Unit 2, Lesson 5
Creating Scale Drawings
Accelerated 7
5.2
Activity
Here is a rough sketch of Noah’s bedroom (not a scale drawing).
Rough sketch of Noah's bedroom. Bottom, horizontal line, labeled Wall C. Left side, vertical line, labeled Wall B. Top, from left to right, horizonal line labeled Wall A, a door, horizontal line, labeled Wall E. Wall E is higher up than Wall A. Right side, vertical line, labeled Wall D.
Noah wants to create a floor plan that is a scale drawing.
- The actual length of Wall C is 4 m. To represent Wall C, Noah draws a segment 16 cm long. What scale is he using? Explain or show your reasoning.
- Find another way to express the scale.
- Discuss your thinking with your partner. How do your scales compare?
- The actual lengths of Wall A and Wall D are 2.5 m and 3.75 m. Determine how long these walls will be on Noah’s scale floor plan. Explain or show your reasoning.
Student Lesson Summary
If we want to create a scale drawing of a room's floor plan that has the scale “1 inch to 4 feet,” we can divide the actual lengths in the room (in feet) by 4 to find the corresponding lengths (in inches) for our drawing.
Suppose the longest wall is 23 feet long. We should draw a line 5.75 inches long to represent this wall, because .
There is more than one way to express this scale. These three scales are all equivalent, because they represent the same relationship between lengths on a drawing and actual lengths:
- 1 inch to 4 feet
- inch to 2 feet
- inch to 1 foot
Any of these scales can be used to find actual lengths and scaled lengths (lengths on a drawing). For instance, we can tell that, at this scale, an 8-foot long wall should be 2 inches long on the drawing because .
The size of a scale drawing is influenced by the choice of scale. For example, here is another scale drawing of the same room using the scale 1 inch to 8 feet.
Notice that this drawing is smaller than the previous one. Since one inch on this drawing represents twice as much actual distance, each side length needs to be only half as long as it was in the first scale drawing.
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