Scale FactorScale FactorA Look at Scale Factor A Look at Scale Factor

and Scale Drawingsand Scale Drawings

What is scale factor?What is scale factor?

a. The factor by which your weight a. The factor by which your weight increases each yearincreases each year

b. A rock bandb. A rock band

c. A game show that is a combination c. A game show that is a combination

of “The Biggest Loser” and of “The Biggest Loser” and

“ “Fear Factor”Fear Factor”

d. The ratio between two sets of d. The ratio between two sets of measurementsmeasurements

That’s right!That’s right!

Scale factor is the ratio between two Scale factor is the ratio between two sets of measurements. sets of measurements.

In a scale drawing, the scale factor is In a scale drawing, the scale factor is the ratio of the measurement on the the ratio of the measurement on the drawing to the measurement of the drawing to the measurement of the actual object. actual object.

For Instance…For Instance…

A blueprint is a A blueprint is a scale drawing of a scale drawing of a

building. When you building. When you buy a home or look buy a home or look for an apartment, for an apartment,

you will look at the you will look at the blueprint. The blueprint. The

scale factor on this scale factor on this is at the bottom. It is at the bottom. It

says ¼” = 1’. says ¼” = 1’. What do you think What do you think

this means?this means?

More Scale Drawings…More Scale Drawings…

LOL! This is on a T-shirt I found LOL! This is on a T-shirt I found online…. online….

How does this relate to scale drawings?How does this relate to scale drawings?

The map shown is a scale drawing. A scale drawing is a picture of a real object that is proportional to the real object. 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.

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

What do you Think?...What do you Think?...

Why are scale drawings and scale Why are scale drawings and scale models useful? When might models useful? When might

they be used in real life?they be used in real life? Maps Maps

BlueprintsBlueprints Representing sizeRepresenting size

One of the most common uses of One of the most common uses of scale factor is a map…scale factor is a map…

Notice that the key says 1 cm = 3mi.Notice that the key says 1 cm = 3mi.

What does that mean?What does that mean?

Is it important to list this on a map? Why?Is it important to list this on a map? Why?

1 cm = 3 mi

Let’s say the distance from the Bus Stop to Let’s say the distance from the Bus Stop to the Shrine is 2 cm. What is the ACTUAL the Shrine is 2 cm. What is the ACTUAL

distance? distance?

If the bus stop is 3 ½ cm from the If the bus stop is 3 ½ cm from the museum, what is the ACTUAL distance?museum, what is the ACTUAL distance?

1 cm = 3 mi

Let’s say the distance from the Bus Stop to Let’s say the distance from the Bus Stop to the Shrine is 2 cm. What is the ACTUAL the Shrine is 2 cm. What is the ACTUAL

distance? distance? 6 miles6 miles

If the bus stop is 3 ½ cm from the museum, If the bus stop is 3 ½ cm from the museum, what is the ACTUAL distance? what is the ACTUAL distance? 10 ½ miles10 ½ miles

1 cm = 3 mi

If Ohmicho-Ichiba is 12 miles from the If Ohmicho-Ichiba is 12 miles from the shrine, how far apart are they on the map?shrine, how far apart are they on the map?

1 cm = 3 mi

If Ohmicho-Ichiba is 12 miles from the If Ohmicho-Ichiba is 12 miles from the shrine, how far apart are they on the map?shrine, how far apart are they on the map?

4 cm4 cm

1 cm = 3 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?

20 in. x mi

_____ 4 in. 1 mi

____ =

x = 5

1. Write a proportion using the scale as one of the ratios. Let x represent your unknown value (actual distance).

2. Multiply by 5.

3. The actual distance is 5 miles.

4 in. 1 mi

____ 20 in. x mi

_____=

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?

8 in.x million km

_________ 1 in. 15 million km

___________ =

120 = x

Write a proportion. Let x be the distance from Mars to Venus.

The actual distance from Mars to Venus is about 120 million km.

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 = 7 cm

4. Sault Ste. Marie to Toronto = 33 cm

5. A state park is being added to this map. If the park is

315 km from Detroit, how far apart are these places on

the map?

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 270 km

2. Duluth to Nipigon = 20 cm 450 km

3. Buffalo to Syracuse = 7 cm 157.5 km

4. Sault Ste. Marie to Toronto = 33 cm 742.5 km

5. A state park is being added to this map. If the park is 315

km from Detroit, how far apart are these places on the map?

14 cm