1. Your students 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? You may choose to give them the following 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 they have solved the Zotbot problem, they 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? You may choose to give them the following 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 your students 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. They could start with the two missions designed for the Robot Challenge. Then they could create their 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. Have your students try various products of prime numbers and also non prime numbers so they 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 might challenge really bright students to figure out why prime numbers were used without giving any explanation. From this extension, students can see how prime numbers can be applied to solve real problems.

3. Your students 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 they make, they can always get back to the original activity by exiting Squeak and starting over, so don't worry. Have your students explore, try what comes to their mind, and have fun exercising their brain. To start, have them click on the Playing button at the left for a introduction to how Squeak works, if they haven't done this already. They must click Escape Browser and their resolution must be set at 800x600 to view this properly. Send your students to Squeakland for tutorials and more information on using Squeak. Here are several references where you can learn more about Squeak and where to get basic information sheets to hand out to your students to guide them using Squeak. You could have them try to figure out how the feedback is given when they click the T buttons. The feedback is very basic, but it could be much more complex and less revealing. For example, the feedback tells them if they need a Norbot or Zotbot if none of the needed parts is in the proper robot. Your students could work on ways to make the feedback more sophisticated. To learn how the feedback is given, your students need to open all the flaps on the right, drag out any scripts they find, and explore.

4. Your students 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 they make, they can always get back to the original activity by exiting Squeak and starting over, so don't worry. Have your students explore, try what comes to their mind, and have fun exercising their brain. To start, have them click on the Playing button at the left for a introduction to how Squeak works, if they haven't done this already. They must click Escape Browser and their resolution must be set at 800x600 to view this properly. Send your students to Squeakland for tutorials and more information on using Squeak. Here are several references where you can learn more about Squeak and where to get basic information sheets to hand out to your students to guide them using Squeak. To learn how the project works, your students need to open all the flaps on the right, drag out any scripts they find, and explore. Once they have learned something about how the project works, you could have them try to reconstruct the project for a even higher order learning experience. For example, you could have your students make new robot parts and have them figure out how to identify the parts (the Mission 1 Squeak project uses prime numbers). Then you could have them determine when the parts are in the robot and create feedback statements for the user.

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.