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October 31, 2011 Deeper Dive into the “Core” Module B (Day 1): Unpacking Gr Math CCSS through “Rich” Lesson Activities/Tasks Teacher Trainers for Content Sessions: Frannie ApelDeborah Arrington Wendy BartlettGreg Fisher Stacy GoodsonRachel Kowalcheck Beth LaytonDenise Poore Fred Thompson K-12 Math Program Manager: Velvet M. Simington 9-12 Math Coach: Melisa Hanks

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Session Goals Review the Common Core State Standards for Mathematical Practice Review the structure of the CCSS for Gr. 9 – 12 Mathematics Understand certain critical ideas from CCSS for Gr. 9 – 12 Mathematics Explore rich tasks that lend themselves to the implementation of the CCSS for Gr. 9 – 12 Mathematics

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Norms & May the “ Horse ” Rest in Peace …. Courtesy & Respect Open mindset New ideas New information Professional conversations Deep thinking Active participation “Can-do” spirit… Collaboration

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1. a) How many Standards for Mathematical Practice are there in the new CCSS? Eight SMPs b) List them. 1. Make sense of problems and perserve 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.

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2. The NCSCOS uses different labels for various components of the standards. What is the CCSS equivalent for the following? GOAL Cluster StrandDomain OBJECTIVE Standard INDICATORS “Unpacking” documents

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3. a) How many conceptual categories are there in the High School CCSS? Six Conceptual Categories b) List them. Number and Quantity; Algebra; Functions; Modeling; Geometry; Statistics and Probability 4. What is unique about the “modeling” Conceptual Category? There is no list of standards for this category; it is integrated within the five remaining conceptual categories. It does not stand alone.

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5. Why are some standards labeled with a “+”? Standards labeled with a “+” indicate additional mathematics that students should learn in order to take advanced courses like AP Calculus, AP Statistics, or discrete mathematics. 6. a) How many model pathways are there in high school? Two model pathways b) List them. Traditional Pathway “International” Integrated Pathway

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7. What is in Appendix A? Appendix A contains model course pathways that include the organization of CCS standards to be taught in high school mathematics courses. It also contains pertinent information concerning middle school accelerated pathways and their associated standards. 8. What does the label F.IF.7 represent? HS Conceptual Category: Functions Domain: Interpreting Functions Standard #7

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9. What are an “Ah Ha” and an “Oh No” you have about the CCSS? _____________________________________

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Mathematical PracticesMathematical Content NumberMeasurementAlgebraGeometryProbability Data & Statistics Design of CCSS for K-12 Mathematics

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Standards for Mathematical Practice Carry across all grade levels (K-12) Describe habits of a mathematically proficient student Standards for Mathematical Content K-8 presented by grade level Organized into domains that progress over several grades Grade introductions give 2-4 focal points at each grade level High school standards presented by conceptual theme (Number & Quantity, Algebra, Functions, Modeling, Geometry, Statistics & Probability)

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Algebra Seeing Structure in Expressions A-SSE Interpret the structure of expressions. 1.Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r) n as the product of P and a factor not depending on P. 2.Use the structure of an expression to identify ways to rewrite it. For example, see x 4 – y 4 as (x 2 ) 2 – (y 2 ) 2, thus recognizing it as a difference of squares that can be factored as (x 2 – y 2 )(x 2 + y 2 ). Write expressions in equivalent forms to solve problems. 3.Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15 t can be rewritten as (1.15 1/12 ) 12t ≈ t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. 4. Derive the formula for the sum of a finite geometric series (when the common ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Format of High School Standards Code Domain StandardA.SSE.2StandardA.SSE.2 Conceptual Category Modeling Symbol Cluster Heading

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CCSS Math Grades Grades 9 – 12 require the application of mathematics to real world situations and issues. Modeling is a requirement under the Standards for Mathematical Practice.

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YearStandards To Be TaughtStandards To Be Assessed NCSCOS NCSCOS CCSSCCSS* CCSSCCSS* CCSSCCSS** Common Core State Standards Adopted June, 2010 * - NC Tests & ** - National Tests

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Focus Key ideas, understandings, and skills are identified Deep learning of concepts is emphasized That is, time is spent on a topic and on learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

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CCSS WSFCS Math Wiki (K-12) To gain access to our WSFCS Math Wiki for CCSS Go to the above website. Click on Request access. Complete the steps on the webpage. Within hours, requestors should receive an that grants them access to the wiki.

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Standards for Mathematical Practice Reflection Why? Students who do not understand the mathematics cannot engage in the mathematical practices. They rely too much on memorizing procedures.

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

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Essential Question What kinds of tasks support the implementation of the CCSS in developing student practitioners of mathematics as they grow in mathematical maturity and expertise?

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