16 + 5 + 7 + 16 =
and please show your working out.
12 November 2006
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Two times sixteen is thirty-two. Plus all the fingers (and thumb) on my right hand make thirty-seven, plus all the fingers (and thumb) on my left hand and two fingers from my right equals forty-four.
Comment by Lucy — 12 November 2006 @ 10:48 am
16+5 is 21, +7 is 28 +10 is 38 +6 is 44
Comment by Merry — 12 November 2006 @ 12:43 pm
I’d look at it and think 32+12 is 44.
Why???
Comment by Alison — 12 November 2006 @ 12:46 pm
I’m with Alison, 2x 16 is 32, plus 12 = 44.
and also with the why?
Comment by HelenHaricot — 12 November 2006 @ 1:10 pm
me three 32 plus 12
Comment by Em — 12 November 2006 @ 1:32 pm
32 + 12
Comment by layla — 12 November 2006 @ 2:00 pm
Probably I’d do 32 plus 12 but all depends on my mood. Just as likely to say why???
Comment by Allie — 12 November 2006 @ 2:56 pm
i wouldn’t know 16*2 was 32 unless i spent time thinking about how to do the sum in the first place, by which time the person who used to spend all day adding up while she worked in a bank could have done it quicker.
Still find it amazing i worked in a bank…
Comment by Merry — 12 November 2006 @ 11:05 pm
It’s weird for me to think about what it would be like not to just *know* that 2 16’s is 32. People’s minds and brains are fascinating 🙂
Comment by Alison — 12 November 2006 @ 11:08 pm
I’m planning a blog post on learning styles – brought on by Ady struggling with his college course and my own fascination with how brains work, how people learn, store and process information. I doubt any of us learnt 16 times table but I think most people added the two 16s together first. Then we mostly seem to have that number bond knowledge that 7 + 5 is 12.
Do we then add the tens from our 32 and our 12 and then the units?
To pick up on Merry’s point about working in a bank I think a lot of maths information we just ‘know’ is what we have used a lot. Having worked on tills for years I know all the number bonds adding up to 100 from giving change. I know if something is 3.57 then the change from whole pounds will be 43 pence odd. I know that to use every coin in the till would be 1.88.
Ady’s maths on subtraction of darts scores is excellent, not because he can work it out out of context but because he’s spent so long playing it in staff canteens over the years that he just *knows*.
People who worked behind a bar in a pub or in greengrocers certainly always used to have awesome maths skills even if they couldn’t tell you what a fraction was. I think everywhere I’ve ever worked in retail has offered 20% staff discount, so telling you what 80% of a total price is would come as second nature.
But I must do the blog post rather than bung it all here…
Interesting stuff.
Comment by Nic — 12 November 2006 @ 11:41 pm
Missed this yesterday! I would have said the same as Alison just by looking at the sum, but with a slightly longer pause before the 44 😉
Comment by Sarah — 13 November 2006 @ 8:06 am
Yes, I’d have done the 16 + 12 route. As you say nic, this is mostly down to just having learnt stuff through useage, though some people certainly do have an aptitude (or not for this sort of thing).
My useless financial skill was being able to weigh out £1 worth of old 10p’s in my hand – picked up in summer job working on an amusement acarde bingo bit where we had to dish out change
Comment by Chris F — 13 November 2006 @ 11:24 am
Fuck, I got 43.
Comment by Chris — 13 November 2006 @ 12:12 pm
Didn’t have enough noughts on the end for you darling 🙂
When I worked in a shop, I used to love it when someone bought stuff that added up to £X.12 – you have to get your thrills where you can when manning a till 😉
These days Nic, I don’t have to separate out tens and units when adding 32 and 12 😉 Sometimes answers come into my head without thinking about it, but I’m not sure whether to trust them, and end up working them out anyway. e.g. 353 – 87 = 466 and then I’ll think “is it???”
Comment by Alison — 13 November 2006 @ 12:47 pm
ROFL, I meant of course 266!!! I was just telling E that it was 4 hours until we went swimming when I was typing that 😆 I’m so suggestible 😆
Comment by Alison — 13 November 2006 @ 12:49 pm
PMSL 😆
Comment by Nic — 13 November 2006 @ 12:55 pm
You are so *not* suggestible. I was making a suggestion to you all day yesterday and got nowhere, not even to 4.
Comment by Chris — 13 November 2006 @ 1:35 pm
You can tell a bookie’s child because they count
1, 3 to 2, 2, 3, 10 to 3, 4 …
Comment by Bob — 13 November 2006 @ 5:08 pm
rofl at your sum.
yeh, I didn’t add tens and units for that, just the whole lot popped into head, but i would have done a quick -90 plus 3 for your sum Alison [i think]
Comment by HelenHaricot — 13 November 2006 @ 5:25 pm
I think i might (possibly) have done it differently before i worked in a bank, but 18 months of solid cashier work probably conditioned me into adding up downwards, as it were, because if you ended up with several thousand pounds in odds and sods, an ordinary additon sum was quickest.
I add up my parcel weights every day (usually about 40-50,000grams) by hand, in my head. I’m far more accurate doing it that way than using a calculator!
Chris made me laugh 😉
Comment by Merry — 13 November 2006 @ 9:43 pm
Interesting.
In answer to “Do we then add the tens from our 32 and our 12 and then the units?”
In general, I think it’s far more natural to work from left to right, even though we seem to insist on teaching children to work from right to left. But then I suppose that looks neater when carrying ten’s etc. For example, 36 + 58, it’s much neater to add 6 and 8, write in the 4 and jot down a little ‘1’ to add to the 3 and 5 next, rather than write down an ‘8’ in the ten’s column, only to have to scribble it out and replace with a ‘9’. But in your head I think it’s easier to think of replacing the 8 with a 9 (cos you can see that carrying’s going to be involved) and be thinking (or saying) ‘ninety…’ whilst working out the units.
This of course for those of us who don’t just ‘see’ the answer. And tbh, I think I’d have to say that I don’t. I’d just run through the above fast enough to pretend I did, if necessary starting to say the answer before I’d finished working it out. 😉 And even if I did just ‘see’ the answer, I wouldn’t trust myself and like Alison insist on ‘checking’ it anyway.
Comment by Barbara — 13 November 2006 @ 10:49 pm
but for yours, I am fairly sure that I add 60 then -2, giving me 94 much more quickly than any other way. but I might not? as I might be doing 30 plus 50 plus 14. hmm?? that one was a looker as it were!
Comment by HelenHaricot — 14 November 2006 @ 12:31 am
I just added it up as I saw it, but I worked behind bars for years where you add drinks up as you pull them. My stepdad was a chartered accountant so give me numbers on a piece of paper and I do something different again – immediately set them under each other and start book-keeping with them.
Fascinating subject Nic. Looking forward to the blog post about it!
Comment by Gill — 14 November 2006 @ 7:47 am
hmm, not sure now Helen, lol. I think the 30+50+14 idea is what I was meaning when I meant working from left to right. (As opposed to thinking 4+30+50+10 which is the order of the written method.) It just makes more sence (to me) to work with the ‘more important’ numbers first, to get to an approximation first which you can then fine tune. (Obviously for sums so trivial that sounds a bit over the top, but they’re not trivial to a small child, and I would apply the same ideas to less trivial problems.)
Comment by Barbara — 14 November 2006 @ 10:00 am
See, again, I wouldn’t really do any conscious working out for 36+58, but I think 36+60-2 is closest. When adding up two 3 or 4 digit numbers, I’d do hundreds or thousands first and then work towards the right. But if there are more than about 7 digits involved it’s probably quicker to do it on paper, as that requires almost zero thought.
Practice certainly helps, but I do think aptitude has a lot to do with it, having watched my kids come up with very efficient methods without having had them shown to them.
Comment by Alison — 14 November 2006 @ 11:18 am
I think the main difference that aptitude makes is whether a child manages to work out their own methods before having methods thrust upon them. In school that often takes a very bright child, but it will be to their advantage, thus broadening the gap with the weaker children. When managing the learning of 30 children, it’s very hard to give every child that opportunity. But give any child long enough, asking them the right questions to guide a little if necessary, and they should also be able to come up with their own methods to experiment with. It’s how (and when) you ask the questions that is the challenge for the educator. When working one-to-one, if I have to spell anything out to my students, I consider it a failure on my part, and usually only happens when the lesson is almost up!
And re the 36+58, I agree it’s hard to analysie exactly how you do it when it’s so automatic, but I think it’s a useful exercise. I pretty sure I think “80+10”. I don’t think I think in terms of taking 2 from 6. The ‘4’ to finish with just comes from the 6+8=14 number bond. Although if I *had* to explain quickly to a child how to do it without pen-and-paper, that’s probably what I’d use.
Also looking forward to your post, Nic.
Comment by Barbara — 14 November 2006 @ 2:19 pm
Well, I started out adding them as they came, got to the 7, saw the second 16, revised it to 32 + 5 + 7 and pretty much left it at that.
With big numbers I do it in units, tens and so ons, complete with carrying. No, not visually, yes, in my head.
Lots of sums break down quicker though, though not in the way Alison does them, mine is more about lots of mental maths from working behind bars as well.
Comment by jax — 14 November 2006 @ 10:47 pm