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

B EYOND R IGHT A NSWERS : M ATH AND THE CCSS Teaching Channel video 2

3 © 2011 Caliornia County Superintendents Educational Services Association Mathematics General Overview 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

Topics and performances are logical over time Based on learning progression 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

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

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

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

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

9 © 2013 Actions Learning Systems, Inc. K 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

© 2011 California County Superintendents Educational Services Association Mathematics General Overview 10

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 Additional standard language or whole standards Bolded and underlined Added to maintain rigor of California expectations 11 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

12 Grade 3 Overview Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. Understand properties of multiplication and the relationship between multiplication and division. Multiply and divide within 100. Solve problems involving the four operations, and identify and Explain patterns in arithmetic. Number and Operations in Base Ten Use place value understanding and properties of operations to perform multi-digit arithmetic. Number and Operations - Fractions Develop understanding of fractions as numbers. Measurement and Data Solve problems involving measurement and estimation of Intervals of time, liquid volumes, and masses of objects. Geometry Reason with shapes and their attributes. Mathematical Practices 1. Make sense of problems and persevere 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.

R EADING THE S TANDARDS 13 © 2011 California County Superintendents Educational Services Association Mathematics General Overview 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. Ratios and Proportional Relationships 3.RP Domain Understand ratio concepts and use ratio reasoning to solve problems. 1. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” 2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”1 Standard CLUSTERCLUSTER

G RADE S HIFTS : E XAMPLES 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 Developed by SCFIRD

M ATHEMATICAL C ONTENT A CTIVITY Discuss the standards which have been added or deleted from the 3 rd grade. Discuss the implications for teaching mathematics. Using the key vocabulary page, look through the standards and highlight where the key terms are found. 15

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 16 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

Problem Solving Computational & Procedural Skills DOING MATH Conceptual Understanding “WHERE” THE MATHEMATICS WORK “HOW” THE MATHEMATICS WORK “WHY” THE MATHEMATICS WORK 17 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

“ …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.” 18 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

S TRUCTURING THE S TANDARDS FOR M AT HEMATICAL P RACTICE 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 California County Superintendents Educational Services Association Mathematics General Overview

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 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 20 © 2011 California County Superintendents Educational Services Association Mathematics General Overview

M ATHEMATICAL P RACTICES A LIGNED TO C OMMON C ORE S TANDARDS Activity Look at the articulation of mathematical practices of grades below and above. How do the practices progress? What are the implications for teaching? 21

R ESOURCES Tulare County Office of Education – Common Core State Standards (mathematics – resources) Common Core Support Tools – Public Schools of North Carolina (unpacking standards) Arizona’s Common Core State Standards for Mathematics Illinois State Board of Education 22

C LASSROOM L ESSON V IDEOS 23