Exploring Proportional and Nonproportional Relationships

The video tutorial covers proportional and non-proportional relationships, focusing on unit rates. It explains how to determine if relationships are proportional by comparing unit rates. The tutorial includes a practical example of a boat rental scenario and compares work scenarios to illustrate proportionality. The conclusion emphasizes that proportional relationships have equal unit rates or equivalent ratios.

What is a unit rate?

• A comparison of two different quantities where the denominator is one.

• A comparison of three different quantities.

• A ratio where the numerator is always greater than the denominator.

• A rate that changes over time.

Which of the following is an example of a unit rate?

• 10 miles per hour

• 5 apples per basket

• 8 students per class

• 3 books per shelf

How do you determine if a relationship is proportional?

• By checking if the quantities are whole numbers.

• By finding the average of the quantities.

• By comparing the total quantities.

• By checking if all unit rates are equal.

In the boat rental example, what is the total cost for renting the boat for 1 hour?

• $62

• $37

• $12

• $25

What is the total cost for renting the boat for 2 hours?

• $50

• $87

• $62

• $74

Why is the boat rental example considered non-proportional?

• Because the unit rates are not equal.

• Because the total cost is too high.

• Because the fuel charge is constant.

• Because the rental fee changes every hour.

What is the unit rate for renting the boat for 3 hours?

• $37 per hour

• $31 per hour

• $29 per hour

• $25 per hour

In the comparison of Matt and Jane's earnings, which one represents a proportional relationship?

• Jane's earnings

• Both Matt and Jane's earnings

• Matt's earnings

• Neither Matt nor Jane's earnings

What makes Jane's earnings proportional?

• The total amount earned is higher.

• The unit rates are equal.

• The hours worked are fewer.

• The earnings increase over time.

What must be true for two quantities to be proportional?

• The unit rates must be the same.

• The total quantities must be equal.

• The quantities must be different.

• The quantities must be whole numbers.