1. April 2011 Building a Deeper Understanding of the Common Core State Standards For Mathematics

2. The Common Core State Standards Initiative (CCSSI) is a state-led effort coordinated by the National Governors Association (NGA) and the Council of Chief State School Officers (CCSSO). www.corestandards.org/the-standards

3. Mission Statement The Common Core State Standards provide a consistent, clear understanding of what students are expected to learn, so teachers and parents know what they need to do to help them. The standards are designed to be robust and relevant to the real world, reflecting the knowledge and skills that our young people need for success in college and careers. With American students fully prepared for the future, our communities will be best positioned to compete successfully in the global economy. - Common Core State Standards Initiative

4. Common Core State Standards for Mathematics Standards for Mathematical Practices Standards for Mathematical Content CCSS Mathematics

5. Mathematical Understanding What does it mean for a student to have mathematical understanding?

6. Building from Past Work The Mathematical Practices rest on “important processes and proficiencies with longstanding importance in mathematics education” (CCSS, 2010, p. 6). –National Council of Teachers of Mathematics (NCTM, 2000) Process Standards –National Research Council (NRC, 2001) Strands of Mathematical Proficiency (Adding It Up)

7. Standards for Mathematical Practice 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.

8. Standards for Mathematical Practice “Acquiring proficiency…involves much more than memorizing.” (Adding It Up, National Research Council, 2001)

9. What do the Mathematical Practices look like in action?

11. Connecting Mathematical Practices to Content Standards “The Standards for Mathematical Content are a balanced combination of procedure and understanding. Expectations that begin with the word ‘understand’ are often especially good opportunities to connect the practices to the content.” - CCSS, Mathematics, p. 8

12. Domain Cluster Standards Content strand across grades: Operations & Algebraic Thinking “Big Idea” that groups together a set of related standards. Statements that define what students should understand and be able to do at a grade level. Standards for Mathematical Content

13. Standards for Mathematical Content: K-8 Domains K12345678 Counting and cardinality Operations and Algebraic Thinking Ratios and Proportional Relationships Number and Operations in Base Ten Number and Operations – Base Ten The Number System Number and Operations - Fractions Expressions and Equations Functions Measurement and Data Statistics and Probability Geometry

14. Standards for Mathematical Content: Learning Progressions “…the development of these Standards began with research-based learning progressions detailing what is known today about how students’ mathematical knowledge, skill, and understanding develop over time.” - CCSS Mathematics, p. 4

15. Standards for Mathematical Content: Learning Progressions K12345678 Counting and Cardinality Number and Operations in Base Ten Ratios and Proportional Relationships Number and Operations - Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Functions Measurement and DataStatistics and Probability Geometry Ohio Department of Education

16. Standards for Mathematical Content: Learning Progressions Fluently add and subtract within 5. K.OA.5 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. 1.OA.6 Know from memory all sums of two one-digit numbers. (basic addition facts) 2.OA.2

17. Arkansas Crosswalk The results of the analysis comparing the Common Core State Standards with the Arkansas Curriculum Frameworks for English language arts and mathematics are available at: http://ccssarkansas.pbworks.com/w/page /32131061/CCSS-Arkansas

18. Design for Mathematics Grade Level Narrative Grade Level Overview Mathematical Practice (in gray box) CCSS – Grade level standards

19. Standards for Mathematical Content: Kindergarten

20. Focus Areas (located in Narrative) Domains and Clusters (located in Overview) StandardsMathematical Practice (located in Overview) Representing and comparing whole numbers, initially with sets of objects Describing shapes and space

21. Grade K Overview

22. Standards for Mathematical Content: Kindergarten Focus Areas (located in Narrative) Domains and Clusters (located in Overview) StandardsMathematical Practice (located in Overview) Representing and comparing whole numbers, initially with sets of objects Counting & Cardinality * Know number names and the count sequence. Describing shapes and space Geometry Identify and describe shapes.

23. Standards for Mathematical Content: Kindergarten

24. Focus Areas (located in Narrative) Domains and Clusters (located in Overview) StandardsMathematical Practice (located in Overview) Representing and comparing whole numbers, initially with sets of objects Counting & Cardinality * Know number names and the count sequence. 1.Count to 100 by ones and by tens. 2.Count forward beginning from a given number within the known sequence (instead of having to begin at 1). 3.Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects). Describing shapes and space Geometry Identify and describe shapes. 1.Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. 2.Correctly name shapes regardless of their orientations or overall size. 3.Identify shapes as two- dimensional (lying in a plane, “flat”) or three-dimensional (“solid”).

25. Changes in Grades K-5 More Numeration and operation intensified as well as introduced earlier Early place value foundations in grade K Regrouping as composing / decomposing in grade 2 Decimals to hundredths in grade 4 All three types of measurement simultaneously – non ‐ standard, English and metric Emphasis on fractions as numbers Emphasis on number line as visualization /structure Less Backed off of algebraic patterns K ‐ 5 Backed off stats and probability in K ‐ 5 Delayed content like percent and ratio and proportion

26. Changes in Grades 6-8 Ratio and Proportion focused on in grade 6 –ratio, unit rates, converting measurement, tables of –values, graphing, missing value problems Percents introduced grade 6 Statistics is introduced in grade 6 –statistical variability (measures of central tendency, distributions, interquartile range, mean and absolute deviation, data shape) Rational numbers in grade 7 One ‐ third of algebra for all students is in grade 8

27. Time to Reflect

28. Common Core State Standards for Mathematics Standards for Mathematical Practices Standards for Mathematical Content (Traditional HS Pathway) CCSS Mathematics

29. Standards for Mathematical Practice 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.

30. CCSS – Math Learning Progressions K12345678HS Counting and Cardinality Number and Quantity Number and Operations in Base Ten Ratios and Proportional Relationships Number and Operations - Fractions The Number System Operations and Algebraic Thinking Expressions and Equations Algebra Functions Statistics and Probability Measurement and Data Geometry Ohio Department of Education

31. Mathematics HS Conceptual Categories and Domains Conceptual Categories Algebra I Domains Geometry Domains Algebra II Domains 4 th Year Courses Domains Number and Quantity The Real Number System * Quantities * The Complex Number System The Complex Number System * Vector Quantities and Matrices Algebra Seeing Structure in Expressions Creating Equations * Reasoning with Equations and Inequalities Seeing Structure in Expressions * Arithmetic with Polynomials & Rational Expressions Creating Equations * Creating Equations * Reasoning with Equations and Inequalities Functions * Interpreting Functions * Building Functions * Linear, Quadratic, and Exponential Models * Interpreting Functions * Building Functions * Linear, Quadratic, and Exponential Models * Trigonometric Functions * Interpreting Functions * Building Functions * Trigonometric Functions

32. CCSS Mathematics Traditional Pathway Conceptual Categories Algebra I Domains Geometry Domains Algebra II Domains 4 th Year Courses Domains Statistics and Probability Interpreting Categorical and Quantitative Data * Conditional Probability and the Rules of Probability * Using Probability to Make Decisions Interpreting Categorical and Quantitative Data * Making Inferences and Justifying Conclusions * Using Probability to Make Decisions Geometry * Congruence * Similarity, Right Triangles, and Trigonometry * Circles * Expressing Geometric Properties with Equations * Geometric Measurement and Dimension * Modeling with Geometry * Expressing Geometric Properties with Equations * Geometric Measurement and Dimension

33. Standards for Mathematical Content: Learning Progressions Apply and extend previous understandings of numbers to the system of rational numbers. (6 th Grade) Know that there are numbers that not rational, and approximate them by rational numbers. (8 th Grade) Perform arithmetic operations with complex numbers. (Algebra II)

34. http://ccssarkansas.pbworks.com/w/page/32131061/CCSS-Arkansas The results of the analysis comparing the Common Core State Standards with the Arkansas Curriculum Frameworks for English language arts and mathematics are available at: http://ccssarkansas.pbworks.com/w/page /32131061/CCSS-Arkansas

35. Mathematics High School Conceptual Categories Number and Quantity –N Algebra –A Functions –F Modeling – (across all conceptual categories) Modeling standards are distributed under the five major headings and are indicated with a (  ) symbol. Geometry –G Statistics and Probability –S

36. CCSS Mathematics: Design for Mathematics Grade Level Narrative Grade Level Overview Mathematical Practice (in gray box) CCSS – Grade level standards

37. Model Course Pathways for Mathematics Courses in higher level mathematics: Precalculus, Calculus (upon completion of Precalculus), Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or other courses to be designed at a later date, such as additional career technical courses. Algebra II Geometry Algebra I Pathway A Traditional in U.S. Mathematics IIIs III Mathematics II Mathematics I Pathway B International Integrated approach (typical outside of U.S.).

38. CCSS Traditional Pathway

42. High School All students must master topics traditionally from Algebra II or beyond –simple periodic functions –polynomials, –radicals –more probability and statistics (correlation, random processes) –introduced to mathematical modeling

43. “Standards and assessments are only the foundation upon which states will construct high-quality curriculum, professional development, and all the other pieces that will support teachers preparing to teach to these new standards and students learning at higher levels.” - Arne Duncan, Education Secretary, September 2010

44. Resources ADE http://ccssarkansas.pbworks.com/w/page/32131061/CCSS-Arkansas http://arkansased.org/educators/curriculum/common_core.html CCSS website http://www.corestandards.org/ Achieve, Inc. http://www.achieve.org/achievingcommoncore Education Service Centers’ state CCSS resource site http://web.me.com/acaciatc/UACC/Intro.html