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Common Core Math7th GradeGeometry

7.G.1: Solve Problems with Scale Drawings

Also written as 7.G.A.1 and CCSS.MATH.CONTENT.7.G.A.1 · Cluster: Draw construct, and describe geometrical figures and describe the relationships between them.

Make a 7.G.1 Scale Drawing GridAll 24 7th Grade Math Standards

The Official Wording

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.

Common Core State Standards, Grade 7, Geometry · Read it at the source · Checked October 14, 2026

What 7.G.1 Means in Plain English

Seventh graders read a scale like 1 inch = 4 feet and turn drawing lengths into real ones. A garden drawn 5 in by 3½ in is really 20 ft by 14 ft, and redrawn at 1 inch = 8 feet it shrinks to 2½ in by 1¾ in.

Area is the trap: each square inch of the drawing stands for 16 square feet, not 4, because the scale stretches both length and width. 8th grade turns scale drawings into dilations on the coordinate plane (8.G.3) and similar figures (8.G.4).

7.G.1 I Can Statements

  • I can use a scale to find actual lengths from a drawing.
  • I can find an actual area, knowing the scale applies twice.
  • I can redraw a scale drawing at a new scale.

7.G.1 Worked Example

One garden plan read three ways: real lengths, real area, and a smaller copy at a new scale.

Problem

A scale drawing of a community garden uses 1 inch = 4 feet. On the drawing the garden is 5 in by 3½ in. Find the garden’s real length, width and area, then give its size on a new drawing at 1 inch = 8 feet.

A garden plan at 1 inch = 4 feet
  1. Every inch on the drawing is 4 real feet, so multiply each drawing length by 4.5 × 4 = 20 ft; 3½ × 4 = 14 ft
  2. Find the real area from the real lengths.A = 20 × 14 = 280 ft²
  3. Cross-check from the drawing. Each square inch on paper is a 4 ft by 4 ft square on the ground, which is 16 ft², not 4.5 × 3½ = 17½ in²; 17½ × 16 = 280 ft²
  4. For the new drawing, go back to the real size and divide by 8, since each inch now stands for 8 feet.20 ÷ 8 = 2½ in; 14 ÷ 8 = 1¾ in
AnswerThe garden is 20 ft by 14 ft, an area of 280 ft², and the new drawing is 2½ in by 1¾ in

Check it: Each inch now stands for twice as many feet, so every drawing length should halve: 5 to 2½ and 3½ to 1¾. Scale back up to confirm: 2½ × 8 = 20 ft and 1¾ × 8 = 14 ft.

Common Mistakes with 7.G.1

Scaling area by the scale once

17½ in² × 4 = 70 ft²

Try this: Sketch one drawing square inch as a 4 ft by 4 ft plot: it holds 16 ft², so multiply drawing areas by 16.

Running the scale backward

The garden is 20 ft long, so it is 20 × 4 = 80 in on the drawing

Try this: Write the scale with units, 1 in : 4 ft, and remember real lengths are bigger: 20 ft ÷ 4 = 5 in.

Doubling the drawing for a bigger scale number

1 inch = 8 feet is twice the scale, so 5 in becomes 10 in

Try this: Go through the real size: 5 in is 20 ft, and 20 ÷ 8 = 2½ in. More feet per inch means a smaller drawing.

Where 7.G.1 Fits

Comes Before6.RP.3Use ratio tables and unit rates, the arithmetic behind every scale.6.G.1Find the area of triangles and polygons, the shapes a plan is made of.
Alongside7.RP.2Real length is a constant times drawing length, a proportional relationship.7.G.6Area and volume problems, often read off a floor plan.
Comes Next8.G.3Dilations on the coordinate plane, a scale drawing with coordinates.8.G.4Similar figures as dilations combined with rigid motions.

Practice 7.G.1

Graph Paper GeneratorFree ToolQuarter-inch grid paper where one square is one foot: the 20 by 14 ft garden is 20 by 14 squares, which is exactly 1 inch = 4 feet.¼ inch squaresLetterPrint
Make Graph Paper
Word Problem GeneratorFree ToolMap and blueprint story problems: 1 inch to 4 feet, so how long is a wall drawn 3½ inches? Students set up the scale before multiplying.Ratios and ratesScale drawingsGrade 7
Make Word Problems

Quick Check

  1. On a map, 1 cm = 5 km. Two towns are 7.5 cm apart on the map. How far apart are they really?
  2. A room is drawn 4 in by 3 in at 1 inch = 3 feet. What is the room’s real area?
  3. A poster drawing is 6 cm by 9 cm at 1 cm = 2 ft. How big is it redrawn at 1 cm = 3 ft?

7.G.1: Other Names

7.G.17.G.A.1CCSS.MATH.CONTENT.7.G.A.1

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.