SWBAT use all four operations to conduct a cost-benefit analysis of items sold at a fundraiser.

Engaging students in analyzing the cost-benefit of selling different food items at a fundraiser provides real-world, two-step word problems!

11 minutes

I ask students to list the five items they think would be most popular at a fundraiser. In this particular instance I do not worry about junk food. The problem of poor diet is far larger than one isolated event, and I spend the rest of the year talking about nutrition.

They write down their five items on a whiteboard or piece of paper and then we list them on the board. As a class, we eliminate ridiculous or difficult choices. The remaining choices are narrowed down to approximately ten items.

I pick one of the items (for example, a bag of chips) and ask the students what they think it should be sold for at the fundraiser. I pick the consensus answer, say 50 cents, and then have a version of the following conversation:

Teacher: *"How much money will we make if we sell this bag of chips for 50 cents?" *

Students: “50 cents!”

Teacher: *“What did I pay for this bag of chips at the store?”* (I hold up the Costco box that contains the 50 chip bags.)

Students: (pause)

Teacher: *“What do I need to know to find out how much I paid for a bag of chips? What would be a reasonable first step? Think.”* I pause of 30 seconds. I watch the clock and signal them that nobody is to talk or answer yet. Then I call on students randomly. I do not have them raise their hands. If, after 3 students, nobody has arrived at the answer yet, I take volunteers. This leads to the next part of the lesson, where we run through a model of how we might calculate the cost of individual items.

**Note: ** Students at my school have a club (PEPA USA) to help refugees and orphans in the eastern Democratic Republic of Congo and Uganda, so we were actually having a fundraiser and that is how I was able to use the real items in class, which they found very exciting.

25 minutes

Students eventually state that to find the cost of a bag of chips we need to know the cost of the entire box and then divide it by the number of bags. I show them the receipt and provide them with the cost of the entire box.

I draw an array model to represent the chips in the box and then fill it in to show a student suggestion that each bag of chips costs 50 cents. This is a reasonable guess and a good starting point as it is an easy number with which to work. This child is fluent with basic facts and has an intuitive understanding of multiplying by tens and using place value understanding.

As he explains his strategy it is clear that he is well on his way to being able to explain **why **one can add a zero when multiplying by a ten. The model provides visual support for the realization that each bag must cost less than fifty cents. I ask them, "Did I pay more or less than fifty cents per bag?

25 minutes

We segue into a discussion of profit as distinct from the total amount (gross) we collect. Once students realize that "our" cost per bag of chips is less than fifty cents, and we have worked through that division calculation, I ask them to state out loud that there is a difference between cost and sale price. Once they understand that what I paid (in this case $11.87) is different than what we will sell the items for (at 50 cents each, a total intake of $25.00) is the basis of understanding that we'll make a profit. I restate that a profit is the amount of money that is earned after the cost has been subtracted (taken into account).

I then give them a hypothetical. I say:

Teacher: *Pretend a bag of chips costs 10 cents. If you sold it for 50 cents, how much profit would you make? The profit is what you earn on top of what you paid. So, the person buying the chips from you may put 50 cents into your hand, but what did you earn for the Magendo family (the refugees in Kampala, Uganda that we are trying to help). Think.*

Students realize that to obtain the actual profit, they need to subtract the cost from the sale price. I let them know that will be our next step, but that we can't do that until we have the cost!

I put them into groups and pass out the items so they can work with this idea hands on. They get very excited because it's real. The cost of the bulk amount of items is on the board, their task is to work, with their groups, to determine individual item cost, as that is how the food will be sold at the fundraiser.

4 minutes

I ask students to write down some notes about what they did today in math. For homework I'd like them to explain at least one part of what we did today to an adult in their home. My proof that they did this is simply an adult's signature. They don't need to write it out, though I certainly encourage them to do so.

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