The Common Core State Standards for Mathematics Transitioning to the Common Core

K-8 Content Standards Grade Domain Cluster Standard

K-8 Grade Level Overview Critical Areas – similar to NCTM’s Curriculum Focal Points

Format of K-8 Standards Grade Level DomainDomain

Format of K-8 StandardsClusterCluster ClusterCluster StandardStandard StandardStandard

DomainK12345 Counting and Cardinality (CC) Operations and Algebraic Thinking (OA) Number and Operations in Base Ten (NBT) Measurement and Data (MD) Geometry (G) Numbers and Operations- Fractions (NF) Domains

Domain678 Ratios and Proportional Relationships (RP) The Number System (NS) Expressions and Equations (EE) Geometry (G) Statistics and Probability (SP) Functions (F) Domains

High School Conceptual Categories The big ideas that connect mathematics across high school – such as Functions or Probability and Statistics A progression of increasing complexity Description of mathematical content to be learned elaborated through domains, clusters, and standards

Number and Quantity Algebra Functions Geometry Statistics and Probability Modeling High School Conceptual Categories

Pathways Four model pathways: –Traditional Pathway (Algebra 1, Geometry, Algebra 2) –Integrated Pathway –Compacted Traditional Pathway* –Compacted Integrated Pathway* *7 th, 8 th, and Algebra 1 standards covered in 2 years See CCSSM APPENDIX A for course descriptions for both pathways.

8 CCSS 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.

SMARTER Balanced Assessment Consortium System Highlights

Assessment Design The Consortium will provide the following by the school year: 3. Formative tools and resources 4. Responsible flexibility 5. Distributed summative assessment a. Content clusters throughout a course b. Most appropriate time for each student c. Scores rolled up Smarter Balanced Assessment Consortium

Link to Practice Standards Four Claims Used in Draft 2 Test Specifications Claim 1 ≈ 40% of assessment Claim 2 ≈ 20% of assessment Claim 3 ≈ 20% of assessment Claim 4 ≈ 20% of assessment

SHIFT #1: Focus Similar to the Oregon standards in Mathematics, the intent of the CCSSM is to narrowly and deeply focus the time and energy spent in the math classroom. The CCSSM emphasizes concepts prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.

The Three-Legged Stool In order to focus on content, you must teach to address all three legs of mathematical learning: Conceptual Understanding Computational Fluency Problem-Solving

Draft Emphases (Sample – Grade 6) Ratios and Proportional Relationships [m] Understand ratio concepts and use ratio reasoning to solve problems. The Number System [m] Apply and extend previous understandings of multiplication and division to divide fractions by fractions. [a] Compute fluently with multi-digit numbers and find common factors and multiples. [m] Apply and extend previous understandings of numbers to the system of rational numbers. Expressions and Equations [m] Apply and extend previous understandings of arithmetic to algebraic expressions. [m] Reason about and solve one-variable equations and inequalities. [m] Represent and analyze quantitative relationships between dependent and independent variables Geometry [s] Solve real-world and mathematical problems involving area, surface area, and volume. Statistics and Probability [a] Develop understanding of statistical variability. [a] Summarize and describe distributions.

Activity: Focus (find a partner or small group at your grade level) Grades K-2 Read through the Critical Areas page of your standards Discuss with a partner how you could better address all three legs of the “mathematics” stool in these areas Grades 3-HS Pick up the appropriate Emphases page from the front Look at the “m” clusters and discuss how you could better address all three legs of the “mathematics” stool in these areas

Deep conceptual understanding of core content at each grade is critical for student success in subsequent years. Each standard is not a new event, but an extension of previous learning. For example, fractions and multiplication build across grade levels and students can scaffold new understanding onto foundations built in previous years. SHIFT #2: Coherence

Activity: Coherence (with same partner or small group at your grade level) Grades K-2 Look at the standards not in your critical areas (may fall in the same domain but be listed at the end) How are these connecting to your grade level while introducing or reinforcing other grade level skills? Grades 3-8 Look at the “s” and “a” clusters. How are these connecting to your grade level while introducing or reinforcing other grade level skills?

Activity: Coherence (Cont) (with same partner or small group at your grade level) High School Only your major emphases are listed on the Emphases handout. Coherence may come from connecting and reinforcing previous grade level standards. How do the additional and supporting (non-major) standards fit into your program(s)?

Shift #4: Modeling Modeling links classroom mathematics and statistics to everyday life, work, and decision-making – Choose and use appropriate mathematics to analyze situations – Better understanding real-world scenarios involving math Teachers at all grade levels should identify opportunities for students to apply math concepts in “real world” situations.

Activity: Modeling 1. Locate your goldenrod stations activity template. 2. Visit between 4-6 stations.  Pink Cards = Elementary Content  Blue Cards = Middle/High School Content 3.While visiting stations, have others sign off on the correctness of your answer. Nobody can sign your paper more than twice. 4. When finished, return to your seat and answer the two questions at the bottom of the page.

Performance Task Choose a new partner or small group: Elementary or Secondary 1.Pick up the appropriate performance task up front. Options: Elementary (4 th Grade) or High School 2.Understand purpose and placement of task in classroom instruction and assessment. 3.Read/Attempt the task. 4.Discuss implications for classroom instruction.

Contact Information Shannon McCaw, SMc Curriculum