MCAP Grade 7 Equations and Expressions Practice

Equations and Expressions skills

7.EE.A Use properties of operations to generate equivalent expressions.

7.EE.B Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

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

At the start of the season, a soccer club roster was divided into three position groups. Exactly $\dfrac{1}{3}$ of the players were forwards, exactly $\dfrac{1}{2}$ were midfielders, and $9$ players were goalkeepers. How many players were on the roster?

Let $x$ be the roster size. Forwards and midfielders account for $\dfrac{1}{3}x + \dfrac{1}{2}x = \dfrac{5}{6}x$ . The goalkeepers are the remaining $\dfrac{1}{6}x = 9$ , so $x = 54$ .

Practice playeasy

A library reading room must keep noise at a level of at most $65.0$ decibels. A meter shows $68.5$ decibels. What is the minimum decrease needed in the noise level, in decibels, so that the room meets the rule?

The noise level must be at most $65.0$ decibels. The minimum decrease is $68.5 - 65.0 = 3.5\textsf{.}$

Practice playeasy

Solve for $k$ : $9k = -27$ .

Isolate $k$ : $k = -3$ .

Practice playmedium

An arena concert used four seating sections. Exactly $\dfrac{1}{6}$ of the seats were in section A, exactly $\dfrac{1}{3}$ were in section B, $22$ seats were in section C, and $18$ seats were in section D. How many seats were in the arena for this concert?

Let $x$ be the total number of seats. Sections A and B account for $\dfrac{1}{6}x + \dfrac{1}{3}x = \dfrac{1}{2}x$ . Sections C and D total $22 + 18 = 40$ seats, so $\dfrac{1}{2}x = 40$ and $x = 80$ .

Practice playeasy

In a school zone, a car must travel at a speed of at most $35.0$ miles per hour. A car is traveling at $38.2$ miles per hour. What is the minimum decrease needed in the car's speed, in miles per hour, so that it meets the speed limit?

The speed must be at most $35.0$ miles per hour. The minimum decrease is $38.2 - 35.0 = 3.2\textsf{.}$

Practice playeasy

What value of $n$ satisfies $5n - 8 = 17$ ?

Add $8$ to both sides: $5n = 25$ . Divide both sides by $5$ : $n = 5$ .

Practice playmedium

A botanical garden is divided into four planted areas. Exactly $\dfrac{1}{4}$ of the garden is vegetables, exactly $\dfrac{1}{5}$ is flowers, $48$ square meters are herbs, and $40$ square meters are fruit trees. How many square meters are in the entire garden?

Let $x$ be the total area. Vegetables and flowers cover $\dfrac{1}{4}x + \dfrac{1}{5}x = \dfrac{9}{20}x$ . The herbs and fruit trees cover $48 + 40 = 88$ square meters, so $\dfrac{11}{20}x = 88$ and $x = 160$ .

Practice playeasy

A shipping company accepts a package only if its mass is at least $2.50$ kilograms. A package has a mass of $2.15$ kilograms. What is the minimum increase needed in the package's mass, in kilograms, so that it can be accepted?