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Rigor & Mathematical Practices in Grades 6-8

Explore the importance of rigor in math education and how it relates to the mathematical practices in grades 6-8. Learn about conceptual understanding, procedural skills, and application in mathematics.

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Rigor & Mathematical Practices in Grades 6-8

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  1. Rigor & Mathematical Practices in Grades 6-8 Summer2017

  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, 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”

  5. RIGOR IN GRADES 6-8This Week “Do the math” Connect to our practice

  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.

  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 6-8What Is Rigor? Stop & Jot: How have you heard the word “rigor” used in your school or district?

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

  11. 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.

  12. RIGOR IN GRADES 6-8 Why Rigor?

  13. RIGOR IN GRADES 6-8 From TIMSS Video Study

  14. RIGOR IN GRADES 6-8 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

  15. 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.

  16. 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.

  17. 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

  18. Transition to Group Time!

  19. 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

  20. Transition to Whole Group!

  21. 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.

  22. 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.

  23. RIGOR IN GRADES 6-8 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

  24. Transition to Group Time!

  25. 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

  26. Transition to Whole Group!

  27. 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.

  28. 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 • 7th grade mini-assessment • Solving for variables • 8th grade mini-assessment • Quick computation practice • “Sprints” and “Rapid White Board Exchanges”

  29. Engagement: Transfer of Learning& Active Participation Facilitation Skills • This morning as we have reviewed aspects of rigor we have asked you to use a protocol (listed on the right) that begins with individual work, moves to group work and finally has whole group share out. • With your table group briefly discuss: • Why was this structure used? • How did the structure support your learning? Protocol: time • 10 min: Individual work time • 10 min: Group collaboration • 10 min: Each group share out

  30. Break

  31. RIGOR IN GRADES 6-8 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 6-8Putting 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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