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Which is more valuable, a pile of pennies equaling your weight or a stack of quarters equaling your height?

Students who are familiar with pocket change will start thinking about such a question because it seems so simple.  However, using coins to measure human weight and height is a bit strange.  Their first inclination will be to guess, but if you require them to support their answers (by asking an additional question like "By how much?"), they'll soon realize that they need more information. You'll undoubtedly hear questions like, "How much does a penny weigh?" and "How thick is a quarter?".  You can answer them, or show them how/where to get the answers.  In any event I'll bet that you end up with a lively discussion and many involved students.

• For coin weights and dimensions

look at the U.S. Mint's specifications on circulating coins
review the 2004 Guidebook of U.S. Coins by R.S. Yeoman

• I've developed an Excel spreadsheet for calculating answers to this question.  You can download it in either Excel 97 or Excel 5/95 format.  If you are unable to open spreadsheets in either of these formats, e-mail me.  In your message tell me what spreadsheet you have, and what formats you can open.  If I can convert my sheet to one that you can use, I will do so and e-mail the file back to you.

Excel 97 version (coins97.xls)
Excel 5/95 version (coins95.xls)

If you are using Microsoft Internet Explorer 4.01 or later to view this page (and have Office XP or later installed on your system), you can use the Excel worksheet in a separate browser window.  However, if you want to save or print the results of your work, you will find it easier to work with one of the XLS files above.

• Instructions for calculating a solution to the coin problem

If this process is too much for your students, urge them to think about and discuss how one would go about solving a problem like this, and what information they'd need to do so.

U.S. coins

 Weight Thickness Diameter grams mm mm ======= ========= ======== Penny (1959-82) 3.11 1.55 19.05 Penny (since 1983) 2.5 1.55 19.05 Nickel 5 1.95 21.21 Dime (through 1964) 2.5 1.35 17.91 Dime (since 1965) 2.268 1.35 17.91 Quarter (through 1964) 6.25 1.75 24.26 Quarter (since 1965) 5.67 1.75 24.26

1 inch=25.4 mm             1 pound=453.59237 grams

To determine an answer for a specific student

1. for the person's weight

a. Multiply 453.59237 (the # of grams in 1 pound) by the person's weight
b. Divide the answer from a. by the weight of the coin in grams
c. Divide the answer from b. by the number of coins in one dollar
d. Round the answer from c. to the nearest penny

2. for the person's height with the coins stacked

a. Multiply the number of feet tall by 12 then add the number of inches
b. Multiply the answer from a. by 25.4 (the number of millimeters in one inch)
c. Divide the answer from b. by the thickness of the coin in millimeters
d. Divide the answer from c. by the number of coins in one dollar
e. Round the answer from d. to the nearest penny

3. for the person's height with the coins laid edge to edge

a. Multiply the number of feet tall by 12 then add the number of inches
b. Multiply the answer from a. by 25.4 (the number of millimeters in one inch)
c. Divide the answer from b. by the diameter of the coin in millimeters
d. Divide the answer from c. by the number of coins in one dollar
e. Round the answer from d. to the nearest penny