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Folding and Cutting a Set of Tangrams. Fold a regular sheet of 8.5 x 11 inch paper so the short side lies along the long side, as illustrated.  Open the paper. Fold the opposite short side at the bottom of that fold.  Open and cut off the rectangle just formed. .

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Presentation Transcript
slide2

Fold a regular sheet of 8.5 x 11 inch paper so the short side lies along the long side, as illustrated.  Open the paper. Fold the opposite short side at the bottom of that fold.  Open and cut off the rectangle just formed.

slide3

Fold the square along one of its diagonals.

    • What two shapes have your made?
    • Cut the two shapes apart.
    • Can you make it back into a square?
slide4

Pick up one of the isosceles right triangles and fold it along its line of symmetry.

    • What two shapes have you made out of the isosceles right triangle?
    • Cut the two shapes apart.
    • Can you make the three pieces back into a square?
    • What is the relationship between the two different isosceles right triangles?
slide5

Pick up the largest isosceles right triangle and locate the midpoint of the hypotenuse by folding. Fold the vertex of the right angle to this midpoint.

    • What two shapes have you made out of the isosceles right triangle?
    • Cut the two shapes apart.
    • Can you make the four pieces back into a square?
slide6

Pick up the isosceles trapezoid and fold it along its line of symmetry.

    • What two identical shapes have you made?
    • Cut the two shapes apart.
    • Can you make the five pieces back into a square?
    • Take one of the right trapezoid (we'll call it a boot) Fold the toe to the heel. Cut along the fold
slide7

Take the other right trapezoid (or boot) and fold the heel to the laces.  Cut along the fold. .

    • What two shapes did you make.
    • Cut them apart.
    • What is the relationship between the three isosceles right triangles?
slide8

Can you put all 7 pieces back together to make a square?

Think about how each piece was created. This could help you put the shapes back into a square.

activity 1
Activity 1
  • Study the seven pieces.
  • Use the communicator template to describe their areas:
    • Place an A is the shape with the smallest area, B is the next largest area, etc,
    • If two shapes have the same area repeat the letter.
    • How many pieces have the same area?
    • How many different areas exist?
  • Suppose the area of the small square is equal to 4 square units.
    • Find the area of each piece.
    • Do your areas make sense?
    • Find the area of the entire tangram puzzle.
activity 110
Activity 1
  • Use the communicator template of the tangram pieces. Study the length of the various sides.
    • How many different lengths are involved?
    • Number the lengths in order from smallest to largest. Start by labeling the smallest side 1, the next largest side 2, etc.
    • How many different length sides exist in the tangram puzzle?
suppose the area of the small square is equal to 2 square units
Suppose the area of the small square is equal to 2 square units.
  • Use the communicator template of the tangram pieces to record your answers.
    • Find the length of each side of each piece.
    • Find the area of each piece.
    • Find the base and height of each piece.
activity 2
Activity 2
  • Place the three isosceles right triangles on top of each other.
    • Compare the corresponding angles.
    • What is the relationship between the three triangles?
    • Suppose the length of the leg on the smallest triangle is equal to 2 unit. How long is each of the nine sides of the three triangles? Use the communicator template to record your lengths.
    • What is the ratio of the corresponding sides of the
      • Smallest to middle triangle?
      • Middle triangle to largest triangle?
      • Smallest triangle to largest triangle?
    • How do the areas of the three triangles compare?
activity 3
Activity 3
  • Suppose the side of the small square is .
  • Use the communicator template to record the
    • Area of each piece.
    • Length of each side of each piece.
activity 4
Activity 4
  • What shapes make up other shapes?
    • What shapes (3) can you make with two small isosceles right triangles?
    • What shapes will make the largest isosceles right triangle?
    • Make the largest isosceles right triangle without using the square piece.
activity 415
Activity 4
  • Without using the two largest isosceles right triangles, make a square from the other 5 pieces.
  • Use the square and small isosceles right triangle to form a right trapezoid. Make a trapezoid that is similar but not congruent to this trapezoid.
activity 416
Activity 4
  • Make a pentagon (2) like the one illustrated.
activity 5
Activity 5

The Tasty Tangram Company has recently opened throughout the US. They sell brownies in the shape of the 7 tangram pieces.

Create a set of directions which will help the employees put the seven shapes of brownies together to form the tangram square.

Other groups can put the directions to the test by following the directions.

If the owner of Tasty Tangram franchises decides she will charge $1 for the small right triangle shape brownie, and all the other shapes will be charged proportionately, how much will she charge for each of the other pieces and how much will the entire brownie tangram cost?