In this section, we will take a look at your own, rather than your students', reasoning about a problem and your methods of proving mathematical statements. As you work through the activity, pay attention to your reasoning methods, the vocabulary you use while thinking about the problem, the questions that come to mind, and any new mathematical insights you develop. This exploration is meant to assist you in reflecting on your own methods related to reasoning and proof, which will help you later when considering how to increase your students' abilities regarding reasoning and proof.

We multiply two or more whole-number factors and get a product. The area of a rectangle with a whole-number length and width can be thought of as the product of two factors. In this Interactive Activity, you will build rectangles that have a given area, and then compile a list of all the possible factors of the given number. Then, most importantly, you will attempt to prove, or explain, how you know that you have found all the possible factors.

Use the following Interactive Activity to find all the factors of 24.

  Extending the Factors of 24 activity