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TANGRAMS. History of Tangrams.

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history of tangrams
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
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
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
Step 3
  • Take one of the halves, fold it in half and cut along the crease.
  • What observations can you make?
step 4
Step 4
  • Take the remaining half and lightly crease to find the midpoint of the longest side.
step 41
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
Step 5
  • Take the trapezoid, fold it in half and cut.
  • What shapes are formed?
  • What types of angles are formed?
step 6
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
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

You should now have seven pieces.

Can you put them together to make a square?

slide12

Put the pieces in order from smallest to largest.

  • What criteria did you use for your arrangement?
slide13
area
  • If the small triangle is our basic unit of area, what are the areas of the other pieces in triangular units?
squares
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?