Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Architects, mapmakers and model builders all rely on scale drawings, pictures in which every length is the same fixed fraction of the real length. A floor plan drawn at 1 inch to 4 feet shrinks a 14-foot wall to 3.5 inches, and anyone reading the plan can reverse the scale to recover the real size. Seventh graders use this idea to compute actual lengths and areas from a drawing and to reproduce a drawing at a different scale.
Lengths scale by the scale factor, but areas do not scale the same way. If every length on a drawing is multiplied by 3 to get the real object, the real area is 3 × 3 = 9 times the area on the drawing, because area involves two dimensions. Redrawing at a new scale usually goes through the real measurements: convert drawing lengths to actual lengths, then convert those to the new scale. Students also learn to read scales written in different ways, such as 1 cm : 25 km, 1:24, or with a scale bar.
If lengths are 3 times larger, many students say the area is 3 times larger. Drawing a 1-by-1 square next to a 3-by-3 square and counting the 9 small squares makes the squaring visible.
With a scale of 1 inch : 4 feet, dividing the drawing length by 4 instead of multiplying gives a tiny real room. Students should ask whether the real object should be bigger or smaller than the drawing.
A scale of 1:24 has no units, so both measurements must be in the same unit. Converting 4.32 m to 432 cm before dividing avoids answers that are off by a factor of 100.
On a floor plan with scale 1 inch : 4 feet, a bedroom measures 3.5 inches by 2.75 inches. Find the room's actual dimensions and floor area, then give its size on a new plan at 1 inch : 8 feet.
Answer: The room is 14 ft by 11 ft with an area of 154 sq ft, and it is drawn 1.75 in by 1.375 in on the new plan.
Hands-on projects make this standard memorable: students measure the classroom and draw it to scale, or enlarge a cartoon using a grid. Comparing the area of a small grid square with the matching enlarged square is a natural moment to discover the squaring of area.
Test items typically give a map or plan and ask for an actual distance or area, or ask students to identify a correct redrawing at a new scale. Encourage a quick table with drawing length, scale and actual length so each conversion step is visible.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 160 (also accepted: 160 km)
Each centimeter stands for 25 km, so 6.4 × 25 = 160 km.
Answer: B) 90 cm²
Area scales by the square of the scale factor: 10 × 3 × 3 = 90 cm².
Answer: 18 (also accepted: 18 cm)
Convert to the same unit: 4.32 m = 432 cm. The model is 1/24 of that: 432 ÷ 24 = 18 cm.
Answer: D) 8 inches
The real wall is 4 × 6 = 24 feet. At 1 inch : 3 feet it is 24 ÷ 3 = 8 inches long.
Answer: 12 (also accepted: 12 cm², 12 cm2)
The drawing is 12 ÷ 3 = 4 cm by 9 ÷ 3 = 3 cm, so its area is 4 × 3 = 12 cm².
Answer: B) Lengths double and the area becomes 4 times as large
Area depends on two lengths, so doubling both multiplies the area by 2 × 2 = 4.
A full lesson with slides, activities and an exit ticket on scale drawings, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.G.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn scale drawings into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It is the number every length is multiplied by to go from the drawing to the real object (or back). A scale of 1 inch : 4 feet means a scale factor of 48, since 4 feet is 48 inches.
Area is length times width, and both are multiplied by the scale factor, so the area is multiplied by the scale factor squared.