1. You can learn about combinations by trying to figure out how many ways certain things can be done.

• Given the parts on the tabs in the Squeak activity, how many different combinations of robot parts can be used to fill the Zotbot robot? Hint: Start by determining how many triangles it takes to fill the Zotbot and then note that a parallelogram is two triangles and a trapezoid is three. Make an organized list of the various parts and ways to fill the space with the given parts.
• Once you have solved the Zotbot problem, you can work on the Norbot. Given the parts on the tabs in the Squeak activity, how many different combinations of robot parts can be used to fill the Norbot robot? Hint: Start by determining how many triangles it takes to fill the Norbot and then note that a parallelogram is two triangles and a trapezoid is three. Make an organized list of the various parts and ways to fill the space with the given parts.
• Lastly, see if you can determine how many different ways the parts can be placed in the Zotbot or Norbot for a given mission with a specific set of parts. Start with the two missions designed for the Robot Challenge. Then create your own missions and parts list and solve for the number of ways to put the parts in the new robot.

2. For this Squeak project, each part was identified by a different prime number. Since the product of prime numbers is unique, it is possible to determine which parts have been used to construct the robot. Try various products of prime numbers and also non prime numbers so you can see that the product of prime numbers will always be unique, but the product of non prime numbers isn't necessarily unique. For example, the product of the prime numbers 5, 7 , and 13 is 455 and can only be made from those numbers. That is, 445 is only divisible by 5, 7, or 13. However, the product of the non prime numbers 4, 6 and 15 is 360. The number 360 has many divisors other than 4, 6, or 15 (e.g. 10 and 12 and 36, to name a few). You can get a book in the library to read about prime numbers.

3. Take the activity apart, which is the power of Squeak. Taking the Squeak project apart and even breaking it is a good way to learn. 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 their mind, and have fun exercising your brain. To start, click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 800x600 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. Try to figure out how the feedback is given when you click the T buttons. The feedback is very basic, but it could be much more complex and less revealing. For example, the feedback tells you if you need a Norbot or Zotbot if none of the needed parts is in the proper robot. Work on ways to make the feedback more sophisticated. To learn how the feedback is given, 0pen all the flaps on the right, drag out any scripts you find, and explore.

4. You can take the activity apart, which is the power of Squeak. Taking the Squeak project apart and even breaking it is a good way to learn. 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 their mind, and have fun exercising your brain. To start, click on the Playing button at the left for a introduction to how Squeak works, if you haven't done this already. You must click Escape Browser and your resolution must be set at 800x600 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. To learn how the project works, you need to open all the flaps on the right, drag out any scripts you find, and explore. Once you have learned something about how the project works, try to reconstruct the project for a even higher order learning experience. For example, make new robot parts and figure out how to identify the parts (the Mission 1 Squeak project uses prime numbers). Then determine when the parts are in the robot and create feedback statements for the user.

5. 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 Exercise 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.