Implementing Common Core Standards in Math Wednesday, March 7th - 4pm Eastern Time Reasoning & Explaining in the Practices Presented by Sara Delano Moore, Ph.D. Sponsored by Join the Implementing Common Core Standards in Math community Tweeting today? #ccss

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 Make sense of problems & persevere in solving them.  Reason abstractly and quantitatively.  Construct viable arguments & critique the reasoning of others.  Model with mathematics.  Use appropriate tools strategically.  Attend to precision.  Look for & make use of structure.  Look for & express regularity in repeated reasoning.

 Mathematics in and out of context  Working with symbols as abstractions  Quantitative reasoning requires number sense  Using properties of operations and objects  Considering the units involved  Attending to the meaning of quantities, not just computation

 Understand and use assumptions, definitions, and prior results › Think about precision (MP6)  Make conjectures and build logical progressions to support those conjectures › Not just two column proofs in high school  Analyze situations by cases › Positive values of X and negative values of X › Two-digit numbers vs three-digit numbers  Recognize & use counter-examples › Maximum area problem

 Provide rich problems where multiple pathways and solutions are possible  Look for the best answer and allow multiple interpretations of best  Recognize the difference between argument and opinion  Provide scaffolds for them

 How can you show that your computation is correct? › Use a different tool or strategy › Compare your work with someone else  How can you explain why your answer is best? › What possibilities did you consider? › What criteria did you use? › Why did you reject some options? › What made you choose this option?  Embedding logic into your thinking › Does one part depend on another part? › Does changing one aspect of the problem change the result? › What are you sure about? What comes next?

 Compare two plausible arguments  Distinguish correct from flawed reasoning › Explain/correct the flaw  Elementary student arguments might depend on concrete referents › Generalize the reasoning at later stage  Ask useful questions to clarify and improve arguments

 Should every lesson address every practice?  How is this practice addressed in this lesson?  What practices does this lesson highlight?  In what ways does this lesson highlight one or more practices?

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