1. A Look at Scale Factor and Scale Drawings

2. What is scale factor?
a. The factor by which your weight increases each year
b. A rock band
c. A game show that is a combination
of “The Biggest Loser” and
“Fear Factor”
d. The ratio between two sets of measurements

3. That’s right!
Scale factor is the ratio between two sets of measurements.
In a scale drawing, the scale factor is the ratio of the measurement on the drawing to the measurement of the actual object.

4. For Instance…
A blueprint is a scale drawing of a building. When you buy a home or look for an apartment, you will look at the blueprint. The scale factor on this is at the bottom. It says ¼” = 1’. What do you think this means?

5. More Scale Drawings…

6. LOL. This is on a T-shirt I found online…
LOL! This is on a T-shirt I found online….  How does this relate to scale drawings?

7. The map shown is a scale drawing
The map shown is a scale drawing. A scale drawing is a picture of a real object that is proportional to the real object it represents. The real object may be smaller or larger.
Since they are proportional, they are also SIMILAR FIGURES.
A scale is a ratio between two sets of measurements.
In the map above, the scale is 1 in:100 mi.
This ratio means that 1 inch on the map represents 100 miles.

8. And Some Scale Models (same concept, just in 3D)…

9. What do you Think?...
Why are scale drawings and scale models useful? When might they be used in
real life?

10. One of the most common uses of scale factor is a map…
1 cm = 3 mi
Notice that the key says 1 cm = 3mi.
What does that mean?
Is it important to list this on a map? Why?

11. Let’s say the distance from the Bus Stop to the Shrine is 2 cm
Let’s say the distance from the Bus Stop to the Shrine is 2 cm. What is the ACTUAL distance?
1 cm = 3 mi
If the bus stop is 3 ½ cm from the museum, what is the ACTUAL distance?

12. If Ohmicho-Ichiba is 12 miles from the shrine, how far apart are they on the map?
1 cm = 3 mi

13. Example: Finding Actual Distances The scale on a map is 4 in: 1 mi
* Example: Finding Actual Distances The scale on a map is 4 in: 1 mi. On the map, the distance between two towns is 20 in. What is the actual distance?
Write a proportion using the scale as one of the ratios. Let x represent your unknown value (actual distance). Make sure the ratios are lined up correctly.
4 in.
1 mi
____
20 in.
x mi
_____ =
4 in.
1 mi
____
20 in.
x mi
_____ =
2. Multiply by 5.
x = 5
The actual distance is 5 miles.

14. Check It Out: Additional Example If a drawing of the planets were made using the scale 1 in:15 million km, the distance from Mars to Venus on the drawing would be about 8 in. What is the actual distance from Mars to Venus?
Write a proportion. Let x be the distance from Mars to Venus.
1 in.
15 million km
___________
8 in.
x million km
_________ =
120 = x
The actual distance from Mars to Venus is about 120 million km.

15. Lesson Review: Try These! 
On a map of the Great Lakes area, 2 cm = 45 km. Find the actual distance of the following, given their distances on the map.
1. Detroit to Cleveland = 12 cm
2. Duluth to Nipigon = 20 cm
3. Buffalo to Syracuse = 10 cm
4. Sault Ste. Marie to Toronto = 33 cm
5. A state park is being added to this map. If the park is
450 km from Detroit, how far apart are these places on
the map?