Scale Drawings and Models

Grade 7 · Math · Study Guide

Learn how to use scale factors to create and interpret scale drawings, maps, and three-dimensional models.

A scale drawing is a representation of an object where all measurements are proportional to the actual object's measurements. The scale tells you the relationship between the drawing's measurements and the real measurements.

A scale is written as a ratio, such as 1:50 or 1 inch = 10 feet. This means every 1 unit in the drawing equals 50 units (or 10 feet) in real life. You can use this ratio to find real distances from a drawing, or to figure out how large to draw something.

To find the actual measurement from a drawing, set up a proportion: (drawing measurement) / (scale unit) = (actual measurement) / (real unit). Cross multiply and solve.

Scale factor is the ratio by which all dimensions are multiplied. If a blueprint uses a scale of 1 cm = 2 m, the scale factor is 1:200 (converting both to centimeters). A scale factor greater than 1 means the drawing is an enlargement; less than 1 means it is a reduction.

Scale models work the same way in three dimensions. Model cars, architectural models, and globes are all real-world examples. Understanding scale helps in reading maps, interpreting blueprints, and creating accurate models.

Key terms

Scale drawing
A proportional representation of an object where dimensions are reduced or enlarged by a consistent ratio
Scale
The ratio comparing a measurement in a drawing or model to the actual measurement
Scale factor
The ratio by which every dimension is multiplied; it is a single number or simplified ratio
Reduction
A scale drawing smaller than the actual object; scale factor is less than 1
Enlargement
A scale drawing larger than the actual object; scale factor is greater than 1

Flashcards

Scale ratio format
Written as drawing : actual, e.g., 1:50 means 1 unit in the drawing = 50 units in real life
Finding actual distance
Actual = drawing measurement × scale factor (real/drawing units)
Finding drawing distance
Drawing = actual measurement ÷ scale factor
Proportion method for scale problems
Set up: drawing/scale = actual/1, then cross multiply to solve
Scale factor < 1
The drawing or model is SMALLER than reality (a reduction)
Scale factor > 1
The drawing or model is LARGER than reality (an enlargement)
Real-world scale examples
Maps, architectural blueprints, model trains, globes, and engineering drawings
Converting scale units
Make sure both units match before computing — convert feet to inches or cm to m as needed

Questions

  1. A map uses a scale of 1 inch = 30 miles. Two cities are 4.5 inches apart on the map. What is the real distance?

    1. 100 miles
    2. 120 miles
    3. 135 miles
    4. 150 miles
    Show answer

    Answer: 135 miles

    4.5 inches × 30 miles/inch = 135 miles.

  2. In a scale drawing, if the scale factor is 1/100, the drawing is an enlargement of the real object.

    Show answer

    Answer: False

    A scale factor of 1/100 means the drawing is 100 times SMALLER than the actual object — that is a reduction, not an enlargement.

  3. A blueprint scale reads 1 cm = 5 m. A wall measures 3 cm on the blueprint. The actual wall is _____ meters long.

    Show answer

    Answer: 15

    3 cm × 5 m/cm = 15 meters.

  4. A model car is built at a scale of 1:24. The actual car is 4.8 meters long. How long is the model?

    1. 0.2 meters
    2. 0.4 meters
    3. 2 meters
    4. 115.2 meters
    Show answer

    Answer: 0.2 meters

    Scale 1:24 means model = actual ÷ 24. So 4.8 m ÷ 24 = 0.2 m.

  5. All scale drawings must have lengths AND widths scaled by the same factor.

    Show answer

    Answer: True

    A scale drawing must use the same scale factor for all dimensions to maintain the correct proportions (shape) of the object.

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