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Lesson 9Creating Scale Drawings

Let’s create our own scale drawings.

Learning Targets:

  • 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.

9.1 Number Talk: Which is Greater?

Without calculating, decide which quotient is larger.

11 \div 23 or 7 \div 13

0.63 \div 2 or 0.55 \div 3

15 \div \frac{1}{3} or 15 \div \frac{1}{4}

9.2 Bedroom Floor Plan

Noah made a rough sketch of the layout of his room (not a scale drawing).

  1. Noah wants to create a floor plan that is a scale drawing. The actual length of Wall C is 4 m. Noah draws a segment 16 cm long to represent Wall C. What scale is he using? Explain or show your reasoning.
  2. Find another way to express the scale.
  3. Pause and discuss your responses with a partner. How do your scales compare?
  4. The actual lengths of Wall A, Wall B, and Wall D are 2.5 m, 2.75 m, and 3.75 m. Determine how long these walls will be on Noah’s scale floor plan.
  5. Use the Point tool
     and the Segment tool
     to draw the walls of Noah's scale floor plan in the applet.
a rough sketch of a floor plan
open applet in presentation mode

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.

9.3 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.

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

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

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

Lesson 9 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.

A scale drawing of a room's floor plan. A scale is shown indicating 1 inch equals 4 feet.

Suppose the longest wall is 15 feet long. We should draw a line 3.75 inches long to represent this wall, because 15 \div 4 = 3.75 .

There is more than one way to express this scale.

These three scales are all equivalent, since they represent the same relationship between lengths on a drawing and actual lengths:

  • 1 inch to 4 feet
  • \frac12 inch to 2 feet
  • \frac14 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 \frac14 \boldcdot 8 = 2 .

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.

A scale drawing of a room's floor plan. A scale is shown indicating 1 inch equals 8 feet.

Notice this drawing is smaller than the previous one. Since one inch on this drawing represents twice as much actual distance, each side length only needs to be half as long as it was in the first scale drawing.

Lesson 9 Practice Problems

  1. An image of a book shown on a website is 1.5 inches wide and 3 inches tall on a computer monitor. The actual book is 9 inches wide.

    1. What scale is being used for the image?
    2. How tall is the actual book?

  2. The flag of Colombia is a rectangle that is 6 ft long with three horizontal strips.

    A rectangular figure that represents a flag. The rectangle is divided by two horizontal lines. The first horizontal line is drawn dividing the rectangle in half and the top half is shaded yellow. The second horizontal line is drawn halfway between the first horizontal line and the base of the rectangle. The middle section is shaded blue and the bottom section is shaded red.
    “Flag of Colombia” by SKopp via Wikimedia Commons. Public Domain.
    • The top stripe is 2 ft tall and is yellow.
    • The middle stripe is 1 ft tall and is blue.
    • The bottom stripe is also 1 ft tall and is red.
    1. Create a scale drawing of the Colombian flag with a scale of 1 cm to 2 ft.
    1. Create a scale drawing of the Colombian flag with a scale of 2 cm to 1 ft.

  3. These triangles are scaled copies of each other.

    Four right triangles labeled F, B, G, and H. Triangle F has the vertical side labeled 8, the horizontal side labeled 6, and the longest side labeled 10. Triangle B has the vertical side labeled 2, the horizontal side labeled 3 halves, and the longest side labeled 5 halves. Triangle G has the vertical side labeled 4, the horizontal side labeled 3, and the longest side labeled 5. Triangle H has the vertical side labeled 8 thirds, the horizontal side labeled 2, and the longest side labeled 10 thirds.

    For each pair of triangles listed, the area of the second triangle is how many times larger than the area of the first?

    1. Triangle G and Triangle F

    2. Triangle G and Triangle B

    3. Triangle B and Triangle F

    4. Triangle F and Triangle H

    5. Triangle G and Triangle H

    6. Triangle H and Triangle B

  4. Here is an unlabeled rectangle, followed by other quadrilaterals that are labeled. 

    1. Select all quadrilaterals that are scaled copies of the unlabeled rectangle. Explain how you know.
    Original dimensions are 2 by 4. Figure A has side lengths of 4, diagonal side down 2, left 1, 4, diagonal side up 2, right 1. Figure B has side lengths 8, 3, 8, 3. C has side lengths 6, 3, 6, 3. D has 2, 1, 2, 1. E has 4, 2, 4, 2. F has 7, diagonal side down 3, right 1, 7, and diagonal side left 1, up 3. G has 5, 2, 5, 2. H has 8, 4, 8, 4.
    1. On graph paper, draw a different scaled version of the original rectangle.