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Q&A #178


Concept of division

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From: mary lou <mderwent@chern.math.nd.edu> (for Teacher2Teacher Service)
Date: May 01, 1998 at 17:43:53
Subject: concept of division

I am not an elementary teacher but I am a math teacher.  I am also the
mother of five grown children.  We did a lot of kitchen math.   Since
you mention that your daughter has no idea of what division is I
suggest that you buy a pound of dry beans.  Using the kitchen table
have her choose say 12 beans and put them in one group.  Choose 12
more and then put them in another group.  Do the process again.  What
she has is three groups of 12 beans each.   Ask her if she puts the
beans to gether, how many beans will she have?   Hopefully, she
recognizes that 12 + 12 + 12 = 36.   As her how many groups she had
before.   The answer is three.   Ask her to make four groups using the
36 beans.   Tell her that she can do it any way she wants.   Examples
of ways that she might attempt is to designate four areas on the table
and  portion them out one bean at a time, or two beans at a time until
she runs out of beans.   When finished, ask her to count the number of
beans in each group.   She should have nine in each group.   

Tell her to put the four groups together and get the 9 + 9 + 9 + 9 =
36 beans again.  This time ask her to put the beans into 6 groups.  
When finished with this.   Tell her that the number of groups that you
choose each time was the divisor and the 36 was divided into the 3, 4,
or 6 groups by the divisor 3, 4, or 6.   The number of beans that were
in each group was the quotient.

If you think that she understand this, ask her to put the 36 beans
into 5 groups with the same number of beans in each group.   She
should check when she is finished that the number of beans in each
group is the same.  She will also notice that there is one bean that
cannot be put into a group.   This is called the remainder  because 
5 * 7 + 1 = 36.   In each of the previous groups there was no
remainder because the number 3, 4, and 6 divided evenly into 36.

Once you do this try to show her how this is written as a division
problem on paper.

Good luck.

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