Tangram in Geometry

  The other day, I described using Tangram in my geometry class to find convex and concave polygons.  I wondered what learning opportunities Tangram offered in Geometry.  Why are they good to use?

Tangram help develop geometric knowledge, reasoning, and improves geometric imagination.  One reason geometric imagination is important is it helps sense the shapes, their position, changes in size, both in the plane and in space.

These are some of the activities that can be used with Tangram.

1.  If all 7 pieces are used to create a square and the square is one inch by one inch, what is the area of each piece.  Show or explain how you arrived at your answer.  This activity requires mathematical reasoning and thinking.

2.  A different way of looking at activity one is to assign a ratio to each part, for instance the largest triangles might be worth 1/4th of the shape each, etc so that once they've got fractions worked out for each shape, they can then figure out the actual area for each piece based on the size of the original square.

3.  This is a great exercise when looking at the specific quadrilaterals as an introduction because once the shapes are made, students can use the resulting piece to determine the characteristics of each one.
Have students use all 7 pieces to create
          a.) a quadrilateral with four equal angles and equal sides that are opposite of each other.
          b.) a quadrilateral with two sets of parallel sides and no right angles.
          c. ) a quadrilateral with one set of parallel sides and no right angles.
          d.) a quadrilateral with four right angles and four equal sides.

4.  Students start with the parallelogram piece and are asked to recreate it using other pieces in the Tangram.  (It uses one square and two small triangles.)  They are then asked to find the formula for the area of a Tangram which they do by rearranging the pieces into a rectangle.

5. Activity three also allows students to create a formula to find the formula for the area and the perimeter based on the shapes they create.  Once they have the formulas, the teacher can give them a worksheet to apply the formulas to the shapes shown on them.

I believe for geometry that when the students work through activities such as this one, they are more likely to understand the concept and remember it.  I told my students to keep their Tangram sets for future activities, so we'll see if they did. Let me know what you think, I'd love to hear.  Have a great day.