Proportionality

Proportionality

Unit 5 Important Vocabulary

Unit Rate

• Definition: A type of ratio that compares a single unit of one thing to another amount that uses different units.

• Facts/Characteristics: When working with Unit Rates you will have two different types of units.

• The one in the unit rate is not usually shown. (like 20 miles/hour)

Open Ended

Driving at a constant speed for 5 hours, a traveler has covered 300 miles. What is the unit rate in miles/hour?

Proportional

• Definition: When quantities have the same relative size (ratio)

• Facts/Characteristics: A proportional graph starts at zero and changes at a constant rate

Multiple Choice

If the traveler drove 300 miles in 5 hours.. How far would that traveler drive in 15 hours?

• 1,500 miles

• 900 miles

• 9,000 miles

Non-Proportional

• Definition: When two or more quantities do not have the same relative size (ratios)

• Facts/Characteristics: A non-proportional graph either doesn't start at zero, or, is not constant.

Multiple Select

Choose all of the fractions (ratios) that are equal to each other.

•  $\frac{4}{5}$  

•  $\frac{20}{24}$  

•  $\frac{40}{50}$  

•  $\frac{60}{70}$  

•  $\frac{80}{100}$  

Constant of Proportionality

• Definition: The rate that a relationship of two numbers increases or decreases

• Facts/Characteristics: often represented by the letter k.

•  $\frac{y}{x}=k$    and/or    $y=kx$  

Multiple Choice

What is the Constant of Proportionality for this table? Remember,

 $k\ =\frac{y}{x}$  

• k = 10

• k = 5

• k = 3

• k = 1

Let's Quizizz!

Multiple Choice

Greg is making 4 apple pies. He has to buy 24 apples.

What is the Unit Rate? (How many apples for every 1 pie?)

• 4 pies/1 apple

• 9 apples/1 pie

• 7 pies/1 apple

• 7 apples/ 1 pie

Multiple Select

Choose which of the following graphs you think represent a proportional relationship.

Multiple Choice

What is the constant of proportionality for this table?

• $\frac{1}{12}$

• $\frac{1}{2}$

• $0$

• $12$

• $24$

Multiple Choice

James just filled up his truck with gas. He paid $28.75 and got 11.5 gallons of gas. What is the Unit Rate? (What is the cost of 1 gallon of gas?)

• $2.00 per Gallon

• $2.50 per gallon

• $3.00 per gallon

• $3.50 per gallon

• $4.00 per gallon