CCSS.Math.Content.HSA-REI.A.2
The standard
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Common Core State Standards for Mathematics
What this standard means
Students need to solve one-variable equations that include fractions with variables or square roots. They should use legal algebra steps, track restrictions like zero denominators and nonnegative radicands, and check answers in the original equation.
Mastery means students can explain why a number found by algebra may not actually work. They often get stuck by multiplying through and forgetting denominator restrictions, or by squaring both sides and keeping false solutions. Insist on a final substitution check, not just a boxed answer.
Ways to teach it
- Hands-on activity: Give pairs equation cards and solution cards, then have them match, check, and sort any extraneous solutions into a discard pile.
- Writing prompt: Solve sqrt(x + 5) = x - 1, then explain why checking in the original equation changes the answer list.
- Quick assessment: Exit ticket with one rational equation and one radical equation, asking students to circle any restricted values before solving.
- Real-world connection: Use a speed, distance, time problem with a rational equation, then have students reject any answer that gives impossible time or speed.
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