## Engage NY Eureka Math 6th Grade Module 3 Lesson 4 Answer Key

### Eureka Math Grade 6 Module 3 Lesson 4 Example Answer Key

Example 1:

Every Number Has an Opposite

Locate the number 8 and its opposite on the number line. Explain how they are related to zero.

Answer:

→ First, start at zero, and move 8 units to the right to locate positive 8. So, the opposite of 8 must be 8 units to the left of zero. What number is 8 units to the left of zero?

– 8

→ 8 and – 8 are the same distance from zero. Since both numbers are the same distance from zero but on opposite sides of zero on the number line, they are opposites.

Example 2:

A Real-World Example

Maria decides to take a walk along Central Avenue to purchase a book at the bookstore. On her way, she passes the Furry Friends Pet Shop and goes in to look for a new leash for her dog. Furry Friends Pet Shop Is seven blocks west of the bookstore. She leaves Furry Friends Pet Shop and walks toward the bookstore to look at some books. After she leaves the bookstore, she heads east for seven blocks and stops at Ray’s Pet Shop to see If she can find a new leash at a better price. Which location, if any, Is the farthest from Maria while she is at the bookstore?

Determine an appropriate scale, and model the situation on the number line below.

Answer:

Answers will vary.

Explain your answer. What does zero represent in the situation?

Answer:

The pet stores are the same distance from Maria, who is at the bookstore. They are each 7 blocks away but in opposite directions. In this example, zero represents the bookstore.

### Eureka Math Grade 6 Module 3 Lesson 4 Exercise Answer Key

Exercise 1:

Walk the Number Line

Each nonzero integer has an opposite, denoted – a; – a and a are opposites if they are on opposite sides of zero and the same distance from zero on the number line.

Answer:

Exercises 2.

Locate and label the opposites of the numbers on the number line.

a. 9

b. – 2

c. 4

d. – 7

Answer:

Exercises 3.

Write the integer that represents the opposite of each situation. Explain what zero means in each situation.

a. 100 feet above sea level

Answer:

– 100; zero represents sea level.

b. 32°C below zero

Answer:

32; zero represents 0 degrees Celsius.

c. A withdrawal of $25

Answer:

25; zero represents no change, where no withdrawal or deposit is made.

Read each situation carefully, and answer the questions.

Exercises 4.

On a number line, locate and label a credit of $15 and a debit for the same amount from a bank account. What does zero represent in this situation?

Answer:

Zero represents no change in the balance.

Exercises 5.

On a number line, locate and label 20°C below zero and 20°C above zero. What does zero represent In this situation?

Answer:

Zero represents 0°C.

Exercises 6.

A proton represents a positive charge. Write an integer to represent 5 protons. An electron represents a negative charge. Write an integer to represent 3 electrons.

Answer:

5 protons: 5

3 electrons: – 3

### Eureka Math Grade 6 Module 3 Lesson 4 Problem Set Answer Key

Question 1.

Find the opposite of each number, and describe its location on the number line.

a. – 5

Answer:

The opposite of – 5 is 5, which is 5 units to the right of (or above) 0.

b. 10

Answer:

The opposite of 10 is – 10, which is 10 units to the left of(or below) 0.

c. – 3

Answer:

The opposite of – 3 is 3, which is 3 units to the right of (or above) 0.

d. 15

Answer:

The opposite of 15 is – 15, which is 15 units to the left of(or below) 0.

Question 2.

Write the opposite of each number, and label the points on the number line.

a. Point A: the opposite of 9

Answer:

– 9

b. Point B: the opposite of – 4

Answer:

4

c. Point C: the opposite of – 7

Answer:

7

d. Point D: the opposite of 0

Answer:

0

e. Point E: the opposite of 2

Answer:

– 2

Question 3.

Study the first example. Write the integer that represents the opposite of each real-world situation. In words, write the meaning of the opposite.

a. An atom’s positive charge of 7

Answer:

– 7, an atom’s negative charge of 7

b. A deposit of $25

Answer:

– 25, a withdrawal of $25

c. 3,500 feet below sea level

Answer:

3, 500, 3,500 feet above sea level

d. A rise of 45°C

Answer:

– 45, a decrease of 45°C

e. A loss of 13 pounds

Answer:

13, a gain of 13 pounds

Question 4.

On a number line, locate and label a credit of $38 and a debit for the same amount from a bank account. What does zero represent ¡n this situation?

Answer:

Zero represents no change in the balance.

Question 5.

On a number line, locate and label 40°C below zero and 40°C above zero. What does zero represent in this situation?

Answer:

Zero represents 0°C.

### Eureka Math Grade 6 Module 3 Lesson 4 Exit Ticket Answer Key

In a recent survey, a magazine reported that the preferred room temperature in the summer is 68°F. A wall thermostat, like the ones shown below, tells a room’s temperature in degrees Fahrenheit.

a. Which bedroom is warmer than the recommended room temperature?

Answer:

The upstairs bedroom is warmer than the recommended room temperature.

b. Which bedroom is cooler than the recommended room temperature?

Answer:

The downstairs bedroom is cooler than the recommended room temperature.

c. Sarah notices that her room’s temperature is 4°F above the recommended temperature, and the downstairs bedroom’s temperature is 4°F below the recommended temperature. She graphs 72 and 64 on a vertical number line and determines they are opposites. Is Sarah correct? Explain.

Answer:

No. Both temperatures are positive numbers and not the same distance from 0, so they cannot be opposites. Both numbers have to be the same distance from zero, but one has to be above zero, and the other has to be below zero in order to be opposites.

d. After determining the relationship between the temperatures, Sarah now decides to represent 72°F as 4 and 64°F as – 4 and graphs them on a vertical number line. Graph 4 and – 4 on the vertical number line on the right. Explain what zero represents in this situation.

Answer:

Zero represents the recommended room temperature of 68°F. Zero could also represent not being above or below the recommended temperature.