Implementing Common Core Standards in Math Wednesday, February 8th- 4pm EST Mathematical Habits of Mind in the Practices: Problem Solving & Attending to Precision Presented by Sara Delano Moore, Ph.D., Director of Mathematics and Science at ETA/Cuisenaire Join the edWeb.net community at:

 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.

Solving Problems Problem Solving

Characteristics Example  Context relevant to students  Incorporates rich mathematics  Entry points/solution pathways not readily apparent   Tommy & Tessa want to fence in a play area for their dog, Moose. Moose is a big dog, and they want to give him as much room as they can. They have 64 feet of fence. They can use up to 36 feet of the side of their barn as one side of the play area. The area must be rectangular and each side must be a whole number of feet. Determine the best size for Moose’s play area.

Mathematically proficient students…  Explain the meaning of the problem to themselves  Look for entry points to the solution  Analyze givens, constraints, relationships, goals

 Tommy & Tessa want to fence in a play area for their dog, Moose. Moose is a big dog, and they want to give him as much room as they can. They have 64 feet of fence. They can use up to 36 feet of the side of their barn as one side of the play area. The area must be rectangular and each side must be a whole number of feet. Determine the best size for Moose’s play area. › Explain the meaning of the problem › Entry points › Givens, constraints, relationships, goals

Mathematically proficient students….  Plan a solution pathway  Consider analogous cases and alternate forms  Monitor progress and change course if necessary

 Tommy & Tessa want to fence in a play area for their dog, Moose. Moose is a big dog, and they want to give him as much room as they can. They have 64 feet of fence. They can use up to 36 feet of the side of their barn as one side of the play area. The area must be rectangular and each side must be a whole number of feet. Determine the best size for Moose’s play area. › Possible solution pathways/strategies › Consider analogous cases & alternate forms

Mathematically proficient students…  Explain correspondence and search for trends  Check their answers using alternate methods  Continually ask themselves, “Does this make sense?”  Understand the approaches of others

 Select rich mathematical tasks › Connected to rigorous mathematics content  Ask good questions › Is that true every time? Explain how you know. › Have you found all the possibilities? How can you be sure? › Does anyone have the same answer but a different way to explain it? › Can you explain what you’ve done so far? What else is there to do?  Finding a solution is only part of the process

Vocabulary Mathematical Symbols Computation Measurement Communication

 Vocabulary › Similar, adjacent  Mathematical Symbols ›=›=  Computation and Measurement › Accurate computation › Estimating when appropriate › Appropriate units of measure  Communication › Formulate explanations carefully › Make explicit use of definitions

 Tommy & Tessa want to fence in a play area for their dog, Moose. Moose is a big dog, and they want to give him as much room as they can. They have 64 feet of fence. They can use up to 36 feet of the side of their barn as one side of the play area. The area must be rectangular and each side must be a whole number of feet. Determine the best size for Moose’s play area. › Vocabulary › Mathematical Symbols › Computation & Measurement › Communication

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