MCAP Algebra I Number and Quantity Practice

Number and Quantity skills

N.RN.B Use properties of rational and irrational numbers.

N.Q.A Reason quantitatively and use units to solve problems.

Standards basis

Maryland College and Career Ready Standards for Mathematics (MCCRSM) — Maryland

How the MCAP reports it

MCAP is Maryland's statewide successor to PARCC, built on the Maryland College and Career Ready Standards for Mathematics (which mirror CCSS-M) — it is not a Smarter Balanced administration despite the claims-style family resemblance. Each grade/course High Level Blueprint (September 2022) organizes the assessment into three subclaims: Content (23-24 one-point machine-scored items, listed per domain/conceptual category as MCCRSM cluster headings), Reasoning (6 items), and Modeling (6 items), the latter two defined by per-grade evidence statements and including constructed-response items. Cluster headings are transcribed verbatim from the blueprints, including their minor typographical deviations from the parallel CCSS-M headings; two evident misprints are normalized (a duplicated sentence fragment on 4.OA.C, and the domain codes printed as G.P.E / T.TF for G.GPE / F.TF). Since March 2025, grade 6-7 students enrolled in a high-school mathematics course may take the corresponding MCAP course assessment instead of the grade-level test.

Blueprint & weighting

Each High Level Blueprint (September 2022) publishes per-domain operational item counts. Content Subclaim (1-point machine-scored items): Grade 3 — OA 7, NBT 2, NF 7, Measurement 5, Geometry 2 (23 items); Grade 4 — OA 4, NBT 5, NF 10, Measurement 3, Geometry 1 (23); Grade 5 — OA 2, NBT 6, NF 9, Measurement 4, Geometry 2 (23); Grade 6 — RP 3, NS 8, EE 8, Geometry 2, SP 2 (23); Grade 7 — RP 8, NS 4, EE 5, Geometry 3, SP 3 (23); Grade 8 — NS 2, EE 10, Functions 5, Geometry 4, SP 2 (23); Algebra I — Number and Quantity 1, Algebra 12, Functions 9, Statistics 2 (24); Geometry — G.CO 7, G.SRT 8, G.C 3, G.GPE 3, G.GMD 1, G.MG 1 (23); Algebra II — Number and Quantity 3, Algebra 8, Functions 11, Statistics 1 (23). Every assessment adds 6 Reasoning Subclaim and 6 Modeling Subclaim operational items — four 1-point machine-scored each, plus two constructed-response items (two 3-point in grades 3-4; one 3-point and one 4-point in grades 5-8; two 4-point in Algebra I, Geometry, and Algebra II) — so a form carries 35 operational items (36 for Algebra I).

Official sources

MSDE — MCAP Mathematics (current program page: grades 3-8, Algebra I, Geometry, Algebra II)
MSDE — MCAP Overview / High Level Blueprints summary
MSDE — MCAP Grade 3 Mathematics High Level Blueprint (September 2022)

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.