The document summarizes the key aspects of the Common Core State Standards for mathematics. It describes the development and adoption process, benefits for states, characteristics of the standards, and their focus on coherence, clarity, and rigor. It also provides examples of the mathematical practices and standards format for different grade levels.

1. The Common Core State Standards August 2010

2. Common Core Development Initially 48 states and three territories signed on Final Standards released June 2, 2010, and can be downloaded at www.corestandards.org As of August 10, 2010, 32 states had officially adopted Adoption required for Race to the Top funds

3. Common Core Development 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 core in English language arts and mathematics. States may add additional standards.

4. Benefits for States and Districts Allows collaborative professional development to be based on best practices Allows the development of common assessments and other tools Enables comparison of policies and achievement across states and districts Creates potential for collaborative groups to get more mileage from: Curriculum development, assessment, and professional development

5. Characteristics 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, so that all students are prepared 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. Research based.

6. Intent of the Common Core The same goals for all students Coherence Focus Clarity and specificity

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

8. Focus Key ideas, understandings, and skills are identified Deep learning of concepts is stressed That is, adequate time is devoted to a topic and learning it well. This counters the “mile wide, inch deep” criticism leveled at most current U.S. standards.

9. Clarity and Specificity Skills and concepts are clearly defined. An ability to apply concepts and skills to new situations is expected.

10. CCSS Mathematical Practices The Common Core proposes a set of Mathematical Practices that all teachers should develop in their students. These practices are similar to the mathematical processes that NCTM addresses in the Process Standards in Principles and Standards for School Mathematics .

11. CCSS Mathematical Practices 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. Common Core Format High School Conceptual Category Domain Cluster Standards K-8 Grade Domain Cluster Standards (No pre-K Common Core Standards)

13. Grade Level Overview Mathematics | Grade 1 In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes. (1) Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with

14. Grade Level Overview Mathematics | Grade 1 In Grade 1, instructional time should focus on four critical areas: (1) developing understanding of addition, subtraction, and strategies for addition and subtraction within 20; (2) developing understanding of whole number relationships and place value, including grouping in tens and ones; (3) developing understanding of linear measurement and measuring lengths as iterating length units; and (4) reasoning about attributes of, and composing and decomposing geometric shapes. (1) Students develop strategies for adding and subtracting whole numbers based on their prior work with small numbers. They use a variety of models, including discrete objects and length-based models (e.g., cubes connected to form lengths), to model add-to, take-from, put-together, take-apart, and compare situations to develop meaning for the operations of addition and subtraction, and to develop strategies to solve arithmetic problems with these operations. Students understand connections between counting and addition and subtraction Cross- Cutting Themes Critical Areas

15. Format of K-8 Standards Operations and Algebraic Thinking 1.OA Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Understand and apply properties of operations and the relationship between addition and subtraction. 3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Grade Level Domain

16. Format of K-8 Standards Operations and Algebraic Thinking 1.OA Represent and solve problems involving addition and subtraction. 1. Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 2 2. Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Understand and apply properties of operations and the relationship between addition and subtraction. 3. Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) 4. Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by finding the number that makes 10 when added to 8. Standard Standard Cluster Cluster

17. 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

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

19. 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

20. Additional Information For grades preK-8, a model of implementation can be found in NCTM’s Curriculum Focal Points for Prekindergarten through Grade 8 Mathematics For the secondary level, please see NCTM’s Focus in High School Mathematics: Reasoning and Sense Making www.nctm.org/cfp www.nctm.org/FHSM

21. Acknowledgments Thanks to the Ohio Department of Education and Eric Milou of Rowan University for providing content and assistance for this presentation