Always, Sometimes, Never

Classify the statement, then prove it with examples.

These starters ask students to decide whether a mathematical statement is always true, sometimes true or never true. They are designed to build precision, expose misconceptions and encourage students to use examples and counterexamples.

Always, Sometimes, Never

Decide, justify, then look for examples.

Students should choose a classification, explain why, and then test the statement with examples and counterexamples.

Starter

Number

Even Numbers

Prompt

1/10

Statement

The sum of two even numbers is even.

Choose Always, Sometimes or Never before revealing the answer.

Choose a prompt

Classroom use

Ask students to vote first, but do not reveal the answer until they have given at least one example or counterexample.

The best follow-up is often: how could we change the statement so it becomes always true?

Encourage students to notice that sometimes is often the hardest answer, because it needs both a supporting example and a counterexample.

Later ideas

Topic filters for number, algebra, geometry and probability.

Teacher-created statement banks.

Printable mini-card versions for group discussion.