Operations with Rational Numbers

Lesson 7

Math

Unit 2

7th Grade

Lesson 7 of 18

Objective


Understand subtraction as addition of the opposite value (or additive inverse).

Common Core Standards


Core Standards

  • 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.

Foundational Standards

  • 6.NS.C.6

Criteria for Success


  1. Understand that adding negative amounts results in moving to the left on the number line, as does subtracting positive amounts.
  2. Understand that adding positive amounts results in moving to the right on the number line, as does subtracting negative amounts.
  3. Rewrite subtraction problems as addition of the opposite value.
  4. Model addition and subtraction problems on the number line (MP.4).

Tips for Teachers


  • There are several different approaches to introducing the concept of subtracting positive and negative values. This lesson focuses on using the number line as a way to “move” according to the problem. On the number line, there are only two directions in which to move; it is the combination of the operation and the sign of the number that will tell students which way to go. This blog by Nathan Kraft, which follows a similar approach, is helpful to read prior to the lesson.
  • In addition to this approach, there are others that may be valuable with a subset of students or the whole class. This blog post by David Wees does a nice job explaining the problem $${4-(-3)=7}$$ in five different ways.
  • If you have introduced the Integer Game used in the EngageNY materials, this could also be incorporated into an Anchor Problem and/or the Problem Set Guidance.

Lesson Materials

  • Optional: Standard deck of playing cards (1 per student or small group)
  • Laminated number line (1 per student)
  • Game piece or token (1 per student)
  • Dry erase marker (1 per student)
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Anchor Problems

25-30 minutes


Problem 1

Use your number line and game piece to model each subtraction problem and answer the questions that follow. 

  1.   $$5-3$$
  2.   $$3-5$$
  3.   $$-3-5$$
  4.   $$-5-3$$

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? 

Guiding Questions

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Student Response

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Problem 2

Use your number line and game piece to model each subtraction problem and answer the questions that follow. 

  1.   $${5-(-3)}$$
  2.   $${3-(-5)}$$
  3.   $$-{3-(-5)}$$
  4.   $$-{5-(-3)}$$

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?

Guiding Questions

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Student Response

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Problem 3

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. 

Guiding Questions

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Student Response

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References

Nathan Kraft's Blog An Alternative to 'Add the Opposite'Andrew Stadel's comment on May 23, 2016

An Alternative to 'Add the Opposite' is made available on Nathan Kraft's Blog. Accessed Aug. 15, 2017, 12:41 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Problem 1

Circle the expressions below that have a value of 2.

$${8+ (-6)}$$             $${6-8}$$             $${-{8-6}}$$             $${-8+(-6)}$$

 

$${8-6}$$             $${-6+8}$$             $${-8+6}$$             $${-6 - (-8)}$$

Student Response

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Problem 2

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.   $${-4 + 16}$$

Student Response

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Additional Practice


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.

  • Include opportunities for students to continue modeling and confirming the conclusions from Anchor Problems #1 and #2.
  • Include problems where students rewrite subtraction problems as addition problems, then model each one and determine the answers are the same. Ensure practice with all variations of adding/subtracting positives/negatives; stick to small integers so students can continue to internalize the concept.
  • Using a deck of playing cards, students can draw two cards, write two problems (addition and subtraction), and find the answer; encourage use of a number line.
  • EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 5Exercises and Problem Set
  • SERP Poster Problems Seeing SumsThere are two handouts with problems where students model addition and subtraction on the number line, as well as a dynamic number line for students to use on the computer.

Next

Find and represent the distance between two rational numbers as the absolute value of their difference.

Lesson 8
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Adding and Subtracting Rational Numbers

Topic B: Multiplying and Dividing Rational Numbers

Topic C: Using all Four Operations with Rational Numbers

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