California Common Core State Standards (CCSS) mathematics Overview

1. CaliforniaCommon Core State Standards(CCSS)mathematicsOverview Walter Lewis wlewis@icoe.org 760.312.6176

2. What is the timeline

3. Welcome /Outcomes /Agenda • Overview-What is the direction of Math Education? • Math CCSS • Standards for Mathematical Practice • Content Standards • Assessment/Consideration/Reflection Agenda

4. But First a Problem…

5. Max bought 2 items in a sale. One item was 10% off. One item was 20% off. Max says he saved 15% altogether. Is he right? Explain. SALE!

6. Max bought 2 items in a sale. One item was 10% off. One item was 20% off. Max says he saved 15% altogether. Is he right? Explain. SALE! (Seventh Grade-SBAC)

7. Wrap the Mummy Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide. Will one toilet roll be enough to wrap a person? Describe your reasoning as fully as possible. (You will need to estimate the average size of an adult person)

8. Wrap the Mummy (Seventh Grade-sbac) Pam is thirteen today. She is holding a party at which she plans to play the game 'Wrap the mummy'. In this game, players try to completely cover themselves with toilet paper. A roll of toilet paper contains 100 feet of paper, 4 inches wide. Will one toilet roll be enough to wrap a person? Describe your reasoning as fully as possible. (You will need to estimate the average size of an adult person)

9. The Perils and Promises of Discovery Learning What should mathematics instruction look like now…MARZANO’S analysis

10. Quality instruction Checking for Understanding T E C H N O L O G y 2 1 st C E N T U R Y L E A R N I N G g California Common Core State Standards

11. Common Core State Standards

13. Ensure that our students are… • meeting college and career expectations with text complexity increased K-12; • provided a vision of what it means to be an academically literate person in the twenty-first century; • prepared to succeed in our global economy and society; and • provided with rigorous content and applications of higher knowledge through higher order thinking skills. Why the Common Core State Standards?

14. Benefits of the CCSS Internationally benchmarked  Evidence and research-based  Expectations clear to students, parents, teachers, and the general public  Costs to the state reduced  Consistent expectations for all—not dependent on a zip code

15. Heart & Soul of CCSS ELA College and Career Readiness Standards Math Standards for Mathematical Practice

16. Standards for Mathematical Practice AND Content Standards MATHEMATICS INCLUDES TWO SETS OF STANDARDS:

17. Professor Jason Phil William Zimba Daro McCallum Ph.D. Authors for the standards…

18. Underlying Frameworks National Council of Teachers of Mathematics 5 ProcessStandards • Problem Solving • Reasoning and Proof • Communication • Connections • Representations NCTM (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

19. 1. Make sense of problems and persevere in solving them …start by explaining the meaning of a problem and looking for entry points to its solution 2. Reason abstractly and quantitatively …make sense of quantities and their relationships to problem situations 3. Construct viable arguments and critique the reasoning of others …understand and use stated assumptions, definitions, and previously established results in constructing arguments 4. Model with mathematics …can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace Standards for Mathematical Practices

20. 5. Use appropriate tools strategically …consider the available tools when solving a mathematical problem 6. Attend to precision …communicate precisely using clear definitions and calculate accurately and efficiently 7. Look for and make use of structure …look closely to discern a pattern or structure 8. Look for and express regularity in repeated reasoning …notice if calculations are repeated, and look for both general methods and for shortcuts Standards for Mathematical Practice

21. Common Core State Standards Mathematical Practices • 2. Reason abstractly and quantitatively. • 3. Construct viable arguments and critique the reasoning of others. 1. Make sense of problems and persevere in solving them. 6. Attend to precision • 4. Model with mathematics. • 5. Use appropriate tools strategically. • 7. Look for and make use of structure. • 8. Look for and express regularity in repeated reasoning.

22. The Standards for Mathematical Practice Take a moment to examine the first three words of each of the 8 mathematical practices…what do you notice? Mathematically Proficient Students… Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

23. The Standards for [Student] Mathematical Practice SMP1: Explain and make conjectures… SMP2: Make sense of… SMP3: Understand and use… SMP4: Apply and interpret… SMP5: Consider and detect… SMP6: Communicate precisely to others… SMP7: Discern and recognize… SMP8: Notice and pay attention to… Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

24. The Standards for [Student] Mathematical Practice The 8 Standards for Mathematical Practice – place an emphasis on student demonstrations of learning… that describe the thinking processes, habits of mind, and dispositions that students need to develop. that describe mathematical content students need to learn. Adapted from Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011.

25. CCSS Domains and Conceptual Categories Findwell, Bradford & Foughty, Zachary. “”Preparing to Implement the Common Core State Standards for Mathematics. Indiana Department of Education and Ohio Department of Education. March 30, 2011

26. CCSS Domains K-8

27. Grade Shifts Examples 6-8

29. The Goal for 8th grade students is Algebra 1. However, there are two sets of standards for grade 8 • Standards for Algebra 1-Taken from 8th grade Common Core, high school Algebra content cluster and CA Algebra standards • 8th grade Common Core-Finalize preparation for students in high school. California Grade 8 Options

30. High School Mathematics The CCSS high school standards are organized in 6 conceptual categories: Number and Quantity Algebra Functions Modeling (*) Geometry Statistics and Probability California additions: Advanced Placement Probability and Statistics Calculus Modeling standards are indicated by a (*) symbol. Standards necessary to prepare for advanced courses in mathematics are indicated by a (+) symbol.

31. Two Mathematics Pathways Courses in higher level mathematics: Precalculus, Calculus*, Advanced Statistics, Discrete Mathematics, Advanced Quantitative Reasoning, or courses designed for career technical programs of study. • Two Regular Sequences: • Traditional Pathway • 2 Algebra courses,1 Geometry course, with Probability and Statistics interwoven • Integrated Pathway • 3 courses that attend to Algebra, Geometry, and Probability and Statistics each year Algebra II Mathematics III Geometry Mathematics II Mathematics I High School Algebra I Traditional Pathway Typical in U.S. Integrated Pathway Typical outside of U.S.

32. Accelerated Pathway • Two additional pathways (one traditional and one integrated) that compact the curriculum and require a faster pace • The traditional compacted pathway has students completing the content of 7th grade, 8th grade, and High School Algebra I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Algebra I), enabling students to finish Algebra II by the end of the sophomore year. • The integrated compacted pathway has students completing the content of 7th grade, 8th grade, and Mathematics I in grades 7 (Compacted 7th Grade) and 8 (8th Grade Mathematics I), enabling them to complete Math III by the end of the sophomore year. • Bothprepare students for Precalculus in their junior year and Calculus in their senior year Getting To Calculus Sooner: Two Compacted Pathways

33. CCSS and California standards crosswalks

35. Overview Page

36. How to Read the Standards Briars, Diane. “Getting Started with the Common Core State Standards.” Power Point Presentation. NCSM Winter Conference, 2011

37. How to Read the Standards

38. Geometry Conceptual Category Example

39. Assessments will begin in 2014 • California has recently signed on with SMARTER Balanced Assessment Consortium • Assessments will include: • Computer Adaptive Assessments (interim & summative) • Performance Assessments (interim & summative) • Selected Response • Constructed Response • Both Two-hour and Extended Performance Assessments Assessment: What We Know

40. 3 Assessments Each Year • Reading • Writing, Listening and Speaking, Language • Math • Optional Interim Assessments in ELA and Math SMARTER Approach

41. Computer-adaptive 2 ELA and 2 Math “performance events” for Grades 3-8 Up to six math and ELA “events” for Grade 11 Grades 9 & 10 Optional Combination of computer and human scoring SMARTER End of Year

42. Computer-adaptive To be implemented based on state and district policy Teacher-administered “performance-events” Combination of human and computer scoring within 2 weeks Items will be non-secure for teacher and principal analysis SMARTER Interims

43. Writing Prompts Constructed Responses Technology-Enhanced Items Standardized Performance Events Single Session; administered within 12 weeks of end of the school year SMARTER Item Types

49. The K‐5 standards provide students with a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions and decimals‐‐which help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into applications. Key Takeaways from the Draft K‐12 ccss Initiative in Mathematics

50. In kindergarten, the standards follow successful international models and recommendations from the National Research Council’s Early Math Panel report, by focusing kindergarten work on the number core: learning how numbers correspond to quantities, and learning how to put numbers together and take them apart (the beginnings of addition and subtraction).