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History of Tangrams • Legend states that a servant of a Chinese emperor was carrying a ceramic tile, extremely expensive and extremely fragile. The servant tripped, shattering the tile. In a panic, the servant desperately tried to reassemble the tile into a square, but could not. He did realize, however, that many other shapes could be formed from the pieces.
Step 1 • Fold your paper so that two adjacentsides meet. • Cut off the rectangle under the folded section. • You now have a square.
Step 2 • Fold the square in half along a diagonal. • Unfold and cut along the crease. • What observations can you make about the two pieces you have? • How can you “prove” your observations are correct?
Step 3 • Take one of the halves, fold it in half and cut along the crease. • What observations can you make?
Step 4 • Take the remaining half and lightly crease to find the midpoint of the longest side.
Step 4 • Take the remaining half and lightly crease to find the midpoint of the longest side. • Fold so that the vertex of the right angle touches the midpoint and cut along the crease.
Step 5 • Take the trapezoid, fold it in half and cut. • What shapes are formed? • What types of angles are formed?
Step 6 • Take one trapezoid. • Fold the acute base angle to the adjacentright base angle. • Cut on the crease. • What shapes are formed?
Step 7 • Take the other trapezoid. • Fold the right base angle to the oppositeobtuse angle. • Cut on the crease. • What shapes are formed?
You should now have seven pieces. Can you put them together to make a square?
Put the pieces in order from smallest to largest. • What criteria did you use for your arrangement?
area • If the small triangle is our basic unit of area, what are the areas of the other pieces in triangular units?
Squares • Create a square using only one piece. • What is its area? • Create a square using two pieces. • What is its area? • Create a square using 3 pieces, 4 pieces, 5 pieces, 6 pieces, and 7 pieces. • Are they all possible? • What are the areas?
