## Engage NY Eureka Math 6th Grade Module 3 Lesson 10 Answer Key

### Eureka Math Grade 6 Module 3 Lesson 10 Example Answer Key

Example 1.
Writing Inequality Statements Involving Rational Numbers
Write one inequality statement to show the relationship among the following shoe sizes: 10$$\frac{1}{2}$$, 8, and 9.
a. From least to greatest:
8 < 9 < 10$$\frac{1}{2}$$

b. From greatest to least:
10$$\frac{1}{2}$$ > 9 > 8

Example 2.
Interpreting Data and Writing Inequality Statements
Mary is comparing the rainfall totals for May, June, and July. The data Is reflected in the table below. Fill in the blanks below to create inequality statements that compare the changes in Total Rainfall for each month (the right-most column of the table).

Write one inequality to order the Changes in Total Rainfall:
From least to greatest:   – 1.4 < 0.3 < 0.5
From greatest to least:   0.5 >0.3 > -1.4

In this case, does the greatest number indicate the greatest change in rainfall? Explain.
No. In this situation, the greatest change is for the month of May since the average total rainfall went down from last year by 1.4 inches, but the greatest number in the inequality statement is 0. 5.

### Eureka Math Grade 6 Module 3 Lesson 10 Exercise Answer Key

Exercise 1.
Graph your answer from the Opening Exercise part (a) on the number line below.

Exercise 2.
Also, graph the points associated with 4 and 5 on the number line.

Exercise 3.
Explain in words how the location of the three numbers on the number line supports the inequality statements you wrote in the Opening Exercise parts (b) and (c).
The numbers are ordered from least to greatest when I look at the number line from left to right. So, 4 is less than 4. 75, and 4.75 is less than 5.

Exercise 4.
Write one inequality statement that shows the relationship among all three numbers.

4 < 4.75 < 5

Exercise 5.
Mark’s favorite football team lost yards on two back-to-back plays. They lost 3 yards on the first play. They lost 1 yard on the second play. Write an inequality statement using integers to compare the forward progress made on each play.
– 3 < – 1

Exercise 6.
Sierra had to pay the school for two textbooks that she lost. One textbook cost $55, and the other cost$75. Her mother wrote two separate checks, one for each expense. Write two integers that represent the change to her mother’s checking account balance. Then, write an inequality statement that shows the relationship between these two numbers.
– 55 and – 75; – 55 > – 75

Exercise 7.
Jason ordered the numbers – 70, – 18, and – 18. 5 from least to greatest by writing the following statement: – 18 < – 18.5 < – 70. Is this a true statement? Explain.
No, it is not a true statement because 18 < 18. 5 < 70, so the opposites of these numbers are in the opposite order. The order should be – 70 < – 18.5 < 18.

Exercise 8.
Write a real-world situation that is represented by the following inequality: – 19 < 40. Explain the position of the numbers on a number line.
The coldest temperature in January was – 19 degrees Fahrenheit, and the warmest temperature was 40 degrees Fahrenheit. Since the point associated with 40 is above zero on a vertical number line and – 19 is below zero, we know that 40 is greater than – 19. This means that 40 degrees Fahrenheit is warmer than – 19 degrees Fahrenheit.

Exercise 9.
A Closer Look at the Sprint
Look at the following two examples from the Sprint.

a. Fill in the numbers In the correct order.
– 1< – <$$\frac{1}{4}$$ < 0 and 0 > – $$\frac{1}{4}$$ > – 1

b. Explain how the position of the numbers on the number line supports the inequality statements you created.
– 1 is the farthest left on the number line, so it is the least value. 0 is farthest right, so it is the greatest value, and – $$\frac{1}{4}$$ is in between.

c. Create a new pair of greater than and less than inequality statements using three other rational numbers.
Answers will vary. 8 > 0. 5 > – 1.8 and – 1.8 < 0.5 < 8

### Eureka Math Grade 6 Module 3 Lesson 10 Problem Set Answer Key

For each of the relationships described below, write an Inequality that relates the rational numbers.

Question 1.
Seven feet below sea level Is farther below sea level than 4$$\frac{1}{2}$$ feet below sea level.
– 7 < – 4$$\frac{1}{2}$$

Question 2.
Sixteen degrees Celsius is warmer than zero degrees Celsius.
16 > 0

Question 3.
Three and one-half yards of fabric Is less than five and one-half yards of fabric.
3$$\frac{1}{2}$$ < 5$$\frac{1}{2}$$

Question 4.
A loss of $500 in the stock market is worse than a gain of$200 in the stock market.
– 500 < 200

Question 5.
A test score of 64 is worse than a test score of 65, and a test score of 65 is worse than a test score of 67$$\frac{1}{2}$$
64 < 65 < 67$$\frac{1}{2}$$

Question 6.
In December, the total snowfall was 13. 2 inches, which is more than the total snowfall in October and November, which was 3.7 inches and 6. 15 inches, respectively.
13.2 > 6.15 > 3.7

For each of the following, use the information given by the inequality to describe the relative position of the numbers on a horizontal number line.

Question 7.
– 0.2 < – 0.1
– 0.2 is to the left of – 0.1, or – 0.1 is to the right of – 0.2.

Question 8.
8$$\frac{1}{4}$$ > -8$$\frac{1}{4}$$
8$$\frac{1}{4}$$ is to the right of – 8$$\frac{1}{4}$$ or – 8$$\frac{1}{4}$$ is to the left of 8$$\frac{1}{4}$$.

Question 9.
– 2 < 0 < 5
– 2 is to the left of zero and zero is to the left of 5, or 5 is to the right of zero and zero is to the right of – 2.

Question 10.
– 99 > – 100
– 99 is to the right of – 100, or – 100 is to the left of – 99.

Question 11.
– 7.6 <- 7$$\frac{1}{2}$$ – 7
– 7.6 is to the left of – 7$$\frac{1}{2}$$ and – 7$$\frac{1}{2}$$ is to the left of – 7, or – 7 is to the right of – 7$$\frac{1}{2}$$ and – 7$$\frac{1}{2}$$ is to the right of – 7.6.

Fill in the blanks with numbers that correctly complete each of the statements.

Question 12.
Three integers between -4 and 0
– 3 < – 2 < – 1

Question 13.
Three rational numbers between 16 and 15
15.3 < 15.6 < 15.7

Question 14.
Three rational numbers between -1 and -2
– 1.9 < – 1.55 < – 1.02

Question 15.
Three integers between 2 and – 2
– 1 < 0 < 1

### Eureka Math Grade 6 Module 3 Lesson 10 Exit Ticket Answer Key

Question 1.
Kendra collected data for her science project. She surveyed people asking them how many hours they sleep during a typical night. The chart below shows how each person’s response compares to 8 hours (which is the answer she expected most people to say).

a. Plot and label each of the numbers in the right-most column of the table above on the number line below.

b. List the numbers from least to greatest
– 1.0, – $$\frac{1}{4}$$, 0, 0.5, 1.5

c. Using your answer from part (b) and inequality symbols, write one statement that shows the relationship among all the numbers.
– 1.0 < –$$\frac{1}{4}$$ < 0 < 0.5 < 1.5 or 0.5 > 0.5 > 0 > –$$\frac{1}{4}$$ > -1.0

### Eureka Math Grade 6 Module 3 Lesson 10 Opening Exercise Answer Key

“The amount of money I have in my pocket is less than $5 but greater than$4.”
a. One possible value for the amount of money in my pocket is ___________ .
$4.75 b. Write an inequality statement comparing the possible value of the money in my pocket to$4.
4.00 < 4.75

c. Write an inequality statement comparing the possible value of the money in my pocket to \$5.
4.75 < 5.00

### Eureka Math Grade 6 Module 3 Lesson 10 Inequality Statements Answer Key

Rational Numbers: Inequality Statements – Round 1
Directions: Work in numerical order to answer Problems 1 – 33. Arrange each set of numbers in order according to the inequality symbols.

Question 1.

Question 2

Question 3.

Question 4.

Question 5.

Question 6.

Question 7.

Question 8.

Question 9.

Question 10.

Question 11.

Question 12.

Question 13.

Question 14

Question 15.

Question 16.

Question 17.

Question 18.

Question 19.

Question 20.

Question 21.

Question 22.

Question 23.

Question 24.

Question 25.

Question 26.

Question 27.

Question 28.

Question 29.

Question 30.

Question 31.

Question 32.