True and False Number Sentences

New York State Common Core Math Grade 6, Module 4, Lesson 23
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Lesson 23 Student Outcomes

Students explain what the equality and inequality symbols including =, <, >, ≤, and ≥ stand for. They determine if a number sentence is true or false based on the given symbol.

Lesson 23 Student 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, 3 < 4, 6 + 8 > 15 > 12, and (15 + 3)² < 1000 - 32 are all true number sentences, while the sentence 9 > 3(4) is false.

Opening Exercise

Determine what each symbol stands for and provide an example.

Example 1:
For each inequality or equation your teacher displays, write the equation or inequality, then substitute 3 for every x. Determine if the equation or inequality results in a true number sentence or a false number sentence.

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. 4 + x = 12. Substitute 8 for x.
2. 3g > 15. Substitute 4 1/2 for g.
3. f/4 < 2. Substitute 8 for f.
4. 14.2 ≤ h - 10.3. Substitute 25.8 for h.
5. 4 = 8/d. Substitute 6 for h.
6. 3 > k + 1/4. Substitute 1 1/2 for k.
7. 4.5 - d > 2.5. Substitute 2.5 for d.
8. 8 ≥ 32p. Substitute 1/2 for p.
9. w/2 < 32. Substitute 16 for w.
10. 18 ≥ 32 - b. Substitute 14 for b.

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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. 3 5/6 = 1 2/3+h. Substitute 2 1/6 for h.
2. 39 > 156g. Substitute 1/4 for g.
3. f/4 ≤ 3. Substitute 12 for f.
4. 121-98 ≥ r. Substitute 23 for r.
5. 54/ = 6. Substitute 10 for q.

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: d Symbol: ≥ The sentence is true when 5 is substituted for d.
7. Variable: y Symbol: ≠ The sentence is true when 10 is substituted for y.
8. Variable: k Symbol: < The sentence is true when 8 is substituted for k.
9. Variable: a Symbol: ≤ The sentence is true when 9 is substituted for a.

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