Florida B.E.S.T. MA.912.AR.7.1
The Standard
Solve one-variable radical equations. Interpret solutions as viable in terms of 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 isolate the radical, remove it with an inverse operation, and solve the resulting equation. They substitute every candidate into the original equation. They also decide whether checked solutions make sense for the stated situation.
What Mastery Looks Like
- A student chooses valid algebraic steps and tracks restrictions such as a nonnegative square root. They check all candidates in the original equation and label false or contextually impossible values.
Common Misconceptions
- Students often accept every root from the transformed equation without substituting back. They may forget that an even root is nonnegative, square terms incorrectly, or reject a valid negative input. They can also confuse an extraneous value with a valid answer that fails a context condition.
How to Assess It
- Exit ticket: Solve √(x + 6) = x, check each candidate in the original equation, and explain which value is viable if x is a length in meters.
Lesson moves
Ways to Teach It
Give pairs equation cards and candidate solution cards; students substitute each value, sort valid and extraneous solutions, then solve to confirm.
Ask students to explain why squaring both sides can create a false answer, then support their claim with one solved example.
Run a four-corner check game: post four candidate answers, display a radical equation, and have students move after testing each answer.
Model a ladder problem with a radical distance equation, then reject any answer that gives a negative length or misses the stated conditions.
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Related Standards
- MA.912.AR.5.2
Solve one-variable equations involving logarithms or exponential expressions. Interpret solutions as viable in terms of the context and identify any extraneous ...
- MA.912.AR.7.4
Solve and graph mathematical and real-world problems that are modeled with radical functions. Interpret key features and determine constraints in terms of the c...
- MA.912.AR.7
Solve and graph radical equations and functions in one and two variables.
- MA.912.AR.8.1
Write and solve one-variable rational equations. Interpret solutions as viable in terms of the context and identify any extraneous solutions.
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