NY Next Generation Math NY-7.EE.1

Math7th GradeUse properties of operations to generate equivalent expressions.

The Standard

Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students use operation properties to combine, subtract, factor, and expand linear expressions with positive and negative rational coefficients. They preserve equivalence at each step.
What Mastery Looks Like: A student expands 3(x − 2) + (1/2)x to (7/2)x − 6 and explains the distribution and combination of like terms. The student factors 6x + 9 as 3(2x + 3).
Common Misconceptions: Students may distribute to only one term or lose a negative sign during subtraction. They may combine unlike terms or remove a factor from only part of an expression.
How to Assess It: Ask students to simplify 2.5(x − 4) − 0.5x and factor 8x + 12, showing which property supports each step.

Lesson moves

Use algebra tiles to expand, combine, and factor expressions with positive and negative terms, then record each symbolic step.
Ask students to compare two solution paths for 4(x + 3) − 2x and explain why both remain equivalent.
Play equivalent-expression match with expanded, factored, and simplified cards containing integers, fractions, and decimals.
Write and simplify expressions for changing service fees, discounts, or repeated costs with rational rates.

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