2. Standards for Mathematical Practice

3. 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

4. Common Core Standards for Mathematical Practice

5. Frayer Model DefinitionCharacteristics ExampleNon-Example

6. MP1 Make sense of problems and persevere in solving them. Work to make sense of your problem. Make a plan. Try different approaches. productive struggle strategy, planning, effort, not giving up How many different plans do you have in your group? Explain them. I can do it. Sí, se puede. I think I can. I think I can… I quit. MP1 DefinitionCharacteristics ExampleNon-Example

7. MP1 Make sense of problems and persevere in solving them. Productive Struggle : “Students are more likely to retain what they learn when they expend effort solving problems that are within reach and grappling with key mathematical ideas that are comprehensible but not yet well formed.”  Carnegie Foundation for the Advancement of Teaching 2013

8. MP6 Attend to precision. Communicate your mathematical thinking clearly and precisely. Be accurate when you count, measure, & calculate. accuracy, vocabulary, attention to detail vocabulary word wall, peer editing “What’s another word for that?” “How might you label the answer?” “that thing” numbers w/o labels “The number on the top of the fraction…” MP6 DefinitionCharacteristics ExampleNon-Example

9. MP2 Reason abstractly and quantitatively. Explain the meaning of numbers, words, pictures, symbols, tables, graphs, and concrete objects. contextualize & decontextualize, in & out of context Singapore bar model, “What do the numbers used in the problem represent?” “This shows…” “Ours is not to reason why, just invert and multiply.” MP2 DefinitionCharacteristics ExampleNon-Example

10. MP3 Construct viable arguments and critique the reasoning of others. Explain both what to do and why it works. Work to make sense of others' mathematical thinking. communicate, back it up, prove it I agree with Paco, because… I see it a different way… What evidence do you see to support…? What I hear you saying is… a silent classroom MP3 DefinitionCharacteristics ExampleNon-Example

11. Resources to Deepen Understanding Frayer Model Standards for Mathematical Practice (Commentary & Elaboration for K-5) Problem Solving Tasks Classroom Implementation Guides

12. Deepening Our Understanding Questions to Consider How does the task elicit that Practice Standard? How can the practices be used to influence instruction?

17. Supporting Mathematical Proficiency Through Student Talk in the Classroom  Provide time for and facilitate discussion  Encourage and facilitate students in justifying their conclusions, communicating, and responding to others  Ask questions to clarify and improve students’ arguments  Expect precision in communication (written and oral)  Provide a variety of tools and technology  Provide opportunities to look for patterns

18. Supporting Mathematical Proficiency Through Problem Solving  Provide time to think and problem solve  Encourage students to check answers using different methods  Provide problems that require flexible use of objects and properties of operations  Provide situations that apply to everyday life  Focus on conceptual understanding  Provide a variety of tools and technology  Provide opportunities to look for patterns