Tangrams

     Notice that the perfect squares formed along leg A and leg B of the small red triangle required 2 of the small triangular units to form each one of them.  Notice that the perfect square formed along the hypotenuse required 4 triangular units.  This is twice as many as it took to form the squares on legs A & B.

     On the legs of the yellow, mid-size triangle, it took 4 triangular units to form each of the squares.  On the hypotenuse of the mid-size triangle it took 8 of the triangular pieces to form a perfect square.  Although using a different size right triangle, it still took twice as many pieces to form the square on the hypotenuse as it did on either leg.

     On the legs of the large, blue triangle, it takes 8 triangular pieces to form a square.  On the hypotenuse of the large triangle, I used all 7 pieces of the tangram to form a square.  Based upon data from the small and medium triangle, we can assume that it would take 16 small triangular pieces to form a square along the hypotenuse.

 

 

     In all right triangles, we notice that it takes the square of A + the square of B to = the square of C(hypotenuse).  Hence, A² + B² = C ².  Students have just discovered the Pythagorean Theorem!
     This is a great introduction to square roots.  This hands on activity walks the students step-by-step through the process of really understanding square roots. 
     I would present this activity as it was presented to us.  I’d have them follow the 6 steps.  Students would be placed in pairs and each pair could work together to unravel the Pythagorean Theorem.  We would use the Tangram Blackline Master, make copies, color and cut out the shapes.  I would use heavyweight paper so the students wouldn’t get as frustrated as I did when placing the pieces together.  They kept moving on me!

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