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Lesson 5

Creating Scale Drawings

Unit 2

Scale Drawings, similarity and slope

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5.1 Warm Up: Number Talk: Which is Greater?

Without calculating, decide which quotient is larger.

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Learning Targets

  • When I know the actual measurements, I can create a scale drawing at a given scale.
  • I know how different scales affect the lengths in the scale drawing.
  • I can determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths.

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5.2 Bedroom Floor Plan

Here is a rough sketch of Noah’s bedroom (not a scale drawing).

Noah wants to create a floor plan that is a scale drawing.

1. 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.

2. Find another way to express the scale.

3. Discuss your thinking with your partner. How do your scales compare?

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5.2 Bedroom Floor Plan

4. 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.

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5.2 Are you ready for more?

If Noah wanted to draw another floor plan on which Wall C was 20 cm, would 1 cm to 5 m be the right scale to use? Explain your reasoning.

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5.3 Two Maps of Utah

A rectangle around Utah is about 270 miles wide and about 350 miles tall. The upper right corner that is missing is about 110 miles wide and about 70 miles tall.

1. Make a scale drawing of Utah where 1 centimeter represents 50 miles.

Make a scale drawing of Utah where 1 centimeter represents 75 miles.

2. How do the two drawings compare? How does the choice of scale influence the drawing?

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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 15 feet long. We should draw a line 3.75 inches long to represent this wall, because 15 ÷ 4 = 3.75.

There is more than one way to express this scale. Any of these scales can be used to find actual lengths and scaled lengths (lengths on a drawing). The size of a scale drawing is influenced by the choice of scale. These three scales are all equivalent, since they represent the same relationship between lengths on a drawing and actual lengths:

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5.4 Cool Down: Drawing a Pool

A rectangular swimming pool measures 50 meters in length and 25 meters in width.

1. Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters.

2. What are the length and width of your scale drawing?

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Reflections

  • Can you create a scale drawing at a given scale?
  • Do you know how different scales affect the lengths in the scale drawing?
  • Can you determine the scale of a scale drawing when I know lengths on the drawing and corresponding actual lengths?

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Practice Problems

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Lesson Video

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