1. Have your students think about how many different ways there are to do something? In this activity there are four cloud cells and four aerosol cells to chose from when calibrating the system. Your students probably selected cell 1 and put it in the test area, then added cell 2 for two cells, then added cell 3 for three cells, and finally for their prediction added cell 4. But there are many other ways they could have done the calibration. They could have picked cell 2, cell 3, or cell 4 for the first cell so there would be 4 different ways to test what Zot would measure for one cell. See if your students can figure out how many different ways there are to chose two cells from the four cells and then how many different ways to chose three cells from the four cells. Now the question is, will all the different ways of picking from the identical cells give the same result? Have your students predict what would happen as they try the different ways and then they should test their predictions by doing the experiment. If you want an even greater challenge for your students, introduce them to probability and combinatorial mathematics and see if they can calculate the number of different ways to pick two and three cells from the four cells. As a final check, how many ways are there to pick four cells from the four cells? This will be easy to answer if you did the other parts.

2. There is a special kind of graph paper that is called log paper. If you plot an exponential function on it, the result will be a straight line. Download an MSWord document that contains a copy of log graph paper and instructions. Have your students plot their data and see if they lie on a straight line.

Before trying Challenge 5, your students and you should read this section. 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, if you haven't done this already. You must click Escape Browser and your resolution must be set at 1024x768 to view this properly. Go to Squeakland for tutorials and more information on using Squeak. Again, taking it 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.

3. Challenge 5: Have your students add a fifth cloud or aerosol test cell that gives the correct result when Norbert and Zot perform the experiment on five cells. They can take apart the Squeak project to see how it works. They should start by looking at the scripts for the yellow test area by clicking the 7th flap down from the top on the right. They can click once on a script tile and drag it out onto the work area to examine it. They can pull parts of the script out and see how it changes what happens. Once they figure out how the scripts work, they should make a fifth test cell to follow the model they have from their analysis. It would also be very helpful to download and print the Etoy Quick Start Guide. Have your students submit their Squeak projects for Challenge 5 to the NASA CONNECT web site. We will post all the good entries that we receive to acknowledge your good work and let others learn from your solution.

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 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.