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CSD Foundations in CCSS Part 2 The Standards of Math Practice

CSD Foundations in CCSS Part 2 The Standards of Math Practice. 8 Standards of Math Practice. Standards for Mathematical Practice. Reasoning and Explaining. Modeling and Using Tools. Seeing Structure and Generalizing. Get into 8 groups.

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CSD Foundations in CCSS Part 2 The Standards of Math Practice

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  1. CSD Foundations in CCSS Part 2The Standards of Math Practice 8 Standards of Math Practice

  2. Standards for Mathematical Practice Reasoning and Explaining Modeling and Using Tools Seeing Structure and Generalizing

  3. Get into 8 groups • Each group take one or two of the standards of math practice at each of the tables. • After reading the description of the standard, jot down an example of this practice being demonstrated at your grade level— • What would the teacher be doing? • What would the students be doing? • label the grade levels. • Visit each others standards and examples • Yes, and…if you have something that comes to mind • circulate

  4. P. 2 of the SMP handout • Look at the grid on p. 2 • Discuss how this might be used at your school

  5. #1: Mathematically Proficient Students … Make sense of problems and persevere in solving them. • Explain the meaning of the problem to themselves • Look for entry points • Analyze givens, constraints, relationships, goals • Make conjectures about the solution • Plan a solution pathway • Consider analogous problems • Try special cases and similar forms • Monitor and evaluate progress, and change course if necessary • Check their answer to problems using a different method • Continually ask themselves “Does this make sense?”

  6. Go to livebinders , the math tasks tab • Go to tab for Math Tasks • Go to the sub-tab for Dan Meyer • #45 Pyramid of Pennies

  7. #6: Mathematically Proficient Students … Attend to precision. • communicate precisely to others; use clear definitions • state the meaning of the symbols they use • specify units of measurement • label the axes to clarify correspondence with problem • calculate accurately and efficiently • Express answers with an appropriate degree of precision Comic: http://forums.xkcd.com/viewtopic.php?f=7&t=66819

  8. P. 5 of SMP handout • Look-fors for students and teachers • Discuss the look-fors we found on our charts

  9. #2: Mathematically Proficient Students … Reason abstractly and quantitatively. • Decontextualize • Represent as symbols, abstract the situation • Contextualize • Pause as needed to refer back to situation 5 Mathematical Problem ½ P x x x x -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

  10. Go to Livebinders • Go to tab for Math Tasks • Go to the sub-tab for Illustrative Math Project • Search for an example that would be quantitative and abstract • Grade 3, fractions 3 and 3a

  11. #3: Mathematically Proficient Students … Construct viable arguments and critique the reasoning of others. Use assumptions, definitions, and previous results Make a conjecture Build a logical progression of statements to explore the conjecture Analyze situations by breaking them into cases Recognize and use counter examples Communicate conclusions Distinguish correct logic Justify conclusions Explain flaws Respond to arguments Ask clarifying questions Whitesides, E. (2011). The CCSS Mathematical Practices. Presentation at the CCSSO Mathematics SCASS meeting, November 2011).

  12. Go to Livebinders • Go to tab for Math Tasks • Go to the sub-tab for K-8 tasks • Go to “by math strand” • Number sense and operations • Class Line Up • Puzzled by Time

  13. Discovery Education • Go to Discovery Education –it is under

  14. #4: Mathematically Proficient Students … Model with mathematics. Problems in everyday life… …reasoned using mathematical methods • Mathematically proficient students • make assumptions and approximations to simplify a situation, realizing these may need revision later • interpret mathematical results in the context of the situation and reflect on whether they make sense -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

  15. Go to Livebinders • Go to tab for Math Tasks • Go to the sub-tab for 6-12 estimates & Number Sense • Estimation 180

  16. #5: Mathematically Proficient Students … Use appropriate tools strategically. • Proficient students • are sufficiently familiar with appropriate tools to decide when each tool is helpful, knowing both the benefit and limitations • detect possible errors • identify relevant external mathematical resources, and use them to pose or solve problems

  17. p. 10 SMP handout • Answer the questions : • How will you ensure these things are happening in your classroom?

  18. #7: Mathematically Proficient Students … Look for and make use of structure. • look closely to discern a pattern or structure • step back for an overview and shift perspective • see complicated things as single objects, or as composed of several objects -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

  19. Go to Livebinders • Go to tab for Math Tasks • Go to the sub-tab for visual patterns

  20. #8: Mathematically Proficient Students … Look for and express regularity in repeated reasoning. • notice if calculations are repeated and look both for general methods and for shortcuts • maintain oversight of the process while attending to the details, as they work to solve a problem • continually evaluate the reasonableness of their intermediate results -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

  21. GMP Flipbooks http://www.livebinders.com/play/play?id=187117 Go to the Content Unpacked ta Go to the KA K-8 Flipbooks Gr 4

  22. Handout • P. 2—fill out Practice 8 row • P. 5 Look-Fors • P. 6-12 good questions to ponder • P. 13 sample lesson plan tool • P. 15 High Level Instructional Practices

  23. P. 13-14 SMP handout • Lesson planning template for the SMPs

  24. Mathematical Practices Posters http://elemmath.jordandistrict.org/mathematical-practices-by-standard/

  25. Henry Ford once observed: “If I had asked people what they wanted, they would have said a faster horse.”

  26. If we cannot truly measure something, it might just be the most important thing.

  27. We laminate our lives to reuse next year.

  28. Video –Expanded Learning EVALUATION FORM

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