Teaching the Concept of Average

Date: 06/20/2003 at 06:21:02
From: Ridya
Subject: Average

How can I use objects to teach averages to students?

Date: 06/20/2003 at 14:18:57
From: Doctor Peterson
Subject: Re: Average

Hi, Ridya.

For a discussion of what averages are, see our archives:

   What Does Average Mean?
   http://mathforum.org/library/drmath/view/52809.html 

As I explain there, the essential idea of averaging is "smoothing 
numbers out." You might introduce the idea by giving each student a 
different number of, say, blocks or balls or cards, and asking how 
many each of them has. Write those numbers down, and point out how 
they vary. Then have them work together to find a way to share them 
equally. (You may or may not have chosen the total number of objects 
such that they CAN be shared exactly.) Eventually they should all 
have about the same number of objects, and you can discuss with them 
how they could have decided ahead of time how many each of them should 
have. The answer, of course, is to find the total number of objects 
and divide by the number of students. The resulting number - the 
number that each has if they share equally - is called the average.

You can also do this as a smaller-scale demonstration. Make piles of 
blocks of different heights, like

         H
    H    H
    H    H              H
    H    H    H         H
    H    H    H    H    H
    H    H    H    H    H
  -------------------------

Then move blocks from the higher piles to the lower ones to make all 
the piles equal:

    H    H    H    H    H
    H    H    H    H    H
    H    H    H    H    H
    H    H    H    H    H
  -------------------------

You have just found the average: on the average, each pile had 4 
blocks in it. And how can you find that number if you just have the 
numbers 5, 6, 3, 2, and 4 from the original piles? You add and then 
divide.  

So, yes, division is central to finding an average. But addition is 
the other half of the work. Does this help clarify the relationship?

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 

Date: 06/23/2003 at 06:55:13
From: ridya
Subject: Thank you (average)

Good Day, Dr.Math!
Thanks for your explanation as it really helps me out to 
solve my problems regarding average.I will use your ideas 
to introduce this topic to my students.Thanks again.
Ridya