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 focused on two-column proofs in our high school geometry class. But we can help our students begin to develop reasoning skills in much earlier grades by giving them many opportunities to explain their thinking in a variety of ways -- through drawing pictures, explaining with words, and listening to their classmates' explanations. Through reasoning, students develop their own sense of the mathematical coherence of the things they are learning.

In this section, we will take a look at your, 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 -- or informed guesses -- and then justify your thinking.

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