Utah Grade 7 Math

A floor plan has a length scale, not an area multiplier

An invented rectangular display space measures 6 cm by 4 cm on a plan. The plan’s scale is 1 cm representing 2 m. Find the actual length, width, and area. A student multiplies the drawing area of 24 cm² by 2 and reports 48 m². Explain the mistake. Then draw the same space using 1 cm to represent 3 m.

Follow the reasoning

The scale converts each length separately: 6 cm represents 12 m, and 4 cm represents 8 m. The actual area is 12 × 8 = 96 m². A 1 cm by 1 cm square on the original plan represents a 2 m by 2 m square, or 4 m². Thus the 24 drawing squares represent 24 × 4 = 96 m². Multiplying the drawing area by the length factor only once ignores the change in the second dimension. On the new plan, divide each actual length by 3 m per centimetre: the length is 4 cm and the width is 8/3 cm. Its area is 32/3 cm², with each square centimetre representing 9 m²; (32/3) × 9 returns 96 m².

Check the units and conditions

The correspondence assumes the same scale in both directions. The actual space stays unchanged when the drawing scale changes. The drawing’s square-centimetre area is not the actual square-metre area. Keep length and area units distinct and use the exact fractional width rather than silently rounding it.

Try a second rectangle

At the original scale, draw a rectangle 5 cm by 3 cm. Its actual dimensions are 10 m by 6 m and its area is 60 m². Explain how 15 drawing squares each represent 4 m². Redraw the same rectangle at the new scale: 10/3 cm by 2 cm, preserving the same actual area.

Utah reference for this worked activity

The Utah mathematics standards directory identifies January 2016 adoption and lists a revision process that is still underway. The elementary PDF says revised April 2016; the middle-school PDF says revised September 2015–April 2016. These file revision labels do not establish adoption of a new 2026 edition. Use the school’s current learning sequence and consult later department updates.

This selected reference identifies the activity focus. The complete standard and grade curriculum include additional work. These labels do not certify alignment of every independent lesson, worksheet, or quiz in the broader directory.

Choose a next task from the student’s explanation

Use a different set of numbers to check whether the student can explain the same relationship. If the explanation is unclear, return to the model; if the reasoning is sound but a calculation is wrong, work through a shorter calculation and check it against the model. Use the related learning resources alongside the teacher’s assigned goals.

The Utah RISE overview lists mathematics summative assessment in Grades 3–8, including this grade. Follow the school’s current directions and accommodations. Independently published practice has its own timing, tools, question count, and scoring; its result does not establish a state performance level. This original activity is not an official state assessment question. Read Utah assessment guidance.

State sources and the selected complete PDF page checked October 6, 2026. Confirm later guidance and local assignments before planning assessment preparation.