

a) How many copies of the medium-size tangram triangle fill the shaded region? Describe how you found your answer.

[[{"fid":"298","view_mode":"default","type":"media","attributes":{"height":276,"width":276,"class":"media-element file-default"}}]]

b) How many copies of the small tangram triangle fill the shaded region? Describe how you found your answer.

[[{"fid":"299","view_mode":"default","type":"media","attributes":{"height":192,"width":192,"class":"media-element file-default"}}]]

c) How many copies of tangram parallelogram fill the shaded region? Describe how you found your answer.

[[{"fid":"300","view_mode":"default","type":"media","attributes":{"height":196,"width":333,"class":"media-element file-default"}}]]

d) Now compare the areas of the three tangram pieces pictured in parts a, b, and c to each other. How does the area of each piece compare to the area of the other 2 pieces?

- Examine the following shapes:

[[{"fid":"301","view_mode":"default","type":"media","attributes":{"height":403,"width":596,"class":"media-element file-default"}}]]

[[{"fid":"302","view_mode":"default","type":"media","attributes":{"height":197,"width":543,"class":"media-element file-default"}}]]

a) Which shapes have the same area?

b) How did you determine these shapes had the same area?

## Tangram Template

If you do not have access to sets of tangrams, then create your own using this template. Make one copy of this template per person on card stock (or some other type of heavy paper), then cut out the tangram shapes.