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Math Common Core Standards Jennie Winters Lake County ROE

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Focus for Today 1.3 types of change 2.Standards for Mathematical Practice 3.Focus, Coherence & Rigor 4.Assessment 5.Curriculum: Quality Units/Lessons 6.Q & A

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Common Core Implementation Curricular Change Instructional Change Assessment Change

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Practice Standards Make sense persevere 1. Make sense of problems and persevere in solving them.

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Practice Standards Reason 2. Reason abstractly and quantitatively.

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Practice Standards arguments critique 3. Construct viable arguments and critique the reasoning of others.

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Practice Standards Model 4. Model with mathematics.

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Practice Standards tools 5. Use appropriate tools strategically.

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Practice Standards precision. 6. Attend to precision.

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Practice Standards structure 7. Look for and make use of structure.

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Practice Standards repeated reasoning 8. Look for and express regularity in repeated reasoning.

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Modes of Representation (Lesh, Post, & Behr, 1987) Pictures Manipulative Models Written Symbols Real-world Situations Oral/Written Language Oral/Written Language

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Modes of Representation Manipulative/ Tools Picture/Graph Table/Chart Symbols (Equations, etc.) Oral & Written Language Real-Life Situations

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14 The CCSS Requires Three Shifts in Mathematics 1.Focus: Focus strongly where the standards focus. 2.Coherence: Think across grades, and link to major topics 3.Rigor: In major topics, pursue conceptual understanding, procedural skill and fluency, and application

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Rigor 15 The CCSSM require a balance of: Solid conceptual understanding Procedural skill and fluency Application of skills in problem solving situations Pursuit of all threes requires equal intensity in time, activities, and resources.

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Solid Conceptual Understanding Teach more than how to get the answer and instead support students ability to access concepts from a number of perspectives Students are able to see math as more than a set of mnemonics or discrete procedures Conceptual understanding supports the other aspects of rigor (fluency and application) 16

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Fluency The standards require speed and accuracy in calculation. Teachers structure class time and/or homework time for students to practice core functions such as single-digit multiplication so that they are more able to understand and manipulate more complex concepts 17

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18 Required Fluencies in K-6 GradeStandardRequired Fluency KK.OA.5Add/subtract within 5 11.OA.6Add/subtract within OA.2 2.NBT.5 Add/subtract within 20 (know single-digit sums from memory) Add/subtract within OA.7 3.NBT.2 Multiply/divide within 100 (know single-digit products from memory) Add/subtract within NBT.4Add/subtract within 1,000, NBT.5Multi-digit multiplication 66.NS.2,3 Multi-digit division Multi-digit decimal operations

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Application Students can use appropriate concepts and procedures for application even when not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in real world situations, recognizing this means different things in K-5, 6-8, and HS. Teachers in content areas outside of math, particularly science, ensure that students are using grade-level-appropriate math to make meaning of and access science content. 19

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Assessment Conceptual Assessment –Includes Observational Tools

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2 nd Grade Example Students each create their own paper airplane and take turns flying them. They use a tape measure to find the distance each has flown to the nearest foot. What concepts are being assessed?

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Assessment Conceptual Assessment –Includes Observational Tools Procedural Skill & Fluency Assessment –Includes Extended Response

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Assessment Conceptual Assessment –Includes Observational Tools Procedural Skill & Fluency Assessment –Includes Extended Response Application –Includes Rich Tasks

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Curriculum Sequence of units (Coherence) Prioritization Sequence within units: –Conceptual before procedural –Application throughout

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The Tri-State Quality Review Rubric Criteria

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4 Dimensions Alignment to the Rigor of the CCSS Key Areas of Focus in the CCSS Instructional Supports Assessment

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1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: Targets a set of grade level mathematics standard(s) at the level of rigor in the CCSS for teaching & learning

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1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: Standards for Mathematical Practice that are central to the unit are identified, handled in a grade- appropriate way, and well connected to the content being addressed.

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1 – Alignment to the Rigor of the CCSS The unit aligns with the letter and spirit of the CCSS: Presents a balance of mathematical procedures and deeper conceptual understanding inherent in the CCSS

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2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. Focus Centers on the concepts, foundational knowledge and level of rigor that are prioritized in the standards.

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2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. Coherence Makes connections and provides opportunities for students to transfer knowledge and skills within and across domains and learning progressions.

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2-Key Areas of Focus in the CCSS The unit reflects evidence of key shifts that are reflected in the CCSS. Rigor Requires students to engage with an demonstrate challenging mathematics in the following ways:

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2-Key Areas of Focus in the CCSS Conceptual Understanding Requires students to demonstrate conceptual understanding through complex problem solving, in addition to writing and speaking about their understanding.

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2-Key Areas of Focus in the CCSS Procedural Skill & Fluency Expects, supports and provides guidelines for procedural skill and fluency with core calculations, mathematical procedures and strategies (when called for in the standards for the grade) to be performed quickly and accurately.

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2-Key Areas of Focus in the CCSS Application Provides opportunities for students to independently apply mathematical concepts in real-world situations and problem solve with persistence, choosing and applying an appropriate model or strategy to new situations.

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3 – Instructional Supports The unit is responsive to varied student needs: Includes clear and sufficient guidance to support teaching and learning of the targeted standards, including, when appropriate, the use of technology and media.

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3 – Instructional Supports The unit is responsive to varied student needs: Uses and encourages precise and accurate mathematics, academic language, terminology, and concrete or abstract representations (e.g. pictures, symbols, expressions, equations, graphics, models) in the discipline.

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3 – Instructional Supports The unit is responsive to varied student needs: Engages students in productive struggle through relevant, thought- provoking questions, problems, and tasks that stimulate interest and elicit mathematical thinking.

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3 – Instructional Supports The unit is responsive to varied student needs: Addresses instructional expectations and is easy to understand and use.

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3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: Supports diverse cultural and linguistic backgrounds, interests and styles.

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3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: Provides extra supports for students working below grade level.

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3 – Instructional Supports Provides appropriate level and type of scaffolding, differentiation, intervention, and support for a broad range of learners: Provides extensions for students with high interest or working above grade level.

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3 – Instructional Supports Recommend and facilitate a mix of instructional approaches for a variety of learners such as using multiple representations, (including models) using a range of questions, checking for understanding, flexible grouping, pair-share, etc.

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3 – Instructional Supports Gradually remove supports, requiring students to demonstrate their mathematical understanding independently.

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3 – Instructional Supports Demonstrate an effective sequence and a progression of learning where the concepts or skills advance and deepen over time.

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3 – Instructional Supports Expects, supports, and provides guidelines for procedural skill and fluency with core calculations and mathematical procedures (when called for in the standards for the grade) to be performed quickly and accurately.

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4 – Assessment The lesson/unit regularly assesses whether students are mastering standards-based content and skills: Is designed to elicit direct, observable evidence of the degree to which a student can independently demonstrate the targeted CCSS.**

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4 – Assessment The lesson/unit regularly assesses whether students are mastering standards-based content and skills: Assesses student proficiency using methods that are accessible and unbiased, including the use of grade level language in student prompts.**

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4 – Assessment The lesson/unit regularly assesses whether students are mastering standards-based content and skills: Includes aligned rubrics, answer keys, and scoring guidelines that provide sufficient guidance for interpreting student performance.

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4 – Assessment The lesson/unit regularly assesses whether students are mastering standards-based content and skills: Use varied modes of curriculum embedded assessments that may include pre-, formative, summative and self-assessment measures.

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Questions and (Hopefully) Answers

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