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## TANGRAMS

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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?

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