Q&A #1217

Basic math fractions

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From: Gail (for Teacher2Teacher Service)
Date: Feb 27, 1999 at 18:03:28
Subject: Re: Basic math fractions

Marylou gave you some terrific resources. As an introduction to the
instruction, you may want to remind your students about what we are trying to
find out when we divide. For example, if we were dividing 138 by four, we
would be trying to find out how many groups of 4 there are in 138, or how
many are in each group, for 4 equal groups, depending on the context of the
problem we were doing the arithmetic for. (You have 138 pairs of sock to put
in boxes, and four pairs will fit into each box.  How many boxes will you
need, vs. You have 138 pairs of socks to store in 4 boxes. How many should
you put into each box, to evenly arrange them.)

When we divide with fractions we are looking for the same sort of
information. 1/2 divided by 1/4 is really asking, "if you have half a pie,
how many fourths of a pie do you have." Since 2 fourths is equivalent to one
half, the answer is two. It forces us to think about the fractions in
relation to the whole.

How about one-fourths divided by one half. That is asking how many halves
there are in one fourth. If you draw a whole, and shade a fourth of it, you
can see that half of a half is in a fourth. So the answer is one half.

Here is where a pitfall enters. Some teachers have taught their students that
when you divide you get a smaller answer. That is true for whole numbers,
but not for fractions and decimals necessarily. When students divide one half
by one fourth, and get the answer "two" it does not seem reasonable to them.
Having them actually cut a half into fourths (fourths of the original whole,
that is, not cutting a half into four equal pieces) will help them see what
is happening when fractions are divided.

 -Gail, for the Teacher2Teacher service

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