Consumer Math

This lesson used in a suburban high school General Math class of 28 students, five of whom were limited English speakers.

Students are directed to bring to class a Thursday newspaper (Thursday is the day, locally, when most supermarket ads appear) and any supermarket ``junk mail'' they have recently received. When class begins, the market ads are collected into two piles: color ads and black-white only ads. The class is polled as to where their families do most of their food shopping. Each student records the results of this poll as the first page of her/his research. For twenty minutes students go through the market advertisements. Students are encouraged to work in groups to collect information from the ads:

1. Find 8 comparable items advertised at each of 10 different markets (five full-color ads and five black-white ads). [for example, you can compare the price of golden delicious apples to red delicious apples at a different store, both fall into the category of ``apples''].
2. On a fresh piece of paper mark off eleven columns - make sure the first one is wide enough for the product name. List the 8 (or more!) items you are comparing and their prices. Indicate whether or not a coupon is required. Your list might look something like this:

   Product and units	color ad prices					black&white ad prices
   of measurement	Ralph's	Vons	...	...	...	Safeway	Smiths	...	...	...
   apples (1 pound)	1.05	1.15	...	...	...	1.25	C .99	...	...	...

After a short discussion of possible ways to compare the numbers they have found I introduce the notion of a statistic: a number derived from other numbers. I show/remind the students how to find an average price for each of their products. I then explain the notion of distance from this average as exemplified by variance. The remainder of the period is spent by the students calculating the averages for their grocery prices.

The next class I reintroduce the notion of variance and ask the class what is ``wrong'' with it, what other method of comparing a price to the average could be used? The students invariably suggest that the variance is too big and soon discover that the squaring of the differences is the reason. They suggest finding the plain old difference. I ask, ``What if the difference is negative?'' By this means a short discussion develops about how to compare things. The rest of the period is spent on the students calculating the standard deviation for each product sample and in writing a short (three paragraph minimum) report on their findings.

They have the following questions to address:

1. What is the collective average and standard deviation in price for the following products in each of the two market categories?
   1. one pound loaf of whole wheat bread
   2. one pound loaf of white bread
   3. $\frac{1}{2}$ pound of tomatoes
   4. 4 apples
   5. 6 oranges
   6. one gallon 2%-fat milk
   7. one dozen eggs
   8. one pound spaghetti
   9. a 2.3 pound package of chicken

2. Compare the prices and coupons at the ``full-color'' and ``plain'' ad markets. Please use complete sentences and give examples that include the contrast between the regular prices at each of the two types of stores as well as the coupon savings prices.
3. Where is it better to shop if you are a single person? ...a couple/roommates? ...a family of four or more? By what standard(s) do you judge one market to be ``better'' than another? Please be specific and write in complete sentences.

Students keep their graded reports and add to them as the semester and their critical observations of supermarket ads on television, radio and in newspaper circulars progress. At the end of the semester, each student has compiled several pages of observations and conclusions. Each student distills his/her collected thoughts into a two page ``term paper'' which is counted as 4% of their semester grade.