NY State Math Algebra I Number & Quantity Practice

NY State Math Algebra I Number & Quantity. Practice it free.

Per the NYSED Algebra I Educator Guide blueprint, the Number & Quantity conceptual category is 4%–10% of credit and includes the domains The Real Number System (N-RN) and Quantities (N-Q). This Algebra I reporting domain maps to 4 practice skills and 8 representative questions from the playable bank.

Algebra IN-RN, N-Q4 mapped skills

Number & Quantity skills

Use properties of rational and irrational numbers

Reason quantitatively and use units to solve problems

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

8 free questions · 0/0 correct

Practice playmedium

Teen volunteers at a food drive packed supply bags so that each volunteer received the same number of water bottles and the same number of granola bars to distribute. The drive had $56$ water bottles and $84$ granola bars in all. Which could be the number of volunteers?

The number of volunteers must divide both totals. Common factors of $56$ and $84$ greater than $1$ include $2$ , $4$ , $7$ , $14$ , and $28$ . Only $14$ appears among the choices: $56 \div 14 = 4$ bottles and $84 \div 14 = 6$ bars per volunteer.

Practice playmedium

Given that $3 \le m \le 8$ , $1 \le n \le 2$ , and $4 \le p \le 6$ , what is the least possible value of $\dfrac{m}{n + p}$ ?

Minimize $m$ with $m = 3$ , and maximize $n + p$ with $n = 2$ and $p = 6$ : $\dfrac{3}{2 + 6} = \dfrac{3}{8}$ .

Practice playhard

Bus route A leaves the station every $20$ minutes, and bus route B leaves every $30$ minutes. Both buses leave together at noon. Over the next $3$ hours, not counting the noon departure, how many times do both buses leave the station at the same time?

Both buses leave together every least common multiple of $20$ and $30$ minutes. Since the GCF of $20$ and $30$ is $10\textsf{,}$ divide their product by the GCF to get that interval: $\dfrac{20 \times 30}{10}=60$ minutes. In $180$ minutes after noon, the shared departures are at $60\textsf{,}$ $120\textsf{,}$ and $180$ minutes, so there are $3$ additional times.

Practice playeasy

A running track is $2$ kilometers long. What is the length of the track in meters?
(Note: $1$ kilometer $= 1{,}000$ meters)

Multiply by a conversion factor so the old unit cancels: $2\,\text{km} \times \dfrac{1{,}000\,\text{m}}{1\,\text{km}} = 2{,}000\,\text{m}$ .

Practice playmedium

A drama club prepared scripts and prop kits for a showcase. Each cast member received the same number of scripts and the same number of prop kits. The club had $54$ scripts and $81$ prop kits in all. Which could be the number of cast members?

The number of cast members must divide both totals. The common factors of $54$ and $81$ greater than $1$ are $3$ , $9$ , and $27$ . Only $9$ appears among the choices: $54 \div 9 = 6$ scripts and $81 \div 9 = 9$ kits per member.

Practice playmedium

Given that $2 \le m \le 5$ and $3 \le n \le 8$ , what is the greatest possible value of $\dfrac{1}{m} + \dfrac{1}{n}$ ?

Each term $\dfrac{1}{m}$ and $\dfrac{1}{n}$ is greatest when its denominator is least: $\dfrac{1}{2} + \dfrac{1}{3} = \dfrac{5}{6}$ .

Practice playhard

A parking-garage gate opens every $9$ minutes, and a ferry docks every $15$ minutes. Both events occur together at noon. Over the next $90$ minutes, not counting noon, how many times do both events occur at the same time?

Both events coincide every least common multiple of $9$ and $15$ minutes. Since the GCF of $9$ and $15$ is $3\textsf{,}$ divide their product by the GCF to get that interval: $\dfrac{9 \times 15}{3}=45$ minutes. In $90$ minutes after noon, the shared times are at $45$ and $90$ minutes, so there are $2$ additional times.