Name _______________________________________________ Date ___________
Math 7
Mrs. L Liddiard
Lesson 1.2 Adding Numbers on a Number Line
Adding Integers
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 represents this
situation?
How would you model your number sentence on a number line? Where should you
start?
Does the order matter when we add numbers? Let’s try it and see!
-2 + 3
3 + (-2)
What can you say about the sum of -2 + 3 and 3 + (-2)? Does order matter when
adding numbers? Why or why not?
The Arrows
What do the arrows on a number line really tell us?
2 + (-4)
How long is the line for 2? ____________________________
What direction does the arrow for 2 point? ____________________________
How long is the line for -4? _____________________
What direction does the arrow for -4 point? ____________________
Arrows actually tell us ________________________ and _______________________.
Consider the following problem: 54 + (-21)
Would you want to draw arrows for this problem? Why or why not?
Can you determine how far away from 54 the answer is?
Can you determine in what direction from 54 the answer lies?
How do you know these answers to be true?
-34 + 82
How far away from -34 and in what direction is the answer?
The Integer Game
Shuffle the cards. Each player is dealt two cards. The remaining cards should be laid
face down with the top card turned over as a discard pile. Each player should keep
their cards to themselves. Using a number line, find the sum of your two cards. On
your turn, decide if you want to pick up the top discard card or pick an unknown card
from the draw pile. Once you have drawn a card, you must discard one card from your
hand in the discard pile.
Goal: The first player to reach a sum of zero wins!
Lesson Summary
Classwork
1. Complete the table.
Change in Temperatures from Morning to Afternoon
Morning
Temperature
Change
Number Sentence
1℃
rise of 3 ℃
1+3=4
2℃
rise of 8 ℃
−2 ℃
fall of 6 ℃
−4 ℃
rise of 7 ℃
6℃
fall of 9 ℃
−5 ℃
fall of 5 ℃
7℃
fall of 7 ℃
Afternoon
Temperature
4℃
2. Terry selected two cards. The sum of her cards is −10.
a. Can both cards be positive? Explain why or why not.
b. Can one of the cards be positive and the other be negative? Explain why or why
not
.
c. Can both cards be negative? Explain why or why not.
3. When playing the Integer Game, the first two cards you selected were −8 and −10.
a. What is the value of your hand? Write an equation to justify your answer.
b. For part (a), what is the distance of the sum from −8? Does the sum lie to the
right or left of −8 on the number line?
c. If you discarded the −10 and then selected a 10, what would be the value of your
hand? Write an equation to justify your answer.
4. Given the expression 67 + (−35), can you determine, without finding the sum, the
distance between 67 and the sum? Is the sum to the right or left of 67 on the number
line?
5.
a. Would the sum change if we changed the order in which we add the numbers, for
example, (−2) + 3 + 5?
b. What would change?
6. 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.
7. In the Integer Card Game, you drew the cards, 2, 8, and −11. Your partner gave you
a 7 from his hand. What is your new total? Model your answer on the number line
below.
What cards would you need to get your score back to zero? Explain.
8.
Find each of the sums below.
Z
9.
10.