Scale, Scale Factor, & Scale Drawings

Scale, Scale Factor, & Scale Drawings

Objective:7.2.01 & 7.3.03Essential Question: How can I use a scale factor to understand distances on a map or the size of a house or object?

Vocabulary:Scale: the ratio between the actual size of an object

and a proportional representation.Scale Factor: the factor by which all components are

multiplied in order to create a proportional enlargement or reduction.

Scale Drawing: a drawing that is similar but either larger or smaller than the actual object.

Scale Model: a model that is used to represent something that is too small or too large for an actual size model.

Scale, Scale Factor, & Scale Drawings

First Things First…Lets get rid of some possible misconceptions we might have about this notion of scale.

We are not talking about the kind of scale you might

see in a grocery store

Scale, Scale Factor, & Scale Drawings

First Things First…Lets get rid of some possible misconceptions we might have about this notion of scale.

We are also not talking about the kind of scale you

get on at a doctors office

Scale, Scale Factor, & Scale Drawings

So What Are We Talking AboutWe are talking about the kind of scale that shows the relationship between two objects.

Examples might include:

Models

Scale, Scale Factor, & Scale Drawings

Blueprints for House

Maps

Where Will I See ThisSome careers or jobs that utilize the math concept of scale include:

Mapmakers (Cartographers) DoctorsModel Makers EngineersContractors Construction Workers

Artists PilotsTruck Drivers Fashion/Clothes DesignersArchitects

Scale, Scale Factor, & Scale Drawings

Scale, Scale Factor, & Scale Drawings

Example 1:

A) 1 inch = 60 miles

1 inch represents an actual distance of 60 miles

B) 1 : 24

1 unit represents an actual distance of 24 units

Scale, Scale Factor, & Scale Drawings

Example 2: Tell whether each scale represents a copy, reduction, or enlargement of the original object.

A) 4 cm = 12 m

B) 1 ft : 8 in

C) 1 yd : 3 ft

REDUCTION

ENLARGEMENT

COPY

b/c every 12m is now represented by only 4cm

b/c every 8in is now represented by 1ft

b/c every 3ft is still being represented by 3ft

Scale, Scale Factor, & Scale Drawings

Example 3: A drawing of a car that is drawn to scale is 1:20. If the drawing of the car is 12 inches long, what is the length of the car in real-life?

240 inches

Scale, Scale Factor, & Scale Drawings

Example 4: On a map of the United States the scale is 1 inch = 120 miles.

A) If the distance from Clinton to Greensboro is 2.5 inches on the map, how many miles apart are the two cities?

300 miles

Scale, Scale Factor, & Scale Drawings

Example 4: On a map of the United States the scale is 1 inch = 120 miles.

B) If the actual distance from Clinton to Wilmington is 60 miles, how far apart should they be on the map?

0.5 inches

Scale, Scale Factor, & Scale Drawings

Example 5: The Washington Monument stands 540 feet tall.

A) If a model of the monument in a souvenir shop is 9 inches tall, what is the model’s scale?

1 inch = 60 feet

Scale, Scale Factor, & Scale Drawings

Example 5: The Washington Monument stands 540 feet tall.

B) What is the scale factor?* scale factor is when both measures have the same unit

1 inch = 720 inches OR 1:720

Scale, Scale Factor, & Scale Drawings

Example 6: Below are two similar rectangles. Find the scale factor of the larger rectangle to the smaller rectangle.

24 cm

12 cm

20 cm

10 cm

6:5

Scale, Scale Factor, & Scale Drawings

Real World: Your Social Studies teacher has asked you to draw a map of North Carolina. You decide that the scale you will use is 1 inch = 30 miles. The actual distance from Charlotte to Raleigh is 144 miles. How far apart should the cities be on your map?

4.8 inches apart

Scale, Scale Factor, & Scale Drawings

Real World: The distance from Springfield to Capital City is 1.4 inches on the map. Find the actual distance.

9.8 miles

HOMEWORK

Scale, Scale Factor, & Scale Drawings