This lesson teaches students about true and false number sentences. Students learn that a number sentence is an equation or inequality between two numerical expressions. A number sentence is true if the expressions evaluate to the same number or satisfy the inequality, and false otherwise. The lesson provides examples of substituting values into variables in number sentences and determining whether the resulting sentences are true or false. Students practice this by substituting values into given number sentences and stating the truth value.

1. Lesson 23: True and False Number Sentences
Date: 4/23/14 S.100
100
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 23
Lesson 23:True and False Number Sentences
Classwork
Opening Exercise
Determine what each symbol stands for and provide an example.
Symbol What the Symbol Stands For Example
Example 1
For each inequality or equation your teacher displays, write the equation or inequality, then substitute 3 for every .
Determine if the equation or inequality results in a true number sentence or a false number sentence.
1.
2.
3.
4.
5.
6.

2. Lesson 23: True and False Number Sentences
Date: 4/23/14 S.101
101
©2013CommonCore,Inc. Some rights reserved.commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 23
Exercises
Substitute the value into the variable and state (in a complete sentence) whether the resulting number sentence is true
or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true
number sentence.
1. . Substitute for .
2. .Substitute for .
3. . Substitute for .
4. .Substitute for .
5. .Substitute for .
6. . Substitute for .
7. . Substitute for .
8. . Substitute for .
9. . Substitute for .
10. . Substitute for .

3. Lesson 23: True and False Number Sentences
Date: 4/23/14 S.102
102
©2013CommonCore,Inc. Some rights reserved.commoncore.org
This work is licensed under a
Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 23
Lesson Summary
Number Sentence: A number sentence is a statement of equality (or inequality) between two numerical
expressions.
Truth Values of a Number Sentence: A number sentence that is an equation is said to be true if both numerical
expressions evaluate to the same number; it is said to be false otherwise. True and false are called truth values.
Number sentences that are inequalities also have truth values. For example, , , and
are all true number sentences, while the sentence is false.
Problem Set
Substitute the value into the variable and state (in a complete sentence) whether the resulting number sentence is true
or false. If true, find a value that would result in a false number sentence. If false, find a value that would result in a true
number sentence.
1. . Substitute for .
2. . Substitute for .
3. . Substitute for .
4. . Substitute for .
5. . Substitute for .
Create a number sentence using the given variable and symbol. The number sentence you write must be true for the
given value of the variable.
6. Variable: Symbol: The sentence is true when is substituted for .
7. Variable: Symbol: The sentence is true when is substituted for .
8. Variable: Symbol: The sentence is true when is substituted for .
9. Variable: Symbol: The sentence is true when is substituted for .