True or False Statements

In True or False Statements topic, 8th Grade students will learn how to decide whether a math statement is always true, sometimes true, or never true. They will practice using counterexamples and proofs with clear reasons. Students will learn to be precise with definitions, because one small detail can change a statement from true to false. They will also learn to explain their decision using math language, not just a final word. Over time, students become more careful and confident thinkers.

What Children Learn

Students learn what it means for a statement to be true for all numbers versus only some numbers. They practice finding a counterexample, which is one example that disproves a statement. Students learn to justify true statements by using rules, definitions, and clear steps. They compare statements about exponents, integers, lines, and angle relationships. Students practice rewriting statements in a clearer form to check meaning. As tasks get harder, students explain whether a statement is always true, sometimes true, or never true and they support their answer with evidence.

Sample Questions Children Practice

1. True or false: If a number is divisible by 6, then it is divisible by 3.

A. True

B. False

C. Sometimes true

D. Cannot be determined

2. Fill in the blank: A counterexample is a single example that shows a statement is ____.

3. True or false: The square of any integer is negative.

A. True

B. False

C. Sometimes true

D. Cannot be determined

4. True or false: If two lines have the same slope, then they must intersect.

A. True

B. False

C. Sometimes true

D. Cannot be determined

5. Thinking question: Give one counterexample to show the statement x squared is greater than x is not always true.

Why This Topic Matters

True and false work trains students to think like mathematicians. Students learn that a single counterexample can disprove a claim, which builds strong logic. This topic improves precision with definitions and vocabulary. It also strengthens explaining skills, because students must give reasons, not just answers. These habits support proofs, algebra reasoning, and high school math success.