Common Core State Standards for Mathematics Webinar Series – Part Four

2. Common Core State Standards for Mathematics Webinar Series – Part Four Office of Superintendent of Public Instruction Randy I. Dorn, State Superintendent

3. Welcome!Agenda for today’s webinar… • Refresher on CCSS in Mathematics • Building state-wide capacity and supports • HS focus on math shifts • Update on Smarter Balanced Assessment Initiatives

4. Before we begin…About You • We’d like to know a little about who is out there. • Time for a poll.

5. Focusing on the Foundation…Washington’s Implementation Timeline & Activities

6. Implementing the Common Core State Standards in Washington State (HANDOUT) Our Vision: Every student will have access to the CCSS standards through high quality instruction aligned with the standards every day; and that all English language arts and mathematics teachers are prepared and receive the support they need to implement the standards in their classrooms every day. Our Purpose: To develop a statewide system with aligned resources that supports all school districts in their preparation of educators and students to implement the CCSS. This includes building system-wide capacity for sustained professional learning that can support CCSS implementation now and be applied to other initiatives in the future. Our Core Values: This vision can only occur through core values of clarity, consistency, collaboration, coordination, and commitment from classrooms, schools, and communities to the state level.

7. Common Core State Standards for Mathematics A Review of Shifts, Design, and Focus

8. Content Progressions and Major Shifts

9. CCSS Design and Organization

10. Critical Areas of Focus

11. HS Conceptual Categories • Number and Quantity • Algebra • Functions • Modeling • Geometry • Statistics and Probability

12. High School Pathways • The CCSSM Model Pathways • Two models that organize the CCSSM into coherent, rigorous courses • NOT required. The two sequences are examples, not mandates • Pathway A: Consists of two algebra courses and a geometry course, with some data, probability and statistics infused throughout each (traditional) • Pathway B: Typically seen internationally that consists of a sequence of 3 courses each of which treats aspects of algebra, geometry and data, probability, and statistics.

13. The Structure is the Standards A Grecian urn You have just purchased an expensive Grecian urn and asked the dealer to ship it to your house. He picks up a hammer, shatters it into pieces, and explains that he will send one piece a day in an envelope for the next year. You object; he says “don’t worry, I’ll make sure that you get every single piece, and the markings are clear, so you’ll be able to glue them all back together. I’ve got it covered.” Absurd, no? But this is the way many school systems require teachers to deliver mathematics to their students; one piece (i.e. one standard) at a time. They promise their customers (the taxpayers) that by the end of the year they will have “covered” the standards. In the Common Core State Standards, individual statements of what students are expected to understand and be able to do are embedded within domain headings and cluster headings designed to convey the structure of the subject. “The Standards” refers to all elements of the design—the wording of domain headings, cluster headings, and individual statements; the text of the grade level introductions and high school category descriptions; the placement of the standards for mathematical practice at each grade level.

14. Common Core State Standards for Mathematics Building Statewide Capacity

15. 2011-12 CCSS Timeline and Foci… OSPI Quarterly Webinar Series August/Sept. 2011 January 2012 March and May 2012

16. Spring and Summer 2012 CCSS Opportunities to Build Statewide… Awareness:

17. Spring and Summer 2012 CCSS Opportunities to Build Statewide… Capacity:

18. http://www.k12.wa.us/CoreStandards/ProfDev.aspx

19. Spring and Summer 2012 CCSS Opportunities to Continue Statewide… Coordination and Collaboration:

20. Washington Implementation Partnerships PLUS… Large School Districts Higher Education Statewide Education and Content Associations

21. Common Core State Standards for Mathematics Classroom Transition Supports

22. Three-Year Transition Plan for Common Core State Standards for Mathematics by Grade Level

23. 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

24. Standards for Mathematical Practices Graphic

25. Professional Development Plan CCSS-M • Three-year transition plan focuses on one or two domain areas for each year. • Domain of focus for year one aligns to the current testing of the MSP and EOC. • Each year additional domains will be added, but the process can be repeated each year of the transition.

27. What does this mean? The Washington State 2008 standards asks students to: A1.4.C • Write and solve systems of two linear equations and inequalities in two variables.

28. In the Common Core State Standards students will need to: Solve systems of Equations A.REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

29. What does this mean? Algebra Critical Area 1: By the end of eighth grade, students have learned to solve linear equations in one variable and have applied graphical and algebraic methods to analyze and solve systems of linear equations in two variables. Now, students analyze and explain the process of solving an equation. Students develop fluency writing, interpreting, and translating between various forms of linear equations and inequalities, and using them to solve problems. They master the solution of linear equations and apply related solution techniques and the laws of exponents to the creation and solution of simple exponential equations.

30. 8. EEAnalyze and solve linear equations and pairs of simultaneous linear equations. • 8.EE.8. Analyze and solve pairs of simultaneous linear equations. • a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. • b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x +2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. • c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

31. What does this mean? A-REI Reasoning with Equations and Inequalities Understand Solving Equations as a process of reasoning and explaining the reasoning Solve equations and inequalities in one variable Solve systems of equations A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g. with graphs), focusing on pairs of linear equations in two variables. HS Algebra: Build on student experiences graphing and solving systems of linear equations from middle school to focus on justification of the methods used.

32. A-REI.6 (Illustrative Math Project) Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said, I wonder whether the dollar belongs inside the cash box or not. The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? Commentary: A variant of this problem would be to describe the context without giving any numbers and have a cash box with play money and ticket stubs available.

33. Statewide Assessment Landscape and Update New Assessment System for CCSS: What we know so far

34. A National Consortium of States • 28 states representing 44% of K-12 students • 21 governing, 7 advisory states • Washington state is fiscal agent

35. A Balanced Assessment System:ELA and Math --Grades 3-8 and High School Summative assessments Benchmarked to college and career readiness Teachers and schools have information and tools they need to improve teaching and learning Common Core State Standards specify K-12 expectations for college and career readiness All students leave high school college and career ready Teacher resources for formative assessment practices to improve instruction Interim assessments Flexible, open, used for actionable feedback

36. A Balanced Assessment System

38. Time and format • Summative: For each content area - ELA & Math • Computer Adaptive Testing • Selected response (MC), Constructed Response (open-ended), Technology enhanced (e.g., drag and drop, video clips, limited web-interface) • Performance Tasks (like our CBAs) • Up to 2 per content area in grades 3-8 • Up to 6 per content area in High School

39. Time and format • Summative: - Administration window is last 12 weeks of school - For each content area - ELA & Math • Shorter option for states (~3 hours ELA, ~2 hours Math) • Scale score on comprehensive test (met/not met determination) • Longer option for states (~5 hours ELA, ~3 hours Math) • Able to report data on claims for individual students

40. Time and format • Interim assessments • Can be used as often as needed • Can be customized by districts/schools • To focus on selected strands • To clone summative test • Will use Computer Adaptive Technology • Released items from summative item bank

41. Smarter BalancedHS Sample Performance Task • During the two sessions of the upcoming performance task, you will be predicting the total costs for tuition and school-related fees, as a combined cost for a college of your choice. Your assignment will include the following: • Choose a college or university that you will use to predict the future cost of tuition. This can either be a local 2-year or 4-year institution or one that you would like to attend in the future. • Find out what the current year’s tuition, including school-related fees, are for the school you chose. This information can often be found by calling the school’s admissions office, obtaining a current school catalog, or doing an Internet search. Be sure to get the cost for in-state students if the school is located in this state. Get the cost for out-of-state students if the school is not located in our state. • Read the news articles “Tuition and fees rise more than 8% at U.S. public colleges,” “Tuition Hikes of the Downturn,” and “The State of the Union on college costs.” • Use the information you obtained about the current year’s tuition at the school you chose and the information you read in the “Tuition and fees rise more than 8% at U.S. public colleges” news article to predict the cost of college tuition at your choice of schools the year you are first eligible to attend college. You should also predict the total tuition amount for the entire college education.

42. Washington’s Testing System Transition Current Testing System • Reading and Math: Grades 3–8 and 10 • Writing: Grades 4, 7, 10 • Science: Grades 5, 8, 10 SBAC/CCSS Testing System (fully operational in 2014-15) • English/Language Arts and Math: Grade 3–8 and 11* • Science exams are required under ESEA but are not included in SBAC *11th grade to measure college and career readiness. We are working with higher ed to explore the possible use of these measures as an alternative for college placement (or entrance). ()

43. Still to be worked out: Washington’s Policy Discussion… • Will 11th grade exam be used for graduation (exit exam) in Washington? • If these exams are our exit exams what will the CAA options be? • Will the Summative SBAC test replace our End of Course exams or will SBAC have End of Course exams too? • How will Washington’s science tests mesh with these tests?

44. Find Out More: www.SmarterBalanced.org State Contact: Robin.Munson@k12.wa.us

45. http://www.smarterbalanced.org/smarter-balanced-assessments/ Zip files with ELA and Math Item Specifications and Sample Student Tasks

46. HS Resources Illustrative Math Project: http://www.illustrativemathematics.org/ Bill McCallum’s Blog: http://commoncoretools.me/ Mathematics Assessment Project (MARS): http://map.mathshell.org/materials/index.php Progressions documents: http://ime.math.arizona.edu/progressions Inside Mathematics: http://Insidemathematics.org Achieve the Core: http://achievethecore.org ()

48. Have a great summer! • Common Core Questions: • Email: corestandards@k12.wa.usOR • Greta Bornemann, OSPI CCSS Project Lead, E-mail: Greta.Bornemann@k12.wa.us