a story of ratios
DESCRIPTION
A Story of Ratios. Grade 8 – Module 7. 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 . - PowerPoint PPT PresentationTRANSCRIPT
© 2012 Common Core, Inc. All rights reserved. commoncore.org
NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios
A Story of RatiosGrade 8 – Module 7
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
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.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Curriculum Overview of A Story of Ratios
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
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
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
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
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
CONCRETE
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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
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
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
Lesson 1 Example 4 – alternate method
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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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
LESSON TRANSCRIPT
ACTIVITY
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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
• 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
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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
Lesson 7
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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
Locating a number with a finite number of decimal digits on the
number line.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Locating a number with a infinite number of decimal digits on the
number line.
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
© 2012 Common Core, Inc. All rights reserved. commoncore.org
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
Biggest Takeaway
Turn and Talk:• What questions were answered for you?• What new questions have surfaced?