1. Module 7

1.40. Page 2

Mathematics 10-3 Module 7 Lesson 8

Module 7: Trigonometry

 

Get Started

 

In this activity you will investigate the tangram puzzle.

 

Try This

 

Work with a partner, if possible.

 

Step 1: Print Tangram Template.

 

Step 2: Glue the printed Tangram Template to the back of an old file folder or heavy cardstock. Then, carefully cut out the seven pieces. You will end up with five triangles, one square, and one parallelogram.

 

Use a blue marker to colour the back of the parallelogram, since you may have to flip the parallelogram over to solve certain puzzles. You will not have to colour the backs of the other pieces, as they will not be flipped over.

 

Step 3: Now that you have cut the pieces apart, see if you can form the square or the other tangram shapes shown at the beginning of this lesson. You must use all seven pieces to form each shape. You must not overlap the pieces, but you can rotate pieces and even flip the parallelogram over. Are you totally stuck? If so, glance at the image Tangram Solutions shown at the end of this activity. Tangram Solutions show the lines separating the shapes so you can see how the shapes were made.

 

Step 4: Come up with your own shapes to challenge your partner. Draw an outline of your shape to show your partner, and then see if she or he can use the tangram pieces to solve your puzzle.

 

To design your own shapes, you can use the pieces you cut out or you can use an online tangram applet. You may find an applet by doing a search with the group of words “standard tangram puzzle.”

 

TANGRAM SOLUTIONS

This illustration shows the geometric shapes of a tangram puzzle assembled into a square. Also shown are many other shapes and figures that can be formed by rearranging the geometric shapes.

© KamiGami/shutterstock

 

Self-Check

 

The areas of the seven tangram pieces are related. Assume that the original square from which you cut the seven pieces was 4 in on each side.

 

SC 1. What is the area of the original square?

 

SC 2. Together, what is the area of the large red triangle and the large yellow triangle? How do you know? What is the area of each of the large triangles?

 

SC 3. What is the area of the green triangle? How do you know?

 

SC 4. What is the area of each of the purple triangles? How do you know?

 

SC 5. How are the areas of the small square and the parallelogram related? What is the area of each?

 

Compare your answers.