FUSD AZCCRS MATHEMATICS CURRICULUM
6/7•3
Lesson 6
Lesson 6: Writing and Interpreting Inequality Statements Involving Rational
Numbers
Date: 10/25/15
S.15
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
Lesson 6: Writing and Interpreting Inequality Statements
Involving Rational Numbers
Opening Exercise
“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 _____________.
b. Write an inequality statement comparing the possible value of the money in my pocket to $4.
c. Write an inequality statement comparing the possible value of the money in my 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 the Opening Exercise, 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, and 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).
Month
This Year’s Total Rainfall
(in inches)
Last Year’s Total Rainfall
(in inches)
Change in Total Rainfall from last year to this
year (in inches)
May
𝟐. 𝟑
𝟑. 𝟕
−𝟏. 𝟒
June
𝟑. 𝟖
𝟑. 𝟓
𝟎. 𝟑
July
𝟑. 𝟕
𝟑. 𝟐
𝟎. 𝟓
Write one inequality to order the Changes in Total Rainfall
_______________ ________________
From least to greatest From greatest to least
In this case, does the greatest number indicate the greatest change in rainfall? Explain.
FUSD AZCCRS MATHEMATICS CURRICULUM
6/7•3
Lesson 6
Lesson 6: Writing and Interpreting Inequality Statements Involving Rational
Numbers
Date: 10/25/15
S.16
© 2014 Common Core, Inc. Some rights reserved. commoncore.org
Exercises 5–8
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.
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 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: −𝟏𝟗 < 𝟒𝟎. Explain the position
of the numbers on a number line.
Exercise 9: A Closer Look at the Sprint
9. Look at the following two examples from the Sprint.
< <
−¼ , −1 , 0
> >
−¼ , −1 , 0
a. Fill in the numbers in the correct order.
b. Explain how the position of the numbers on the number line supports the inequality statements you created.
c. Create a new pair of greater than and less than inequality statements using three other rational numbers.