1. Have your students exchange theorems with one another and check each other's theorems out by using the Squeak Theorem Challenge web activity tools. If they don't agree about the theorem, have them work together to figure out whether the theorem is correct or not. Repeat until they check all the theorems they created. Go to the NASA CONNECT web site to have your students submit their theorems once they have checked them out and we will post them if they are correct and respond if they are wrong.

2. Have your students use pictures (like in the Squeak Theorem Challenge book on page 6) to visualize their theorems. For a super challenge, have them look in some math textbooks where theorems are proved and use that type of mathematical reasoning to try to prove their theorems.

3. Have your students explain their theorems to the class or to their group. To prepare students for their oral presentation, assign as homework the task to explain the process of arriving at their theorem(s), explain their theorem(s), and show examples of using their theorem(s). Encourage them to accompany their words with pictures they draw. This will take them through inductive and deductive reasoning and will be quite an accomplishment.

4. You and your students can take the activity apart, which is the power of Squeak. Click on the Playing button at the left for a introduction to how Squeak works. You must click Escape Browser and your resolution must be set at 768x1024 to view this properly. Have your students view the introduction. Then have them open the Theorem Challenge web activity and try to take it apart and see how it works and then construct their own activity by modifying the Theorem Challenge web activity. You might have them try to make an activity for theorems about triangles or hexagons. No matter how bad a mess they make, they can always get back to the original activity by exiting Squeak and starting over, so don't worry. Have them explore, try what comes to your mind, and have fun exercising their brains. When they are done go to the NASA CONNECT web site and have them submit the project they constructed and we will post it.

5. It is important to foster individual aesthetic growth in your students. The sense of beauty seen in art is equally important in mathematics. Symmetry is part of beauty and it runs throughout art and mathematics. Theorems have a sense of beauty because they represent truth. Beauty gives us a sense of balance and well-being in our lives. The Squeak project was organized on the page to be functional and that often leads to a kind of beauty. But beauty is in the eye of the beholder, so challenge your students to recreate the Squeak project in a way that leaves them with a sense of balance and beauty. With the tools in Squeak, they can make their own drawings. Any of the objects can be moved and resized and their colors can often be changed. Click on any object while holding down the alt key on a PC or the command key on a Mac and a halo of handles will appear. Click on the red handle at the upper left to explore many options for changing the object. Go to Squeakland for tutorials and more information on using Squeak. When they are done go to the NASA CONNECT web site and have them submit their version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open their project.