MCAP Geometry Modeling with Geometry Practice

Modeling with Geometry skills

G.MG.A Apply geometric concepts in modeling situations.

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

Lakeview has a population of $37{,}800$ people and an area of $84$ square miles. What is the population density, in people per square mile?

Set up the proportion $\dfrac{x\text{ people}}{1\text{ square mile}} = \dfrac{37{,}800\text{ people}}{84\text{ square miles}}\textsf{.}$ Cross-multiplying gives $84x = 37{,}800\textsf{,}$ so $x = 450\text{ people per mile}^{2}\textsf{.}$

Practice playmedium

A metal sample has a mass of $540$ kilograms and a density of $12$ kilograms per cubic meter. What is the volume of the sample, in cubic meters?

Set up the proportion $\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.}$ Cross-multiplying gives $12x = 540\textsf{,}$ so $x = 45\text{ m}^{3}\textsf{.}$

Practice playeasy

Riverside has a population density of $1{,}250$ people per square mile and an area of $48$ square miles. What is the population of Riverside?

Set up the proportion $\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.}$ Cross-multiplying gives $x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}$

Practice playeasy

A ranch has $414$ cattle and a density of $18$ cattle per acre. What is the area of the ranch, in acres?

Set up the proportion $\dfrac{18\text{ cattle}}{1\text{ acre}} = \dfrac{414\text{ cattle}}{x\text{ acres}}\textsf{.}$ Cross-multiplying gives $18x = 414\textsf{,}$ so $x = 23\text{ acres}\textsf{.}$

Practice playeasy

A city park has a density of $35$ picnic tables per acre and covers $24$ acres. How many picnic tables are in the park?

Set up the proportion $\dfrac{35\text{ picnic tables}}{1\text{ acre}} = \dfrac{x\text{ picnic tables}}{24\text{ acres}}\textsf{.}$ Cross-multiplying gives $x = 35 \times 24 = 840\text{ picnic tables}\textsf{.}$

Practice playmedium

A storage tank holds liquid at a density of $8$ pounds per cubic foot. If the tank contains $1{,}920$ pounds of liquid, what is the volume of the liquid, in cubic feet?

Set up the proportion $\dfrac{8\text{ pounds}}{1\text{ cubic foot}} = \dfrac{1{,}920\text{ pounds}}{x\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $8x = 1{,}920\textsf{,}$ so $x = 240\text{ ft}^{3}\textsf{.}$

Practice playmedium

A shipping crate has a volume of $160$ cubic feet and holds $4{,}800$ identical packages. What is the packaging density, in packages per cubic foot?

Set up the proportion $\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $160x = 4{,}800\textsf{,}$ so $x = 30\text{ packages per ft}^{3}\textsf{.}$

Practice playmedium

A room heater uses energy at a density of $25$ BTUs per cubic foot. For a room with volume $120$ cubic feet, how many BTUs does the heater use?

Set up the proportion $\dfrac{25\text{ BTUs}}{1\text{ cubic foot}} = \dfrac{x\text{ BTUs}}{120\text{ cubic feet}}\textsf{.}$ Cross-multiplying gives $x = 25 \times 120 = 3{,}000\text{ BTUs}\textsf{.}$

MCAP Geometry Modeling with Geometry. Practice it free.

Modeling with Geometry skills

G.MG.A Apply geometric concepts in modeling situations.

Topics mapped to this domain

Density from area and volume

8 free questions · 0/0 correct

Turn modeling with geometry into game time.

More Geometry domains