In this activity Norbert and Zot are mathematics professors. They challenge your students to exercise their minds by trying to create theorems about parallelograms. A theorem is a statement about mathematics that can be proved (or shown) to be true. Norbert and Zot have tools to help students explore parallelograms. The tools allow users to draw parallelograms of various shapes and sizes and measure the areas of the parallelograms. From their explorations, your students should be able to come up with some statements about parallelograms that seem like they should be true. It is great if your students' theorems are true; but don't worry so much about whether their theorems are right or wrong, but worry that your students are exploring in a logical and productive fashion.

Be sure Squeak is installed successfully on your computer. It may take up to 20 seconds for the project to load for a fast connection (up to 6 minutes for a slow modem connection). Wait until you see an orange flap at the lower left labeled Navigation. Click the flap to open and close it and access some neat tools. You need to click Escape Browser so you will have more space. Click Browser Reentry to get back your Browser controls. Click on the button at the left to try the activity so you will be better prepared to help your students.

After students explore parallelograms, they should be able to use their theorems and what they learned to draw a very symmetrical kite using just parallelograms. They should explore, create, and have fun learning. Be sure to return to this page for extensions once your students are familiar with the activity.

We would like to see the theorems your students prove, the kites they draw and the challenges they meet. Go to the NASA CONNECT web site and have your students submit their results and we will post them.

Math Objectives

1. Students will explore parallelograms and create theorems.
2. Students will learn about parallelograms from the theorems they create.
3. Students will measure and learn about the area of parallelograms.
4. Students will explore and learn about mirror reflection.
5. Students will draw a kite using parallelograms and the theorems they created.

Teacher Information

• Check the national math standards for this activity.
• This activity is inquiry based. An effective approach is to: ENGAGE, EXPLORE, EXPLAIN, EXTEND, and EVALUATE.
• This activity employes many research-based strategies. Check them out for valuable tips.
• Involve other students and have them work cooperatively. Follow the link for advice.
• After your students are familiar with the Squeak theorems project, have them try these extensions.
• Check these basic tips for help 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.