MathematicsOperations with Rational Numbers: Fractions & Decimals

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Unit Information

Content Map: 1b: Operations with Rational Numbers: Fractions & Decimals

Checklist: 1b: Operations with Rational Numbers: Fractions & Decimals Checklist

Unit 1: Examples and Explanations of Standards

CCGPS Unit Standards or Troup County Version (TCV):

  • CC.7.NS.1b Understand p = q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

  • CC.7.NS.1c Understand subtraction of rational numbers as adding the additive inverse,
    p – q = p + (-q) Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

  • CC.7.NS.1d Apply properties of operations as strategies to add and subtract rational numbers.

  • TCVCC.7.NS.2b Interpret products and quotients of rational numbers by describing real-world contexts.

  • TCVCC.7.NS.2d Convert a fraction to a decimal using long division knowing that the decimal form of a rational number terminates in 0s or eventually repeats.

  • CC.7.NS.3 Solve real-world and mathematical problems involving the four operations with rational numbers.

Prerequisites: As identified by the CCGPS Frameworks

  • quantities can be shown using + or – and having opposite directions or values

  • points on a number line show distance and direction

  • opposite signs of numbers indicate locations on opposite sides of 0 on the number line

  • the opposite of an opposite is the number itself

  • the absolute value of a rational number is its distance from 0 on the number line

  • the absolute value is the magnitude for a positive or negative quantity

  • coordinates can be located and compared on a coordinate grid using negative and positive rational numbers

Unit Length: 14 Days

Resources by Concept: (click on a concept)

Concept 1: Multiplication and Division of Fractions (NS.2d & NS.2b)
Essential Questions:
  • 1. Why does the process of invert and multiply work when dividing fractions?
  • 2. When I divide one number by another number, do I always get a quotient smaller than my original number?
  • 3. How do I convert a rational number to a decimal using long division?
  • 4. Why is the product often smaller than the original numbers when I multiply fractions?
Key Vocabulary:
divisor reciprocal
product repeating decimal
dividend terminating decimal
  • CC.7.NS.2d
    • CCGPS Frameworks The Repeater vs. the Terminator TE p. 87-94
      Student  |  Teacher
    • Glencoe Math Text (McGraw-Hill, 2013) p. 263-271
    • Algebraic Thinking Lesson 99
  • CC.7.NS.2b
    • Glencoe Math Text (McGraw-Hill, 2013) - Multiplying - p. 311-318
    • Glencoe Math Text (McGraw-Hill, 2013) - Dividing - p. 327-334
    • McDougall Littell Text Lesson 5.4

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Concept 2: Addition and Subtraction of Fractions (NS.bcd & NS.3)
Essential Questions:
  • 1. What models can be used to show addition and multiplication of positive and negative rational numbers?
  • 2. What strategies are most useful in helping me develop algorithms for all operation with positive & negative integers?
Key Vocabulary:
additive inverse
  • CC.7.NS.1b
  • CC.7.NS.1c
    • CCGPS Frameworks “Helicopters & Submarines” TE p. 30-35
      Student  |  Teacher
    • Glencoe Math Text (McGraw-Hill, 2013) p. 211-224
    • McDougal Littell Text Lesson 2.3
    • McDougal Littell Text Lesson 5.1 Subtract Only
    • McDougal Littell Text Lesson 5.6 Subtract only
    • 7 Station p. 18-20
    • Integer Card Games: Largest Difference Wins
      Instructions  |  Student Sheet
  • CC.7.NS.1d
    • CCGPS Frameworks Hot Air Balloons -TE p. 36-45
      Student  |  Teacher
    • CCGPS Frameworks Debits & Credits -TE p. 46-52
      Student  |  Teacher
    • Glencoe Math Text (McGraw-Hill, 2013) p. 199-224
    • McDougal Littell Text Page 85 (# 7,8,10,11)
    • McDougal Littell Text Page 86 (# 23, 24, 25, 31,32,33)
  • CC.7.NS.3
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