An infinite number of correct answers

[lovingboth]

From a SATS key stage 2 (i.e. for 6-7 year olds) practice question...

[Poll #1386206]

Comments

[valkyriekaren.livejournal.com]

Wow, way to ask a non-specific question! I'm assuming the kids will get points for any two numbers that have a product of 120, though. Otherwise that's just cruel.

[lovingboth]

Yes, you get a point (or you would, if this weren't a practice question) for any correct answer. But which answer people pick is quite interesting.

[barakta]

Bugger you've hidden the responses ;)

I specifically said I was only dealing in integers.

That's also quite hard for a KS2 child - they only really seem to have started multiplication tables by then. I'm not sure I could have done that at 6 or 7 cos we didn't do tables properly till I was about 8 when I crunched through them rapidly and got my stupid certificate out of the way.

[ciphergoth.livejournal.com]

If you said integers, did you consider answers like -6*-20?

[barakta]

No, you got me on those.

[ciphergoth.livejournal.com]

A useful term here is [[natural number (http://en.wikipedia.org/wiki/Natural_number)]]

[valkyriekaren.livejournal.com]

I've never understood why minus numbers behave that way.

[ciphergoth.livejournal.com]

I'll show you next time we're in the same place. The short answer is: draw a graph of -2x against x and it should be clear!

[valkyriekaren.livejournal.com]

It's OK, I don't think I really need to know why. Multiplying minus numbers in my head isn't something I need to do regularly, anyway.

[lovingboth]

Yeah, I wanted to avoid biasing answers. I'll post something about the answers tomorrow or so, but the first five people asked 'in real life' here gave five different (correct) answers.

I was expecting Paul to say something like '120 pi and 1 / pi' :)

[barakta]

I await your answers with interest.

I definitely want to see what the mathmos answered and see if my poor little brain can make sense of it without going *boom*.

[ciphergoth.livejournal.com]

I think I gave good answer :-)

[a-musing-amazon.livejournal.com]

(1,120),(2,60),(3,40),(4,30),(5,24),(6,20),(8,15),(10,12) are the positive integers.
While (-1,-120),(-2,-60),(-3,-40),(-4,-30),(-5,-24),(-6,-20),(-8,-15),(-10,-12) are the negative integer solutions,
also (x,120/x) where x is a rational number,
also irrational solutions such as (120^1/2,120^1/2),
also transcendental numbers such as (Pi, 120/Pi),(e,120/e).
also complex numbers, such as (120i, -i).

I suppose the most general answer would be something like (x, 120/x) where x is a complex number a +bi where a and b are real numbers and a+bi <> 0. But this does seem a bot beyond the comprehension of most 5-6 yeat olds.

[nitoda]

Help ... a monster swallowed my partner! ;-)

[trishpiglet.livejournal.com]

I'd give the quickest answer I could think of and then move on to see if the other questions were any more challenging

But then I'm not 6

[haggis.livejournal.com]

An infinite number of correct answers. But also a larger infinite number of wrong answers presumably?

[ergotia.livejournal.com]

I would not have had a clue about that when I was 6.

[badriya.livejournal.com]

I had 30x40 as one but knew it looked too big and had to do it on paper :) I got 10x12 ok at once. I think that was the expected answer if they do tables. Ten times table is one of the first you learn, isn't it?

[lovingboth]

You weren't the only one to say 30x40.

I'm not sure they do 10x as a formal table, but yes, it's an early one although there are some children in te age range who won't have done much wth numbers greater than a 100 yet.