RISE Grade 7 Expressions and Equations Practice

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

Utah Core Standards for Mathematics (CCSS-aligned Utah math standards) — Utah

How the RISE reports it

Utah’s RISE mathematics assessment is a state assessment aligned to Utah Core Standards rather than a separately branded national framework. The official Utah pages point to Utah Core standards resources and the RISE administration guidance, with no separate public math blueprint published on the assessment page itself.

Blueprint & weighting

RISE mathematics weighting by domain was not located on the official Utah assessment page; the official page only points to the RISE assessment overview/administration resources and the Utah Core Standards resources. Grade 6 administration guidance notes a two-segment math test with Segment 1 no calculator and Segment 2 calculator allowed, and the proctor guide states Mathematics has an expected testing time of 90 minutes for most students and 135 minutes for all students.

Official sources

Utah State Board of Education Assessments
Utah State Board of Education Learning Resources for Families
Utah State Board of Education Assessment Contacts PDF

8 free questions · 0/0 correct

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

Airline rules allow a carry-on bag to weigh at most $50.0$ pounds. A bag weighs $52.8$ pounds. What is the minimum decrease needed in the bag's weight, in pounds, so that it meets the rule?

The bag must weigh at most $50.0$ pounds. The minimum decrease is $52.8 - 50.0 = 2.8\textsf{.}$

Practice playeasy

Solve for $m$ : $m - 4 = 2$ .

Subtract 4 from both sides: $m = 6$ .

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?