NY Next Generation Math AI-A.APR.1

MathGrades 9–12Perform arithmetic operations on polynomials.

The Standard

Add, subtract, and multiply polynomials and recognize that the result of the operation is also a polynomial. This forms a system analogous to the integers.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What This Standard Means

What Students Need to Do: Students add, subtract, and multiply polynomials fluently in Algebra I. They combine like terms and use the distributive property while recognizing that each result remains a polynomial.
What Mastery Looks Like: The student produces an equivalent polynomial with terms combined and signs handled correctly. Work shows an efficient method for multiplication and a quick check by degree or substitution.
Common Misconceptions: Students may combine unlike terms, lose a negative while subtracting, or distribute incompletely. They may assume multiplying two binomials always produces three nonzero terms.
How to Assess It: Ask students to simplify (3x squared minus 2x plus 1) minus (x squared plus 4x) and multiply (x minus 2)(2x plus 3), showing checks.

Lesson moves

Ways to Teach It

Arrange polynomial term cards to model addition and subtraction before combining like terms.
Ask students why multiplying two polynomials cannot create a nonpolynomial result.
Play error hunt with polynomial operation solutions containing one sign, distribution, or like-term mistake.
Model the area of a rectangular garden with polynomial side lengths and expand the area expression.

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