Lesson 2: Using the Number Line to Model the Addition

Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Lesson 2: Using the Number Line to Model the Addition of
Integers
Classwork
Exercise 1: Real-World Introduction to Integer Addition
Answer the questions below.
a.
Suppose you received $10 from your grandmother for your birthday. You spent $4 on snacks. Using addition, how
would you write a number sentence to represent this situation?
b.
How would you model your equation on a number line to show your answer?
Example 1: Modeling Addition on the Number Line
Complete the steps to finding the sum of −2 + 3 by filling in the blanks. Model the number sentence 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 0.
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 ________.
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.6
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
f.
Circle the number at which the second arrow ends to indicate the ending value.
g.
Repeat the process from parts (a)–(f) for the expression 3 + (−2).
h.
What can you say about the sum of −2 + 3 and 3 + (−2)? Does order matter when adding numbers? Why or why
not?
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?
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.7
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
c.
7•2
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.

−

a.
Write an equation to express the sum.
b.
What three cards are represented in this model? How did you know?
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.8
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
c.
In what ways does this model differ from the ones we used in Lesson 1?
d.
Can you make a connection between the sum of 6 and where the third arrow ends on the number line?
e.
Would the sum change if we changed the order in which we add the numbers, for example, (−2) + 3 + 5?
f.
Would the diagram change? If so, how?
7•2
Exercise 3
Play the Integer Game with your group. Use a number line to practice “counting on”.
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.9
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
7•2
Lesson 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 combining integers in the Integer Game.
The sum of several arrows is the final position of the last arrow.
Problem Set
For Questions 1–3, represent each of the following problems using both a number line diagram and an equation.
1.
David and Victoria are playing the Integer Card Game. David drew three cards, −6, 12, and −4. What is the sum of
the cards in his hand? Model your answer on the number line below.
2.
3.
In the Integer Card Game, you drew the cards, 2, 8, and −11. Your partner gave you a 7 from his hand.
a.
What is your total? Model your answer on the number line below.
b.
What card(s) would you need to get your score back to zero? Explain. Use and explain the term “additive
inverse” in your answer.
If a football player gains 40 yards on a play, but on the next play, he loses 10 yards, what would his total yards
be for the game if he ran for another 60 yards? What did you count by to label the units on your number line?
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.10
Lesson 2
NYS COMMON CORE MATHEMATICS CURRICULUM
4.
5.
7•2
Find the sums.
a.
−2 + 9
b.
−8 + −8
c.
−4 + (−6) + 10
d.
5 + 7 + (−11)
Mark an integer between 1 and 5 on a number line, and label it point . Then, locate and label each of the
following points by finding the sums.
a.
Point :  + 5
b.
Point :  + (−3)
c.
Point : (−4) + (−2) + 
d.
Point : −3 +  + 1
6.
Write a story problem that would model the sum of the arrows in the number diagram below.
7.
Do the arrows correctly represent the equation 4 + (−7) + 5 = 2? If not, draw a correct model below.
Lesson 2:
Date:
Using the Number Line to Model the Addition of Integers
10/27/14
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
S.11