Directions   Math Question Illustration
Preparation Step: 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 and cut off the rectangle just formed.

 

You have the square sheet of paper we need to begin the construction of our set of tangrams.

   What mathematical name can you give this fold?  (diagonal or a line of symmetry)
       
Step 1:  Cut the square sheet of paper along the diagonal.   What shapes have your created?  (two congruent isosceles right triangles)
       
Step 2:  Take one of the isosceles right triangles and fold it along its line of symmetry.   What shapes have you created?  (two more congruent isosceles right triangles.)

How are these two isosceles right triangles related to the other isosceles right triangle?
(Similar)
       
Step 3: Return to the largest isosceles right triangle.  Fold the midpoint of the hypotenuse or longest side.  Fold the vertex of the right angle to this midpoint.  Open and cut along the fold.   What two shapes have you created?  (another isosceles right triangle and an isosceles trapezoid)

What is the relationship between the two types of isosceles right triangles?  (Similar)
 
Step 4a: Fold the isosceles trapezoid along it line of symmetry.  Cut along the fold.

 

 

   What do you call these two shapes?  (Right trapezoids)  We'll call the two shapes boots.

Can you locate where the heel, laces, and toe would be located?

 
Step 4b:  Take one of the right trapezoid (we'll call it a boot) Fold the toe to the heel. Cut along the fold.   What two shapes have you created out of the right trapezoid? (another isosceles right triangle and a square)

What is the relationship between the three isosceles right triangles? (similar to each other)
       
Step 5:Take the other right trapezoid (or boot) and fold the heel to the laces.  Cut along the fold.   What two shapes have you created out the second right trapezoid?
(an isosceles right trapezoid and a parallelogram)

What is the relationship between the two smallest isosceles right triangles?  (congruent)
       
Step 6: You have just created a set of tangrams.  Try to reassemble the 7 pieces back to a square.   Think about the shapes that created as you dissected the square.  This may help you reassemble the square.