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7. Look for and make use of structure.In all grade levels mathematically proficient students will:1.discern a pattern or structure2.understand complex structures as single objects or as being composed of several objects3.check if the answer is reasonableAlaska Standards for Mathematical Practice (June 2012) Page 107

To help students build confidence and rely on their ownunderstanding, ask…• Why is that true?• How did you reach that conclusion?• Does that make sense?• Can you make a model to show that?To help students learn to reason mathematically, ask…• Is that true for all cases? Explain.• Can you think of a counterexample?• How would you prove that?• What assumptions are you making?To check student progress, ask…• Can you explain what you have done so far? What else is there todo?• Why did you decide to use this method?• Can you think of another method that might have worked?• Is there a more efficient strategy?• Why did you decide to organize your results like that?• Do you think this would work with other numbers?• Have you thought of all possibilities? How can you be sure?To help students collectively make sense of mathematics, ask…• What do you think about what_____said?• Do you agree? Why or why not?• Does anyone have the same answer but a different way to explainit?• Do you understand what_____is saying?• Can you convince the rest of us that your answer makes sense?To encourage conjecturing, ask…• What would happen if…? What if not?• Do you see a pattern? Can you explain the pattern?• What are some possibilities here?• Can you predict the next one? What about the last one?• What decision do you think s/he should make?To promote problem solving, ask…• What do you need to find out?• What information do you need? How can you obtain it?Developing Mathematical Thinking, page 2-3

Patterns and Reasonableness

Grannynannycook lost at sea! Don't know where she's goin', but knows where she's been!

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