NY Next Generation Math AI-A.REI.1.a
The Standard
Explain each step when solving a linear or quadratic equation 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 explain why each step in solving a linear or quadratic equation preserves equality. They build a logical argument from the assumption that the original equation has a solution.
What Mastery Looks Like
- The student names the property or equivalent operation behind each transformation and reaches a correct solution. Substitution checks the result, and the explanation forms a connected argument.
Common Misconceptions
- Students may describe steps as moving terms without justifying equality or apply an operation to only one side. They may verify arithmetic without explaining why the method is valid.
How to Assess It
- Give 3(x minus 2) equals x plus 8 with a completed solution. Ask students to annotate every step with its equality-preserving reason and verify the result.
Lesson moves
Ways to Teach It
Arrange equation-step cards in a valid order and attach a property card to every transition.
Ask students why subtracting the same expression from both sides preserves the solution set.
Play invalid-step hunt with linear and quadratic solution chains containing one unjustified transformation.
Explain the reasoning in an equation used to find an unknown measurement in a design problem.
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