Engage NY Eureka Math 6th Grade Module 3 Lesson 13 Answer Key

Example 1. Ordering Numbers In the Real World
A $25 credit and a$25 charge appear similar, yet they are very different.
Describe what is similar about the two transactions.
The transactions look similar because they are described using the same number. Both transactions have the same magnitude (or absolute value) and, therefore, result in a change of $25 to an account balance. How do the two transactions differ? Answer: The credit would cause an increase to an account balance and, therefore, should be represented by 25, while the charge would instead decrease an account balance and should be represented by – 25. The two transactions represent changes that are opposites. Example 2: Using Absolute Value to Solve Real-World Problems The captain of a fishing vessel is standing on the deck at 23 feet above sea level. He holds a rope tied to his fishing net that is below him underwater at a depth of 38 feet. Draw a diagram using a number line, and then use absolute value to compare the lengths of rope in and out of the water. Answer: The captain is above the water, and the fishing net is below the water’s surface. Using the water level as reference point zero, I can draw the diagram using a vertical number line. The captain is located at 23, and the fishing net is located at – 38. |23| = 23 and |- 38| = 38,so there is more rope underwater than above. 38 – 23 = 15 The length of rope below the water’s surface is 15 feet longer than the rope above water. Example 3: Making Sense of Absolute Value and Statements of Inequality A recent television commercial asked viewers, “Do you have over$10,000 in credit card debt?”

What types of numbers are associated with the word debt, and why? Write a number that represents the value from the television commercial.
Negative numbers; debt describes money that is owed; – 10,000

Give one example of “over $10,000 in credit card debt.” Then, write a rational number that represents your example. Answer: Answers will vary, but the number should have a value of less than – 10,000. Credit card debt of$11,000; – 11,000

How do the debts compare, and how do the rational numbers that describe them compare? Explain.
The example $11, 000 is greater than$10, 000 from the commercial; however, the rational numbers that represent these debt values have the opposite order because they are negative numbers. – 11,000 < – 10, 000. The absolute values of negative numbers have the opposite order of the negative values themselves.

Exercise 1.
Scientists are studying temperatures and weather patterns in the Northern Hemisphere. They recorded
temperatures (in degrees Celsius) in the table below as reported in emails from various participants. Represent each reported temperature using a rational number. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately represent the given temperatures.

– 13 < – 8 < – 6 < – 5 < – 4 < 0 < 2 < 12
The words “below zero” refer to negative numbers because they are located below zero on a vertical number line.

Exercise 2.
Jami’s bank account statement shows the transactions below. Represent each transaction as a rational number describing how it changes Jami’s account balance. Then, order the rational numbers from greatest to least. Explain why the rational numbers that you chose appropriately reflect the given transactions.

5.5 > 4.08 > – 1.5 > – 3 > – 3.95 > – 12.2 > – 20
The words “debit,” “charge,” and “withdrawal” all describe transactions in which money is taken out of Jami’s account, decreasing its balance. These transactions are represented by negative numbers. The words “credit” and “deposit” describe transactions that will put money into Jami’s account, increasing its balance. These transactions are represented by positive numbers.

Exercise 3.
During the summer, Madison monitors the water level in her parents’ swimming pool to make sure it is not too far above or below normal. The table below shows the numbers she recorded In July and August to represent how the water levels compare to normal. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately reflect the given water levels.

$$-1 \frac{1}{4}<-\frac{3}{4}<-\frac{1}{2}<-\frac{3}{8}<\frac{1}{8}<\frac{1}{4}<\frac{1}{2}$$
The measurements are taken in reference to normal level, which is considered to be 0. The words “above normal” refer to the positive numbers located above zero on a vertical number line, and the words “below normal” refer to the negative numbers located below zero on a vertical number line.

Exercise 4.
Changes in the weather can be predicted by changes in the barometric pressure. Over several weeks, Stephanie recorded changes in barometric pressure seen on her barometer to compare to local weather forecasts. Her observations are recorded In the table below. Use rational numbers to record the indicated changes In the pressure in the second row of the table. Order the rational numbers from least to greatest. Explain why the rational numbers that you chose appropriately represent the given pressure changes.

Eureka Math Grade 6 Module 3 Lesson 13 Problem Set Answer Key

Question 1.
Negative air pressure created by an air pump makes a vacuum cleaner able to collect air and dirt into a bag or other container. Below are several readings from a pressure gauge. Write rational numbers to represent each of the readings, and then order the rational numbers from least to greatest.

– 13 < – 7.8 < – 6.3 < – 1.9 < 2 < 7.8 < 25

Question 2.
The fuel gauge in Nic’s car says that he has 26 miles to go until his tank is empty. He passed a fuel station 19 miles ago, and a sign says there is a town only 8 miles ahead. If he takes a chance and drives ahead to the town and there isn’t a fuel station there, does he have enough fuel to go back to the last station? Include a diagram along a number line, and use absolute value to find your answer.
No, he does not have enough fuel to drive to the town and then back to the fuel station. He needs 8 miles’ worth of fuel to get to the town, which lowers his limit to 18 miles. The total distance between the fuel station and the town is 27 miles; |8| + |- 19| = 8 + 19 = 27. Nic would be9miles short on fuel. It would be safer to go back to the fuel station without going to the town first.

Eureka Math Grade 6 Module 3 Lesson 13 Exit Ticket Answer Key

Question 1.
Loni and Daryl call each other from different sides of Watertown. Their locations are shown on the number line below using miles. Use absolute value to explain who is a farther distance (in miles) from Watertown. How much closer is one than the other?

Loni’s location is – 6, and |- 6| = 6 because – 6 is 6 units from 0 on the number line. Daryl’s location is 10, and |10| = 10 because 10 is 10 units from 0 on the number line. We know that 10 > 6, so Daryl is farther from Watertown than Loni.
10 – 6 = 4; Loni is 4 miles closer to Watertown than Daryl.

Question 2.
Claude recently read that no one has ever scuba dived more than 330 meters below sea level. Describe what this means in terms of elevation using sea level as a reference point.