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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.
Here are some resources that will help you and your students go about answering the question.
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.
To download one of the files below, right click on its link then choose Save
Target As and specify the location to which you want it saved. You may also
click on the file's link. If you have Quick View+ installed on your
computer, you will see an error message; choose the Save option it gives
you, then save the file to a folder on your hard drive from that window. If
you do not have this viewing program installed, a small window should open. One of the options presented should be to save the file.
Click on that option. You should then be prompted to specify where on your hard
drive you want to save the file. Put it in the folder where you save and open Excel
spreadsheets. Once the file has completed downloading, the small window will close
on its own.
Excel 97 version (coins97.xls)
Excel 5/95 version (coins95.xls)Click here to view a GIF image of the spreadsheet running under Excel 97
To return to this page after you finish viewing the GIF image, close the window that will open without closing your browser software.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 penny2. 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 penny3. 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
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original web posting: Tuesday, March 14, 2000
last modified:
Thursday, April 10, 2008