Keeping in mind the Reasoning and Proof Standard and the methods and goals discussed in this section, read the following questions and answer one in light of the students and content you teach.

• What is the role of conjectures in the upper elementary mathematics classroom? Who makes conjectures?
• What are the characteristics of good mathematical tasks that encourage students to develop habits of sound reasoning and proof?
• How can you incorporate reasoning and proof, including justification, into everyday math lessons?
• Describe a problem where students can generate and organize data, look for patterns, make a conjecture, state a general rule related to the conjecture, and possibly state reasons why it should always hold. How might students develop their reasoning as they solve this problem?
• Could you define the key elements of reasoning and proof in the upper elementary school classroom, if, for instance, you were asked to explain them to a colleague?

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