Observing Student Reasoning and Proof
"In grades 6-8, students should sharpen and extend their reasoning skills by deepening their evaluations of their assertions and conjectures and using inductive and deductive reasoning to formulate mathematical arguments."

## (NCTM, 2000, p. 262)

Students in the elementary grades should have had experience in formulating conjectures and assessing those conjectures in various ways, such as looking for evidence, making models or diagrams, or finding counter-examples. In the middle grades, our goal is for students to refine and extend these experiences, for example, by developing arguments to support their conclusions, evaluating their classmates' assertions, and considering the limitations of their conclusions. The role of the teacher is to engage student thinking and reasoning in the classroom.

We begin with a problem for you to consider. Later in this part, you will observe student thinking on this problem, but here, please consider the mathematical content and the reasoning process you are using to solve it.

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