Proportional Relationships and Rates

This lesson introduces proportional relationships through various activities, including adjusting recipes, calculating park entrance costs, comparing running times, and analyzing costs of apples and pizza. The lesson emphasizes constructing tables to understand proportional and non-proportional relationships, using constant rates, and applying these concepts to real-world scenarios.

What is the constant of proportionality when scaling the lemonade recipe to have a stronger lemon taste?

• 4/5

• 3/5

• 2/5

• 1/5

How is the entrance fee per person calculated when entering the state park?

• By dividing the total cost by the number of people

• By adding a fixed vehicle fee to the per person fee

• By multiplying the number of people by the vehicle fee

• By using a constant of proportionality

In the running laps activity, what indicates that Claire is running at a constant rate?

• Her time per lap decreases

• Her time per lap remains constant

• Her time per lap increases

• Her distance per lap varies

What is the constant of proportionality for the cost of apples per pound?

• 2.50

• 2.00

• 1.88

• 1.50

Why is the cost of pizza with toppings not a proportional relationship?

• The base price of the pizza changes

• The total cost is divided by the number of toppings

• The cost per topping is constant

• The cost per topping decreases as more toppings are added

What is the key factor in determining if a relationship is proportional?

• The presence of a constant of proportionality

• The complexity of the equation

• The size of the values involved

• The number of variables

In the context of taxi fares, what makes the relationship not proportional?

• The fare is calculated per mile

• The fare decreases over time

• The fare increases with distance

• The initial fixed cost

How does the rabbit's speed change throughout the race?

• It remains constant

• It increases steadily

• It decreases over time

• It fluctuates randomly

What happens to the diagonal of a rectangle if both its length and width are doubled?

• The diagonal is halved

• The diagonal remains the same

• The diagonal is doubled

• The diagonal is tripled

What is the reciprocal of 54 meters per minute in terms of time per distance?

• 54 meters per second

• 1 minute per 54 meters

• 54 minutes per meter

• 1/54 minutes per meter