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January 2018

Rigor & Mathematical Practices in Grades 6–8. January 2018. RIGOR IN GRADES 6–8 Welcome Back!. RIGOR IN GRADES 6–8 Thank You for Your Feedback!. +. RIGOR IN GRADES 6–8 Norms That Support Our Learning. Take responsibility for yourself as a learner.

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January 2018

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  1. Rigor & Mathematical Practices in Grades 6–8 January 2018

  2. RIGOR IN GRADES 6–8Welcome Back!

  3. RIGOR IN GRADES 6–8Thank You for Your Feedback! +

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

  5. RIGOR IN GRADES 6–8This Week “Do the math” Equity for all Connect to our practice 5

  6. RIGOR IN GRADES 6–8 Today • Morning: Rigor in Grades 6–8 • Afternoon: Rigor and the Mathematical Practices in Grades 6–8

  7. RIGOR IN GRADES 6–8Morning Objectives • Participants will be able to define the procedural skill and fluency, conceptual understanding, and application aspects of mathematics understanding. • Participants will be able to recognize signals of procedural skill and fluency, conceptual understanding, and application within language of standards. • Participants will be able to identify characteristics of tasks that emphasize conceptual understanding, procedural skill and fluency, and modeling/application. • Participants will be able to explain how attending to the shift of rigor is an equitable practice in Standards-aligned math instruction.

  8. RIGOR IN GRADES 6–8Morning Agenda • What Is Rigor? • Why Rigor? • Deep Dive into Rigor: Conceptual Understanding • Deep Dive into Rigor: Procedural Skills and Fluency • Deep Dive into Rigor: Application • Putting It All Together

  9. RIGOR IN GRADES 6–8 Equity Equity is engaging in practices that meet students where they are and advance their learning by giving them what they need. It’s about fairness, not sameness. Equity ensures that all children—regardless of circumstances—are receiving high-quality and Standards-aligned instruction with access to high-quality materials and resources. We want to ensure that Standards-aligned instruction is a pathway to the equitable practices needed to close the gaps caused by systemic and systematic racism, bias, and poverty. All week, we will explore our learning through an equity lens, and we will capture those moments visibly here in our room. 9

  10. RIGOR IN GRADES 6–8I. What Is Rigor? Stop & Jot: How have you heard the word “rigor” used in your school or district?

  11. “Rigor refers to deep, authentic command of mathematical concepts, not making math harder or introducing topics at earlier grades.”

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

  13. RIGOR IN GRADES 6–8 II. Why Rigor?

  14. “Lessons for [marginalized] students commonly focus primarily on rote skills and procedures, with scant attention to meaningful mathematics learning.” • –National Council for Teachers of Mathematics, 2014 Addressing equity and access includes both ensuring that all students attain mathematics proficiency and increasing the numbers of students from all racial, ethnic, linguistic, gender, and socioeconomic groups who attain the highest levels of mathematics achievement.

  15. RIGOR IN GRADES 6–8 III. Deep Dive into Rigor: Conceptual Understanding • Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes conceptual understanding. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify the conceptual understanding. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  16. RIGOR IN GRADES 6–8Sample Task • 8.EE.B.5 The graphs below show the cost y of buying x pounds of fruit. One graph shows the cost of buying x pounds of peaches, and the other shows the cost of buying x pounds of plums. Which kind of fruit costs more per pound? Explain. Bananas cost less per pound than peaches or plums. Draw a line alongside the other graphs that might represent the cost y of buying x pounds of bananas.

  17. RIGOR IN GRADES 6–8 Identifying Rigor in the Standards Conceptual Understanding 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

  18. RIGOR IN GRADES 6–8 Conceptual Understanding • Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes conceptual understanding. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  19. Transition to Group Time!

  20. RIGOR IN GRADES 6–8 Conceptual Understanding • Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for conceptual understanding. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify the conceptual understanding. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  21. Transition to Whole Group!

  22. RIGOR IN GRADES 6–8 Conceptual Understanding Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out • Goals for This Activity: • Chart the characteristics of the tasks that exemplify the conceptual understanding aspect of rigor.

  23. RIGOR IN GRADES 6–8 Characteristics of Conceptual Understanding in Grades 6–8 • Students explain their thinking with words, drawings, and/or equations. • “Equivalent Ratios” • Students understand the meaning of equivalence. • “Equivalent Ratios” • “Cups of Water, Cups of Flour” • “Matching” • “Orders of Magnitude” • Students use or interpret models and drawings. • “Many Ways to Say It” • “Bike Race” • “Temperature Change” • Students use and apply mathematical rules. • “Function Rules” • Students apply properties.

  24. RIGOR IN GRADES 6–8 IV. Procedural Skills and Fluency • Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes procedural skills and fluency. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and fluency. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  25. Transition to Group Time!

  26. RIGOR IN GRADES 6–8 Procedural Skills and Fluency • Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for procedural skills and fluency. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify procedural skills and fluency. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  27. Transition to Whole Group!

  28. RIGOR IN GRADES 6–8 Procedural Skills and Fluency Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out Goals for This Activity: • Chart the characteristics of the tasks that exemplify the procedural skills and fluency aspect of rigor.

  29. RIGOR IN GRADES 6–8 Characteristics of Procedural Skills and Fluency in 6–8 • Students perform procedures often with the expectation of speed and accuracy: • Multiplying/Dividing Fractions and Decimals • “Tenths of (and So On)” • Rewriting Expressions • Grade 7 mini-assessment • Solving for variables • Grade 8 mini-assessment • Quick computation practice • “Sprints” and “Rapid White Board Exchanges”

  30. Break

  31. RIGOR IN GRADES 6–8 V. Application • Goals for This Activity: • Do the math for each task. • Identify the language/wording of the task that emphasizes application. • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application. • Identify how the task aligns to the standard. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  32. Transition to Group Time!

  33. RIGOR IN GRADES 6–8 Application • Goals for This Activity: • Determine the standard(s) aligned with each task, and identify the language of the standard(s) that calls for application. • Identify how the task aligns to the standard. • Chart the characteristics of the tasks that exemplify application. Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  34. Transition to Whole Group!

  35. RIGOR IN GRADES 6–8 Application Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out Goals for This Activity: • Chart the characteristics of the tasks that exemplify the application aspect of rigor.

  36. RIGOR IN GRADES 6–8 Characteristics of Application in 6–8 • Students ratio and rate reasoning to solve real-world math problems. • “Buying Bananas” • “Solving Percent Problems” • “Data Transfer” • Students apply understanding of concepts, rules, and equations (e.g., ratio, percent, functions) to solve word problems and mathematical problems. • “Sharing Prize Money” • “Firefighter Allocation” • “High Jump Competition” • “High School Graduations”

  37. RIGOR IN GRADES 6–8Balance of Rigor • The three aspects of rigor are not always separate in materials and standards. • Nor are the three aspects of rigor always together in materials and standards. “The Standards…set high expectations for all three components of rigor in the major work of each grade.”

  38. RIGOR IN GRADES 6–8VI. Putting It All Together What would you expect to see, in terms of rigor, in a unit on ratio or functions at your grade level?

  39. RIGOR IN GRADES 6–8Why EngageNY? The only curriculum rated fully aligned for Grades K–8, based on Gateways 1 and 2.

  40. RIGOR IN GRADES 6–8 Curriculum Map

  41. RIGOR IN GRADES 6–8Module + Topic Overviews

  42. RIGOR IN GRADES 6–8 Lessons + Assessments

  43. RIGOR IN GRADES 6–8 Rigor in the Modules Independently examine the standards for these modules: Grade 6: Module 1 Grade 7: Module 1 Grade 8: Module 5 1. What are the aspects of rigor associated with each standard? (There may be more than one!) 2.Predict the kinds of problems and activities you’d expect to see associated with each standard.

  44. SESSION 1 (111M): WHAT IS RIGOR AT THIS GRADE LEVEL? – FORMULA FOR MATH SUCCESS K-2Share Out Share aspects of rigor you found in the standards with a partner.

  45. RIGOR IN GRADES 6–8 Rigor at This Grade Level

  46. RIGOR IN GRADES 6–8 Teacher Version

  47. RIGOR IN GRADES 6–8 Student Version

  48. RIGOR IN GRADES 6–8 Student Outcomes

  49. RIGOR IN GRADES 6–8 Examples

  50. RIGOR IN GRADES 6–8 Problem Set

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