In order for teachers to increase their effectiveness in helping students develop skills in reasoning and proof, it's helpful to explore how reasoning and justifying relate to developing a deeper understanding of mathematical concepts. Our own experience with reasoning and proof may have been limited to two column proofs in a geometry class. Giving students opportunities to reason by noting patterns and structure in a variety of mathematical contexts, to make conjectures based on these patterns, and to test their conjectures and justify their thinking enables students to develop a much deeper understanding of the mathematical concepts they are studying.

In this section, we will take a look at your own, rather than your students', approach to applying reasoning skills to a mathematical activity. As you complete this activity, you will need to make some conjectures and justify your thinking.

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