Italicized links open a new window to an external site

What is the average age of those currently in the room?

This question is effective with students at many ability levels.  In addition to arithmetic practice, it is a good way to introduce small group organization, and discussion and information gathering skills.  Before using it, be sure to get a birth date for each student, then calculate the average(s) before you get to class so you can verify the answer your students present.

If your students know little or nothing about averages, use this question as an introduction to calculating a simple mean.  Explain what a mean is, then ask them how they might calculate one for their ages.  This discussion should result in a plan to list their ages in years, total the list, then to divide the result by the number of people who contributed ages.  If averaging the entire class seems too much of a challenge, divide the class into small groups and have each group calculate its mean.  When each has finished and reported its result to the whole class, you might consider having them attempt a class mean.

If the above works well enough that you'd like to try it again, do so by asking the group to determine their average pulse rate.  Be warned though, you'll most likely have to show many students how to take a pulse.

If your students are familiar with mean averages, and competent at arithmetic, ask them to figure out the group's average age in days or months.  To start, you should ask them to calculate their individual ages to the day (i.e. 15 years, 8 months, 16 days).  If you like, make this an assignment to be completed prior to the class period where you'll use this activity.  An assignment like this should stimulate a good discussion about calendars and leap years.

To get an average once each person knows his/her age to the day, each will have to convert that age to the total number of days s/he has lived.  To do so, each student will need to know the number of days in each month (to arrive at the number of days in their first year of life, and in the current year), and the number of days in leap and non-leap years (to get the number in the whole years they've lived).  Once each person knows his/her age in days, the class can prepare a list and calculate a mean.  This mean can then be converted to the class mean in years, months and days.  To do so, divide the total day mean by 365.25.  Drop any decimal portion to get the mean in years.  Multiply the decimal portion you dropped by 12 to get the months portion of the average age (again dropping any decimal portion).  Finally, multiply the decimal portion of the months by 30.4375 (which is 365.25 divided by 12 - the average number of days in a month) to get the mean age to the day.  This may result in a day number different from that calculated by the workbook below which calculates it using an Excel function.  A note to purists.  I am aware that the length of the mean solar year is a matter of debate among astronomers. I gather that the general consensus now places it at 365.24218967 days.  I have chosen to use 365.25 as it is an easier number with which to work.  However, if you choose, use the more precise number.  To read a description of the issues involved in the calculation of the length of the mean solar year, go to http://www.hermetic.ch/cal_stud/cal_art.html#Variation.

For those choosing to undertake the more complicated tasks, I've prepared an Excel 97/2000 workbook that will calculate the mean for up to 50 students.  Once you know your students' birth dates, all you need do is enter them; the workbook will complete all calculations for you.  For simplicity's sake, and since most of us do not know the exact time of day at which we were born, the workbook counts the day each was born and the current day as whole days when computing the total number of days each person has lived.

To save the workbook file below (avage.xls), right click on its link above then choose Save Target As and specify the location to which you want it saved. If you click on its link and have QuickView+ 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.

avage.xls

Should you have problems with the file, or should you need a version in a different file format, please e-mail me.  I will help in any way I can.

If you want your students to see the differences among mean, median and mode averages; have them go back to the data they've collected and compute median and mode averages for it.  Once they've finished, lead a discussion to explore the situations in which the different types of averages are most useful.  Robert Niles' site is a very good place to find information with which to begin.  See especially his explanations for mean and medianThe American Heritage Book of English Usage also provides a clear explanation of the differences.

For another activity using averages (among other things), have a look at How Much Do They Make?  For more about calendars, see Putting Time in Perspective.  For more about time and standards, see How Long is a Second?

From the Let's Give Credit Where Credit Is Due Department

Thanks to Gene Stanford for the idea on which I based this activity.  He published it in his Developing Effective Classroom Groups: A Practical Guide for Teachers (Hart Publishing Co., 1977), pages 87-88.