This math activity is from the Math
for All—Plus video series. Tape 6  "We've Got Your Number", Activity #2
There are several chinese legends about Master Tan. In one version, he is the best tile artist in all of the land. Master Tan was asked to make a special tile as a present for his Emperor. On his way to the castle, the tile is broken.
When the broken tile is presented to the emperor, Master Tan is embarrassed and sad. Later, the Emperor sends for him and thanks him and gives him many gifts. He tells Master Tan that he is enjoying the beautiful tile pieces because of all the things he can make with them. In this activity we are going to create Master Tan's tile pieces, called "tangrams" by folding and cutting paper. 
2 sheets of 8 1/2" x 11" colored paper
each cut into an 8 1/2" square
scissors
pen or pencil
CONGRUENT:
the same lengths and the same angles
SIMILAR:
proportional lengths and the same angles

In this activity... you will construct a 7piece "tangram" from one of the 8 1/2" paper squares, and figure out what fractional part each shape is of the total square. Do the following steps:
 Fold the square by bringing corner A to corner B, cut along fold line. You will work with these two triangular shaped pieces.
 Put the long side of triangle #1 toward you, fold lower right hand corner A over to lower left hand B; cut along fold. Set aside these two large congruent (same size) triangles.
 Take triangle #2 and fold corner A to point B, cut along fold. This makes 1 medium triangle and 1 trapezoid.
 Using the trapezoid, fold corner A to corner B, cut along the fold.
 Using one of the new pieces, fold corner A to corner B and cut. This gives us 1 small triangle and 1 parallelogram.
 On the other piece, fold corner A to corner B and cut along fold. This gives you 1 small triangle and 1 small square.
You now have 7 pieces in various sizes and shapes.
 Look carefully at the pieces; using the uncut 8 1/2" paper square, what fractional part of the square do each of the large triangle represent? Write your answer on each part.
 Knowing what fractional part each piece is, how many of these triangles will it take to fill up the large square?
 do the same steps with each of the other pieces.

Did you know...
 You can make several tangram sets and arrange the pieces to make a Tangram Zoo—which includes a cat, giraffe, polar bear, rocket ship and more.
 You can make each letter of the alphabet using all 7 tile pieces. Give it a try!
 Although we cut our square into seven pieces, we didn't create 1/7. Why? Because not all pieces are the same size or the same area—some are 1/4 of the original square and some are as small as 1/16.
 Some pieces have the same fractional name but don't have the same shape. Can you name the fractional names of each tangram piece?

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