1. Scale factors and similarity
Ratios Proportions
Scale
Scale diagrams

2. Ratios???
Ratios are basically a comparison of two quantities with the same units.
Ratios can be expressed:
as a fraction ⅓
as a comparison ratio 1 : 3

3. Proportions???
A proportion is simply two ratios that are equivalent to each other. 
Proportions are usually used in Algebra to solve for some missing information.
Proportions are solved using cross multiplication

4. Scale
Scale is a comparison between the actual size of an object and the size of the diagram
The first number in the scale represents the drawing, while the second number represents the actual measurement of the object
So, a scale of 1 : 45 means that 1 unit on the drawing represents 45 units on the actual object. The size of the unit depends on the information provided. It could be cm, m, km, thousands of miles…..
Scale can also be stated
as a percent - for example: the diagram represents a 66% reduction
or in words: the diagram is two thirds the size of the actual object

5. From scale diagrams to actual measurements
When provided with a scale diagram, it will state the scale.
This diagram of a skateboard uses a scale of 1 : 14
5.5 cm
To determine actual size, either use the scale ratio provided and multiply (5.5cm x 14 = 77cm)
or use a proportion and cross multiply
1 = 5.5
14 x x = 77

6. Determining scale factor
Scale = diagram measurement
actual measurement
If you are given a diagram, and know the actual measurement of an object, you can determine the scale factor!
Example: an actual Canadian quarter has a diameter of mm. Measure the diagram of the quarter that you have been given.
Set up the proportion for scale: 14
≈ o.586… ≈ 0.6 scale factor

7. Practice makes perfect
Homework:
Page #1 – 10, 13, 18, 19