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A Story of Ratios

A Story of Ratios. Implementation in a Transition Year Principal’s Session. Session Objectives. Closely examine a series of lessons in order to make choices regarding implementation.

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A Story of Ratios

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  1. A Story of Ratios Implementation in a Transition Year Principal’s Session

  2. Session Objectives • Closely examine a series of lessons in order to make choices regarding implementation. • Understand how specific choices support successful pacing while bridging gaps in prior knowledge and honoring the balance of rigor. • Share strategies and successes in implementation of A Story of Ratios. • Practice using the information in our daily administrative routines

  3. Agenda Tuesday • Getting Focused • Grade 6 • Grade 7 • Grade 8 Wednesday • Implementation in a Transition Year Panel • Grade 9 • Professional Development for SY 14-15

  4. A Story of Ratios Implementation in a Transition Year

  5. Getting Started Introductions What are the issues I would love to have time to discuss with colleagues? Synthesize learning goals Share out focus for SY 14-15 PD

  6. A Story of Ratios Module Focus Grade 6

  7. CCLS Checklist for A Story of Ratios

  8. CCLS Checklist for A Story of Ratios

  9. CCLS Checklist for A Story of Ratios

  10. CCLS Checklist for A Story of Ratios

  11. CCLS Checklist for A Story of Ratios

  12. What’s In a Module? • Teacher Materials • Module Overview • Topic Overviews • Daily Lessons • Assessments • Student Materials • Daily Lessons with Problem Sets • Copy Ready Materials • Exit Tickets • Fluency Worksheets / Sprints • Assessments

  13. Types of Lessons • Problem Set Students and teachers work through examples and complete exercises to develop or reinforce a concept. • Socratic Teacher leads students in a conversation to develop a specific concept or proof. • Exploration Independent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge. • Modeling Students practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined.

  14. What’s In a Lesson? • Teacher Materials Lessons • Student Outcomes and Lesson Notes (in select lessons) • Classwork • General directions and guidance, including timing guidance • Bulleted discussion points with expected student responses • Student classwork with solutions (boxed) • Exit Ticket with Solutions • Problem Set with Solutions • Student Materials • Classwork • Problem Set

  15. Grade 6 Module 4

  16. G6-M4: Module Overview

  17. G6-M4: Module Overview

  18. Lesson 1 – Introduction to Fluency Activities

  19. Lesson 2 – Exploratory Challenge! • Work in pairs or small groups to determine number sentences to show the relationship between multiplication and division. Use tape diagrams to provide support for your findings. • Create two number sentences to show the relationship between multiplication and division. These number sentences should be identities and include variables. Use the squares to develop these number sentences. • Write your number sentences on large paper. Show a series of tape diagrams to defend each of your number sentences.

  20. Lesson 4Tape Diagram Demonstration

  21. Lesson 4

  22. Lesson 5

  23. Lesson 6

  24. Lesson 8: Replacing Numbers with Letters • Students understand that a letter in an expression can represent a number. When that number is replaced with a letter, an expression is stated. • Students discover the commutative properties of addition and multiplication, the additive identity property of 0, and the multiplicative identity property of 1. They determine that g÷ 1 = g, g ÷ g = 1, and 1 ÷ g = 1/g.

  25. Lesson 8

  26. Tape Diagram Demonstration Lesson 9

  27. Lesson 11: Factoring Expressions • Students model and write equivalent expressions using the distributive property and move from a factored form to an expanded form of an expression.

  28. Lesson 11: Factoring Expressions

  29. Tape Diagram Demonstration Lesson 11

  30. Lesson 12 + 4x 5 4xy 5y y

  31. Lesson 23 – True and False Number Sentences • Students explain the meaning of equality and inequality symbols. They determine if a number sentence is true or false based on the meaning of the equality/inequality symbol.

  32. Tape Diagram Demonstration Lesson 26 This lesson serves as a means for students to solve one-step equations through the use of tape diagrams. Through the construction of tape diagrams, students create algebraic equations and solve for one variable. In this lesson, students continue their study of the properties of operations and identity and develop intuition of the properties of equality. This lesson continues the informal study of the properties of equality students have practiced since first grade and also serves as a springboard to the formal study, use, and application of the properties of equality seen in seventh grade. While students will intuitively use the properties of equality, understand that diagrams are driving the meaning behind the content of this lesson. This lesson purposefully omits focus on the actual properties of equality, which is reserved for Grade 7. Students will relate an equation directly to diagrams and verbalize what they do with diagrams to construct and solve algebraic equations.

  33. Tape Diagram Demonstration Lesson 27 This lesson teaches students to solve one-step equations using tape diagrams. Through the construction of tape diagrams, students will create algebraic equations and solve for one variable. This lesson not only allows students to continue studying the properties of operations and identity, but also allows students to develop intuition of the properties of equality. This lesson continues the informal study of the properties of equality students have practiced since first grade, and also serves as a springboard to the formal study, use, and application of the properties of equality seen in Grade 7. Understand that, while students will intuitively use the properties of equality, diagrams are the focus of this lesson. This lesson purposefully omits focusing on the actual properties of equality, which will be covered in Grade 7. Students will relate an equation directly to diagrams and verbalize what they do with diagrams to construct and solve algebraic equations.

  34. Your Most Important Takeaway from Grade 6 Module 4 Take a moment to reflect on this module and make a note of the key takeaways.

  35. Grade 6 Module 5

  36. Module’s Foundation • Standards: • Pages 18-20 in the Progressions Document (K-6,Geometry,) serves as a foundation.

  37. G6-M5: Module Overview

  38. G6-M5: Module Overview

  39. Terminology New or Recently Introduced Terms • Triangular region • Altitude and base of a triangle • Pentagon • Hexagon • Line Perpendicular to a plane • Parallel planes • Right rectangular prism • Cube • Surface of a prism

  40. Building upon prior work

  41. Students discover through manipulation that the area of all triangles is exactly half the area of its corresponding rectangle.

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