Eureka Math Grade 7 Module 2 Lesson 2 Answer Key

Engage NY Eureka Math 7th Grade Module 2 Lesson 2 Answer Key

Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key

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 __ .
Answer:
0

b. Draw the arrow 2 units to the left of 0, and stop at __. The direction of the arrow is to the ___ left since you are counting down from 0.
Answer:
-2, left

c. Start the next arrow at the end of the first arrow, or at __ .
Answer:
-2

d. Draw the second arrow __ units to the right since you are counting up from -2.
Answer:
3

e. Stop at __ .
Answer:
1

f. Circle the number at which the second arrow ends to indicate the ending value.
Answer:
Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key 1

g. Repeat the process from parts (a)–(f) for the expression 3+(-2).
Answer:
Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key 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?
Answer:
-2 + 3 is the same as 3 + (-2) because they both equal 1. The order does not matter when adding numbers because addition is commutative.

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? Use the number line provided to support your answer.
Answer:
|-2|=2, so the arrow is 2 units long. Because -2 is a negative number, the arrow points to the left.
Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key 3

b. How does the absolute value determine the arrow length for 3? Use the number line provided to support your answer.
Answer:
|3| = 3, so the arrow is 3 units long. Because 3 is positive, the arrow points to the right.
Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key 4

c. Describe how the absolute value helps you represent -10 on a number line.
Answer:
The absolute value can help me because it tells me how long my arrow should be when starting at 0 on the real number line. The |-10| = 10, so my arrow will be 10 units in length.

Example 3.
Finding Sums on a Real Number Line Model
Find the sum of the integers represented in the diagram below.
Eureka Math Grade 7 Module 2 Lesson 2 Example Answer Key 5

a. Write an equation to express the sum.
Answer:
5 + (-2) + 3 = 6

b. What three cards are represented in this model? How did you know?
Answer:
The cards are 5, -2, and 3 because the arrows show their lengths.

c. In what ways does this model differ from the ones we used in Lesson 1?
Answer:
In Lesson 1, a movement of 5 units was shown with 5 separate hops. In this lesson, 5 units are shown as one total movement with a straight arrow. Both represent the same total movement.

d. Can you make a connection between the sum of 6 and where the third arrow ends on the number line?
Answer:
The final position of the third arrow is 6. This means that the sum is 6.

e. Would the sum change if we changed the order in which we add the numbers, for example, (-2)+3+5?
Answer:
No, because addition is commutative. Order does not matter.

f. Would the diagram change? If so, how?
Answer:
Yes, the first arrow would start at 0 and point left 2 units. The second arrow would start at -2 and point right 3 units. The third arrow would start at 1 and point 5 units right but still end on 6.

Eureka Math Grade 7 Module 2 Lesson 2 Exercise Answer Key

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 an equation to represent this situation?
Answer:
10 + (-4) = 6

b. How would you model your equation on a number line to show your answer?
Answer:
Eureka Math Grade 7 Module 2 Lesson 2 Exercise Answer Key 5.1

Exercise 2
Create a number line model to represent each of the expressions below.
a. -6 + 4
Answer:
Eureka Math Grade 7 Module 2 Lesson 2 Exercise Answer Key 6

b. 3 + (-8)
Answer:
Eureka Math Grade 7 Module 2 Lesson 2 Exercise Answer Key 8

Eureka Math Grade 7 Module 2 Lesson 2 Exit Ticket Answer Key

Eureka Math Grade 7 Module 2 Lesson 2 Exit Ticket Answer Key 9

Jessica made the addition model below of the expression (-5)+(-2)+3.
a. Do the arrows correctly represent the numbers that Jessica is using in her expression?
Answer:
No. Jessica started her first arrow at -5 instead of 0. Negative numbers should be shown as counting down, so the arrow should have started at 0 and pointed left, ending on -5. The other arrows are drawn correctly, but they are in the wrong places because the starting arrow is in the wrong place.

b. Jessica used the number line diagram above to conclude that the sum of the three numbers is 1. Is she correct?
Answer:
Jessica is incorrect.

c. If she is incorrect, find the sum, and draw the correct model.
Answer:
The sum should be -4. -5 + (-2) + 3 = -4.
Eureka Math Grade 7 Module 2 Lesson 2 Exit Ticket Answer Key 9.1

d. Write a real-world situation that would represent the sum.
Answer:
Answers will vary. A football team lost 5 yards on the first play. On the second play, the team lost another 2 yards. Then, the team gained 3 yards. After three plays, the team had a total yardage of -4 yards.

Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key

Represent Problems 1–3 using both a number line diagram and an equation.

Question 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.
Answer:
(-6) + 12 + (-4) = 2
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 10

Question 2.
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.
Answer:
2 + 8 + (-11) + 7 = 6
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 11

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.
Answer:
You would need any combination of cards that sum to -6 because the additive inverse of 6 is -6.
6 + (-6) = 0

Question 3.
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?
Answer:
90 yards because 40+(-10)+60=90. Student answers may vary, but they should not choose to count by 1.
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 12

Question 4.
Find the sums.
a. -2 + 9
Answer:
7

b. -8 + -8
Answer:
-16

c. -4 + (-6) + 10
Answer:
0

d. 5 + 7 + (-11)
Answer:
1

Question 5.
Mark an integer between 1 and 5 on a number line, and label it point Z. Then, locate and label each of the following points by finding the sums.
Answer:
Answers will vary. Sample student response below.
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 50

a. Point A: Z+5
Answer:
Point A: 3+5=8

b. Point B: Z+(-3)
Answer:
Point B: 3+(-3)=0

c. Point C: (-4) + (-2) + Z
Answer:
Point C: (-4) + (-2) + 3 = -3

d. Point D: -3 + Z + 1
Answer:
Point D: -3 + 3 + 1 = 1

Question 6.
Write a story problem that would model the sum of the arrows in the number diagram below.
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 51
Answer:
Answers will vary. Jill got on an elevator and went to the 9th floor. She accidently pressed the down button and went back to the lobby. She pressed the button for the 5th floor and got off the elevator.

Question 7.
Do the arrows correctly represent the equation 4 + (-7) + 5 = 2? If not, draw a correct model below.
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 52
Answer:
No, the arrows are incorrect. The correct model is shown.
Eureka Math Grade 7 Module 2 Lesson 2 Problem Set Answer Key 53

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