VTCAP Grade 7 Expressions and Equations Practice

VTCAP Grade 7 Expressions and Equations. Practice it free.

Grade 7 Expressions and Equations standards; reported jointly with the number system as 'The Number System, Expressions and Equations' performance indicator. Blueprint target: 8-16 points (15-30% of the grade 7 test). This Grade 7 reporting domain maps to 3 practice skills and 8 representative questions from the playable bank.

Grade 77.EE3 mapped skills

Expressions and Equations skills

Use properties of operations to generate equivalent expressions

Solve real-life and mathematical problems using numerical and algebraic expressions and equations

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)

8 free questions · 0/0 correct

Practice playmedium

A warehouse manager sorted a shipment of shirts into four color groups. Exactly $\dfrac{1}{5}$ of the shirts were red, exactly $\dfrac{1}{4}$ were white, $42$ shirts were green, and $24$ shirts were blue. How many shirts were in the shipment?

Let $x$ be the total number of shirts. Red and white shirts make $\dfrac{1}{5}x + \dfrac{1}{4}x = \dfrac{9}{20}x$ . Green and blue shirts total $42 + 24 = 66$ , so $\dfrac{11}{20}x = 66$ and $x = 120$ .

Practice playeasy

A band competition allows an instrument case's length, width, and height to total at most $62.0$ inches. A case measures $65.4$ inches in total. What is the minimum decrease needed in that total, in inches, so that the case meets the rule?

The total must be at most $62.0$ inches. The minimum decrease is $65.4 - 62.0 = 3.4\textsf{.}$

Practice playeasy

Solve for $k$ : $k + 3 = 5$ .

Isolate $k$ : $k = 2$ .

Practice playmedium

A public library counted every book checked out on one busy Saturday. Exactly $\dfrac{1}{6}$ of the checkouts were fiction, exactly $\dfrac{1}{2}$ were nonfiction, $14$ checkouts were reference books, and $10$ checkouts were magazines. How many books were checked out that day?

Let $x$ be the total checkouts. Fiction and nonfiction account for $\dfrac{1}{6}x + \dfrac{1}{2}x = \dfrac{2}{3}x$ . Reference and magazines total $14 + 10 = 24$ , so $\dfrac{1}{3}x = 24$ and $x = 72$ .

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

A car dealership's lot held four types of vehicles. Exactly $\dfrac{1}{3}$ of the vehicles were sedans, exactly $\dfrac{1}{4}$ were SUVs, $45$ vehicles were compacts, and $35$ vehicles were trucks. How many vehicles were on the lot?

Let $x$ be the total number of vehicles. Sedans and SUVs account for $\dfrac{1}{3}x + \dfrac{1}{4}x = \dfrac{7}{12}x$ . Compacts and trucks total $45 + 35 = 80$ , so $\dfrac{5}{12}x = 80$ and $x = 192$ .

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?