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.
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:
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.