The Common Core State Standards for Mathematics

1. The Common Core State Standards for Mathematics Grades4–5

2. The Development of the CCSS • Sponsored by the Council of Chief State School Officers (CCSS) and the National Governors Association (NGA) • Written by a small group of authors from Sept 2009 – June 2010 • NCTM among the groups that provided feedback and review as part of public review process

3. Potential Benefits for States and Districts • Creates potential for collaborative groups to get more mileage from: • Curriculum development, assessment, and professional development • Encourages collaborative professional development to be based on best practices • Allows for the development of cross-state formative and summative assessment tools

4. Common Core Development • Initially 48 states and three territories signed on. • As of March 1, 2011, 42 states, District of Columbia, and Virgin Islands have adopted. • Final Standards released June 2, 2010 can be downloaded at www.corestandards.org. • Adoption is required for Race to the Top funds.

5. Common Core Implementation • Each state adopting the Common Core either directly or by fully aligning its state standards may do so in accordance with current state timelines for standards adoption, not to exceed three (3) years. • States that choose to align their standards with the Common Core Standards accept 100% of the corein English language arts and mathematics. States may add additional standards.

6. Characteristics Claimed by CCSS (compared to most State Standards) • Fewer and more rigorous. The goal was increased clarity. • Aligned with college and career expectations – prepare all students for success on graduating from high school. • Internationally benchmarked, to prepare all students for succeeding in our global economy and society. • Includes rigorous content and application of higher-order skills. • Builds on strengths and lessons of current state standards and on NCTM’s documents: Curriculum Focal Points, PSSM, and Focus on Reasoning and Sense Making • Research based

7. Stated Intentions of the Common Core • Coherence • Focus • Clarity and specificity • The same goals for all students

8. Coherence According to CCSS • Articulated progressions of topics and performances that are developmental and connected to other progressions • Conceptual understanding and procedural skills stressed equally NCTM states that coherence means that instruction, assessment, and curriculum are aligned.

9. Focus According to CCSS • Key ideas, understandings, and skills are identified. • Deep learning of concepts is emphasized. • That is, adequate time is devoted to a topic to counter the “mile wide, inch deep” criticism leveled at most current U.S. standards.

10. CCSS Standards for Mathematical Practice The Common Core proposes a set of Standards for Mathematical Practice that all teachers should develop in their students. The Mathematical Practice Standards in the CCSS resonate well with the NCTM Process Standards in Principles and Standards for School Mathematics.

11. CCSS Standards for Mathematical Practice • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

12. NCTM Process Standards • Problem Solving is an integral part of mathematics learning. • Reasoning and Proof are ways of expressing justification. • Communication is an essential part of mathematics education. • Connections are critical in mathematics, both across mathematical topics and to contexts outside mathematics. • Representations of mathematical ideas are fundamental to enhancing mathematical understanding.

13. NCTM Process Standards and theCCSS Mathematical Practice Standards

14. Clarity and Specificity for CCSS • Skills and concepts are clearly defined. • An ability to apply concepts and skills to new situations is expected.

15. Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (No pre-K Common Core Standards)

16. Common Core - Domain • Overarching “big ideas” that connect topics across the grades • Descriptions of the mathematical content to be learned, elaborated through clusters and standards

17. Common Core - Clusters • May appear in multiple grade levels with increasing developmental standards as the grade levels progress • Indicate WHAT students should know and be able to do at each grade level • Reflect both mathematical understandings and skills, which are equally important

18. Common Core - Standards • Content statements • Progressions of increasing complexity from grade to grade

19. CCSSM and NCTM Focal Points:Differences in Format CCSSM NCTM Focal Points Three focal points per grade level Connections to other strands • Five Domains • Clusters of standards

20. CCSSM Domains CCSSM - Grade 4 1. Operations and Algebraic Thinking 2. Number and Operations in Base Ten 3. Number and Operations--Fractions 4. Measurement and Data 5. Geometry CCSSM - Grade 5 1. Operations and Algebraic Thinking 2. Number and Operations in Base Ten 3. Number and Operations--Fractions 4. Measurement and Data 5. Geometry

21. Domain 1: Operations and Algebraic Thinking CCSS - Grade 4 NCTM Focal Points - Grade 4 Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication • Use the four operations with whole numbers to solve problems. • Gain familiarity with factors and multiples • Generate and analyze patterns.

22. Domain 1: Operations and Algebraic Thinking CCSS - Grade 5 NCTM Focal Points - Grade 5 Students use patterns, models, and relationships as contexts from which to write and solve simple equations and inequalities. • Write and interpret numerical expressions. • Analyze patterns and relationships.

23. Domain 2: Number and Operations in Base Ten CCSS - Grade 4 NCTM Focal Points - Grade 4 Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication • Generalize place value understanding for multi-digit whole numbers. • Use place value understanding and properties of operations to perform multi-digit arithmetic.

24. Domain 2: Number and Operations in Base Ten CCSS - Grade 5 NCTM Focal Points - Grade 5 Developing understanding of and fluency with whole number division. • Understand the place value system. • Perform operations with multi-digit whole numbers and with decimals to hundredths.

25. Domain 3: Number and Operations – Fractions CCSS - Grade 4 NCTM Focal Points - Grade 4 Developing understanding of decimals, including connections between fractions and decimals. • Extend understanding of fraction equivalence and ordering. • Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. • Understand decimal notation for fractions, and compare decimal fractions.

26. Domain 3 Number and Operations – Fractions CCSS - Grade 5 NCTM Focal Points - Grade 5 Developing understanding of and fluency with addition and subtraction of fractions and decimals. • Use equivalent fractions as a strategy to add and subtract fractions. • Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

27. Domain 4:Measurement and Data CCSS- Grade 4 NCTM Focal Points – Grade 4 Students measure and classify angles. • Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit. • Represent and interpret data. • Geometry measurement: understand concepts of angle and measure angles.

28. Domain 4: Measurement and Data CCSS- Grade 5 NCTM Focal Points – Grade 5 Describing and analyzing properties of three-dimensional shapes, including volume and surface area. Students apply all whole number operations as they construct and analyze double bar and line graphs. • Convert like measurement units within a given measurement system. • Represent and interpret data. • Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

29. Domain 5:Geometry CCSS - Grade 4 NCTM Focal Points - Grade 4 As part of understanding two-dimensional shapes, students measure and classify angles. • Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

30. Domain 5: Geometry CCSS - Grade 5 NCTM Focal Points - Grade 5 Students use ordered pairs on coordinate grids. • Graph points on the coordinate plane to solve real-world and mathematical problems. • Classify two-dimensional figures into categories based on their properties.

31. Implementation Support for Teachers from NCTM Making It Happen: A Guide to Interpretingand Implementing the Common Core State Standards for Mathematics

32. Making It Happen Includes • How the content of CCSSM fits with NCTM’s Standards documents—including a road map to NCTM’s resources • A deep analysis of the connections between NCTM’s Process Standards and the CCSS Standards for Mathematical Practice • Examples of using NCTM resources to interpret and implement CCSS

33. Implementation Support for Teachers from NCTM Possible actions under current discussion • Development of resource toolkit linked to a mobile or e-conference package • A focus on Professional Development with respect to both content and mathematical processes • Grade band specific PowerPoints available on the NCTM Web site

34. NCTM Standards and CCSS The pre-eminent message from both these sets of standards is, and for NCTM always has been, the importance of nurturing the mathematical thinking and reasoning processes as set forth in the NCTM Process Standards, and in the CCSS Standards for Mathematical Practice. No collection of specific standards bullets will hold together without interweaving mathematical processes for our students.