NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
A Story of Ratios
Grade 8 – Module 7
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Types of Lessons
1. Problem Set
Students and teachers work through examples and complete
exercises to develop or reinforce a concept.
2. Socratic
Teacher leads students in a conversation to develop a specific
concept or proof.
3. Exploration
Independent or small group work on a challenging problem
followed by debrief to clarify, expand or develop math knowledge.
4. Modeling
Students practice all or part of the modeling cycle with real-world
or mathematical problems that are ill-defined.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Curriculum Overview of A Story of Ratios
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
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)
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Lesson 1 Example 4 – alternate method
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
Turn and Talk
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 7
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Locating a number with a finite number
of decimal digits on the number line.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
A Story of Ratios
Locating a number with a infinite number
of decimal digits on the number line.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios
NYS COMMON CORE MATHEMATICS CURRICULUM
Biggest Takeaway
Turn and Talk:
• What questions were answered for you?
• What new questions have surfaced?
© 2012 Common Core, Inc. All rights reserved. commoncore.org
A Story of Ratios