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# Buying Coffee

Alignments to Content Standards:
7.RP.A.2

## Task

Coffee costs \$18.96 for 3 pounds.

- What is the cost for one pound of coffee?
- At this store, the price for a pound of coffee is the same no matter how many pounds you buy. Let $x$ be the number of pounds of coffee and $y$ be the total cost of $x$ pounds. Draw a graph of the relationship between the number of pounds of coffee and the total cost.
- Where can you see the cost per pound of coffee in the graph? What is it?

## IM Commentary

The purpose of this task is for students to find a unit rate in a context where two quantities are in a proportional relationship and to draw the graph of that proportional relationship.

This is a task where it would be appropriate for students to use technology such as a graphing calculator or GeoGebra, making it a good candidate for students to engage in MP5, Use appropriate tools strategically. A variant of this problem is appropriate for 8th grade; see 8.EE.5 Coffee by the Pound.

## Solution

- You can find the cost for one pound of coffee by dividing the total cost by 3. Coffee costs \$6.32 per pound.
- We may graph the proportional relationship between the total cost and the number of pounds by plotting the line through the origin and (3, 18.96).
- The cost of one pound, \$6.32, may be seen on the graph in two ways:
- As the point (1, 6.32)
- As the slope of the line: \$6.32 per pound.

Note: Students aren't explicitly required to see the connection between the unit rate and the slope until 8th grade (see 8.EE.5) but they may still see it in 7th grade.

## Buying Coffee

Coffee costs \$18.96 for 3 pounds.

- What is the cost for one pound of coffee?
- At this store, the price for a pound of coffee is the same no matter how many pounds you buy. Let $x$ be the number of pounds of coffee and $y$ be the total cost of $x$ pounds. Draw a graph of the relationship between the number of pounds of coffee and the total cost.
- Where can you see the cost per pound of coffee in the graph? What is it?

## Comments

Log in to comment## Heather_Brown says:

over 4 yearsThis stem seems to be missing a word. Right now there is nothing stating that this relationship is proportional. It is very possible (and in most stores, likely) that a related bag of 2 pounds of coffee is \$15. The ratios and proportions progressions document states: "without further information "2 pounds for a dollar" is ambiguous." Unless we say every 3 pounds of coffee costs \$18.96. (Even then, you could potentially argue that it must be purchased in 3 pound units, but I think this would be close enough that I would argue less :)

## Kristin says:

over 4 yearsThanks Heather. We had debated whether explicitly naming it as a proportional relationship would be sufficient to make it unambiguous and decided that it was. However, since you didn't think so, I reworded it. How is it now?

## Heather_Brown says:

over 4 yearsThis is fine. But did the original say that it was a "proportional relationship"? If it did, then I must have missed it and it wouldn't have needed anything additional... hmmm... maybe I didn't read it very well.

## Kristin says:

over 4 yearsIt was awkward--this is better I think. Thanks!

## Heather_Brown says:

over 4 yearsremoved