THE CCLS AND CIE IN Mathematics 2012-2013 SETTING UP THE YEAR 6-8

1. THE CCLS AND CIE IN Mathematics 2012-2013SETTING UP THE YEAR 6-8 CFN 609 Karen Cardinali, Achievement Coach

2. PD schedule Institute for Learning, University of Pittsburgh Professional Development Support. Series of 3 focused and iterative workshops Dates: December ?, January 22, March 5th: Conklin Building Topics to be covered:  • Examining our vision of CCSS-aligned instruction • Deepening our understanding of the content standards related to ratios and proportional relationships within the context of a lesson. • Learning about assessing and advancing questions • Learning and applying accountable Talk Moves to the share, discuss and analyze phase of a lesson • Understanding  performance-based assessment & practice creating instruction tasks (Strategies for modifying textbook tasks to increase the cognitive demand of the tasks.) • Facilitator moves

3. AGENDA PROBLEM OF THE DAY ACTIVITY # 1: TEACHER TEAMS AND THE QUALITY REVIEW RUBRIC ACTIVITY # 2: THE CITYWIDE EXPECTATIONS, CCLS AND GUIDANCE DOCUMENTS BREAK ACTIVITY # 3: PLANNING: ADJUSTING SCOPE AND SEQUENCE TO ALIGN TO THE MAJOR WORK OF THE GRADE IDENTIFYING GAPS. LUNCH ACTIVITY # 4: PLANNING: COMMON CORE ALIGNED UNITS OF STUDY ACTIVITY # 5: IMPROVING TEACHER PRACTICE THROUGH PLANNING: DANIELSON COMPONENTS 1E, 3B ANB 3D REFLECTIONS AND ACTION PLAN

4. Guess the color of your hat Materials: A bag of hats: 3 are red; 2 are blue Rules for play: • There are three players. • They stand in a line. • The host takes three hats from the bag and places one on the head of each player. • Each player must guess the color of his party hat without looking. • Play begins with the third person in line.

5. The third person in line can see the hats on the heads of the two players in front of him. • The second person in line can see the hat on the head of the first person. • The first person cannot see anyone’s head.

6. The third person goes first, and says, “ I don’t know the color of my hat.” The second person goes and says, “ I also don’t know the color of my hat.” The first person thinks for a moment and says. “ I know the color of my hat.” HOW CAN THIS BE?

7. Solve on your own. Please do not talk to a neighbor. • After 5 minutes, you will be asked to share your strategy with a neighbor • After 5-7 minutes of sharing, you will be asked to reflect on where you are in the problem solving process.

8. Recording Sheet

9. Problem solving in mathematics Where are you in the problem solving process? What is your emotional state? Did communicating with your neighbor help develop you? Hinder you?

10. Problem solving in Mathematics At your table (in small groups) share your strategy and create a group solution and chart it. Be ready to share your solution with the rest of the community. Keep in mind: Can your poster stand alone?

11. 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. What is the relationship among mathematical problem solving, reasoning, modeling and talk? How do we develop mathematical problem solving, reasoning, modeling and talk in our classrooms? What’s the starting place? What supports math reasoning in classrooms?

13. Creating Effective Mathematics lessons • There’s a strong relationship between: • The development of mathematical models and modeling and Problem solving; • The development of mathematical models and modeling and reasoning; and • The development of mathematical models and modeling and a student’s ability to create a viable argument.

14. Activity 1: Quality review RubricIndicators 1.1, 1.2, 1.3, 2.2, 4.2, 5.1 Highlight the words or key phrases through out the well- developed columns that connect to the work of teacher teams or that reflect or are evidence of the work being done in teacher teams. What would/could evidence that your school was well developed in this area look like? Be specific What structures need to be in place to reach these expectations?

15. Recording sheet

16. Citywide Expectations for Mathematics 2012-2013 1. In grades 6-12, students will experience eight Common Core-aligned units of study: two in math, two in ELA, two in social studies, and two in science.

17. Content oF the units Each unit will provide points of access for all students and culminate in a performance task aligned to the Common Core. Schools may choose to upgrade existing units, engaging in cycles of inquiry and looking closely at student work to make adjustments to curriculum, assessment, and instruction. Oneof each teacher’s Common Core-aligned units of study in 2012-13 should focus on Mathematical Practices 3 and/or 4 and the selected domain of focus. The other unit may center on standards in the same domain or on other major work of the grade as well as the above mentioned and other relevant Standards for mathematical practice.

18. Domains of Focus 4-5-Number and Operations—Fractions 6-7-Ratios and Proportional Relationships 8-Expressions and Equations Standards for Mathematical Practice MP.3 Constructing Viable arguments and critique the Reasoning of others and MP.4 Modeling with Mathematics

19. Snapshot of Grade 6 standards Domain Cluster Standard

20. Major Work Grade 6 Domain Cluster

21. “In depth” Opportunities

22. Parcc Model Content Frameworks for Mathematicshttp://www.parcconline.org/ PARCC Model Content Frameworks For Mathematics For Grade 6 The Model Content Frameworks for Grade 6 highlight examples of key content dependencies, examples of key instructional emphases, opportunities for in-depth work on key concepts, and connections to the mathematical practices.  While they provide additional context to the grade 6 standards, the frameworks are not meant to replace engaging with the standards themselves. For this reason, readers are advised to have a copy of the Common Core State Standards to use in conjunction with the Model Content Frameworks.  The Model Content Frameworks for Grade 6 include the following components.  Click the links below to read more about grade 6. • Examples of Key Advances from Grade 5 to Grade 6 • Fluency Expectations or Examples of Culminating Standards • Examples of Major Within-Grade Dependencies • Examples of Opportunities for Connections among Standards, Clusters or Domains • Examples of Opportunities for In-Depth Focus • Examples of Opportunities for Connecting Mathematical Content and Mathematical Practices • Content Emphases by Cluster

23. recommendations for using the cluster‐level emphases. DO: • Use the guidance to inform instructional decisions regarding time and other resources spent on clusters of varying degrees of emphasis. •  Allow the focus on the major work of the grade to open up the time and space to bring the Standards for Mathematical Practice to life in mathematics instruction through sense‐making, reasoning, arguing and critiquing, modeling, etc. •  Evaluate instructional materials taking the cluster‐level emphases into account. The major work of the grade must be presented with the highest possible quality; the supporting work of the grade should indeed support the major focus, not detract from it. • Set priorities for other implementation efforts taking the emphases into account, such as staff development; new curriculum development; or revision of existing formative or summative testing at the school level. -Content Emphases by cluster, DOE

24. Do NoT: • Neglect any material in the standards. (Instead, use the information provided to connect Supporting Clusters to the other work of the grade.) •  Sort clusters from Major to Supporting, and then teach them in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters. •  Use the cluster headings as a replacement for the standards. All features of the standards matter — from the practices to surrounding text to the particular wording of individual content standards. Guidance is given at the cluster level as a way to talk about the content with the necessary specificity yet without going so far into detail as to compromise the coherence of the standards. Content Emphasis by Cluster- DOE

25. 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

26. Opportunities for connecting mathematical practice Mathematical practices should be evident throughout mathematics instruction and connected to all content areas addressed at this grade level. Mathematical tasks (short, long, scaffolded, and unscaffolded) are an important opportunity to connect content and practices. Some brief examples of how the content of this grade might be connected to the practices follow.

27. Based on experience and expectations from the Quality Review Rubric What components support a common core aligned unit of study that meets the needs of all students?

28. Key Components of a Unit: • Content and skills students need to know and be able to perform that align to three to six primary standards to be assessed by a culminating task; • A pre-assessment that helps to surface students’ understanding of the concepts and where understanding ends/breaks down. The pre-assessment should delineate the linguistic and content needs of ELLs; • Formative assessments/checkpoints throughout the units. • A series of learning experiences that build students toward accomplishing the goals of the unit and that reveal a conceptual progression and connection to relevant previously learned and future concepts; • A culminating task that assesses the unit’s primary standards; • A mix of explicit teaching and student investigation; • Explicit teaching of academic vocabulary; • Access for all students through multiple means of representation, action and expression, and engagement (refer to http://www.cast.org/udl/index.html); • Instructional supports, as needed, for ELLs (refer to these ELA and Math resources).

29. CIE continued 2. In grades PK-8, schools will use guidance from the DOE to review their scope and sequence and: Reorganize math content to teach fewer topics and allow for more time to focus on the major work of the grade.

30. DOE Guidance Documents • 1. 2. Scope and Sequence Samples (K-8) • 3. Mathematics Overviews for Impact Math (6-8) • http://schools.nyc.gov/Academics/CommonCoreLibrary/CommonCoreClassroom/Mathematics/default.htm

31. DOE Guidance Documents • These documents provide a CCLS-aligned scope and sequence for Mathematics that take into account the differences in and transitionfrom the New York State Standards to the CCLS. • The scope and sequence is aligned to the Common Core and demonstrates a focus on the major work of the grade which the State has indicated will be the focus of next year’s 3-8 State exams. • This scope and sequence represents one way that a school may choose to organize and teach the full range of the standards before the state test. It is not based on any additional information about the changes in next year’s tests.

32. Core Curriculum Alignment Guidance 6-8

33. Omitted concepts ( & impact Lessons)

34. Bridge Concepts

35. Changes to Unit overviews

36. New York state: Story OF UNITSK-5 Curriculum MapS

37. Alignment?

38. Activity 2: In order to teach a sequence of instruction that fully addresses the standards represented… • How are your teacher teams using these documents as a support when refining existing pacing and scope and sequence? • What supports do teacher teams need in order to make use of this guidance? • If this work is underway, how might you go deeper, incorporating elements of the instructional shifts and the mathematical practices?

39. Talking Points for Middle • How might teacher teams use the documents we’ve looked at as a support • What supports do teacher teams need to go deeper? What are your next steps? • Based on the schools data and the major work of the grade where might you incorporate the 2 common core aligned units with formative and culminatingtasks? • How do we keep the focus on rich tasks and developing connected units of study with a mix of explicit teaching and student investigation so that students get to explore mathematics deeply? • How do we keep an emphasis on changing pedagogy: developing classrooms where students see math as connectedand engage in deep explorations as opposed to skill lesson by skill lesson. • How can we keep the instructional shifts alive both in daily and curriculum planning? Particularly focus, Fluency and Deep Understanding? • What logistics need to be set? Year long pacing, expected start and end dates, common assessments, benchmark assessments?

40. 3. In 2012-2013 the DOE is asking that Teachers focus their Pedagogical growth on Instructional Shifts that: Require fluency, application and conceptual understanding. These shifts focus on the ability to think with mathematics and mathematically, particularly targeting the ability to transfer understanding from one context to another, to select the right mathematical tools and to be able to make mathematical arguments and explain why certain decisions were made proposing solutions to “real-world” problems.

41. Crosswalk of Common Core Instructional Shifts: Mathematics Refresh and review the instructional shifts.

42. To date, curricula have not always been balanced in their approach to these three aspects of rigor… Some curricula stress fluency in computation, without acknowledging the role of conceptual understanding in attaining fluency. Some stress conceptual understanding, without acknowledging that fluency requires separate classroom work of a different nature. Some stress pure mathematics, without acknowledging first of all that applications can be highly motivating for students, and moreover, that a mathematical education should make students fit for more than just their next mathematics course. At another extreme, some curricula focus on applications, without acknowledging that math doesn’t teach itself. -K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics

43. Fluency Expectations or Examples of Culminating standards:parcconline.org. Highlights individual standards that set expectations for fluency or that represent culminating masteries. Fluency standards are highlighted to stress the need to provide sufficient supports and opportunities for practice to help students meet these expectations. Culminating standards are highlighted to help give a sense of where important progressions are headed.  Fluency is not meant to come at the expense of understanding but is an outcome of a progression of learning and sufficient thoughtful practice. It is important to provide the conceptual building blocks that develop understanding in tandem with skill along the way to fluency; the roots of this conceptual understanding often extend one or more grades earlier in the standards than the grade when fluency is finally expected.

44. Key FLuencies

45. Grade level fluencies • 6.ns.2 Students fluently divide multi-digit numbers using the standard algorithm. This is the culminating standard for several years’ worth of work with division of whole numbers. • 6.NS.3 Students fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. This is the culminating standard for several years’ worth of work relating to the domains of Number and Operations in Base Ten, Operations and Algebraic Thinking, and Number and Operations — Fractions. • 6.NS.1 Students interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions. This completes the extension of operations to fractions.

46. Grade 7 fluencies • 7.EE.3 Students solve multistep problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. This work is the culmination of many progressions of learning in arithmetic, problem solving and mathematical practices. • 7.EE.4 In solving word problems leading to one-variable equations of the form px + q = r and p(x + q) = r, students solve the equations fluently. This will require fluency with rational number arithmetic (7.NS.1-3), as well as fluency to some extent with applying properties operations to rewrite linear expressions with rational coefficients (7.EE.1). • 7.NS.1 Adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. The number system will continue to develop in grade 8, expanding to become the real numbers by the introduction of irrational numbers, and will develop further in high school, expanding to become the complex numbers with the introduction of imaginary numbers. Because there are no specific standards for rational number arithmetic in later grades and because so much other work in grade 7 depends on rational number arithmetic (see below), fluency with rational number arithmetic should be the goal in grade 7.

47. Grade 8 Fluencies • 8.EE.7 Students have been working informally with one-variable linear equations since as early as kindergarten. This important line of development culminates in grade 8 with the solution of general one-variable linear equations, including cases with infinitely many solutions or no solutions as well as cases requiring algebraic manipulation using properties of operations. Coefficients and constants in these equations may be any rational numbers. • 8.G.9 When students learn to solve problems involving volumes of cones, cylinders, and spheres — together with their previous grade 7 work in angle measure, area, surface area and volume (7.G.4-6) — they will have acquired a well-developed set of geometric measurement skills. These skills, along with proportional reasoning (7.RP) and multistep numerical problem solving (7.EE.3), can be combined and used in flexible ways as part of modeling during high school — not to mention after high school for college and careers.[1]

48. Standards for Mathematical practices and Instructional shifts Focus Coherence Rigor: fluency, application and Deep understanding. Table talk: How can we keep these at the forefront of our planning and daily instruction? What would this look like in the classroom? In planning? Give specific evidence/examples.

49. Standards and instruction The goal is to balance concepts, skills and application. We can adopt standards for students, but we also need to be aware that implicit in these standards are new standards for teaching. This will be a profound shift in practice for most teachers. Ignoring this will seriously affect the implementation of the CCLS. The common core standards focus on in depth learning. This will mean a focus on the big ideas in mathematics, how they build, and how students develop them. For teachers, this means knowing the big ideas in mathematics and understanding how children develop these big ideas. This also means that teachers need to have pedagogical tools to scaffold student thinking and ways of using classroom discourse to promote the deepest kind of reasoning.

50. Activity 3: Reworking the pacing Materials Needed: • Scope and sequence documents (Curriculum specific guidance documents) • Testing Guidance • Curriculum • CCLS • Additional resources • Calendar • Template