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Overview 1 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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General Content Overview ◦ Focus and Coherence ◦ Similarities ◦ Shifts ◦ Structure/Organization ◦ Activity Objectives 2 Mathematical Practices Overview ◦ Purpose ◦ Structure ◦ 8 Practices ◦ Standards Alignment ◦ Activity

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3 Avoid the problem of “mile wide and an inch deep” Recognize that “fewer standards” are no substitute for focused standards Aim for clarity and specificity © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Topics and performances are logical over time Based on learning progressions research on how students learn Reflect hierarchical nature of the content Evolve from particulars to deeper structures 4 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Define what students should understand and be able to do in their study of mathematics ◦ Is the ability to justify appropriate to student’s math maturity ◦ Understanding and procedural skill are equally important and can be assessed using tasks of sufficient richness Are internationally benchmarked ◦ Reflect rigor, focus and coherence of standards in top-performing countries 5 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Do: ◦ Set grade-level standards K-8 ◦ Identify standards for Algebra 1 ◦ Provide conceptual cluster standards in high school ◦ Provide clear signposts along the way toward the goal of college and career readiness for all students 6 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Do not: ◦ Define intervention methods or materials ◦ Define the full range of supports for English learners, students with special needs and students who are well above or below grade level expectations ◦ Dictate curriculum or teaching methods 7 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Mathematical Content (different at each grade level) Mathematical Practice (recurring throughout the grades) 8 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Mathematical Content 9

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Common Core State Standards for CA DOMAINS California Standards Grades K-7 STRANDS K-5 Counting and Cardinality (K only) Operations and Algebraic Thinking Number and Operations in Base 10 Number and Operations-Fractions Measurement and Data 6-8 Ratio and Proportional Relationships (grade 6-7) The Number System Expressions and Equations Functions (Grade 8) Geometry Statistics and probability Number Sense Algebra and Functions Measurement and Geometry Statistics, Data Analysis and Probability Mathematical Reasoning Mathematical Content Comparison 10 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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11 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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12 © 2013 Actions Learning Systems, Inc. K12345678 Counting & Cardinality x Operations & Algebraic Thinking xxxxxX Number & Base Ten xxxxXx Numbers & Operations- Fractions xxX Ratios & Proportional Relationships xx The Number system xxx Expressions & Equation xxX Functions x Geometry xxxxxxxxX Measurement & Data xxxxxX Statistics & Probability xxx

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13 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Grade Shifts: Examples Developed by SCFIRD Concept1997 StandardsCCCS Compose simple shapes to form larger shapes (e.g., 2 triangles to form a rectangle) Grade 2 K Introduction to Probability Grade 3 Grade 7 Introduction of fractions as numbers Grade 2 Grade 3 Add and subtract simple fractions Grade 3 Grade 4 Introduction of integersGrade 4 Grade 6 14 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Teaching Algebra and Functions https://www.teachingchannel.org/videos/alg ebra-lesson-planning Example of Common Core Math in an Intermediate Classroom © 2011 California County Superintendents Educational Services Association Mathematics General Overview 15

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Overview page ◦ Lists domains, clusters and mathematical practices Domains ◦ Larger groups of related standards. Standards from different domains may be closely related. Standards-by grade level ◦ Defines what students should understand and be able to do Clusters ◦ Groups of related standards. Standards from different clusters may be closely related 16 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Reading the Standards 18 Standards-by grade level: Defines what students should understand and be able to do Clusters: Groups of related standards. Standards from different clusters may be closely related Domains: Larger groups of related standards. Standards from different domains may be closely related. Domain Standard CLUSTERCLUSTER Operations and Algebraic Thinking 5.OA Write and interpret numerical expressions. 1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 2. Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Analyze patterns and relationships. 3. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so. Number and Operations in Base Ten 5.

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Label the Domain, Standards, and Clusters for Grade 5 Common Core Mathematics. Circle, underline or highlight key academic vocabulary within the standards and compare to DOK chart. Go to U Drive, Curriculum, Common Core State Standards, Common Core Unpacked Math, k- 12_math_crosswalk pgs. 77-96. Using the CCSS Math and the crosswalk, choose a standard and compare similarities and differences. Be prepared to discuss. Mathematical Content Activity 19

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Mathematical Practice 20

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Standards for Mathematical Practice ◦ Describe habits of mind of a mathematically expert student ◦ Relate to mathematical proficiency as defined by the California Framework ◦ Consistent throughout grade levels 21 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Problem Solving Computational & Procedural Skills DOING MATH Conceptual Understanding “WHERE” THE MATHEMATICS WORK “HOW” THE MATHEMATICS WORK “WHY” THE MATHEMATICS WORK 22 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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“ …describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high schools years.” 23 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

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Structuring the Standards for Mat hematical Practice 24 1. Make sense of problems and persevere in solving them. 6. Attend to precision 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of other Reasoning and explaining 4.Model with mathematics 5.Use appropriate tools strategies Modeling and using tools 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning Seeing structure and generalizing

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1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning 4. Model with mathematics 25

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5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for an express regularity in repeated reasoning Standards for Mathematical Practice Mathematically proficient students: 26

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Example of Mathematical Practices in the 5 th Grade Classroom: Proportions and Ratios http://www.insidemathematics.org/index.ph p/exemplary-lessons-integrating-practice- standards Inside Mathematics Video © 2011 California County Superintendents Educational Services Association Mathematics General Overview 27

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Activity #1 ◦ Label the Mathematical Practices that align with specific standards. ◦ Choose a standard and its Mathematical Practice(s) ◦ Go to U Drive, Curriculum, Common Core State Standards, Common Core Unpacked Math, Find your grade level ◦ Brain storm how you can integrate the Mathematical Practice with the Common Core Standard you chose. ◦ Be prepared to share. Mathematical Practices Aligned to Common Core Standards 28

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Activity #2 ◦ Choose a standard and its Mathematical Practice(s) ◦ Go to U Drive, Curriculum, Common Core State Standards, Common Core Unpacked Math, Find CCSSMathTasks_Grade5 ◦ Review a performance task and brainstorm how you might be able to integrate one into a lesson. ◦ Be prepared to share. Mathematical Practices Aligned to Common Core Standards © 2011 California County Superintendents Educational Services Association Mathematics General Overview 29

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SBAC Math Test http://www.smarterbalanced.org/practice-test/ SCROLL DOWN AND CLICK ON PRACTICE TEST 30

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