Sorting algorithm that a fifth grader could do in his head

[BaNa]

one of the doods im tutoring has the following calculator-free problem : Sort the following 8 fractions from smallest to largest (a list of 8 fractions with denominators >1 and <10 follow. no easy to come by common denominator, its like 5 X 7 X 9 X 8 ). I'm having trouble explaining it to him in a fashion that he will remember, other than "look at them and try to guess". pair-by-pair comparation seems too work-intensive. Any easy to explain ideas?

[BrainDamage]

tell him to do a first rough preliminary check:
count how many times the denominator fits in the numerator, using only integers, approximating to floor

so 3/5 becomes 0, 2/8 becomes 0, 7/2 becomes 3

then have the fractions sorted by that identifying number

3/5 ~ 0, 2/8 ~ 0, 7/2 ~ 3

unless he has 2 or more with the same number he's set, otherwise continue the sorting only on the ambiguity cases ( like in the case of 3/5 and 2/8 )

even if he goes the "rough" way using common denominator, given the numerical range he should have a smaller range of fractions to find common denominator for

otherwise you can do more tricks to solve those ambiguities without resorting to common denominator, but atm I feel lazy so I'll wait for your answer if you think the first rough sorting is not enough

[BaNa]

Sadly the fractions are all between 0 and 1.

[lurker]

How big can the numerators be? All the way up to 8/9?

[SinbadEV]

one way would be to estimate then check... like 3/7 is just a little under 1/2... 5/8 is just a little over 1/2 etc... 3/5 is over 1/2 and just a little under 2/3...

or if the kid understands decimal form that's the best//

[Relative]

You might want to try something other than an algorithm. Some people work better with spatial representations rather than entirely abstract thinking. So maybe you could use a visual aid so he can get a sense of a fraction's relative size. Something like this:



or this:



You might be able to make a game of sorts - get him to try and figure out how to make a whole number with mixed denominator blocks etc...

My teacher used this sort of thing when I was learning fractions in primary school, and to this day I still think of fractions as coloured blocks

[Lancefighter]

Have him divide them out to 2-3 decimal places.

Its relatively easy to sort them at that point, and not too hard to do division to that far.

[Boirunner]

Have him draw a line, marking one end with zero and the other end with one.

Now, for each fraction, do the following: Put a point at one [denominator]th of the line, then use a compass to multiply the stretch from zero to that point [numerator] times. Mark the resulting point.

Then, simply go through the marked points from zero to one, and voila: sorted fractions.

edit: the idea of the exercise probably isn't using a sorting algorithm, but to get a intuitive feeling for the size of fractions. You should really just play around with fractions with him, maybe with a pizza example.

[BattleMonk]

i have no idea what any of this means

[MidKnight]

i have no idea what any of this means

they are trying to teach a fifth grader how to do fractions, that's all.

I'd suggest translating everything you just said into simple english. that'd make explaining much easier

[BaNa]

Thanks guys, I had him do a bit of playing about with those colorfuul fraction pieces. The problem is that his math curriculum is a total piece of shit called everyday mathematics. First time he met the problem was on a test. Most complicated thing they had before was "is x bigger than y?". He is not the best with numbers and has trouble focusing on anything like this.

[Forboding Angel]

Years ago there used to be a game called mathblaster or something like that, you could try something like that.

Additionally as one of the people that do best with visual aid, I can back up what relative said. I have trouble with complex math if I can't see it. I mean hell I had a really really tough time passing my N+ certification because powers are really tough for me (even though it's really quite simple, when the numbers get big, I start getting confused).

I had a lot of trouble focusing on math in school too. I still made straight A's but I had a lot more trouble than most of the kids. Visual aids were key for me, because then I could see the problem, and work it out using math and plain ol' logic.

THis might sound a lil silly, but you could try using the apple demonstration, worked for a lot of kids (including me).

As an example (if you've never heard of it, and you should prolly look it up online as this example is prolly gonna suck), the apple represents the number 1 (or whatever), now you cut it up into pieves, and there is your fraction. Imo (and I could be wrong) it helps because it's not completely boring and gave me something to latch onto as a visual.

Good luck! And big kudos to you for taking the initiative and spending time to flush the public school system down the toilet and actually teach your kid some stuff. Too few parents do that anymore.

[Sabutai]

I remember AlgeBlaster...