## Thursday, December 29, 2016

### Evenly Odd or Oddly Even

If there's one thing that drives me crazy in maths it's the sayings and phrases we've come up with over the years to supposedly help students learn maths more efficiently. Two, in particular drive me nuts.

"You can't take 5 from 2" is a particularly useless thing to say when you are doing the subtraction algorithm such as 62 - 25. Children typically learn this when they are in second grade but then have to unlearn it when they get to 5th or 6 th grade and encounter negative numbers. It should be immediately apparent 5 is more than 2 so you regroup 62 into 50 + 12 so you can subtract 5 from 12 and 2 tens from 5 tend to get 37. Actually it's easier to use negative numbers. Just say 2 minus 5 is -3; 60 - 20 is 40, then 'subtract' the -3 and you get 37.

The other one that really gets to me is "an even number is a number that is divisible by 2".  This pearl of wisdom often crops up in crossword puzzles and should include "to give another whole number" to be accurate, Every number is divisible by 2 in some way, except 0. We can, of course say that even numbers end in 0,2,4,6,or 8 while odd numbers end in 1,3,5,7 or 9. Conceptually, even numbers comprise  pairs of things in them while odd numbers always have one thing by itself.

One way to think about this is to see the school bus on the left as if it was made of cubes. One at the front for the hood and then pairs stacked on top of each other for the rest of the bus. No matter how long the bus is, or how  many pairs you add, the number of cubes will always be odd.

Now look at the second school bus without the hood, or the odd block at the front. No matter how long the bus is, or how many pairs of blocks you add the number of blocks will always be even.

Another interesting thing about odd and even numbers is the way they impact our culture. For example, in Japan odd numbers are preferred while in the the US we prefer even numbers.

Odd and even numbers even elicit emotions as this Guardian report illustrates. Odds and evens even have gender assignments as this Kellogg study reports