Unit 1, Lesson 7
Scale Drawings
Grade 7
Preparation
Lesson Narrative
In this lesson, students 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.
They see that the principles and strategies they used when reasoning about scaled copies are applicable to scale drawings. 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. First students work with a drawing on which the scale is given in words (“1 cm represents 2 m”). Then they work with a drawing on which the scale is shown as a line segment on the drawing. As students use scales and scale drawings to find actual and scaled lengths, they reason quantitatively and abstractly (MP2).
Today’s community building centers on the teacher sharing their draft commitments as part of the mathematical community. At the end of the lesson, students are invited to suggest additions to the teacher sections of the chart.
- 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.
Required Materials
Activity 1
Activity 2
Activity 3
Required Preparation
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).
In the “Doing Math” teacher section of the Math Community Chart, add 2–5 commitments you have for what your teaching practice “looks like” and “sounds like” this year.
A scale tells how the measurements in a scale drawing represent the actual measurements.
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 represent 16 feet, and inch represents 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.