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A teacher of economics has been working with me to find ways to incorporate online technologies into her teaching. As part of our consultative process, she explains to me the content and method she currently uses to teach certain concepts in the classroom, and I suggest ways that online technologies might be used to enhance or extend those methods. Last week we ended up baking bread.

At the Bakery

The teacher uses the example of a bakery to teach the concept of economies of scale: the fact that the more loaves you produce per day using the same oven and baker, the less is your cost per loaf. To teach this concept in the classroom she puts numbers on the board indicating the per-day fixed cost of the oven, and the fixed daily pay of the baker (which are the same no matter how many loaves are baked), as well as the variable costs of the flour and other supplies that go up and down depending on how many loaves are baked. Then she does the math with the students on the board at different loaf-numbers, and plots the results on a graph. Classic economics teaching.

"I would love for my students to be able to simulate this bakery operation on the computer," said the teacher, but I am sure that it would take many months and a trained professional to develop this into an interactive simulation." She had seen some economics simulations like this, developed in Flash or Java, that allowed students to play the role of a business owner, decide how much to produce, and see the results returned in terms of sales and profit margins and unit costs. "But I'm new to computers, and there's no way I could develop something like that."

With a Spreadsheet

This teacher was not a computerist, but due to the nature of her subject, she was a regular user of the Excel spreadsheet. Teachers of economics find the spreadsheet an important tool in their teaching and research. You probably have a spreadsheet like Excel on your computer as part of the Microsoft Office suite, or as part of AppleWorks. This article explains how we used a spreadsheet to build a simulation of the bakery.

In the simulation, the student decides how many loaves of bread to bake each day, and enters it into a cell in the spreadsheet. (If spreadsheets are brand new to you, look at How to Make Graphs with Excel in this series, at http://www.powertolearn.com/articles/
teaching_with_technology/how_to_make_graphs_with_excel.shtml.) The spreadsheet then calculates the cost per loaf, based on the fixed costs of the oven and baker, and the variable cost of the flour. It also plots these values on a graph. The student tries again and again, entering different numbers down the column of the spreadsheet, until he sees clearly how the trend toward economies of scale works. A simulation-in-progress might look like this:

(Click the image to see a full-size version.)

As you can see, the cost per loaf decreases as you bake more bread. (You can download the spreadsheet and try this yourself, if you have Excel.)

Creating the Spreadsheet

This simulation took about an hour to create. After entering the title and the explanatory text, we labeled the six columns as shown in the illustration. We left the first column, Loaves, blank -- that's where the student will enter her data. Just under the label in the Oven column, in cell C7, we entered a formula: =IF(B7<101,30,60). This formula tells the spreadsheet what number to display in this cell, based on what the student entered in cell B7. It says, "If the number in B7 is less than 101, then put 30 here, or else put 60 here." 30 is the cost of the oven for one day, a fixed cost. But since the oven can bake only 100 loaves per day, you must purchase an additional oven (30 more) to bake more than 100 loaves.

For the baker, the formula is similar. Into cell D7 we enter the formula =IF(B7<101,60,90). This should make sense to you if you understood the first formula.

Into cell E7 we enter the flour formula, the variable cost: =B7*0.2. This means, "Take the number in B7 (the number of loaves that the student entered) and multiply it by 0.2, or twenty cents, and put the result here. For ten loaves, the result, as you see in the illustration, is 2.

Now we can add up the costs of the oven, the baker, and the flour with a formula in the next column. At F7 we enter the formula =C7+D7+E7. Simple addition, with the result for 10 loaves it cost a total of 92. Expensive bread! To figure the cost per loaf, we divide the total cost by the number of loaves, by entering a formula of =F7/B7 into cell G7. This means F7 (total cost) divided by B7 (number of loaves.)

Next we copy the formulas form row 7 down to row 27, and the calculative aspects of the simulation are complete. Next we create the chart.

Creating the Chart

First we select the data that we want to appear on the chart, which is from two columns: the number of loaves (column B) and the cost per loaf (column G). So we select those two columns, from rows 7 to 27. (To select non-adjacent columns, hold down the command key as you select the second column.)

With the columns selected, we choose Insert -- Chart from the menubar. We select the X-Y scatter type of chart, click the Finish button, and we have it.

The chart starts out blank, and as the student enters data, the cost per loaf is plotted against the number of loaves. the axes scale themselves automatically. Try it.

Other simulations

You can use a spreadsheet to construct many other types of educational simulations. Find the maximum area of a rectangle with a fixed perimeter, for instance. A simulation may also be created in programs such as Flash, but that is a subject for another article. In the meantime, try this Flash simulation of the same bakery.