1. ENGAGE:
   There are several ways to engage students in this activity. You could start by showing The Centennial of Flight Special Edition: Problem Solving: The "Wright" Math, which can be streamed from the the South Carolina Educational TV website or the Apple Learning Interchange to show your students the importance of math in desigining exciting NASA advanced aerospace vehicles. This could be followed by the hands-on activity in the Educators Guide or the kite web activity or both found at the NASA CONNECT web site. Start the Theorem Challenge web activity with a story involving Norbert and Zot as theorem hunters, where you introduce the concept of a theorem in the context of geometry. Squeak, an engaging multimedia authoring environment, will grab the attention of young learners.
2. EXPLORE:
   Norbert and Zot challenge your students to explore and create theorems about parallelograms. They have tools to help students explore parallelograms which 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. They will have created a theorem. This whole activity is one big exploration. If you choose to do the extensions involving modifying Squeak, you can challenge your students to explore how the Squeak Theorem Challenge works.
3. EXPLAIN:
   Have your students explain their theorems to the class or to their group. To prepare students for their oral presentation, assign as homework the task to explain the process of arriving at their theorem(s), explain their theorem(s), and show examples of using their theorem(s). Encourage them to accompany their words with pictures they draw. This will take them through inductive and deductive reasoning and will be quite an accomplishment.
4. EXTEND:
   Close this window and follow the link in the Teacher Information area for a list of extensions with ideas ranging from straightforward to very challenging. You can modify the suggested extensions to fit the class time you have available.
5. EVALUATE:
   Both inductive (abstracting a principle from a set of specific observations) and deductive (using a principle to predict a specific result) reasoning can be used to advantage to promote learning. In this case the inductive reasoning process is made very concrete by implementing it with a highly visual tool like Squeak. To close the loop you should have the students use deductive reasoning with their theorems to predict what will happen when certain changes are made in the appropriate values of the parallelogram properties. With this process, they will be able to better evaluate whether or not their theorems are true. This could be homework or an in class group assignment. Finally, go to the NASA CONNECT web site to have your students submit their theorems once they have checked them out and we will post them if they are correct and respond if they are wrong.