Curriculum / Math / 7th Grade / Unit 2: Operations with Rational Numbers / Lesson 7
Math
Unit 2
7th Grade
Lesson 7 of 18
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Understand subtraction as addition of the opposite value (or additive inverse).
The core standards covered in this lesson
7.NS.A.1.C — 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.
7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.
The foundational standards covered in this lesson
6.NS.C.6 — Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Use your number line and game piece to model each subtraction problem and answer the questions that follow.
a. What does each part of the subtraction problem tell you to do on the number line?
b. What answer do you get for each subtraction problem?
c. Rewrite each subtraction problem as an addition problem of the opposite value. Use your number line and game piece to model the addition problem and show it has the same value. What changes and what stays the same?
On a number line, you start at $${{-4}}$$.
a. Explain how you can get to $${-9}$$. Write an addition problem and a subtraction problem to represent this.
b. Explain how you can get to 1. Write an addition problem and a subtraction problem to represent this.
An Alternative to 'Add the Opposite' is made available on Nathan Kraft's Blog. Accessed Aug. 15, 2017, 12:41 p.m..
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Circle the expressions below that have a value of 2.
$${8+ (-6)}$$ $${6-8}$$ $${-{8-6}}$$ $${-8+(-6)}$$
$${8-6}$$ $${-6+8}$$ $${-8+6}$$ $${-6 - (-8)}$$
Rewrite each subtraction problem as an addition problem and each addition problem as a subtraction problem.
a. $${-8-7}$$
b. $${11+(-3)}$$
c. $${20-(-2)}$$
d. $${-4 + 16}$$
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The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 6
Lesson 8
Topic A: Adding and Subtracting Rational Numbers
Represent rational numbers on the number line. Define opposites, absolute value, and rational numbers
7.NS.A.1
Compare and order rational numbers. Write and interpret inequalities to describe the order of rational numbers.
Describe situations in which opposite quantities combine to make zero.
7.NS.A.1.A
Model the addition of integers using a number line.
7.NS.A.1.B 7.NS.A.1.D
Determine efficient ways to add rational numbers with and without the number line.
Efficiently add and reason about sums of rational numbers.
7.NS.A.1.C 7.NS.A.1.D
Find and represent the distance between two rational numbers as the absolute value of their difference.
7.NS.A.1.C
Subtract rational numbers with and without the number line.
Add and subtract rational numbers efficiently using properties of operations.
7.NS.A.1.D
Add and subtract rational numbers using a variety of strategies.
7.NS.A.1 7.NS.A.1.A 7.NS.A.1.B 7.NS.A.1.C 7.NS.A.1.D
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Topic B: Multiplying and Dividing Rational Numbers
Determine the rules for multiplying signed numbers.
7.NS.A.2.A 7.NS.A.2.C
Multiply signed rational numbers and interpret products in real-world contexts.
Determine the rules for dividing signed numbers.
7.NS.A.2.B 7.NS.A.2.C
Divide signed rational numbers and interpret quotients in real-world contexts.
Convert rational numbers to decimals using long division and equivalent fractions.
7.NS.A.2.D
Multiply and divide with rational numbers using properties of operations.
7.NS.A.2 7.NS.A.2.C
Topic C: Using all Four Operations with Rational Numbers
Solve problems with rational numbers and all four operations.
7.NS.A.3
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