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Volume 2 #2 October
resist the temptation near Hallowe’en to digress
from reading for a minute for a quickie on math because
of my infatuation with disguises, specifically, disguised
ones. A proper math teacher uses correct terms when she
teaches, many of which leave the hapless dyslectic or math-phobic
student feeling as though he has had a bucketful of words
dumped on his head. Tell him that he must get a least common
denominator to add fractions, or take out the greatest
common factor to reduce a fraction to lowest terms and
You need to teach
him that the bottom of a fraction is called the denominator
because it is the NAME of the fraction. (If
you nominate someone for office, you name him, etc.) Then
make sure he knows that you can’t add things unless
they have the same name. Two peaches and three pears does
not make five peaches, etc. Two pieces of fruit and three
pieces of fruit, though, does make five pieces of fruit.
The other fact that he needs to know is that you can multiply
anything by one and get the same amount: 1 x 23 = 23.
Next, tell him
that you can disguise the number one any way you want.
You can call it 100 – 99, or 23 over 23,
or 1/2 + 1/2. Be sure he knows that a fraction with a matching
top and bottom always equals one, whether you are talking
3 over 3 or a happy face over a happy face, or a roaring
lion over a roaring lion, or seventeen thousand over seventeen
thousand. The disguised ones you will be using are fractions
with matching numbers top and bottom. (Skip numerator and
denominator for the moment. Top and bottom are just as accurate.)
Show him that he can change the looks of any fraction
by multiplying it by some sort of disguised one: 1/2
= 4/8. (Write them with the divisor line horizontal,
I can’t do that on my computer.) Pick a few fractions
like 2/3 or 1/4 and have him put lots of disguises on them
by multiply them with different disguised ones. Now show
him that just as when he puts on a costume at Hallowe’en,
he looks different, he is still the same person inside. The
disguise doesn’t change him into somebody else. When
he puts a costume (disguise) on a fraction, he doesn’t
change the amount, just the looks.
That said, you
are ready to show him why he can’t add
1/2 with 3/5 with 2/3. They have different names (bottoms).
You have to pick some disguise that will turn them into fractions
with matching bottoms. Each one will need a different “costume”.
Make him write the problem out with the each disguised one
written next to its fraction so that he doesn’t
try to multiply just the bottoms and leave the tops
The next step,
of course, is to get rid of the disguises and find out
what the original fraction looked like
before you started monkeying with it. That needs
which I will write if anybody wants me to.
I got some colored construction paper and cut an 8 inch
circle out of each color. Then I left the black circle whole,
cut the blue circle into halves, the pink one into quarters,
the tan one into eighths, the purple one into thirds, and
the chartreuse one into sixths. Now I called the whole
one my burnt pizza and the others by their colors. Each
fraction’s NAME was its color. Obviously you couldn’t
add two pinks to three purples and get either pink or purple.
You had to find smaller ones that fit both so all the pieces
had the same name (color). Color coding makes it much clearer
than black-and-white diagrams.