In previous lessons, students have used scale drawings to calculate actual distances. This is the first lesson where students use the actual distance to calculate the scaled distance and create their own scale drawings. They see how different scale drawings can be created of the same actual thing, using different scales. They also see how the choice of scale influences the drawing. For example, a scale drawing with a scale of 1 cm to 5 m will be smaller than a scale drawing of the same object with a scale of 1 cm to 2 m (since each cm represents a larger distance, it takes fewer cm to represent the object). This prepares them for future lessons where they will recreate a given scale drawing at a different scale.
Noticing how scaled drawing change with the choice of scale develops important structural understanding of scale drawings (MP7).
- Compare and contrast (orally) different scale drawings of the same object, and describe (orally) how the scale affects the size of the drawing.
- Create a scale drawing, given the actual dimensions of the object and the scale.
- Determine the scale used to create a scale drawing and generate multiple ways to express it (in writing).
Let’s create our own scale drawings.
Ensure students have access to geometry toolkits.
- I can determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths.
- I know how different scales affect the lengths in the scale drawing.
- When I know the actual measurements, I can create a scale drawing at a given scale.
A scale tells how the measurements in a scale drawing represent the actual measurements of the object.
For example, the scale on this floor plan tells us that 1 inch on the drawing represents 8 feet in the actual room. This means that 2 inches would represent 16 feet, and \(\frac12\) inch would represent 4 feet.
A scale drawing represents an actual place or object. All the measurements in the drawing correspond to the measurements of the actual object by the same scale.