Operations with Rational Numbers

Lesson 6

Math

Unit 2

7th Grade

Lesson 6 of 18

Objective


Efficiently add and reason about sums of rational numbers.

Common Core Standards


Core Standards

  • 7.NS.A.1.B — 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.
  • 7.NS.A.1.D — Apply properties of operations as strategies to add and subtract rational numbers.

Foundational Standards

  • 5.NF.A.1
  • 6.NS.B.3

Criteria for Success


  1. Understand that point B, located $$x$$ units from point A, is $$|x| $$ units in either the positive direction or the negative direction from point A. 
  2. Write addition problems for real-world situations.
  3. Find sums of rational numbers.
  4. Make sense of problems using understanding of distance, order, magnitude, direction, etc. (MP.1).

Tips for Teachers


  • In this lesson, students move away from using the number line as a tool to find the sums of rational numbers, and they begin to reason more abstractly about the relationship of numbers on a number line (MP.2), as seen in Anchor Problem 2. Students should also be more comfortable adding rational numbers without the support of a number line. 
  • Students may need to review adding and subtracting positive decimals and fractions. 
  • In terms of pacing, this lesson may be extended to allow for additional practice, review of prior grade-level computation expectations, or development of skills. 
  • Continue building fluency with mental math and other activities.
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Anchor Problems

25-30 minutes


Problem 1

In each problem, point A is shown on the number line and point B is a given distance from point A.

For each problem, write two addition equations that could be used to determine the location of point B.

a.   Point B is 4 units away from point A.

b.   Point B is $${6 {1\over4}}$$ units away from point A.

c.   Point B is $${5 {1\over3}}$$ units away from point A. (A = $${3 {2\over3}}$$)

Guiding Questions

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Student Response

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Problem 2

Two numbers, $$p$$ and $$q$$, are shown on the number line below, and $${|p|<|q|}$$.

Determine if the sums below are positive or negative. Explain your reasoning.

a.      $${p+q}$$

b.      $$-{p+q}$$

c.      $${p+(-q)}$$

d.      $$-{p+(-q)}$$

Guiding Questions

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Student Response

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Problem 3

The temperature of water in a lake at 9:00 a.m. is $$-2.6$$ËšC. By noon, the temperature of the water had risen by $$5.1$$ËšC. By 9:00 p.m., the temperature of the water had fallen by $$12.8$$ËšC from what it had been at noon. 

Write an addition problem to represent the changing temperature of the water, and find the temperature of the water at 9:00 p.m.

Guiding Questions

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Student Response

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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

Point A is located at $$-4.5$$, and point B is $$3.25$$ units from point A. Write two addition equations that could be used to determine the location of point B. Model this on the number line below.

Student Response

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Problem 2

Find the sums.

a.   $${-3+ \left (-2 {1\over4} \right )}$$

b.   $${5.7 + (-12.2)}$$

c.   $${-9 + 3 {2\over5}}$$

d.   $${-{10\over3} + 18}$$

e.   $${-2+3+(-1)+5}$$

Student Response

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Next

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

Lesson 7
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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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