Relating Scale Drawings to Ratios and Rates

Videos, examples, lessons, and solutions to help Grade 7 students learn how to relate scale drawings to ratios and rates.

New York State Common Core Math Grade 7, Module 1, Lesson 16

Worksheets for Grade 7

Student Outcomes

Students understand that a scale drawing is either the reduction or the enlargement of a two-dimensional picture.

Students compare the scale drawing picture with the original picture and determine if the scale drawing is a reduction or an enlargement.

Students match points and figures in one picture with points and figures in the other picture.

Intro Activity: Can You Guess the Image?

Example 1

For the following problems, (a) is the actual picture and (b) is the scale drawing. Is the scale drawing an enlargement or a reduction of the actual picture?

Key Idea:

Scale Drawing: a reduced or enlarged two-dimensional drawing of an original two-dimensional drawing.

Example 2

Derek’s family took a day trip to a modern public garden. Derek looked at his map of the park that was a reduction of the map located at the garden entrance. The dots represent the placement of rare plants. The diagram below is the top-view as Derek held his map while looking at the posted map.

What are the corresponding points of the scale drawings of the maps?

Example 3:

Cleleste drew the outline of a building for a diagram she was making and then drew a second one mimicking her original drawing. State the coordinates of the vertices and fill in the table.

Lesson Summary:

Scale Drawing: A drawing in which all lengths between points or figures in the drawing are reduced or enlarged proportional to the lengths in the actual picture. A constant of proportionality exists between corresponding lengths of the two images.

Reduction: The lengths in the scale drawing are smaller than those in the actual object or picture.

Enlargement/Magnification: The lengths in the scale drawing are larger than those in the actual object or picture.

One-to-one Correspondence: Each point in one figure corresponds to one and only one point in the second figure.

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