Illustrative Math Constant of Proportionality

The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

What is the correct title for the graph?

• Cost (in dollars)

• Calories

The graphs below show some data from a coffee shop menu. One of the graphs shows cost (in dollars) vs. drink volume (in ounces), and one of the graphs shows calories vs. drink volume (in ounces).

What is the correct title for the graph?

• Cost (in dollars)

• Calories

Which quantities appear to be in a proportional relationship? Explain how you know.

• The first graph because the points lie on a straight line and would go through the origin

• The second graph because the points lie on a straight line and would go through the origin.

• Both because the points lie on a straight line and would go through the origin

• Neither because the points do not lie on a straight line and/or would not go through the origin

For the proportional relationship, find the constant of proportionality. What does that number mean?

• 15, 15 calories in 1 ounce

• 15, 1 calorie for 15 ounces

• 1/15, 1/15 calories in 1 ounce

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is t= 1/500d . How long will it take the airplane to travel 800 miles?

• 1.6 hours

• 40000 hours

• 0.625 hours

• 1.3 hours

The graph shows the amounts of almonds, in grams, for different amounts of oats, in cups, in a granola mix. Find the value of k, and explain its meaning.

• For every 25 cups of oats, there is 1 almond.

• For every 0.4 almonds, there is 1 cup of oats.

• For every 25 almonds, there is one cup of oats.

• For every 0.4 cups of oats, there is one almond.

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information. *Hint: Make a table.

How many packets would be needed to transmit 30,000 bytes of information?

• 1500

• 20

• 45,000,000

• 0.05

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information. *Hint: Make a table.

How much information could be transmitted in 30,000 packets?

• 1500

• 20

• 45,000,000

• 0.05

To transmit information on the internet, large files are broken into packets of smaller sizes. Each packet has 1,500 bytes of information. An equation relating packets to bytes of information is given by b = 1,500p where p represents the number of packets and b represents the number of bytes of information. *Hint: Make a table.

Each packet contains 8 bytes of information. Write an equation to represent the relationship between the number of packets and the number of bytes.

• x = 12,000p

• p = 12,000x

• b = 1,500p

• p = 1,500b

Select all of the pieces of information that would tell you and have a proportional relationship. Let y represent the distance between a rock and a turtle's current position in meters and x represent the number of minutes the turtle has been moving.

• Y = 3x

• After 4 minutes, the turtle has walked 12 feet away from the rock

• The turtle walks for a bit, then stops for a minute before walking again.

• The turtle walks away from the rock at a constant rate.