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Opposite Quantities Combine to Make Zero

Videos and solutions to help Grade 7 students learn how opposite quantities combine to make zero.

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Common Core For Grade 7

New York State Common Core Math Grade 7, Module 2, Lesson 1

Student Outcomes

Students add positive integers by counting up and negative integers by counting down (using curved arrows on the number line).

Students play the Integer Game to combine integers, justifying that an integer plus its opposite add to zero.

Students know the opposite of a number is called the additive inverse because the sum of the two numbers is zero.

Lesson Summary

Add positive integers by counting up and, add negative integers by counting down.

An integer plus its opposite sum to zero.

The opposite of a number is called the additive inverse because the two numbers’ sum is zero.

Exercise 1: Positive and Negative Numbers Review

Use the graphic organizer below to record what you know about positive and negative numbers.

Example 2: Counting Up and Counting Down on the Number Line

Use the number line below to practice counting up and counting down.

Counting up corresponds to positive numbers.
Counting down corresponds to negative numbers.

a. Where do you begin when locating a number on the number line?
b. What do you call the distance between a number and on a number line?
c. What is the relationship between 7 and −7?

Example 3: Using the Integer Game and the Number Line

What is the value of the sum of the card values shown? Use the counting on method on the provided number line to justify your answer.

Exercise 2: The Additive Inverse

Use the number line to answer each of the following:

a. How far is from and in which direction?
b. What is the opposite of ?
c. How far is −7 from 0 and in which direction?

For all numbers there is a number –a, such that a + (-a) = 0

The additive inverse of a real number is the opposite of that number on the real number line. For example, the opposite of −3 is 3. A number and its additive inverse have a sum of 0. The sum of any number and its opposite is equal to zero.

Problem Set Sample Solutions
5. During a football game, Kevin gained five yards on the first play. Then he lost seven yards on the second play. How many yards does Kevin need on the next play to get the team back to where they were when they started? Show your work.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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