Tangrams

Tangrams are an excellent tool for the development of spatial sense, as well as being a creative, geometric medium. They are also beneficial in developing mathematical connections to other culture, as well as an excellent example of geometric problem solving. They can be connected to measurement when used as area problems, and also have applications as a model for fractional relationships. In short, tangrams are engaging, versatile manipulatives that are readily available in the elementary classroom.

Some might argue that using virtual tangrams is not as effective as having children manipulate the tans themselves. I agree that using the hands-on tans help children develop fine motor skills, and give them experience in using the isometric transformations of the plane. However, my thought is that making my PST aware of places on the internet where they can access virtual manipulatives will be useful for them to practice with and develop lesson plans at home when classroom manipulatives are not available. In addition, I feel that manipulating the tans in a dynamic environment helps to make the geometric transformations more explicit to the user. Deciding to rotate or flip and then using the computer commands to do it is different than moving the shapes by hand.

There are several places to access virtual tangrams on the web. This link will take you to the website for The National Library for Virtual Manipulatives where you can find a wide variety of manipulatives including a tangram applet. I also include a link which will allow you to download a GSP file I designed containing a set of tangrams and possible activities to use with PST.

In my methods classroom I try to connect mathematics to literature and I often use Grandfather Tang's Story, by Ann Tompert, as a means to introduce the cultural connection of tangrams to my students. After reading through the story, discussing some of the culture connections, and explaining the rules to creating tangrams, I'll turn them loose to think about some of these activities.

Activities

There are three different levels of tangram activities that I use with my PST and suggest that they use with children.

Level One - Outlined Figures: Examples of this type of activity would be the Parallelogram, Hexagon and Drinking Duck sketches in the GSP file. There is an outline of the figure to be made with each shape outlined. for young children, this activity can be challenging as they gain experience with spatial visualization, rotations, and flips.

Level Two - Full sized Shapes: Examples of this activity would be the Running Man, Dinosaur, Swan, Iron, and Candle sketches in the GSP file. Here the target figure is presented in full size, but without the individual shapes outlined in their positions.

Level Three - Scaled figures: Examples of this level are found on the Challenges sketch in the GSP file. In this case, the figures are proportional to the tans, but not the same size. This level is by far the most difficult for children as well as PST.