Videos and solutions to help Grade 6 students
learn how to determine if a number sentence is true or false based on the given the equality and inequality symbols.
New York State Common Core Math Module 4, Grade 6, Lesson 23
Plans and Worksheets for Grade 6
Plans and Worksheets for all Grades
Lessons for Grade 6
Common Core For Grade 6
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
: A number sentence is a statement of equality (or inequality) between two numerical
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.
Determine what each symbol stands for and provide an example.
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.
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
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.
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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