NY State Math Grades 3–8 Operations and Algebraic Thinking Practice

What the test measures

Operations and Algebraic Thinking skills

Represent and solve problems involving addition and subtraction
Represent and solve problems involving multiplication and division
Understand properties of multiplication and the relationship between multiplication and division
Solve problems involving the four operations
Generate and analyze patterns

Standards basis

New York State Learning Standards / New York State Next Generation Learning Standards (NGLS) — New York

How the NY State Math reports it

New York’s Grades 3–8 math tests and Regents math exams are state-developed assessments rather than a shared national framework. The grades 3–8 exams are aligned to New York State learning standards, and the Regents math sequence includes Algebra I, Geometry, and Algebra II, with the June 2026 Algebra II exam explicitly based on the New York State Next Generation Learning Standards.

Blueprint & weighting

Grades 3–8: the official page and the retrieved administration guide describe item/credit structure and timing, but no published domain-by-domain blueprint weighting was located in the primary sources used here. Regents (high school): NYSED publishes a per-conceptual-category 'percent of test by credit' blueprint for each course in its Educator Guides. Algebra I — Number & Quantity 4%–10%, Algebra 48%–61%, Functions 24%–32%, Statistics & Probability 7%–15%. Geometry (single conceptual category, by domain) — Congruence (G-CO) 27%–34%, Similarity, Right Triangles, & Trigonometry (G-SRT) 29%–37%, Circles (G-C) 2%–8%, Expressing Geometric Properties with Equations (G-GPE) 12%–18%, Geometric Measurement & Dimensions (G-GMD) 2%–8%, Modeling with Geometry (G-MG) 8%–15%. Algebra II — Number & Quantity 4%–8%, Algebra 30%–39%, Functions 38%–45%, Statistics & Probability 14%–22%.

Official sources

NYSED Grades 3–8 ELA and Math Test Manuals
NYSED Directions for Administering Regents Examinations
NYSED High School Regents Examinations

Practice by skill

Topics mapped to this domain

Properties of operations

Grade 316 questions

Try it now

8 free questions · 0/0 correct

Practice playeasy

Which property is $\color{red}{4\times}\color{blue}{(3+2)}\color{black}{\,=\,}\color{red}{4\times}\color{blue}{3+}\color{red}{4\times}\color{blue}{2}$ ?

$\color{red}{4\times}\color{blue}{(3+2)}\color{black}{\,=\,}\color{red}{4\times}\color{blue}{3+}\color{red}{4\times}\color{blue}{2}$ shows multiplying across a sum does not change the answer, so the expressions are equal in value. This is the distributive property.

Practice playeasy

Which property is $7 + 0 = 7$ ?

$7 + 0 = 7$ shows adding $0$ does not change the answer, so the expressions are equal in value. This is the identity property.

Practice playeasy

Which property is $3 + (6 + 2) = (3 + 6) + 2$ ?

$3 + (6 + 2) = (3 + 6) + 2$ shows the grouping of the addition does not change the answer, so the expressions are equal in value. This is the associative property.

Practice playeasy

Which property says $6 \times 4 = 4 \times 6$ ?

$6 \times 4 = 4 \times 6$ shows the order of the multiplication does not change the answer, so the expressions are equal in value. This is the commutative property.

Practice playeasy

Which property is $\color{red}{2\times}\color{blue}{(3+5)}\color{black}{\,=\,}\color{red}{2\times}\color{blue}{3+}\color{red}{2\times}\color{blue}{5}$ ?

$\color{red}{2\times}\color{blue}{(3+5)}\color{black}{\,=\,}\color{red}{2\times}\color{blue}{3+}\color{red}{2\times}\color{blue}{5}$ shows multiplying across a sum does not change the answer, so the expressions are equal in value. This is the distributive property.

Practice playeasy

Which property is $6 \times 1 = 6$ ?

$6 \times 1 = 6$ shows multiplying by $1$ does not change the answer, so the expressions are equal in value. This is the identity property.

Practice playeasy

Which property is $(2 \times 3) \times 4 = 2 \times (3 \times 4)$ ?

$(2 \times 3) \times 4 = 2 \times (3 \times 4)$ shows the grouping of the multiplication does not change the answer, so the expressions are equal in value. This is the associative property.