A Story of Ratios

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NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios

A Story of RatiosGrade 8 – Module 7


N YS C O M M O N CO R E M AT H E M AT I C S C U R R I C U LU M A Story of Ratios

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.



What’s In a Module?Teacher Materials• Module Overview• Topic Overviews• Daily Lessons• AssessmentsStudent Materials• Daily Lessons with Problem SetsCopy Ready Materials• Exit Tickets • Fluency Worksheets / Sprints• Assessments



Types of Lessons1. Problem Set

Students and teachers work through examples and complete exercises to develop or reinforce a concept.

2. SocraticTeacher leads students in a conversation to develop a specific concept or proof.

3. ExplorationIndependent or small group work on a challenging problem followed by debrief to clarify, expand or develop math knowledge.

4. ModelingStudents practice all or part of the modeling cycle with real-world or mathematical problems that are ill-defined.



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 SolutionsStudent Materials• Classwork• Problem Set



Curriculum Overview of A Story of Ratios



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.



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.



CONCRETE



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)



Lesson 1 Example 4 – alternate method



Turn and Talk

• 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.

Topic B: Decimal Expansion of Numbers



LESSON TRANSCRIPT

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.

Round Robin Activity



Lesson 7



Locating a number with a finite number of decimal digits on the

number line.



Locating a number with a infinite number of decimal digits on the

number line.



Biggest Takeaway

Turn and Talk:• What questions were answered for you?• What new questions have surfaced?

A Story of Ratios

Documents

Transcript of A Story of Ratios