Q&A #6302

Teachers' Lounge Discussion: Using pattern blocks to understand fractions

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From: loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2001060808:10:13
Subject: Re: reducing/simplifying fractions

In the old days they called it reducing fractions. But now they call
it simplifying fractions.  In Layman's terms you can divide the
numerator by a number if you divide the denominator by the same
nonzero number.  Thus, 2/4 is equal in value to 1/2.  What we have
done is to multiply or divide the fraction by "one" in the form of
2/2.   The concept of "one" is very important in math.  You can write
"one" as a ratio of any numbers you want as long as you do not divide
by zero.

In the above example, 2/4 x 2/2 could be called 4/8 by multiplying
numerators together and denominators together.  What I did, to reduce
is to divide instead of multiplying and the result is 1/2.

I suggest you let students play with manipulatives like fraction
circles and fraction stacks and come up with equivalent fractions. 
Give them examples with circles divided like pizzas.  All kids know
intuitively that 2 pieces out of 8 slices is the same as one out of 4
slices because that is in their realm of experience.  If a kid wants
half of a pizza he will know if 4 slices or 2 slices is half.  But if
you teach it like abstract math, they may not see the connection.  Let
the kids make fraction circles (representing pizzas) on large poster
boards and if they are neat enough, post them on a bulletin board.  

When I was young, we reduced/simplified by placing fraction inside two
straight lines something like absolute value symbols and if we wanted
to reduce by 2, we placed a 2 outside the lines and then we knew to
divide top and bottom by two.  This algorithmic method is not
considered appropriate nowadays, but it was very useful in jogging the
students memory and in a way, told the student the procedure to use.

Here is something else you can do: Make a sheet of fraction families
with the students help.  On the first two lines you could have
something like:
1/2, 2/4, 3/6, ...7/14 etc.
1/3, 2/6.,3/9, 4/12 etc.

As you can see all the fractions on the same line have the same value.
The first line has been multiplied by 2/2, 3/3. 4/4 etc.

Making a table in reverse would be the same as simplifying or reducing

I am sure there are better ways than I have presented.

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