There are many effective hands-on models for fractions. Two of the most popular are Cuisenare rods and pattern blocks. Tangrams are another effective model for fractions. They are similar to pattern blocks in that they are an area model and they are fun to play with.

A tangram is a seven-piece puzzle that originated in China. No one is sure of the exact origin of the puzzle, but Chinese books on tangrams date back to 1813. Ronald Read, the author of a modern book on tangrams, claims that his 1813 Chinese book refers to tangrams as if they were old at that time. It is possible that this Chinese puzzle's origin is many centuries old.

The tangram pieces can be used to make pictures of things, including animals, people, boats, letters of the alphabet, or numbers. The seven pieces of the tangram can be cut from one square. Cut out the square below and then cut the individual pieces to make your puzzle. Tangram sets are also available in school supply stores and catalogs. These are usually made of plastic and tend to be easier to work with.

An Example of a Tangram

CREATIVE PLAY WITH TANGRAMS

Both children and adults enjoy playing with tangrams. The manipulation of the tangram pieces can help develop spatial skills in mathematics.

After all seven pieces are cut out, you should have two small triangles, one medium triangle, two large triangles, one square, and one parallelogram. Let's see what we can create with them. In each case, be sure to use ALL SEVEN TANGRAM PIECES.

1. Make as many letters of the alphabet as you can with your tangram pieces. Trace or sketch your results. Share with a partner!

2. Make as many numbers (Hindu-Arabic numerals) as you can with your tangram pieces. Trace or sketch your results. Share your results!

3. Be creative! Create tangram animals, people, or objects. Share your results!

4. Rearrange all seven pieces to make a large rectangle.

MATHEMATICS ACTIVITIES

1. What are the measures of the angles in all the triangles?

2. Are all the triangles congruent? Are they all similar?

3. Compare the areas of the small triangle, the medium triangle, and the large triangle. What conclusions can you draw?

4. Compare the areas of the small triangle, the square, and the parallelogram. What conclusions can you draw?

5. Use your results in #3 and 4 above to compare the areas of the medium triangle, the square, and the parallelogram.

6. Suppose the large triangle has area 1 and therefore represents one whole. What is the area of the small triangle? What is the area of the medium triangle? What is the area of the square? What is the area of the parallelogram? Explain your answers.

7. Suppose the medium triangle has area 1. What is the area of the small triangle? The large triangle? What is the area of the square? The parallelogram?

8. Suppose two large triangles are put together to form a square and this square represents one whole and has area 1. What is the area of the large triangle? The medium triangle? The small triangle? What is the area of the square? The parallelogram?

9. Compare the use of pattern blocks and tangrams to represent fractions. Which representation is easier to use? Which is more fun? Why?

CONNECTIONS TO CHILDREN'S LITERATURE

Grandfather Tang's Story is a wonderful tale that uses tangrams to tell a story within a story. Students can learn about Chinese culture while learning to use tangrams to make the figures depicted in the story.