1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Grade 8 – Module 4

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Session Objectives Examine the development of mathematical understanding across the module using a focus on concept development within the lessons. Identify the big idea within each topic in order to support instructional choices that achieve the lesson objectives while maintaining rigor within the curriculum.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story of Ratios

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Writing and Solving Linear Equations Focus on transcription and use of properties of equality Begin with identifying linear expressions Using Distributive Property to expand and compress expressions/equations Solve multi-step linear equations Identify characteristics of equations that lead to a unique solution, one solution, or no solution

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 5 Review Identify skill gaps Discuss strategies to overcome gaps Consider the objectives of the lesson; which parts are critical to achieving the objectives? Lesson A, Concept Development

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Linear Equations in Two Variables and Their Graphs Transcription of equation in two variables Prediction about graphs of linear equations Graphs of equations of the form ax + by = c, when x = 0, and when y = 0 Lesson B, Concept Development

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lesson 11 Review Identify skill gaps Discuss strategies to overcome gaps Consider the objectives of the lesson; which parts are critical to achieving the objectives? Lesson A, Concept Development

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Mid-Module Assessment Spend about 10 minutes working on the mid-module assessment and review the rubric for scoring.

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Slope and Equations of a Line Relationship of unit rate and slope The slope formula in terms of similar triangles The graph of the equation y = mx + b has slope m The existence of one line through a point with a given slope Linear equations graph as lines and lines are graphs of linear equations Focus on graphing equations using a table, point- slope form Lesson C, Concept Development

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Lessons 15-17: Slope In Lesson 15 as the unit rate of a graph In Lesson 16 as being found between any two points on the graph of a line In Lesson 17 with respect to y=mx and y=mx+b

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic D: Systems of Linear Equations and Their Solutions System is defined as two or more related linear equations If a solution exists, then it is the point of intersection of the graphs of the lines that comprise the system If no solution exists, the graphs of the lines are parallel and therefore do not intersect If infinitely many solutions exist, the graphs of the lines coincide Lesson D, Concept Development

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic E: Pythagorean Theorem Pythagorean triples, and regular old triples Triples explained in terms of similarity and algebraically System of equations that produces triples Lesson D, Concept Development

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios End-of-Module Assessment Spend about 20 minutes working on the end-of- module assessment and review the rubric for scoring.

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Agenda

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Biggest Takeaway Turn and Talk: What questions were answered for you? What new questions have surfaced?

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Key Points Module begins with transcribing and solving linear equations in one variable, then linear equations in two variables, then systems of linear equations. Geometric concepts are reinforced in word problems, diagrams, and graphs.