Tuesday, 6 March 2012

PWR: Denominonsense

I have come up with a simple idea as an adjunct to teaching kids algebra. The name itself is a portmanteau of denomination and nonsense*. The idea occurred to me during my own senior cycle when I asked myself,  'what is 3 cars * 4 dinosaurs?' The answer, either 12 car-dinosaurs or 12 dinosaur-cars, is usually scoffed at until I point out the usefulness of man-hours.* We can continue with 12 car-dinosaurs / 4 houses gives us 3 car-dinosaurs per house.

* Seconds squared also seems a bit ridculous when you think about it.

The value for me came in the premature discovery of what I subsequently learned is call Dimesional Analysis. I used this to easily remember formulas. For example:

  • speed is measured in km/hour (therefore km/hour = km/hour)
  • km = distance
  • hour = time
  • speed = distance/time
I recently watched the Prof. Brian Cox lecture "A Night with the Stars". In the 44th minute he puts an equation on the board involving Planck's Constant. If you use s (for second) instead of time and p to represent Planck's Constant, the equation is similar to:

  • s   = cm*cm*g/p
  • sp = cm2g
  • p   = cm2g/s
Planck's Constant is actually given as Kgm2/s. So without having seen Planck's Constant before, I was able to work out its unit.

My idea is simple: teach algebra with words (which could be the NATO phonetic alphabet to increase the power-weight ratio). The units are actually called denominations because of the first rule of Denominonsense is similar to multiplying farctions:
number * number; denominantion * denomination
For fractions* that is:
numerator * numerator; denominator * denominator
Again, I think this helps increase the PWR as if a student can handle one it gives them an entry into the other.

* Furthermore for fractions 1/3 + 1/3 = 2/3 just as 1cm + 1cm = 2 cm. But for 1/3 + 1/4 or 1cm + 1km you need to find a common denomination/denominator

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