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

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CSD Foundations in CCSS Part 2 The Standards of Math Practice

Standards for Mathematical Practice
Proficiencies Adaptive Reasoning The capacity for logical thought, reflection, explanation, and justification. Strategic Competence Conceptual Understanding Procedural Fluency Productive Disposition Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Strategic Competence – ability to formulate, represent, and solve mathematical problems Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ( this includes have recall of basic facts but goes beyond to also include knowing when a calculator is most efficient, knowing when a remainder is important, having good number –whole number and fraction sense) Productive Disposition – habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy.

The ability to formulate, represent, and solve problems.
Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence The ability to formulate, represent, and solve problems. Conceptual Understanding Procedural Fluency Productive Disposition Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Strategic Competence – ability to formulate, represent, and solve mathematical problems Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ( this includes have recall of basic facts but goes beyond to also include knowing when a calculator is most efficient, knowing when a remainder is important, having good number –whole number and fraction sense) Productive Disposition – habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy.

The comprehension of mathematical concepts, operation, and relations.
Standards for Mathematical Practice Proficiencies Adaptive Reasoning Strategic Competence Conceptual Understanding The comprehension of mathematical concepts, operation, and relations. Procedural Fluency Productive Disposition Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Strategic Competence – ability to formulate, represent, and solve mathematical problems Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ( this includes have recall of basic facts but goes beyond to also include knowing when a calculator is most efficient, knowing when a remainder is important, having good number –whole number and fraction sense) Productive Disposition – habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy.

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 Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Strategic Competence – ability to formulate, represent, and solve mathematical problems Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ( this includes have recall of basic facts but goes beyond to also include knowing when a calculator is most efficient, knowing when a remainder is important, having good number –whole number and fraction sense) Productive Disposition – habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy.

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 one’s own efficacy. Adaptive Reasoning – capacity for logical thought, reflection, explanation, and justification Strategic Competence – ability to formulate, represent, and solve mathematical problems Conceptual Understanding – comprehension of mathematical concepts, operations, and relations Procedural Fluency – skill in carrying out procedures flexibly, accurately, efficiently, and appropriately ( this includes have recall of basic facts but goes beyond to also include knowing when a calculator is most efficient, knowing when a remainder is important, having good number –whole number and fraction sense) Productive Disposition – habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence and one’s own efficacy.

Standards for Mathematical Practice
Reasoning and Explaining Modeling and Using Tools MPs 1 & 6 are the overarching habits of mind of a productive mathematical thinker. MPs 2 & 3 relate to reasoning and explaining. MPs 4 & 5 relate to modeling and using tools. MPs 7 & 8 relate to seeing structure and generalizing. Seeing Structure and Generalizing

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

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

#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?” MPs 1… overarching habit of mind of a productive mathematical thinker. The adaptive reasoning and strategic competence proficiency that we spoke of earlier are evidenced here. Gather Information Make a plan Anticipate possible solutions Continuously evaluate progress Check results Question sense of solutions

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

#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:

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

#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 MPs 6 are the overarching habits of mind of a productive mathematical thinker. The Adding it Up proficiencies relate to this MP Strategic Competence Conceptual Understanding Procedural Fluency Comic:

#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 P x x x x -- Ellen Whitesides (University of Arizona, Institute for Mathematics and Education). Presentation to the CCSSO Mathematics SCASS, November 2011.

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

#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).

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

Discovery Education Go to Discovery Education –it is under

#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.

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

#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

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

#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.

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

#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.

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

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

P SMP handout Lesson planning template for the SMPs

Mathematical Practices Posters

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

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

We laminate our lives to reuse next year.

Video –Expanded Learning
EVALUATION FORM

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 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 = , 1.10, 2.3, 3.1, 3.5 – 3.8 (Provide the handout for participants.) These examples illustrate some of the Standards for Mathematical Practice and some of the elements of a classroom—whether it’s elementary, middle, or high school—in which high-quality mathematics instruction and learning are taking place. Although the content changes as students progress through the grades, these statements for teachers and students are common characteristics that you should see in any mathematics classroom where there are connections between the content and practices. (Allow participants 3 or 4 minutes to complete then project the next slide with the answers.) Administrator’s Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

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 don’t 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) The very important role of the teacher plays is evident. While giving students plenty of opportunities to think for themselves and come up with their own solutions, the teacher is crucial to facilitating and guiding the mathematical tasks and conversations. Administrator’s Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

Fostering Engagement 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. Achieving this kind of classroom requires much skill and judgment of the teacher, as well as a solid understanding of the mathematics content. WE have much to share today and throughout the series related to both content and practices. Please do not hesitate to ask questions and ask for clarifications along the way…  Administrator’s Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

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