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Coffee by the Pound


Alignments to Content Standards: 8.EE.B.5

Task

Lena paid \$18.96 for 3 pounds of coffee.

  1. What is the cost per pound for this coffee?
  2. How many pounds of coffee could she buy for \$1.00?
  3. Draw a graph in the coordinate plane of the relationship between the number of pounds of coffee and the total cost.
  4. In this situation, what is the meaning of the slope of the line you drew in part (c)?

IM Commentary

A slight modification to this problem would make this appropriate for the 7th grade level (see 7.RP.2.d Coffee by the Pound). At the 8th grade level, the solver would be expected to identify the slope of the line with the unit rate.

Solution

  1. If you divide the cost for three pounds by three, you will get the cost per pound. Coffee costs \$6.32 per pound.
  2. If you divide the number of pounds by the cost for three pounds, you will get the amount of coffee one can purchase for \$1.00. You can buy approximately 0.16 pounds of coffee for a dollar.
  3. There are two possible graphs depending on what you choose x to represent and what you choose y to represent.

    If we let x indicate the number of pounds of coffee and let y indicate the total price, then the solver may produce a graph by drawing a line through the origin and the point (3, 18.96); see below. 1_ce802f4dd42fcec09ae94368a038c58d If we let x indicate the total price and let y indicate the number of pounds of coffee, then the solver may produce a graph by drawing a line through the origin and the point (18.96, 3).
  4. With the choice for x and y we made, the slope is the cost per pound of coffee, which is \$6.32. If we had chosen the other order, the slope would have been the amount of coffee one could buy for a dollar, which is 0.16 pounds.

Martin says:

over 1 year

kgolan: I totally agree. I don't want students to get hung up on how to make accurate intervals on the graph and love your suggested modification. I want them to discover that the slope is the unit rate. I think I am going to use your variation of this problem.

Middle School Math Teacher says:

almost 2 years

Because this task meets the standard of graphing proportional relationships, I am going to have my students use a ratio table to show the proportional relationship. My students are used to graphing points from a table and it brings back or connects the concept of ratio tables from 7th grade.

kgolan says:

over 3 years

When we used this task, we were concerned that students might struggle to create an appropriate scale for the graph. We changed the numbers to be $19.50 per 3lbs, so that the students could use a scale that involved 6.5 (which is more intuitive than 6.32).

We also cut out the question about how much coffee they could purchase for $1, I think in part because at the 8th grade level, we were concerned about students getting confused about which unit rate represents the slope of their graph.

We used our modified problem on an assessment.

Kristin says:

over 3 years

Thanks for letting us know how you modified the problem to suit your needs.