# Ordering Integers and Other Rational Numbers

Videos and solutions to help Grade 6 students learn how to write, interpret, and explain statements of order for rational numbers in the real-world.

Related Topics:
Lesson Plans and Worksheets for Grade 6
Lesson Plans and Worksheets for all Grades

### New York State Common Core Math Module 3, Grade 6, Lessons 7 & 8

Lessons 7 & 8 Student Outcomes

• Students write, interpret, and explain statements of order for rational numbers in the real-world.
• Students recognize that if a < b, then -a > -b, because a number and its opposite are equal distances from zero; and moving along the horizontal number line to the right means the numbers are increasing.

Lesson 8 Summary
When we order rational numbers, their opposites will be in the opposite order. For example, if seven is greater than five, negative seven is less than negative five.

Lesson 7 Classwork

Exercise 1
1. a. Graph 7 and its opposite on the number line. Graph 5 and its opposite on the number line.
b. Where does 7 lie in relation to 5 on the number line?
c. Where does the opposite 7 of lie on the number line in relation to the opposite of 5?
d. I am thinking of 2 numbers. The first number lies to the right of the second number on a number line. What can you say about the location of their opposites? (If needed, refer to your number line diagram.)

Example 1
The record low temperatures for a town in Maine for January and February are -20 and -19 degrees Fahrenheit respectively. Order the numbers from least to greatest. Explain how you arrived at the order.

Exercises 2–4
For each problem, order the rational numbers from least to greatest. First read the problem, then draw a number line diagram, and finally, write/explain the answer. (Allow time for whole-group presentations.)
2. Jon’s time for running the mile in gym class is 9.2 minutes. Jacky’s time is 9.18 minutes. Who ran the mile in less time?

3. Mrs. Rodriguez is a teacher at Westbury Middle School. She gives bonus points on tests for outstanding written answers and deducts points for answers that are not written correctly. She uses rational numbers to represent the points. She wrote the following on the students' papers: Student A: -2 points, Student B: -2.5 points. Did Student A or Student B perform worse on the test?

4. A carp is swimming approximately 8 1/4 feet beneath the water’s surface, and a sunfish is swimming approximately 3 1/2 feet beneath the water’s surface. Which fish is swimming further beneath the water's surface?

Example 2
Henry, Janon, and Clark are playing a card game. The object of the game is to finish with the most points. The scores at the end of the game are: Henry: -7, Janon: 0 and Clark: -5. Who won the game? Who came in last place? Use a number line model and explain how you arrived at your answer.

Exercises 5–6
For each problem, order the rational numbers from least to greatest by first reading the problem, then drawing a number line diagram, and finally, explaining your answer.
5. Henry, Janon, and Clark are playing another round of the card game. Their scores this time are as follows: Clark: -1, Janon: -2, and Henry: -4. Who won? Who came in last place?

6. Represent each of the following elevations using a rational number. Then order, the numbers from least to greatest.
Cayuga Lake, 122 meters above sea level
Mount Marcy, 1,629 meters above sea level
New York Stock Exchange Vault, 15.24 meters below sea level

Lesson 7 Problem Set

1. In the table below, list each set of rational numbers in order from least to greatest. Then list their opposites. Then list the opposites in order from least to greatest. The first example has been completed for you.

2. For each row, what pattern do you notice between the numbers in the 2nd and 4th columns? Why is this so?

Lesson 8 Concept Development

Example 1: Ordering Rational Numbers from Least to Greatest
Sam has \$10 in the bank. He owes his friend Hank \$2.25. He owes his sister \$1.75. Consider the three rational numbers related to this story of Sam's money. Write and order them from least to greatest.

Exercises 2–4
For each problem, list the rational numbers that relate to each situation. Then, order them from least to greatest; and explain how you made your determination.

2. During their most recent visit to the optometrist (eye doctor), Kadijsha and her sister Beth had their vision tested. Kadijsha’s vision in her left eye was -1.50 and her vision in her right eye was the opposite number. Beth’s vision was -1.00 in her left eye and +0.25 in her right eye.

3. There are three letters in Ms. Thomas's mailbox: a bill from the phone company for \$38.12, a bill from the electric company for \$67.55, and a tax refund check for \$25.89. (A bill is money that you owe someone and a tax refund check is money that you receive from someone.)

4. Monica, Jack and Destiny each had their arm length measured for an experiment in science class. They compared their arm lengths to a standard of 22 inches. The listing below shows in inches how each student's arm length compares to 22 inches. Order these rational numbers from least to greatest.

Example 2
Jason is entering college and has opened a checking account, which he will use for college expenses. His parents gave him to deposit into the account. Jason wrote a check for to pay for his Calculus book and a check for to pay for miscellaneous school supplies. Write the three rational numbers related to the balance in Jason’s checking account in order from greatest to least.

Exercise 5–6
For each problem, list the rational numbers that relate to each situation in order from greatest to least. Lastly, explain how you arrived at their order.
5. The following are the current monthly bills that Mr. McGraw must pay:
\$122.00, Cable and Internet
\$73.45, Gas and Electric
\$45.00, Cell phone

6. Arrange the following rational numbers in order from greatest to least: -1/3, 0, -1/5, 1/8.

Problem Set
1. a. In the table below, list each set of rational numbers from greatest to least. Then, in the appropriate column, state which number was farthest right and which number was farthest left on the number line.
Rational Numbers Ordered from Greatest to Least Farthest Right on the Number Line Farthest Left on the Number Line
b. For each row, describe the relationship between the number in Column 3 and its order in Column 2. Why is this?
c. For each row, describe the relationship between the number in Column 4 and its order in Column 2. Why is this?

2. If two rational numbers, a and b, are ordered such that a is less than b, then what must be true about the order for their opposites: -a and -b?

3. Read each statement, and then write a statement relating the opposites of each of the given numbers:
a. 7 is greater than 6.
b. 39.2 is greater than 30.
c. -1/5 is less than 1/3.

4. Order the following from least to greatest: -8, -19, 0, 1/2, 1/4.
5. Order the following from greatest to least: -12, 12, -19, 1 1/2, 5.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.