# Tangrams Part I

Posted February 23, 2010

on:NOTE: All shapes were manipulated in Microsoft PowerPoint and it is harder than you think to get the lines to match up but I tried.

After comparing the three drawings I came up with the following table to show the areas of each square in each step.

Area of Square on Side A | Area of Square on Side B | Area of Square on Side C | |

Step 2 | 2 | 2 | 4 |

Step 3 | 4 | 4 | 8 |

Step 4 | 8 | 8 | 16 |

The sum of the areas of the squares on the legs (side A and side B) is equal to the square of the hypotenuse (side C).

After completing this activity I would hope that students would realize that the number of small triangles that is required to create the square on each side of the original triangle is equal to the area of the square on the hypotenuse side.

This activity allows students to use concrete examples to illustrate a complex concept. Once students realize that the sum of the areas of the squares on each leg is equal to the sum of the square on the hypotenuse. This can be demonstrated by showing the area of each square in terms of length times width. This would be a great introduction into squares and square roots. After completing all the steps students should understand that a square is a number times itself and that in inverse is called square root.

I really liked the way that this lesson was presented to us. I would have the students work in pairs or small groups. Once they are in their groups I would provide them with a handout (directions like we did for this assignment) and multiple sets of tangrams. I would then expect them to do all the steps we did. I used virtual manipulatives but I would want my students to trace the shapes on paper for each step and label all the sides. After the groups have completed steps 1-4, I would pull them back together and do steps 5 and 6 together. While doing steps 5 and 6 I would introduce the appropriate vocabulary.

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