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Inequality Statements Involving Rational Numbers


Videos to help Grade 6 students learn to write and explain inequality statements involving rational numbers.

Students justify inequality statements involving rational numbers.

New York State Common Core Math Grade 6, Module 3, Lesson 10

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Lesson Plans and Worksheets for Grade 6

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More Lessons for Grade 6

Common Core For Grade 6

Opening Exercises

“The amount of money I have in my pocket is less $5 than but greater than $4.”

1. One possible value for the amount of money in my pocket is:_____

2. Write an inequality statement comparing the possible value of the money in your pocket to $4.

3. Write an inequality statement comparing the possible value of the money in your pocket to $5

Exercises 1–4

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

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

3. Explain in words how the location of the three numbers on the number line supports the inequality statements you wrote in parts (b) and (c).

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

Example 1: Writing Inequality Statements Involving Rational Numbers

Write one inequality statement to show the relationship between the following shoe sizes: 10 1/2, 8, 9

a. From Least to Greatest:
b. From Greatest to Least:

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).

Order the Changes in Total Rainfall: From Least to Greatest and rom Greatest to Least
In this case, does the greatest number indicate the greatest change in rainfall? Explain.

Exercises 5–8

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

6. Sierra had to pay the school for two textbooks that she lost. One textbook costs$55 and the other cost $75. Her mother wrote two separate checks 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.

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.

8. Write a real-world situation that is represented by the following inequality:-17 < 40. Explain the position of the numbers on a number line.


What can you do before writing an inequality statement involving three numbers that makes it easier to write the inequality statement? For example, explain the process for writing one inequality statement comparing ,-3 ,8 and -10.

If you know the order of a set of numbers, how can you represent the order using inequality symbols?

If two negative numbers are ordered using the < symbol, what must be true about their positions on a horizontal number line? On a vertical number line?

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.

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