Exploring the Constant of Proportionality in Mathematics

This video lesson introduces the concept of the constant of proportionality, explaining it through examples such as the cost per apple and walking distance. The lesson includes a mini-lesson, practice problems, and word problems to help students understand and apply the concept. The video emphasizes setting up fractions to find unit rates and constants of proportionality, and it concludes with practice problems involving book costs and broken crayons.

How is the cost per apple calculated for Garin?

• Subtracting the number of apples from the total cost

• Dividing the total cost by the number of apples

• Multiplying the number of apples by the total cost

• Adding the total cost to the number of apples

Did Garin and Farren pay the same price per apple?

• No, because the apples were of different quality

• Yes, but only after negotiating

• No, they paid different amounts per apple

• Yes, both paid 25 cents per apple

What does setting up a fraction help in finding the constant of proportionality?

• It simplifies the calculation process

• It automatically provides the unit rate

• It helps in correctly ordering the numerator and denominator

• It eliminates the need for division

Why is the concept of constant of proportionality important?

• It is only used for complex mathematical problems

• It helps in understanding relationships between quantities

• It is not important, just a mathematical curiosity

• It simplifies addition and subtraction

What is the unit rate of walking 2 miles in 30 minutes?

• 30 miles per hour

• 1 mile per 15 minutes

• 2 miles per hour

• 0.0667 miles per minute

How far can one expect to walk in 90 minutes at the given rate?

• 9 miles

• 4.5 miles

• 6 miles

• 3 miles

How is the concept of constant of proportionality applied to walking speed?

• By calculating the distance walked per unit of time

• By estimating the time it takes to walk a certain distance without calculation

• By dividing the time by the distance

• By multiplying the distance by the time taken

What is the cost per book when buying a trilogy for $11.97?

• $4.99

• $5.99

• $3.99

• $2.99

How much would it cost to buy a five-book series at the same rate per book?

• $15.95

• $23.95

• $19.95

• $29.95

Is the amount of crayons broken by students this year proportional to last year?

• No, last year had a higher rate

• Yes, but only after adjusting for student count

• Yes, both years had a rate of 5 crayons per student

• No, this year had a higher rate