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Volume 2 • #2 • October 2002


I can’t 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 he’s gone.

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 x 4/4 = 4/8. (Write them with the divisor line horizontal, not slanted. 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 unchanged.

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 another newsletter, which I will write if anybody wants me to.

Teaching Tip:

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.



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