Teacher Guide: True and False Statements
Learn to identify and evaluate statements as true or false.
Use this lesson with your class
Free, no student accounts needed.
Share with students
Students open the lesson and practise with instant feedback.
Class quiz
10 questions on Boolean Logic. Students join with a name, you see everyone's score.
For Teachers
- Define what makes a sentence a statement
- Distinguish between true and false statements
- Evaluate mathematical statements for truth value
- Identify sentences that are NOT statements (questions, commands)
- • Basic arithmetic operations (addition, subtraction, multiplication)
- • Understanding of equality and inequality symbols
- • Knowledge of basic geometric shapes
- 1. Can you think of a statement that is true today but might be false tomorrow?
- 2. Why is it important to know if something is true or false?
- 3. What is the difference between a false statement and a lie?
- 4. How do scientists figure out if a statement is true?
Thinking all sentences are statements
Believing false statements are "bad"
For Struggling Students:
- • Start with simple numerical statements only (, )
- • Use visual number lines to verify comparisons
- • Provide answer choices: TRUE or FALSE only
For On-Level Students:
- • Evaluate statements involving basic operations
- • Identify non-statements (questions, commands)
- • Create their own true and false statements
For Advanced Students:
- • Explore statements about properties ("All even numbers are divisible by 2")
- • Find counterexamples to prove statements false
- • Discuss statements with unknown truth values
- CCSS.MATH.PRACTICE.MP3 (MP3)
Construct viable arguments and critique the reasoning of others
- CCSS.MATH.PRACTICE.MP6 (MP6)
Attend to precision
- activityTrue or False Sorting Game
Students sort statement cards into true and false piles
- worksheetStatement Detective
Find the false statements hidden among true ones
- activityReal vs. Fake Claims
Analyze statements from everyday life
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Lesson Content
Everything students see: definition, examples, common mistakes, applications. Tap to open.
Definition
- "" is true
- "A square has 4 sides" is true
- "" is false
- "A triangle has 5 sides" is false
Worked Examples
Is the statement "" true or false?
Identify the statement
The statement claims that 8 plus 5 equals 13 →
Calculate the left side
→ 13
Compare with the right side
Left side: 13, Right side: 13 → 13 = 13
Determine if true or false
Both sides are equal → TRUE
Answer: The statement "" is TRUE.
Common Mistakes
Thinking questions can be true or false
Why it's wrong: "What is 5 + 3?" is a question, not a statement. It asks for information rather than making a claim.
Correct: Only declarative sentences that make a claim can be true or false. "5 + 3 = 8" is a statement.
Confusing "sometimes true" with true statements
Why it's wrong: "It is raining" is sometimes true and sometimes false depending on the weather.
Correct: In math logic, a true statement is ALWAYS true. "" is always true, not just sometimes.
Thinking false means "bad" or "wrong to say"
Why it's wrong: False simply means the statement does not match reality. It is not a judgment about the person.
Correct: False is a logical classification. "" is false because 3 is not greater than 5.
Why It Matters
- Problem Solving: When you check your math work, you evaluate whether your answer makes the statement true
- Science: Scientists test hypotheses to determine if they are true or false
- Computer Programming: Computers use true/false logic to make decisions
- Daily Life: You constantly evaluate claims - "The store closes at 9 PM" is either true or false
Real World Applications
Fact-Checking Information
When you read news or information online, you evaluate whether statements are true or false.
Example:
If someone says "The Earth is the largest planet in our solar system," you can check: Is this true or false? (It is false - Jupiter is the largest.)
Testing Answers in Math
When you solve a math problem, you can check your answer by substituting it back.
Example:
If you solve and get , check: Is "" true? Yes! Your answer is correct.
Computer Programs
Computers use true/false logic constantly to make decisions.
Example:
A game checks: "Is the player's score greater than the high score?" If TRUE, save new high score. If FALSE, keep the old one.
Key Takeaways
- 1A statement is a sentence that is either true or false, but not both
- 2True statements are correct and match mathematical rules or reality
- 3False statements are incorrect and do not match reality
- 4Questions and commands are NOT statements
- 5In math, true statements are ALWAYS true, not just sometimes
Frequently Asked Questions
Can a statement be both true and false?
Is "I like pizza" a statement?
What about statements we do not know yet?
Glossary
- Statement
- A sentence that is either true or false, but not both
- True
- A statement that correctly describes reality or follows mathematical rules
- False
- A statement that does not correctly describe reality
- Evaluate
- To determine whether a statement is true or false
- Counterexample
- An example that proves a statement is false