NY State Math Geometry Modeling with Geometry. Practice it free.

Per the NYSED Geometry Educator Guide blueprint, Modeling with Geometry (G-MG) is 8%–15% of credit, applying geometric concepts in modeling situations. This Geometry reporting domain maps to 1 practice skill and 8 representative questions from the playable bank.

GeometryG-MG1 mapped skills
What the test measures

Modeling with Geometry skills

  1. Apply geometric concepts in modeling situations

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%.

Practice by skill

Topics mapped to this domain

Density from area and volume

Grade 910 questions
Try it now

8 free questions · 0/0 correct

Practice playeasy

A ranch has 414414 cattle and a density of 1818 cattle per acre. What is the area of the ranch, in acres?

Set up the proportion 18 cattle1 acre=414 cattlex acres.\dfrac{18\text{ cattle}}{1\text{ acre}} = \dfrac{414\text{ cattle}}{x\text{ acres}}\textsf{.} Cross-multiplying gives 18x=414,18x = 414\textsf{,} so x=23 acres.x = 23\text{ acres}\textsf{.}

Practice playeasy

A city park has a density of 3535 picnic tables per acre and covers 2424 acres. How many picnic tables are in the park?

Set up the proportion 35 picnic tables1 acre=x picnic tables24 acres.\dfrac{35\text{ picnic tables}}{1\text{ acre}} = \dfrac{x\text{ picnic tables}}{24\text{ acres}}\textsf{.} Cross-multiplying gives x=35×24=840 picnic tables.x = 35 \times 24 = 840\text{ picnic tables}\textsf{.}

Practice playmedium

A storage tank holds liquid at a density of 88 pounds per cubic foot. If the tank contains 1,9201{,}920 pounds of liquid, what is the volume of the liquid, in cubic feet?

Set up the proportion 8 pounds1 cubic foot=1,920 poundsx cubic feet.\dfrac{8\text{ pounds}}{1\text{ cubic foot}} = \dfrac{1{,}920\text{ pounds}}{x\text{ cubic feet}}\textsf{.} Cross-multiplying gives 8x=1,920,8x = 1{,}920\textsf{,} so x=240 ft3.x = 240\text{ ft}^{3}\textsf{.}

Practice playmedium

A shipping crate has a volume of 160160 cubic feet and holds 4,8004{,}800 identical packages. What is the packaging density, in packages per cubic foot?

Set up the proportion x packages1 cubic foot=4,800 packages160 cubic feet.\dfrac{x\text{ packages}}{1\text{ cubic foot}} = \dfrac{4{,}800\text{ packages}}{160\text{ cubic feet}}\textsf{.} Cross-multiplying gives 160x=4,800,160x = 4{,}800\textsf{,} so x=30 packages per ft3.x = 30\text{ packages per ft}^{3}\textsf{.}

Practice playmedium

A room heater uses energy at a density of 2525 BTUs per cubic foot. For a room with volume 120120 cubic feet, how many BTUs does the heater use?

Set up the proportion 25 BTUs1 cubic foot=x BTUs120 cubic feet.\dfrac{25\text{ BTUs}}{1\text{ cubic foot}} = \dfrac{x\text{ BTUs}}{120\text{ cubic feet}}\textsf{.} Cross-multiplying gives x=25×120=3,000 BTUs.x = 25 \times 120 = 3{,}000\text{ BTUs}\textsf{.}

Practice playmedium

Lakeview has a population of 37,80037{,}800 people and an area of 8484 square miles. What is the population density, in people per square mile?

Set up the proportion x people1 square mile=37,800 people84 square miles.\dfrac{x\text{ people}}{1\text{ square mile}} = \dfrac{37{,}800\text{ people}}{84\text{ square miles}}\textsf{.} Cross-multiplying gives 84x=37,800,84x = 37{,}800\textsf{,} so x=450 people per mile2.x = 450\text{ people per mile}^{2}\textsf{.}

Practice playmedium

A metal sample has a mass of 540540 kilograms and a density of 1212 kilograms per cubic meter. What is the volume of the sample, in cubic meters?

Set up the proportion 12 kilograms1 cubic meter=540 kilogramsx cubic meters.\dfrac{12\text{ kilograms}}{1\text{ cubic meter}} = \dfrac{540\text{ kilograms}}{x\text{ cubic meters}}\textsf{.} Cross-multiplying gives 12x=540,12x = 540\textsf{,} so x=45 m3.x = 45\text{ m}^{3}\textsf{.}

Practice playeasy

Riverside has a population density of 1,2501{,}250 people per square mile and an area of 4848 square miles. What is the population of Riverside?

Set up the proportion 1,250 people1 square mile=x people48 square miles.\dfrac{1{,}250\text{ people}}{1\text{ square mile}} = \dfrac{x\text{ people}}{48\text{ square miles}}\textsf{.} Cross-multiplying gives x=1,250×48=60,000 people.x = 1{,}250 \times 48 = 60{,}000\text{ people}\textsf{.}

Keep practicing

Turn modeling with geometry into game time.

The NY State Math placement starts with this test's real coverage map and finds the right difficulty.

Batting Cage game coverBatting CagePlay →Blossom Leap game coverBlossom LeapPlay →Buzzer Beater game coverBuzzer BeaterPlay →Minecart Junction game coverMinecart JunctionPlay →
Source and test overview
All NY State Math prepOfficial test source
Reporting categories

More Geometry domains

CongruencePer the NYSED Geometry Educator Guide blueprint, Congruence (G-CO) is 27%–34% of credit, covering transformations in the plane, congruence in terms of rigid motions, geometric theorems, and constructions.8 QsPractice →Similarity, Right Triangles, & TrigonometryPer the NYSED Geometry Educator Guide blueprint, Similarity, Right Triangles, & Trigonometry (G-SRT) is 29%–37% of credit, covering similarity transformations, theorems involving similarity, right-triangle trigonometry, and trigonometry of general triangles.8 QsPractice →CirclesPer the NYSED Geometry Educator Guide blueprint, Circles (G-C) is 2%–8% of credit, covering theorems about circles and arc lengths and areas of sectors.8 QsPractice →Expressing Geometric Properties with EquationsPer the NYSED Geometry Educator Guide blueprint, Expressing Geometric Properties with Equations (G-GPE) is 12%–18% of credit, covering conic-section equations and coordinate proofs.8 QsPractice →Geometric Measurement & DimensionsPer the NYSED Geometry Educator Guide blueprint, Geometric Measurement & Dimensions (G-GMD) is 2%–8% of credit, covering volume formulas and relationships between two- and three-dimensional objects.8 QsPractice →