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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students isolate the variable in equations with variable denominators or square roots. They track restrictions, solve the resulting equation, and substitute each candidate into the original equation.
What Mastery Looks Like
- A student clears denominators or isolates a radical and squares both sides accurately. They identify restricted values, check each candidate in the original equation, and explain any rejected result.
Common Misconceptions
- Students may cancel terms across addition or forget values that make a denominator zero. They may treat squaring as reversible and accept every result. Some check candidates only in the transformed equation, not the original.
How to Assess It
- Exit ticket: Solve √(x + 6) = x, check both candidates in the original equation, and explain why one must be rejected.
Lesson moves
Ways to Teach It
Give students equation, transformation, candidate, and check cards to arrange into valid solution chains.
Ask students to explain, with an example, why squaring both sides can produce a value that fails the original equation.
Run a partner check game where one student solves an equation and the partner tests every candidate in the original.
Use a 120-mile round trip with speeds x and x + 10 to write a time equation and reject impossible speeds.
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Printable HSA-REI.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSA-REI.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSA-REI.A.1
Justifying equation steps supports recognizing when multiplying or squaring can change the solution set and create extraneous answers.
- CCSS.Math.Content.HSA-REI.B.3
Solving rational and radical equations requires isolating expressions and solving resulting one-variable linear equations after clearing denominators or roots.
- CCSS.Math.Content.HSN-RN.A.2
Rewriting radicals and rational exponents supports isolating and transforming radical equations before checking for extraneous solutions.
What This Unlocks
Mastery here sets students up for these next.
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Related Standards
- CCSS.Math.Content.HSA-REI.B
Solve equations and inequalities in one variable
- CCSS.Math.Content.HSA-CED.A.1
Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rati...
- CCSS.Math.Content.8.EE.C.7b
Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and ...
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