A Story of Ratios

1. A Story of Ratios Grade 8 – Module 7

2. Session 5 Objectives • Understand the mathematical concepts developed within Grade 8 Module 7. • Practice collecting evidence of effective instruction using exemplar transcripts of classroom instruction. • Uncover strategies for supporting teachers with their implementation of the Standards for Mathematical Practice.

3. 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

4. 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.

5. 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

6. Curriculum Overview of A Story of Ratios

13. Topic A: Square and Cube Roots • Learning is motivated by the Pythagorean Theorem and need to get a precise length of a side of a right triangle. • Square roots are defined. • Square and cube roots exist and are unique. • Students simplify square roots (optional). • Students solve equations using roots.

14. Before Beginning the Module: • Pythagorean Theorem Lessons from Modules 2 and 3 must be taught: • Module 2, Lesson 15 • Module 2, Lesson 16 • Module 3, Lesson 13 • Module 3, Lesson 14 • Lessons contain proofs and practice.

15. Concrete

16. Lesson 1 Example 4 • Consider the math that students needed to know in order to answer this question: • Knowledge/Properties of Equilateral Triangle • Understanding of Congruence (M2) • Triangle Sum Theorem (M2) • Laws of Exponents (M1) • Properties of Equality/Solving Equations (M4) • Estimating Square Roots (M7)

17. Lesson 1 Example 4 – alternate method

22. Turn and Talk Topic B: Decimal Expansion of Numbers • Rational numbers are defined as numbers whose decimal expansions eventually repeat. • Irrational numbers are defined as numbers that are not rational. • Focus of Topic B is writing decimal expansions of numbers. • Students learn why the long division algorithm leads to the decimal expansion of a number. • Students learn how to determine the decimal expansion of irrational numbers, including pi.

23. Lesson Transcript Activity

24. Round Robin Activity • In your table groups, share the observations you made using the CCSS Instructional Practice Guide. • Each group member shares one observation and the supporting evidence. Then the group member to his/her right shares. • Continue this process until all • observations have been shared.

25. Lesson 7

26. Locating a number with a finite number of decimal digits on the number line.

27. Locating a number with a infinite number of decimal digits on the number line.

38. Biggest Takeaway • Turn and Talk: • What questions were answered for you? • What new questions have surfaced?