You do the curly whirly and you turn around ...

Most Maths teachers would be familiar with the following algorithm for converting mixed numbers into improper fractions. Improper fractions are those where the numerator (top number) is greater than the denominator (bottom number). Thanks to Mr. Person for the illustration.

Basically, you get the numerator of the improper fraction by multiplying the whole number by the denominator and adding the result to the numerator. Fabulous and very sensible! I am being sarcastic, in case you cannot tell :-)

Every year I revise this topic with my year 8s and they all know some part of this algorithm by heart and usually forget another. They fumble through "you times by the bottom and plus by the top". The poor souls get to repeat this, until they use proper verbs (add to, not plus by)!
Not one of them can explain why this works, or is interested in knowing why this works.

This year, I have the fortune of having a year 7 class instead of my usual year 8s. They were happy thinking: one and a quarter is the same as 4 quarters plus another quarter. This can be written as 5 quarters. After they all understood this, I thought I would show them the obligatory shortcut illustrated above. They had seen it in primary school but could not fully remember it.

For the first time, I was the first teacher they had who called it the "curly whirly", and they were not interested. They wanted to think about it logically, turning the whole number into a fraction. So, this leaves us with one good use for the algorithm:
Oh, the curly whirly
Oh, the curly whirly

May your Maths classes be filled with song!
Elias.

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Comments

Anonymous said…
or..."you put the numerator in, you put the numerator out, you put the numerator in & you shake it all about"

and what about,
"You can call me Al...gebra"
by Paul Simon

or

"Pi Pi Miss pythagoras pi"
by Don McLean

and of course,

"Trigonometry...I'm not half the maths i used to be..." by the Beatles

it's endless....just like a teacher's day

ciao elias
keep on bloggin'
TB
8:50 pm
Rambling Teacher said…
LOL, this is hilarious, TB. You've brightened up my weekend. Thank you.
8:50 am
Anonymous said…
i thought of a new song for you maths teachers...

"we can work it out.. we can work it out.. " - the beatles
2:02 pm
Anonymous said…
Good brief and this fill someone in on helped me alot in my college assignement. Say thank you you as your information.
5:03 pm
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