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Working with
Tangrams
I. Spatial Sense -- Initial
Geometric Development
A. Literature Connection
Read Grandfather Tang's Story. This is a Chinese folk tale, with
a moral, that tells of two foxes who play a game in which they change
into different animals. Some interesting results occur.
Have students build the figures in the story. Students often have some
difficulty playing close attention to the orientation of certain pieces.
After students have made all the figures in the story, have them create
other figures of their choice. You could have them write a story or
a few paragraphs about the figures they created.
Extension: What do you know about the areas of each of the figures you
made? Justify your answer.
B. Problem-solving
Consider the table below. Try to build a square using just 2 pieces
or 3 pieces. What shapes can you build using 5 pieces? Sketch out your
solutions.
II. Number and Area Relationships
A. Relationships among the pieces
Find all the relationships you can among the pieces. Which pieces can
be used to make other pieces? What does this tell you about area?
B. Number values
Now that you know the relationships among the pieces, give a value to
one piece. Ask the students what would be the appropriate value of another
piece. For instance,
a) if the square has a value of 6, then what is the value of the medium
triangle? of the little triangle? of the parallelogram?
b) if the parallelogram has a value of 2/3, what is the value of the
medium triangle? of the large triangle?
c) if the medium triangle has a value of T, what is the value of the
large triangle?
Suppose you build a cake out of several tangram pieces. Assign a value
or cost to the entire cake. Determine what would be fair costs for each
of the pieces.
C. Angle Measures
Find the measures of the angles in each of the pieces. Now use that
knowledge to measure the angles of other objects in your room using
the tangram pieces.
D. Pythagorean Theorem
Use appropriate tangram pieces to illustrate the Pythagorean theorem
-- the sum of the squares on the two legs equals the square on the hypotenuse.
References
Marilyn Burns Manipulative Videos (Six Models)
Charles, Linda Holden and Micaelia Randolph Brummett. Connections:
Linking Mathematics with Manipulatives. Sunnyvale, CA: Creative
Publications, 1989.
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