VTCAP Grade 7 Ratios and Proportional Relationships Practice

What the test measures

Ratios and Proportional Relationships skills

Analyze proportional relationships and use them to solve real-world and mathematical problems

Standards basis

Common Core State Standards for Mathematics (CCSS-M) — Vermont

How the VTCAP reports it

Vermont administered the Smarter Balanced summative through spring 2022, then replaced it with the Cognia-developed Vermont Comprehensive Assessment Program (VTCAP) beginning spring 2023 — this landing slug predates the switch. VTCAP mathematics is an adaptive, CCSS-M-aligned assessment in grades 3-9. It is NOT a Smarter Balanced administration: its reporting categories are groupings of the CCSS grade-level domains (e.g. 'The Number System, Expressions and Equations'), not SBAC claims, though two cross-grade Mathematical Practices indicators ('Problem Solving, Reasoning, and Argument'; 'Modeling, Patterns, and Structure') echo the old claim structure. Per the test specifications, the grades 3-8 test may assess any CCSS-M standard at the grade; the grade 9 test assesses a prioritized subset of the high school CCSS-M within the conceptual categories of Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability (the assessed focus areas are published in the grade 9 Performance Level Descriptors).

Blueprint & weighting

VTCAP Test Specifications (Spring 2026) operational test blueprint, target percent of points per grade — Grade 3: OA 24-35%, NBT 10-14%, NF 16-20%, MD 22-29%, G 6-10%, constructed-response Mathematical Practices 12%. Grade 4: OA 20-31%, NBT 16-20%, NF 20-31%, MD 12-20%, G 6-10%, practices 12%. Grade 5: OA 14-22%, NBT 14-25%, NF 22-29%, MD 20-27%, G 8-16%, practices 12%. Grade 6: RP 15-22%, NS 15-22%, EE 15-22%, G 11-19%, SP 11-19%, practices 11%. Grade 7: RP 15-22%, NS 11%, EE 15-30%, G 11-19%, SP 19-22%, practices 11%. Grade 8: F 18-29%, NS 7%, EE 20-31%, G 18-29%, SP 18-22%, practices 11%. Grade 9 (all machine-scored): Number and Quantity/Algebra 18-27%, Algebra/Functions 31-40%, Geometry 20-29%, Statistics and Probability 13-20%; the two practices indicators are dual-aligned targets of >18% of points each. Identical figures appear in the Spring 2025 specifications.

Official sources

VTCAP Test Specifications, Spring 2026 (Vermont AOE / Cognia)
VTCAP Test Specifications, Spring 2025 (Vermont AOE / Cognia)
VTCAP Performance Level Descriptors: Mathematics, Grades 3-9 (Vermont AOE)

Practice by skill

Topics mapped to this domain

Try it now

8 free questions · 0/0 correct

Practice playmedium

An herbicide spray uses concentrate and water in a ratio of $6$ to $24$ . How many cups of concentrate should be added to $2$ quarts of water to make the spray in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Two quarts of water is $2 \times 4 = 8$ cups. With a $6$ to $24$ ratio, $\dfrac{6}{24} = \dfrac{x}{8}$ , so $24x = 48$ and $x = 2$ cups of concentrate.

Practice playeasy

What is $30\%$ of $90$ ?

Convert: $30\% = 0.3$ . Then $0.3 \times 90 = 27$ .

Practice playmedium

After a $25\%$ discount, a board game costs $\text{\char36}45$ . What was the original price, in dollars, before the discount?

The sale price is $75\%$ of the original: $0.75p = 45$ , so $p = 45 \div 0.75 = 60$ dollars.

Practice playmedium

A recipe uses $3$ cups of flour to make $18$ muffins. At this rate, how many cups of flour are needed to make $30$ muffins?

Set up a proportion: $\dfrac{3}{18} = \dfrac{x}{30}$ , so $18x = 90$ and $x = 5$ cups.

Practice playeasy

$x$ and $y$ are in the ratio $8$ to $3$ . Given that $y = 45$ , what is $x$ ?

$\dfrac{x}{y} = \dfrac{8}{3}$ . With $y = 45$ , $\dfrac{x}{45} = \dfrac{8}{3}$ , so $3x = 360$ and $x = 120$ .

Practice playeasy

Find the simple interest on $\text{\char36}100$ at $10\%$ per year for $1$ year.

$I = 100 \times 0.1 \times 1 = \$10$ .

Practice playmedium

The table shows miles driven and gasoline used over two weeks. At the same miles-per-gallon rate, how many gallons are needed to drive $150$ miles?
$\begin{array}{l|c|c} \text{Week} & \text{Miles} & \text{Gallons} \\ \hline 1 & 240 & 8 \\ 2 & 180 & 6 \end{array}$

Week $1$ : $\dfrac{240}{8}=30$ miles per gallon. Week $2$ : $\dfrac{180}{6}=30$ miles per gallon. So $\dfrac{150}{30}=5$ gallons.

Practice playmedium

A pool treatment uses chlorine concentrate and water in a ratio of $9$ to $72$ . How many cups of chlorine concentrate should be added to $5$ gallons of water to make the treatment in this ratio? ( $4$ cups $=$ $1$ quart, $4$ quarts $=$ $1$ gallon.)

Five gallons of water is $5 \times 16 = 80$ cups. With a $9$ to $72$ ratio, $\dfrac{9}{72} = \dfrac{x}{80}$ , so $72x = 720$ and $x = 10$ cups of concentrate.