Summer 2017

1. Global Neutral 01001a Global Warm Neutral d3d1c8 Global Accent On Dark ffbf00 Global Accent on Light ff9800 Global Accent Alt 97c410 ELA - Coral ff5147 Math 009f93 Leadership 7872bf Leadership Pathway: Rigor in Grades 6–8 Summer 2017

2. RIGOR IN GRADES 6–8 Norms That Support Our Learning • Take responsibility for yourself as a learner. • Honor timeframes (start, end, activity). • Be an active and hands-on learner. • Use technology to enhance learning. • Strive for equity of voice. • Contribute to a learning environment where it is “safe to not know.”

3. RIGOR IN GRADES 6–8 Feedback on Feedback

4. RIGOR IN GRADES 6–8 Parking Lot Let’s go back and see if questions were addressed…

5. RIGOR IN GRADES 6–8 Equity Equity isn’t giving every student the same thing; it’s giving every student what they need. It is about fairness. Ensuring all children – regardless of circumstance – are receiving high-quality and Standards-aligned instruction is an equitable practice. We want to ensure Standards-aligned instruction is causing the equitable practices needed to close the gaps caused by racism, bias, and poverty. All week, we will explore our learning through this lens, and we will capture those moments visibly here in our room.

6. RIGOR IN GRADES 6–8 Share Your Learning Don’t forget to jot down ideas for • Light bulb moments • Why I teach/lead

7. RIGOR IN GRADES 6–8 The Week at a Glance

8. Objectives and Agenda Objectives • Participants will be able to describe the three aspects of rigor and why rigor is important. • Participants will be able to evaluate Standards, tasks, and lessons for aspects of rigor. • Participants will be able to observe and coach the rigor Shift in teacher practice. Agenda • Opening • Activator • Rigor: What and Why? • Finding Rigor in the Standards • Observing for Rigor • Apply an equity lens to our understanding of Rigor RIGOR IN GRADES 6–8

9. Teachable Moments Activator Step One – Pair Stand and find a partner. Remain standing. Step Two – Count At the facilitator’s direction, count off 1–6. Step Three – Analyze 4 min. – Analyze your assigned statement for its misconceptions. Step Four – Role Play 3 min. – Practice coaching to undo the misconception(s). 3 min. – Provide feedback RIGOR IN GRADES 6–8

10. RIGOR IN GRADES 6–8 3. I’m going to make sure I spend at least half my time this year teaching the major work of the grade. Teachable Moments Activator 1. Ratios and Proportions aren’t relevant in 8th grade because there is no RP domain in 8th—only 6th and 7th. . 2. I decided to skip the Statistics and Probability domain because everything in there is a supporting or additional cluster. 6. I’m going to make sure all the problems/tasks that I assign always align to at least two different Standards. 4. My kids can’t do 7.EE so I’m teaching 6.EE first. 5. To strengthen connections, I’ll make sure that my students are solving each problem in as many different ways as possible.

11. Rigor: What and Why? “Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.” From the Common Core State Standards

12. RIGOR IN GRADES 6–8 From the CCSS for Mathematics “Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like?” “There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from. The student who can explain the rule understands the mathematics and may have a better chance to succeed at a less familiar task such as expanding (a + b + c)(x + y).” “Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness.”

13. RIGOR IN GRADES 6–8 Paired Learning Activator Is there a time when you learned a procedure or a mnemonic or a way of doing the math without understanding why or what math you were doing? And what impact did that have on your future learning—if any?

14. From “Adding It Up” RIGOR IN GRADES 6–8

15. RIGOR IN GRADES 6–8 From TIMSS Video Study

16. RIGOR IN GRADES 6–8 From TIMSS Video Study

17. RIGOR IN GRADES 6–8 Consider This Contrast USA How can I teach my kids to get the answer to this problem? Japan How can I use this problem to teach the mathematics of this unit?

18. Three Aspects of Rigor RIGOR IN GRADES 6–8 • Procedural Skill and Fluency: The Standards call for speed and accuracy in calculation. • Conceptual Understanding: The Standards call for conceptual understanding of key concepts, such as place value and ratios.  • Modeling/Application: The Standards call for students to use math in situations that require mathematical knowledge.

19. RIGOR IN GRADES 6–8 Finding Rigor in the Standards Protocol: • Do the math. • For each, what aspects of rigor are emphasized and how do you know? • What are the grade-level Standards associated with each one?

20. RIGOR IN GRADES 6–8 Task #1 A mixture of concrete is made up of sand and cement in a ratio of 5:3. How many cubic feet of each are needed to make 160 cubic feet of concrete mix? 6.RP.3.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems (e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations).

21. RIGOR IN GRADES 6–8 Task #2 Hippos sometimes get to eat pumpkins as a special treat. If 3 hippos eat 5 pumpkins, how many pumpkins per hippo is that? Lindy made 24 jelly-bread sandwiches with a 16-ounce jar of jelly. How many ounces of jelly per sandwich is that? Purslane bought 350 rolls of toilet paper for the whole year. How many rolls of toilet paper per month is that? 6.RP.A.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is ¾ cup of flour for each cup of sugar” or, “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

22. RIGOR IN GRADES 6–8 Task #3 6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

23. RIGOR IN GRADES 6–8 Identifying Rigor in the Standards Procedural Skill Application 6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions (e.g., by using visual fraction models and equations to represent the problem). Conceptual Understanding

24. One Final Point: A Balance of Rigor The Standards set high expectations for all three components of rigor in the major work of each grade. (1) The three aspects of rigor are not always separate in materials. (2) Nor are the three aspects of rigor always together in materials. (3) EVERY student MUST have opportunities to work at achieving the balance of rigor RIGOR IN GRADES 6–8

25. Observing for Rigor

26. RIGOR IN GRADES 6–8 Key Supervision Questions for Rigor WHAT TO LOOK FOR Opportunities for students to: become more fluent (efficient and accurate) with procedures Fluency activities build upon conceptual understandings students already have Students practice, many times, with facts and procedures build their conceptual understanding Students being asked “why” to rationalize their thinking Students working with models to process their thinking apply their thinking, particularly in real world situations Students working on rich math problems Students use math absent of external prompts (e.g. “use addition to solve this problem”)

27. RIGOR IN GRADES 6–8 Observing for Rigor Ms. Morey - 7th Grade Standards: 6.RP.A.2, 6.RP.A.3, 7.RP.A.2 Prepare Look up the Standard(s) Determine the aspects of rigor embedded in the Standard(s) Capture Evidence of Rigor Aligned to the Standard Procedural skill and fluency Conceptual understanding Modeling/application How is the instruction equitable?

28. RIGOR IN GRADES 6–8 Observing for Rigor 6.RP.A.2 - Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. 6.RP.A.3 - Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. 7.RP.A.2 - Recognize and represent proportional relationships between quantities.

29. RIGOR IN GRADES 6–8 Observing for Rigor

30. RIGOR IN GRADES 6–8 After the Observation Procedural skill and fluency evidence Students practice, many times, with facts and procedures Fluency activities build upon conceptual understandings students already have Conceptual understanding evidence Students being asked “why”and to rationalize their thinking Students working with models to process their thinking Application/modeling evidence Students working on rich math problems Students use math absent of external prompts

31. RIGOR IN GRADES 6–8 After the Observation What questions would you now want to ask Ms. Morey?

32. RIGOR IN GRADES 6–8 Questions That Develop Rigor

33. RIGOR IN GRADES 6–8Thumb Rating: Did we meet our objectives? Objectives: • Participants will be able to describe the three aspects of rigor and why rigor is important. • Participants will be able to evaluate Standards, tasks, and lessons for aspects of rigor. • Participants will be able to observe and coach the rigor Shift in teacher practice. • Apply an equity lens to observe and coach the rigor Shift in teacher practice.

34. RIGOR IN GRADES 6–8Processing & Application STOP AND JOT • What important understanding do you want to take away from our discussion about Shift 3? • What implications does the importance of rigor have for your work? Consider: Professional development Planning Curriculum Equity Systems/Structures Policy & Programming

35. Global Neutral 01001a Global Warm Neutral d3d1c8 Global Accent On Dark ffbf00 Global Accent on Light ff9800 Global Accent Alt 97c410 ELA - Coral ff5147 Math 009f93 Leadership 7872bf Leadership Pathway: Observing the Standards and Shifts in Grades 6–8 Summer 2017

36. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8Objectives and Agenda Objectives: • Participants will be able to observe and coach teachers on the Standards and the Shifts in mathematics. Agenda: • Observing for Standards and Shifts • Lunch • Coaching Role Play • Apply an equity lens to Observing and Standards • Summary and Reflection

37. Observing for Standards and Shifts

38. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts Ms. Posada, 6th Grade Standard: ? During the observation: Find and look up the Standard Determine: Focus (major work) Coherence (linked learning) Aspects of Rigor

39. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts

40. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts Step One—Focus What Standard(s) are being taught?

41. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts Cluster: Investigate chance processes and develop, use, and evaluate probability models. 7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.C.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. Is this major work for the grade?

42. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts Step Two—Coherence • What prerequisite Standards should students who are getting it be making connections to, or should the teacher be leading struggling students to make connections to? • Are supporting or additional Standards being taught in service of major work?

43. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. 7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. 7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

44. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts Step Three—Rigor Cluster: Investigate chance processes and develop, use, and evaluate probability models. 7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. 7.SP.C.8.a Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs. What aspect(s) of rigor should be addressed in instruction for this Standard?

45. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts LOOK FORs: • Students being asked “why”to rationalize their thinking • Students working with models to process their thinking • Fluency activities build upon conceptual understandings students already have • Students practice, many times, with facts and procedures • Students working on rich math problems • Students use math absent of external prompts (e.g. “use addition to solve this problem”) • Conceptual Understanding: • Procedural Skill & Fluency: • Application:

46. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 Observing for Standards and Shifts

47. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 After the Observation Step One—Focus What Standards are being taught? Is it major work for the grade? Are both teacher instruction and student work aligned to the language of the intended Standard(s)? What questions could we ask the teacher to coach her on focus?

48. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 After the Observation Step Two—Coherence • Are the students who are “getting it”making connections to previous learning? • For students who are are working harder to “get it”, how is the teacher supporting students to make connections to previous learning? • Are supporting or additional Standards being taught in service of major work? • What questions could we ask the teacher to coach her on coherence?

49. OBSERVING THE STANDARDS AND SHIFTS IN GRADES 6–8 After the Observation LOOK FORs: • Students being asked “why”to rationalize their thinking • Students working with models to process their thinking • Fluency activities build upon conceptual understandings students already have • Students practice, many times, with facts and procedures • Students working on rich math problems • Students use math absent of external prompts (e.g. “use addition to solve this problem”) • Step Three - Rigor • What aspects of rigor are embedded in the Standard(s)? • What evidence did you capture of the aspect(s)? • What questions could we ask the teacher to coach her on rigor? • Taking all aspects of the tasks, how would you address equity?

50. Lunch!