Teaching Notes 3.10: Classifying Inequalities as True or False
To determine if an equality is true or false, students must first compare quantities. Combined
inequalities and use of the symbols≤and≥can be particularly confusing.- Provide an example of a number line for your students. Review the number line’s properties:
- A number is greater than any number to its left.
- A number is less than any number to its right.
- Review the information and examples on the worksheet with your students. Discuss the
meaning of the inequality symbols. Particularly emphasize the meanings of the≤and≥
signs. Note how some inequalities can be combined. Encourage your students to sketch a
number line to help them recognize the relationship between the numbers.
EXTRA HELP:
Read the inequality. Use words in place of the symbol to clarify your thinking.ANSWER KEY:
Answers may vary. One correct answer for each false inequality follows.
(1)F; 3< 4 (2)F; 3≤ 4 (3)T (4)T
(5)T (6)F;|− 4 |≤ 4 (7)T (8)F; (−3)^2 < 10
(9)T (10)T (11)F;− 5 <− 22 < 4 (12)T
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(Challenge)Joe is incorrect. He did not understand the meaning of the≤symbol. He seemed to
interpret it as− 2 < 0 and− 2 =0insteadof− 2 < 0 or− 2 =0, which is a true statement.
------------------------------------------------------------------------------------------106 THE ALGEBRA TEACHER’S GUIDE