 # Using the Number Line to Model the Addition of Integers

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Common Core for Mathematics
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Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to use the number line to model the addition of integers.

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

Lesson 2 Student Outcomes

Students model integer addition on the number line by using horizontal arrows; e.g., an arrow for is a horizontal arrow of length pointing in the negative direction.

Students recognize that the length of an arrow on the number line is the absolute value of the integer.

Students add arrows (realizing that adding arrows is the same as combining numbers in the Integer Game). Given several arrows, students indicate the number that the arrows represent (the sum).

Lesson 2 Summary

On a number line, arrows are used to represent integers; they show length and direction.

The length of an arrow on the number line is the absolute value of the integer.

Adding several arrows is the same as combing integers in the Integer Game.

The sum of several arrows is the final position of the last arrow.

Exercise 1: Real-World Introduction to Integer Addition

a. Suppose you received \$10 from your grandmother for your birthday. You spent \$4 on snacks. Using addition, how would you write an equation to represent this situation?

Example 1: Modeling Addition on the Number Line

Complete the steps to find the sum of -2 + 3 by filling in the blanks. Model the equation using straight arrows called vectors on the number line below.

a. Place the tail of the arrow on ___.
b. Draw the arrow 2 units to the left of 0, and stop at ___. The direction of the arrow is to the ___ since you are counting down from .
c. Start the next arrow at the end of the first arrow or at ___ .
d. Draw the second arrow ___ units to the right since you are counting up from -2.
e. Stop at ___.

Example 2: Expressing Absolute Value as the Length of an Arrow on the Real Number Line

a. How does absolute value determine the arrow length for -2
b. How does the absolute value determine the arrow length for 3?
c. How does absolute value help you to represent -10 on a number line?

Exercise 2

Create a number line model to represent each of the expressions below.

a. -6 + 4
b. 3 + (-8)

Example 3: Finding Sums on a Real Number Line Model

Find the sum of the integers represented in the diagram below. Write an equation to express the sum

a. What three cards are represented in this model? How did you know?
b. In what ways does this model differ from the ones we used in Lesson 1?
c. Can you make a connection between the sum of and where the third arrow ends on the number line?
d. Would the sum change if we changed the order in which we add the numbers, for example, (-2) + 3 +5 ?
e. Would the diagram change? If so, how?
Exercise 3
Play the Integer Game with your group. Use a number line to practice “counting on.”

Problem Set Sample Solutions

8. Do the arrows correctly represent the equation 4 + (-7) + 5 = 2? If not, draw a correct model below.

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