Burhoe 6-A-1 The Pythagorean Theorem with Tangrams

Direct link to activity: http://www.math.wichita.edu/history/activities/geometry-act.html#pyth-tan

Step #1: A small triangle is labeled with the longest side as c (hypotenuse) and the other two sides, the legs a and b.   The 90^o angle forms at the intersection of the two shorter sides, the legs a and b.  The other two angles are acute angles which each measure 45^o

Step #2:  On the sides a and b, two small triangles are needed to create squares.  On side c, four small triangles are needed to create a square.   The two squares of a and b combined make the perfect square on side c. 

Step #3: Using the medium triangle in the middle,  four small triangles are used on sides a and b.  Eight small triangles are needed for side c.

Step #4: Using the large triangle, two large triangles are used on sides a and b.  All seven tangram pieces are used for side c.

Step #5: The amount of figures needed to create a square for one leg of a triangle equals the amount of figures needed to create a square for the other leg of a triangle.  The amount of figures needed to create a square for the hypotenuse of a triangle equals  the sum of those two amounts.  Therefore, the sum of the areas of the squares along each leg of the right triangle  equals the area of the square along the hypotenuse.  This activity is a good introduction to square roots and rational numbers.  Students need knowledge of both in order to use the formula a squared + b squared = c squared.  This activity would be great for my students.  Instead of using “parrot math” and having them plug the numbers into the Pythagorean formula, they would be able to see and understand the concept for themselves.  I would use the activity to introduce the formula as well as square roots and rational numbers.  They would enjoy playing with the tangrams (whether hands-on or computer) which would give me their attention to start this activity.