NYS COMMON CORE MATHEMATICS CURRICULUM A Story of

NYS COMMON CORE MATHEMATICS CURRICULUM Agenda Introduction to the Module Concept Development Module Review

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Curriculum Overview of A Story

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module’s Foundation • Standards: 7.

NYS COMMON CORE MATHEMATICS CURRICULUM G 7 -M 2: Module Overview © 2012 Common

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G 7 -M 2: Vocabulary

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G 7 -M 2 Rational

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic A: Addition and Subtraction

NYS COMMON CORE MATHEMATICS CURRICULUM Agenda Introduction to the Module Concept Development – Topic

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Using the Number Line to

NYS COMMON CORE MATHEMATICS CURRICULUM Understanding Addition of Integers Lesson 3 © 2012 Common

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Addition of Integers Lesson

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Subtraction of Integers and

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios The Distance Between Two Rational

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Addition and Subtraction of Rational

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Applying the Properties of Operations

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic B: Multiplication and Division

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding the Multiplication of Integers

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Develop Rules for Multiplying Signed

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Converting Rational Numbers to Decimals

NYS COMMON CORE MATHEMATICS CURRICULUM Mid-Module Assessment Question 6 © 2012 Common Core, Inc.

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Topic C: Applying Operations with

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Comparing Tape Diagram Solutions to

NYS COMMON CORE MATHEMATICS CURRICULUM If-Then Moves with Integer Cards Lesson 21/ Exercises 1

NYS COMMON CORE MATHEMATICS CURRICULUM Solving Equations Using Algebra Lesson 23/Exercise 2 © 2012

NYS COMMON CORE MATHEMATICS CURRICULUM Solving Equations Using Algebra Lesson 23/Exit Ticket © 2012

NYS COMMON CORE MATHEMATICS CURRICULUM End-of-Module Assessment Questions 2 and 3 © 2012 Common

NYS COMMON CORE MATHEMATICS CURRICULUM Biggest Takeaway Turn and Talk: • What questions were

NYS COMMON CORE MATHEMATICS CURRICULUM Key Points • • A Story of Ratios The

Slides: 46

Download presentation

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. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Module’s Foundation • Standards: 7. NS. A. 1, 7. NS. A. 2, 7. NS. A. 3, 7. EE. A. 2, 7. EE. B. 4 • Pages 9 – 13 in the Progressions Document (The Number System, 6 -8) serves as a foundation. • Using vectors to represent the addition of rational numbers on the number line; arriving at the additive inverse: p + (-p) = 0. • Representing subtraction as distance on the number line; and |p – q | is the distance between p and q on the number line. • Students use the properties of operations to justify multiplication and division of rational numbers. © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios G 7 -M 2 Rational Numbers – Topic Overview Topic A: Addition and Subtraction of Integers and Rational Numbers Topic B: Multiplication and Division of Integers and Rational Numbers Topic C: Applying Operations with Rational Numbers to Expressions and Equations © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Outcomes: Zero • Students add positive integers by counting up and negative integers by counting down (using curved arrows on the number line). • Students play the Integer Game to combine integers, justifying that an integer plus its opposite add to zero. • Students know the opposite of a number is called the additive inverse because the sum of the two numbers is zero. Lesson 1 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Zero The Integer Game Lesson 1, Concept Development © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Opposite Quantities Combine to Make Zero Let’s Play the Integer Game! Lesson 1, Concept Development © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Understanding Subtraction of Integers and Other Rational Numbers Outcomes: • Students justify the Rule for Subtraction: Subtracting a number is the same as adding its opposite. • Students relate the subtraction to the Integer Game. • Students justify the Rule for Subtraction for all rational numbers, using the inverse relationship between addition and subtraction. Lesson 5 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Applying the Properties of Operations to Add and Subtract Rational Numbers Outcomes: • Students use properties of operations to add and subtract rational numbers without the use of a calculator. • Students recognize that any problem involving addition and subtraction of rational numbers can be written as a problem using addition and subtraction of only positive numbers. • Students use the commutative and associative properties of addition to rewrite numerical expressions in different forms. They know the opposite of a sum is the sum of its opposites: -(3 + (-4)) = -3 + 4. the opposite Lessons 8 and 9 © 2012 Common Core, Inc. All rights reserved. commoncore. org

NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Ratios Applying the Properties of Operations to Add and Subtract Rational Numbers Lessons 8 and 9 © 2012 Common Core, Inc. All rights reserved. commoncore. org

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

NYS COMMON CORE MATHEMATICS CURRICULUM Key Points • • A Story of Ratios The additive inverse is the opposite of a number because, when added to a number, the sum is zero. We can use arrows on a number line to show the sum, p + q, on a number line. The sum is the distance|q|from p to the right of p is positive, and to the left of p is negative. Subtracting a number is the same as adding its opposite. The properties of operations justify the rules for multiplication and division of integers. (-1) = 1 can be justified using the distributive property and additive inverse. The opposite of a sum is the sum of its opposites. Ex. : –(-3 + 4) = 3 + (-4). Distance between 2 rational numbers p and q on a number line is |p - q| Every rational number can be written as a decimal that either terminate s in zeros or repeat. © 2012 Common Core, Inc. All rights reserved. commoncore. org