An infinite number of correct answers, part two

[lovingboth]

OK, I looked at the question, thought that 'maths is about finding the simplest and easiest answer' and said '120 x 1'. I'm kicking myself slightly for not thinking of sqrt(120) x sqrt(120) first :)

JA(7) saw that 120 is a multiple of 20 and worked out that '20 x 6' was 120.

L said '2 x 60'.

Adult visitor P said that seven year olds probably wouldn't know anything higher than their twelve times tables and said '12 x 10'.

You lot had...

10 x 12 - two people
6 x 20 - three people
3 x 40 - one person
2 x 60 - two people
1 x 120 - one person

Three people gave lots of answers, typically all the natural (1, 2, 3, ..) ones

One person said that 'number' doesn't mean 'integer', which is true, but you weren't asked to give every possible answer, just (at least) one possible one. The marking notes said that (for example) 240 x 1/2 was to be treated as correct, for example.

One person said 30 x 40, which alas is 1,200. Of course, those could have been the numbers Harry picked too - it doesn't say he got the sum right :)

I'm afraid I suspect Paul's attempt (two complex numbers) would get no marks, although this is partly my prejudice about the maths of infant school teachers: would they recognise the answer as being correct?

Comments

[ciphergoth.livejournal.com]

Are you confident that my answer is correct?

didn't anyone else try for a "weird" answer?

[lovingboth]

I will confess to not expanding it out, but it ends up as 60+60, doesn't it?

Let's see...

(10, −10)⋅(6, 6) = (10x6 - -10x6, -10x6 + 10x6)

= (60 - -60, -60 + 60)

= (60 + 60, 0)

= (120, 0)

aka 120, so yep.

I'll leave it to you to explain complex numbers to people :)

Nope, including the square root was as wierd as anyone else got. Mind you, I haven't had a response from some of the other maths people yet.

[a-musing-amazon.livejournal.com]

My full response was in the comments: which in addition to lots of example depending on what type of number was allowed also gave what I thought was the general complex number solution a+bi x 120/(a+bi), a+bi <>0.

Though of course 120/(a+bi) is not expresed in standard complex form which would, I think, be 120a/(a^2+b^2) - 120b/(a^2+b^2)i.

[vampwillow]

So far as teaching is required, I think the one answer that would *not* be accepted is '120 x 1' as that wouldn't show "multiplication" as teachers usually describe / teach it (even though, formally, it is a correct statement).

[lovingboth]

No, I think that was the first correct answer in their marking scheme (then 2x60, 3x40 etc).

Teaching children that one times 'something' = 'something' now happens before any other multiplication from what I've seen.