1. Take a few minutes to complete the survey on your desk.

2. UNPACKING THE STANDARDS 2 ND QUARTER MATHEMATICS COLLABORATIVE September 18, 2015 7 th Grade Math 8 th Grade Math

3. OBJECTIVE To strengthen the teaching and learning of mathematics by - Examining effective mathematics teaching practices - Identifying the skills and concepts that are embedded in the 2nd quarter standards - Developing an understanding of how to use Eureka Math modules and other resources to plan rigorous, engaging lessons that are fully aligned to the current standards

4. RATIONALE “Mathematics learning is an active process, in which each student builds his or her own mathematical knowledge from personal experiences, coupled with feedback from peers, teachers and other adults, and themselves.” Research from both cognitive science (Mayer 2002; Bransford, Brown, and Cocking 2000; National Research Council 2012a) and mathematics education (Donovan and Bransford 2005; Lester 2007)

5. RATIONALE Learners should have experiences that enable them to— engage with challenging tasks that involve active meaning making and support meaningful learning connect new learning with prior knowledge and informal reasoning and, in the process, address preconceptions and misconceptions acquire conceptual knowledge as well as procedural knowledge, so that they can meaningfully organize their knowledge, acquire new knowledge, and transfer and apply knowledge to new situations

6. RATIONALE Learners should have experiences that enable them to— construct knowledge socially, through discourse, activity, and interaction related to meaningful problems receive descriptive and timely feedback so that they can reflect on and revise their work, thinking, and understandings develop metacognitive awareness of themselves as learners, thinkers, and problem solvers, and learn to monitor their learning and performance.

7. EIGHT MATHEMATICS TEACHING PRACTICES Practices that represent a core set of high- leverage practices and essential teaching skills necessary to promote deep learning of mathematics.

8. OVERVIEW OF MATHEMATICS TEACHING PRACTICES MTP1 - Establish mathematics goals to focus learning. MTP2 - Implement tasks that promote reasoning and problem solving. MTP3 - Use and connect mathematical representations. MTP4 - Facilitate meaningful mathematical discourse. MTP5 - Pose purposeful questions. MTP6 - Build procedural fluency from conceptual understanding. MTP7 - Support productive struggle in learning mathematics. MTP8 - Elicit and use evidence of student thinking.

9. MTP 1 Establish mathematics goals to focus learning. Effective teaching of mathematics establishes clear goals for the mathematics that students are learning, situates goals within learning progressions, and uses the goals to guide instructional decisions.

11. MTP 2 Implement tasks that promote reasoning and problem solving. Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

13. MTP 3 Use and connect mathematical representations. Effective teaching of mathematics engages students in making connections among mathematical representations to deepen understanding of mathematics concepts and procedures and as tools for problem solving.

16. MTP 4 Facilitate meaningful mathematical discourse. Effective teaching of mathematics facilitates discourse among students to build shared understanding of mathematical ideas by analyzing and comparing student approaches and arguments.

18. Levels of Classroom Discourse

19. Teacher RoleQuestioningExplaining mathematical thinking Mathematical representations Building student responsibility within the community Level 0Teacher is at the front of the room and dominates the conversation. Teacher is only questioner. Questions serve to keep students listening to teacher. Students give short answers and respond to teacher only. Teacher questions focus on correctness. Students provide short answer-focused responses. Teacher may give answers. Representations are missing, or teacher shows them to students. Culture supports students keeping ideas to themselves or just providing answers when asked. Level 1Teacher encourages the sharing of math ideas and directs speaker to talk to the class, not to the teacher only. Teacher questions begin to focus on student thinking and less on answers. Only teacher asks questions. Teacher probes student thinking somewhat. One or two strategies may be elicited. Teacher may fill in an explanation. Students provide brief descriptions of their thinking in response to teacher probing. Students learn to create math drawings to depict their mathematical thinking. Students believe that their ideas are accepted by the classroom community. They begin to listen to one another supportively and to restate in their own words what another student has said. Level 2Teacher facilitates conversation between students, and encourages students to ask questions of one another. Teacher asks probing questions and facilitates some student-to-student talk. Students ask questions of one another with prompting from teacher. Teacher probes more deeply to learn about student thinking. Teacher elicits multiple strategies. Students respond to teacher probing and volunteer their thinking. Students begin to defend their answers. Students label their math drawings so that others are able to follow their mathematical thinking. Students believe that they are math learners and their ideas and the ideas of their classmates are important. They listen actively so that they can contribute significantly. Level 3Students carry the conversation themselves. Teacher only guides from the periphery of the conversation. Teacher waits for students to clarify thinking of others. Student-to-student talk is student initiated. Students ask questions and listen to responses. Many questions ask “why” and call for justification. Teacher questions may still guide discourse. Teacher follows student explanations closely. Teacher asks students to contrast strategies. Students defend and justify their answers with little prompting from the teacher. Students follow and help shape the descriptions of others’ math thinking through math drawings and may suggest edits in others’ math drawings. Students believe that they are math leaders and can help shape the thinking of others. They help shape others’ math thinking in supportive, collegial ways and accept the same support from others.

20. MTP 5 Pose purposeful questions. Effective teaching of mathematics uses purposeful questions to assess and advance students’ reasoning and sense making about important mathematical ideas and relationships.

22. MTP 6 Build procedural fluency from conceptual understanding. Effective teaching of mathematics builds fluency with procedures on a foundation of conceptual understanding so that students, over time, become skillful in using procedures flexibly as they solve contextual and mathematical problems.

24. MTP 7 Support productive struggle in learning mathematics. Effective teaching of mathematics consistently provides students, individually and collectively, with opportunities and supports to engage in productive struggle as they grapple with mathematical ideas and relationships.

26. MTP 8 Elicit and use evidence of student thinking. Effective teaching of mathematics uses evidence of student thinking to assess progress toward mathematical understanding and to adjust instruction continually in ways that support and extend learning.

28. TEM ALIGNMENT Work with a partner… Review the Mathematics Teaching Practices on your desk. Identify where these practices align to the TEM 4.0 Rubric. Write your findings on the TEM Alignment Chart (Purple Sheet).

29. OUR FINDINGS

30. THINK ABOUT IT Of the eight Mathematics Teaching Practices, which one will you commit to implement immediately? You and your assigned mathematics coach will discuss this further.

31. OBJECTIVE To strengthen the teaching and learning of mathematics by - Examining effective mathematics teaching practices - Identifying the skills and concepts that are embedded in the 2nd quarter standards. - Developing an understanding of how to use Eureka Math modules and other resources to plan rigorous, engaging lessons that are fully aligned to the current standards

32. 2 ND QUARTER STANDARDS 7 th Grade Math Standards 8 th Grade Math Standards

33. 7 TH GRADE MATH 7.RP.A.1 - Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2 / 1/4 miles per hour, equivalently 2 miles per hour.

34. EMBEDDED SKILLS Compute a unit rate by iterating (repeating) (doubling, etc.) or partitioning (halving, etc.) given rate. Compute a unit rate by multiplying or dividing both quantities by the same factor. Determine whether two quantities are proportional by examining the relationship given in a table, graph, equation, diagram, or verbal description. Identify the constant of proportionality when presented with a proportional relationship given in a table, graph, equation, diagram, or verbal description.

35. RESOURCES Eureka Module 1: Ratios and Proportional Relationships engageNY - Module 1, Topic C, Lessons 11-12

36. 8 TH GRADE MATH 8.F.B.4 - Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

37. EMBEDDED SKILLS Construct a function to model a relationship between quantities. Interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Calculate the average rate of change of a function (either symbolically or as a table) over a specified interval.

38. RESOURCES Eureka Module 1: Integer Exponents and Scientific Notation engageNY - Module 6, Part A, Lesson 2

39. EDULASTIC

40. WORK SESSION Work within your group to do the following for your assigned standards: Identify the objective(s) embedded in the standard Discuss which elements of the Eureka Module(s) can be used to teach this standard Go to the izonemathematicstop25.weebly.com website and identify additional resources that could be used to teach this standardizonemathematicstop25.weebly.com