Back to Identify when two expressions are equivalent — Problem 2 · Task Set 29

6.EE.A.4 Tutor Intake -- Identifying Equivalent Expressions

This short check helps your tutor see where to start. Work each problem on
your own, without a calculator unless a problem says otherwise. If you are
not sure, give your best try — every answer helps your tutor plan your
first few sessions.

Grade 6·10 problems·~11 min·Common Core Math - Grade 6·standard·6-ee-a-4

Work through problems with immediate feedback

Procedures

A student is testing whether $6c + 2$ and $2(3c + 2)$ are
equivalent. At $c = 1$ : $6c + 2 = 8$ and $2(3c + 2) = 10$ . What
should the student conclude?

The expressions might be equivalent — try more values before deciding.

The student made an arithmetic error, since equivalent-looking expressions should always match.

The result is inconclusive — a single test can never determine equivalence either way.

The expressions are not equivalent — the mismatch at $c = 1$ is a counterexample, and one mismatch is enough to settle the question.