NY Next Generation Math AII-A.REI.1.b
The Standard
Explain each step when solving rational or radical equations as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students justify each equality-preserving step when solving rational or radical equations in Algebra II. They explain restrictions and check for extraneous solutions introduced by transformations.
What Mastery Looks Like
- The student states domain restrictions, names the reason for each step, and solves accurately. Every candidate is checked in the original equation before the final solution set is accepted.
Common Misconceptions
- Students may multiply by an expression that can be zero without recording restrictions or assume squaring is reversible. They may check candidates only in a transformed equation.
How to Assess It
- Give square root of x plus 5 equals x minus 1 with a proposed solution chain. Ask students to justify each step and reject any extraneous candidate.
Lesson moves
Ways to Teach It
Arrange rational or radical equation steps with reason cards and mark transformations that need a final check.
Ask students why squaring both sides can create a solution the original equation does not have.
Play valid-step audit with rational and radical solutions containing one restriction or equivalence error.
Justify solution steps in a rational rate or radical distance model and interpret the valid answer.
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