Florida B.E.S.T. MA.912.AR.8.1
The Standard
Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find excluded values before clearing denominators. They solve the resulting equation, substitute candidates into the original, and reject values that are undefined or do not fit the situation.
What Mastery Looks Like
- A student identifies denominator restrictions, uses a least common denominator correctly, and solves the resulting equation. The student checks each candidate in the original equation and explains why each answer is viable, extraneous, or impossible in context.
Common Misconceptions
- Students may cancel terms across addition or forget that a denominator cannot equal zero. They may accept every root from the cleared equation without substitution, or reject negative answers even when the context allows them.
How to Assess It
- Give: “For 2 < x ≤ 5, solve x/(x−2) = 2/(x−2) + x−3.” Ask students to show restrictions, test each candidate, and identify the viable solution.
Lesson moves
Ways to Teach It
Give pairs denominator-factor cards and solution cards; students build an LCD, solve the equation, then discard values that make a denominator zero.
Students write a response to: Why can clearing denominators create a value that fails when substituted into the original equation?
Run a sorting relay where teams match rational equations to domain restrictions, algebraic solutions, extraneous values, and final solution sets.
Model shared trip cost with 120/x = 120/(x+2) + 5, then decide whether each solution is a possible group size.
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Printable MA.912.AR.8.1 Worksheet
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Related Standards
- MA.7.AR.2.2
Write and solve two-step equations in one variable within a mathematical or real-world context, where all terms are rational numbers.
- MA.912.AR.7.1
Solve one-variable radical equations. Interpret solutions as viable in terms of context and identify any extraneous solutions.
- MA.912.AR.8
Solve and graph rational equations and functions in one and two variables.
- MA.7.AR.2
Write and solve equations and inequalities in one variable.
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