1. Exchange theorems with another student (or friend or family member if you are working at home) and check each other's theorems out by using the Squeak Theorem Challenge web activity tools. If you don't agree about the theorem, work together to figure out whether the theorem is correct or not. Repeat by checking all the theorems you and others create. Go to the NASA CONNECT web site to submit your theorems once you have checked them out and we will post them if they are correct and let you know if they are wrong.

2. See if you can use pictures (like in the Squeak Theorem Challenge web activity's book on page 6) to visualize yours. For a super challenge, look in some math textbooks where theorems are proved and use that type of mathematical reasoning to try to prove your theorems.

3. You 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. Then try to take the Theorem Challenge web activity apart and see how it works and then construct your own activity by modifying this one. You might try to make an activity for theorems about triangles or hexagons. No matter how bad a mess you make, you can always get back to the original activity by exiting Squeak and starting over, so don't worry. Explore, try what comes to your mind, and have fun exercising your brain. When you are done go to the NASA CONNECT web site to submit your project and we will post it.

4. You may think mathematics and art aren't related, but nothing could be farther from the truth. The sense of beauty you see 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 you a sense of balance and well-being in your life. 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 we challenge you to recreate the Squeak Theorem Challenge project in a way that leaves you with a sense of balance and beauty. With the tools in Squeak, you can make your 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 you will see the halo of handles. 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 you are done go to the NASA CONNECT web site to submit your version of the Squeak project and we will post it to bring beauty and balance into the lives of all who choose to open your project.