NY Next Generation Math AI-A.REI.3

MathGrades 9–12Solve equations and inequalities in one variable.

The Standard

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students solve single linear equations and inequalities in Algebra I, including formulas with letter coefficients. They preserve inequality direction except when multiplying or dividing by a negative quantity.
What Mastery Looks Like: The student isolates the variable, states any needed coefficient conditions, and represents an inequality solution correctly. Work stays within single inequalities rather than compound inequalities.
Common Misconceptions: Students may reverse an inequality after adding a negative instead of multiplying by one, or forget to reverse it after negative division. They may divide by a letter coefficient without noting it cannot be zero.
How to Assess It: Ask students to solve ax plus b equals c for x with a not equal to zero, then solve negative 3x plus 5 greater than 14.

Lesson moves

Use balance tiles to model a linear equation, then record the matching symbolic operations.
Ask students exactly when and why an inequality sign reverses.
Play solution-set match with equations, single inequalities, symbolic answers, and number-line graphs.
Write and solve one inequality for a spending limit or minimum attendance requirement.

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