Up to this point, students have been exploring scaled copies, or two-dimensional images that have been recreated at certain scale factors. In this lesson, they begin to look at scale drawings, or scaled two-dimensional representations of actual objects or places. Students see that although scale drawings capture three-dimensional objects or places, they show scaled measurements in only two of the dimensions, and that all information is projected onto a plane.
In this and upcoming lessons, students see that the principles and strategies they used to reason about scaled copies are applicable to scale drawings (MP7). For example, previously they saw scale factor as a number that describes how lengths in a figure correspond to lengths in a copy of the figure (and vice versa). Now they see that scale serves a similar purpose: it describes how the lengths in an actual object are related to the lengths on a drawn representation of it. They learn that scale can be expressed in a number of ways, and use scale and scale drawings to find actual and scaled lengths.
Students begin by interpreting given scale drawings. In subsequent lessons, they will create or reproduce scale drawings at specified scales, as well as determine appropriate scales to use, given restrictions in the size of drawing.
- Describe (orally) what a “scale drawing” is.
- Explain (orally and in writing) how to use scales and scale drawings to calculate actual and scaled distances.
- Interpret the “scale” of a scale drawing.
Let’s explore scale drawings.
Prepare to display the examples and non-examples of scale drawings for all to see. Consider adding to the collection a local map showing the actual route of a train or bus line (example of scale drawing) and a diagrammatic transit map (non-example).
Ensure students have access to geometry toolkits, especially centimeter rulers and index cards or paper to use as a measuring tool.
You will need the Sizing Up a Basketball Court blackline master for this lesson. Prepare one copy per student.
- I can explain what a scale drawing is, and I can explain what its scale means.
- I can use actual distances and a scale to find scaled distances.
- I can use a scale drawing and its scale to find actual distances.
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.