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Use appropriate tools strategically.

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Look for and make use of structure.

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Make sense of problems and persevere in solving them.

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Construct viable arguments and critique the reasoning of others.

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See relationships between various representations.

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Listen to the arguments of others and ask useful questions to determine if an argument makes sense.

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Use available tools; recognizing the strengths and limitation of each.

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Look for the overall structure and patterns in mathematics.

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In what ways does this problem connect to other mathematical concepts?

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In what situations might it be more informative or helpful to use…?

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How did you decide to try that strategy?

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How might you use one of your previous problems to help you begin?

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Encourages multiple representations, such as visual diagrams, manipulatives, symbols, and problem situations. Making connections among multiple representations to develop meaning.

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Expects students to give feedback and ask questions of others’ solutions.

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Expects students to recognize and identify structures from previous experience(s) and apply this understanding in a new situation.

Ex: 7 x 8 = (7 x 5) + (7 x 3)

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Lends itself to multiple learning tools. (Tools may include; concrete models, measurement tools, graphs, diagrams, spreadsheets, statistical software, etc.)

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Expects students to explain the overall structure of the problem and the big math idea used to solve the problem.

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Demonstrates and provides students experiences with the use of various math tools. A variety of tools are within the environment and readily available.

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Creates various instructional opportunities for students to engage in mathematical discussions (whole group, small group, partners, etc.)

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Continually asks students if their plans and solutions make sense.