[Note: Most of what we did today comes from Bridges materials.]
The Greedy Triangle, in which a shape takes on one additional side after another, transforming from a triangle to a quadrilateral to a pentagon, etc. I then asked the kids to consider what they already knew about geometry. They recorded their thoughts (words and/or pictures) in a 2-flap book. (We made our own flap books--photo left--but you can see a template under "Flip Flap with 2 flaps.") They wrote what they knew under the left flap and questions or things they wonder about under the right flap.
We then compiled our information on a class chart. It was exciting to see lightbulbs begin to go on; several kids had little to nothing on their individual flaps as they thought "geometry" was something totally new. As they heard ideas from other kids, our list became longer and longer as they began to make connections.
We began thinking about Tangrams by reading Three Pigs, One Wolf, and Seven Magic Shapes. After the book, I slowly took them through the process of cutting their own Tangrams from 6x6" pieces of wallpaper. Here are instructions if you'd like to make your own. As they worked, we used a lot of mathematical vocabulary in context. Two words we especially highlighted: congruent and similar. A debate arose as to whether all triangles are "right triangles" or not. Some children were certain that they are; others were positive that there are exceptions. I told them to think about that for a time.
Another challenge? To put the seven pieces back into their original square. This will be made easier by the fact that we used wallpaper with a pattern on one side. We finished with a reading of Agatha's Feather Bed.
iPad/Touch/Phone or select from the following:
Cyberchase Tangram Game
NCTM Tangram Puzzles
NCTM Illuminations Tangram Lesson
Tangram Puzzles to Print
Online Tangram Puzzles
We also have several tangram puzzle kits and a game called Classic Tangoes. Manipulating the puzzles by hand definitely uses a different set of skills than doing them on the computer. If you'd like to read some more books with Tangrams, pick up Grandfather Tang's Story or The Tangram Magician.
P.S. We talked quite a bit about the properties of a trapezoid. Please have them look at this site. It allows you to manipulate a figure so that it remains a trapezoid but allows you to see the wide range of possible figures.