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

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Standards for Mathematical Practice Proficiencies Adaptive Reasoning The capacity for logical thought, reflection, explanation, and justification. Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition

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Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence The ability to formulate, represent, and solve problems. Conceptual Understanding Procedural Fluency Productive Disposition

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Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence Conceptual Understanding The comprehension of mathematical concepts, operation, and relations. Procedural Fluency Productive Disposition

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Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Skill in carrying out procedures flexibly, accurately, efficiently, and appropriately – including quick recall of basic facts, knowing when using a calculator is most efficient, knowing when a remainder is important – having good whole number and fraction sense. Productive Disposition

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Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition The habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief that diligence and ones own efficacy.

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

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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

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

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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? #1: Mathematically Proficient Students … Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions

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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

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Attend to precision. #6: Mathematically Proficient Students … 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=66819http://forums.xkcd.com/viewtopic.php?f=7&t=66819

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

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Attend to precision. #6: Mathematically Proficient Students … 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=66819http://forums.xkcd.com/viewtopic.php?f=7&t=66819

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

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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

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Construct viable arguments and critique the reasoning of others. #3: Mathematically Proficient Students … 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 Whitesides, E. (2011). The CCSS Mathematical Practices. Presentation at the CCSSO Mathematics SCASS meeting, November 2011). Justify conclusions Respond to arguments Communicate conclusions Distinguish correct logic Explain flaws Ask clarifying questions

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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

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Discovery Education Go to Discovery Education –it is under

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Model with mathematics. #4: Mathematically Proficient Students … Problems in everyday life… 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 …reasoned using mathematical methods -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

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

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Use appropriate tools strategically. #5: Mathematically Proficient Students … 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

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

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-- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011. Look for and make use of structure. #7: Mathematically Proficient Students … 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

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

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Look for and express regularity in repeated reasoning. #8: Mathematically Proficient Students … 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.

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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

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Handout P. 2fill 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

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

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

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

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

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We laminate our lives to reuse next year.

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Video –Expanded Learning EVALUATION FORM

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Elements of High Quality K – 12 Mathematics Classrooms S = student learning T = teacher instruction Instruction and Learning Elements in K – 12 Mathematics Classrooms MP = Mathematical Practices SP = Show-Me Process Standards A.Using questioning techniques to facilitate learning MP = 3, 6 SP = 1.4, 1.7, 1.8, 2.2, 2.3, 3.3, 3.5, 3.8 B. Actively engaging in the learning process MP = 1 SP = 3.1 – 3.7 C. Choosing good problems – ones that invite exploration of an important mathematical concept and allow the chance to solidify and extend knowledge MP = 1, 4, 7, 8 SP = 1.6, 1.7, 1.8, 1.10,2.1, 2.3, 3.1 – 3.7, D. Using existing mathematical knowledge to make sense of the task MP = 1, 2, 3 SP = 1.7, 1.8, 1.10, 3.1 – 3.8 E. Making connections among mathematical concepts MP = 2, 7, 8 SP = 1.6 - 1.8, 1.10, 2.3, 3.1, 3.5 – 3.8 Administrators Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

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Fostering Engagement The teacher creates a climate that supports mathematical thinking and communication (MP 2 and 3). Students are accustomed to explaining their ideas and questioning solutions that dont make sense to them (MP 3). Students are not afraid to take risks and know that it is acceptable to struggle with some ideas and to make mistakes (MP 1) Administrators Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

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The teacher responds in a way that keeps the focus on thinking and reasoning rather than only getting the right answer (MP2). Incorrect answers and ideas are not simply judged wrong – the teacher helps identify parts of student thinking that may be correct, sometimes leading students to a new idea and solutions that are correct. Fostering Engagement Administrators Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

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