Scale Drawings and Proportional Relationships
Scale drawings are representations of real objects that maintain the same shape as the original but are either larger or smaller in size. They're used everywhere—from maps and blueprints to model cars and scientific diagrams.
Lesson Objectives
- Understand what scale and scale factor mean
- Learn to convert between different scale notations (ratio, fraction, verbal description)
- Learn to find unknown measurements using proportions
- Discover how scale affects lengths, areas, and volumes
- Apply scale to the coordinate plane (dilation/scaling transformations)
What is a Scale?
A scale is the ratio that compares the measurements in a drawing to the actual measurements of the object being represented. It's typically written in one of these forms:
- As a ratio - 1:100 (read as "1 to 100")
- As a fraction - 1/100
- As a unit ratio - 1 cm on the drawing = 100 cm in reality (that is, 1 cm = 1 m)
For example, if a map has a scale of 1:1000, this means that 1 centimeter on the map represents 1000 centimeters (or 10 meters) in real life.
Types of Scale and Reading Scale Notation
- Numerical scale: 1:1000 (1 unit on the drawing corresponds to 1000 of the same units in reality)
- Fractional notation: 1/1000 (same as 1:1000)
- Verbal description: 1 cm on the plan = 10 m in reality
- Linear (graphic) scale: a scale bar with segments on the drawing that can be measured with a ruler
Converting between forms:
- 1:2500 ⇔ 1/2500 ⇔ 1 cm on the plan = 2500 cm = 25 m
- 1 cm : 2 m ⇔ 1:200 (since 2 m = 200 cm)
Linear scale with markings up to 2 km