Proportional Relationships and Rates

The video tutorial covers a math lesson on proportional relationships, focusing on equations, ratios, and constant of proportionality. It includes activities like adjusting lemonade recipes and analyzing state park entry costs to explore these concepts. The lesson also examines running laps to identify constant pace and concludes with a summary and cool down activity.

What is the constant of proportionality in the equation y = 1/5x?

• x

• 5

• 1/5

• 1

If a lemonade recipe is doubled, what happens to the taste?

• It becomes more sour

• It becomes less sweet

• It remains the same

• It becomes sweeter

How much does it cost for a vehicle with four people to enter the state park?

• $16

• $14

• $12

• $10

What is the cost per person if 10 people share the total entrance cost of $26?

• $2.60

• $2.00

• $3.00

• $2.50

Is the relationship between the number of people and the total entrance cost proportional?

• Yes, because the total cost increases linearly

• No, because the vehicle cost is fixed

• No, because the cost per person varies

• Yes, because the cost per person is constant

What is Claire's pace per lap if she runs 8 laps in 20 minutes?

• 2.5 minutes per lap

• 2.0 minutes per lap

• 3.0 minutes per lap

• 2.25 minutes per lap

Which equation represents Claire's constant pace?

• t = 2.5d

• d = 2.5t

• t = d/2.5

• d = t/2.5

Which smoothie shop has a proportional relationship between size and price?

• Shop A

• Shop B

• Both shops

• Neither shop

What is the unit rate for Shop A's smoothies?

• $0.70 per ounce

• $0.67 per ounce

• $0.75 per ounce

• $0.80 per ounce

Why is Shop B's relationship not proportional?

• Sizes are inconsistent

• Different cost per ounce for each size

• Same cost per ounce for each size

• Prices are too high