Implementing Common Core Standards in Math Tuesday, May 15th - 4pm Eastern Time Seeing Structure & Generalizing in the Practices Presented by Sara Delano Moore, Ph.D., Director of Mathematics and Science at ETA/Cuisenaire Sponsored by Join the Implementing Common Core Standards in Math community at Tweeting today?

 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.

 Patterns, patterns, patterns  Properties of Operations › = › 7 x 8 = 7 x x 3  Geometric Structure › Sorting geometric shapes › Reasoning about the attributes of shapes

 Properties of Operations › Commutative Property › Distributive Property  Properties of Equality › Transitive Property (if a=b and b=c, then a=c)  Properties of Inequality › Exactly one of the following is true:  a > b, a = b, a < b

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 Level 0 (Pre-recognition) › Students do not yet see shapes clearly enough to compare with prototypes  Level 1 (Visualization) › Students understand shapes by comparing to prototypes › Students do not see properties › Students make decisions based on perception, not reasoning  Level 2 (Analysis) › Students see shapes as collections of properties › Students do not identify necessary and sufficient properties

 Level 3 (Abstraction) › Students see relationships among figures and properties › Students can create meaningful definitions and reason informally  Level 4 (Deduction) › Students can construct proofs › Students understand necessary & sufficient conditions  Level 5 (Rigor) › Students can understand non-Euclidean systems › Students can use indirect proof and formal deduction

 Focus on computation here  1 ÷ 3 =  Examining points on a line and slope › (1,2), m=3 (y-2)/(y-1) = 3  Attending to intermediate results

 These practices are about seeing the underlying mathematical principles and generalizations.  These practices have more subtlety.