In this lesson, students see that a scale can be expressed without units. For example, the scale “1 to 60” means that every length on the scale drawing represents an actual length that is 60 times its size, whatever the unit may be (inches, centimeters, etc.). Students analyze various scales and find that sometimes it is helpful to rewrite scales with units as scales without units in order to compare them. 

Expressing the scale without units, such as “1 to 60,” highlights the scale factor that relates the scale drawing to the actual object. Each measurement on the scale drawing is multiplied by 60 to find the corresponding measurement on the actual object. They see that equivalent scales relate scaled and actual measurements by the same scale factor, even though the scales may be expressed differently. For example, the scale 1 inch to 2.5 feet is equivalent to the scale 5 m to 150 m, because they are both at a scale of 1 to 30. As students identify equivalent scales, they construct arguments (MP3) and attend to precision (MP6).

There is a blackline master that gives some information about equal lengths that students may want to refer to during these activities.