1. Math 10 Chapter 1 – Linear Measurement and Proportional Reasoning
Lesson 1 – Ratio and Proportional Reasoning

2. Todays Objectives Provide referents for linear measurements
Solve problems that involve linear measurement using:
SI and imperial units of measure
Estimation strategies
Measurement strategies
Provide referents for linear measurements
Justify the choice of units used for determining a measurement in a problem
Apply proportional reasoning to problems that involve conversions between SI and imperial units of measure

3. Lesson 1.6 – Ratio and Proportional Reasoning
We will soon use proportional reasoning to convert linear units in one measurement system to units in the other.
Before doing this, it is important to review the concept of ratio and how it relates to proportion.

4. Ratio
A ratio compares one number to another, showing a relationship between the two.
It is usually shown as a fraction where the first number is the numerator and the second number is the denominator.
Eg: ratio of 7 to 11 
Ratio of 8 to 3 
Ratio of 5 to 7 

5. Sometimes ratios are shown with a colon between the numbers where the first is the numerator and the second the denominator
7:9  :3 

6. Proportion
When one ratio is equal to another, it is called a proportion
Notice that in a proportion, the “diagonal products” are equal. 
1 x 16 = 2 x 8  16 = 16
Finding the products of numerators and denominators of alternate ratios and then setting them equal to each other is sometimes called “cross multiplication”

7. Proportional Reasoning
Proportional reasoning involves the ability to understand and compare ratios, and to predict and produce equivalent ratios.
It requires comparisons between quantities and also between the relationships between quantities.

8. Examples - Ratios
There are 11 boys and 9 girls in a soccer club. Find the following ratios:
Ratio of boys to girls
Ratio of girls to boys
Ratio of boys to all
members of the club
The number of boys is 11, it is the numerator
The number of girls is 9, it is the denominator
The ratio is
The number of girls is 9, it is the numerator
The number of boys is 11, it is the denominator
The ratio is
The number of boys is 11, it is the numerator The number of all members of the club is 20, it is the denominator
The ratio is

9. Examples – Proportion 1. Find the value of n if
Solution: the diagonal products are equal so we will use cross multiplication
5 x 9 = 3 x n
45 = 3n
15 = n

10. 2. If 4 L of juice are needed for 6 people, how many litres are needed for 9 people?
Solution: We set up a proportion and solve.
The ratio of 4 litres to 6 people is equal to the ratio of n litres to 9 people
litres litres
people people
4 x 9 = 6 x n
36 = 6n
n = 6
There are 6 litres of juice needed for 9 people

11. Choosing appropriate units of measure
There are 2 systems of measurement and many units to choose from when we are measuring distances:
Metric System: millimeter (mm), centimeter (cm), meter (m), kilometer (km)
Imperial System: inches (in. or “), feet (ft. or ‘), yards (yd.), miles (mi.)

12. Units of measure: Distance
Metric Units
1 km = 1000 m
1 m = 100 cm
1 cm = 10 mm
Imperial Units
1 mi = 1760 yd
1 yd = 3 ft
1 ft = 12 in

13. When should we use each unit?
We should use different units when measuring things of different sizes
Example: GOOD! 
The length of my walk to school is about 2 km, or 2000 m
Example: BAD!  !
The length of my walk to school is about 200,000 cm, or 2,000,000 mm

14. When should we use each unit?
Example: GOOD! 
My pen is about 5.5 inches in length
Example: BAD!  !
My pen is about 8.68 x 10^ -5 miles in length

15. Referents
We can use everyday objects to act as referents for various units of measure
A referent is something we can use to estimate a given unit of measure
Example: We can use the width of our pinkie finger as a referent for 1 cm

16. Homework
In your Vocabulary books, make entries for the words listed at the start of your handout
Provide a referent for each unit of measure listed at the end of your handout
Pg. 11, #2-6, pg. 12, Reflect Question