Curriculum  /  Math  /  7th Grade  /  Unit 2: Operations with Rational Numbers  /  Lesson 3

Operations with Rational Numbers

Lesson 3

Math

Unit 2

7th Grade

Lesson 3 of 18

Objective

Describe situations in which opposite quantities combine to make zero.

Common Core Standards

Core Standards

  • 7.NS.A.1.A — Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Foundational Standards

  • 6.NS.C.5
  • 6.NS.C.6

Criteria for Success

  1. Understand that opposites are additive inverses, meaning that when two opposite numbers are added together, they equal 0.
  2. Represent additive inverses on a number line.
  3. Describe situations involving money, elevation, temperature, distance, etc., where opposite quantities make 0.

Tips for Teachers

The Integer Game is an activity in EngageNY, Module 2. It is an optional activity for this lesson, which may also be used again in later lessons. It requires some preparation. The number line and game piece from Lesson 1 is also a good tool to use in this lesson.

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Anchor Problems

25-30 minutes

Problem 1

Four people all started out with a positive balance in their checking accounts. The chart below shows the starting balance for each person and the banking activity they had in the last week. 

  Andrea Blake Cameron Dakota
Starting Balance $56 $100 $56 $56
Activity Deposited $56 Spent $56 Spent $100 Spent $56

Describe what each person’s balance in their checking account looks like at the end of the week.

Guiding Questions

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Student Response

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Problem 2

A cabin is located on a mountain at an elevation of 215 feet above sea level. A hiker leaves the cabin and goes on a hike that increases her altitude by 30 feet. Which situations would bring the hiker back to her original elevation at the cabin? Select all that apply.

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Guiding Questions

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Student Response

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Problem 3

Consider the equation: $${8+(-8)=0}$$

a.   Write a situation that could be described using the equation.

b.   Represent your situation on a number line. Use labels and arrows to show changes in value.

c.   Two numbers that add together to get 0 are called additive inverses of each other. Name 2 more examples of additive inverses. 

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

Rami leaves his house to drive to school. After driving west for $$8\frac{3}{4}$$ miles, he realizes that he forgot his backpack at home. 

How far and in what direction does Rami have to travel to get back to his house? Represent the situation on a number line, including labels for Rami’s house and school, and arrows to show his trips.

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 problems similar to Anchor Problem #2.

  • Include problems where students model situations on the number line.

  • EngageNY Mathematics Grade 7 Mathematics > Module 2 — Overview, "Integer Game" (This is optional; it requires some preparation and explanation—found in Lesson 1, Example 3.)
  • EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic A > Lesson 1 — Exercises, Examples, and Problem Set (Note that some of the problems refer to the Integer Game, explained in the module. These can be skipped if the game is not incorporated into class.)
  • Open Middle Creating Zero — Challenge

Next

Model the addition of integers using a number line.

Lesson 4
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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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