When do kids typically grasp number sense?

[RoboJesus]

Is it before starting school or because of starting school?

Doesn’t this depend slightly on which aspect of number sense you are talking about? Babies less than a year old have a rudimentary sense of number. And I know a fair number of adults, who can carry out calculations but whose number sense is a bit suspect.

Mrz, I have read that article you posted and it is OK (is the woman selling her services, so to speak?), however I must stress that "poor number sense" is NOT an inevitability, nor are there kids wity innately "poor number sense". Instead there are kids who have been taught following an unsatisfactory method. Just like, you guessed it, with phonics, EVERY child will be able to read, we should have the same goal with numbers, but starting from preschoolers and early years, where most of the damage is done (and where kids who "don't get numbers" are created).

Also, I am not convinced by one thing you said: small children do have an innate sense of "oneness" and "twoness" and "hundredness", but they don't have a sense of what "1", "2" or "100" mean. The two things are quite different and unrelated.
An author said that the best numeric system for small kids is Roman numerals, because that is the way their mind works. For a small child "100" is a one digit number, so you might as well use the notation "C". However a (very) young child will have no problems at identifying the hundredness of 100 balls ordered in 10 rows of 5+5 balls (like a bookshelf), and by extension the "thousandness" of 10 bookshelves. They may not know that that is a Thousand and call it "ten hundreds", but that doesn't mean the child doesn't get the concept of "thousandness".

Just like literacy, we need a numeracy revolution ;)

I don’t think that article is claiming that poor number sense is an inevitability. It’s from a Singapore maths based scheme, so it’s coming from the point that poor number Sense isn’t inevitable and can at least be improved with good teaching.

@rafals, yes, of course it can be improved, but we shouldn't be in a position to need the improvement. The improvement has to happen in the way maths is taught to avoid kids wity "poor number sense".
Singapore maths is most certainly a good (or is it THE best? I wonder...) place to start, but for older kids. Attention has to be given to preschooler and YR.

I’m interested in this as I work with kids in year 7 who cannot reliably do number bonds to 10 - so to me the idea that reception kids could do these things is a bit mind boggling! What the children I work with seem to lack is the conceptual basis for maths, even simple ideas such as halving something really test them - I’d have thought that age 5 the actual ability to do calculations could come second to understanding concepts of sharing out, making numbers bigger and smaller, recognising similarities in shapes etc. Am I setting the bar super low though? Interested in people’s experience in this.

No Arkadia she isn't selling her services. It's simply an article published on the Maths no problem ( a scheme used in many primary schools) site.
https://nrich.maths.org/2477. university of Cambridge site
Or you could try

The Number Sense: How the Mind Creates Mathematics* Paperback – 31 Jan 2000
by Stanislas Dehaenee

Oh hang in I’ve just recognised the OP and am remembering some other threads that got dead weird.

And no Arkadia not all small children do have an understanding of the oneness of one when they start school I'm afraid.

That’s what he’s advocating though. That good number sense is developed by good teaching from the school and throughout school.

To take your example of phonics. Yes, we can teach 99% of children to read using a phonics approach, but that journey isn’t the same for every child. We know there are some children who will grasp the code just through exposure to text and most just need some good quality explicit, systematic teaching. But some children will need a lot more support and practice and might take much longer to get there.

The same is probably true of maths. Not all number sense is Inate and some children really need a lot of experience before they get the ‘oneness of one’ thing.

Well, I don't want to get bogged down in a discussion, however, mrz, some people swear that ALL kids do. It is just a matter of teaching them properly. Bear in mind, though, that children in England start school a full two years before other countries, so that might have an impact. However, that makes it even MORE critical to get the right approach to avoid a situation like the one described by @PinguDance.
I have seen wityh my own eyes small kids juggle four figure numbers with ease and have spoken with several primary maths teachers who swear that ALL kids can count and do basic arithmetic if instructed properly. (Alas I don't have anything in English, but I am looking)

@Rafals, of course some kids will get things more quickly than others, however, I insist that the concept of "oneness" is innate and not taught. But leaving that aside, otherwise we get nowhere, one concept that is NOT innate is "zero" as a number. Children understand the absence of something, but "zero" is not seen as a number. The classical example that many give you, is the number line starting at "0" which most kids don't get because to say that the little vertical line with a "0" above it means "absence of something" is meaningless to them - and a number line without a 0 is only marginally better.
(They used it at my school, but at the time I was young and naive :) )

One can try this: get 5 objects, like 5 lights in a row with 5 individual switches and explain how the lights are switched on. The switch, say, 2 lights on and then ask the child to switch on another one and then another one and see what happens ;)

IMO that’s exactly where the bar should be set, Pingu. I think there’s been a tendency to think harder maths = bigger numbers. So children grasp counting to ten, counting ten items and some basic calculation and then there’s a temptation to move them onto 20, 30 etc. Whereas there’s some quite difficult concepts you can explore without going beyond 10.

Number bonds in reception, I’d mainly do practically and start by looking at different ways of partitioning the same number. There’s a fairly unlimited number of contexts for this as well as things like towers of cubes and double sided counters.

@arkadia - yes I’m sure there are kids who have good maths skills age 5 - equally there are some age 11 who struggle despite a lot of high quality maths teaching. I’m not sure all Children start school with decent number sense is what I’m saying. So thinking about the OP for some they won’t be able to do basic arithmetic without explicit teaching.

Simple answer to original question - there is no specific age. Some will have a reasonably good number sense at 18 months, some at 3 years old, some at 7 years old. Certainly not ALL children will have 'it' before starting Reception. It's not as if a light switches on in the brain. Just like so much else in child development, it's a mixture of exposure, parenting, natural skills and interest. And of course, quality teaching from parents, childminders, nursery workers, teachers.

Why do you need to know your number bond to 10? Why not 18?

I worked for about 5 years as a TA in EYFS/ reception class. I reckon that by the end of the year most of the 4/5 year olds could have figured out that if they had 1 screw and wanted 5 screws then they needed 4 more. I can only think of one or two who could have deducted 1 from 150! I'd say about a quarter of the classes I worked with struggled with very simple addition/ subtraction (and didn't have any recorded additional needs). Maybe a bit less, maybe a fifth. Certainly not uncommon though. Generally when they started school the teachers expected (or hoped) that they would know the alphabet, numbers to 10, and how to spell their own names. Some could do much more, others couldn't do that yet. I'm not sure if that helps at all as I've not heard the term "number sense" before.

I'm not sure I know what "number sense" is or follow OP's examples but that is standard for this OP
I think one of the goals for reception is for children to know their number bonds to 10 but by no means all of them will be secure in it.
DC2 is in Yr1 and his teacher was really impressed recently as he was able to say that 32 was 3 x 10 and 2 x unit and it was the same as 20 + 12 or 10 + 22 or 30 + 2.

If you can do number bonds to 10, partitioning and have an understanding of place value you can add and subtract all kinds of stuff quickly.

Arguably adding pairs of single digits quickly and knowing the related subtraction facts helps with column addition and subtraction.

But tbh if you know 2+6=8 and understand place value, then you can do 12+6=18 without any effort. The same for 32+6 or 152+6 or 0.02+0.06 or 20+60.

You picked an example where 2+6 give a result less than 10. How about 37 + 8. How does knowing number bond to 10 make it quicker?
How about 37 + 98?

@ghgn - you do 37+3 = 40 ( number bond knowledge required) then think, oh I’ve got 5 left better add that to 30 = 35. It’s obviously useful to know number bonds up to and including 10.

Interestingly, doing maths with very low ability year 7s we have to give them lots of ‘strategies’ like the above to help them, I find that many of them are ways I actually do maths myself. I had a disrupted primary school career so probably missed the consistent maths teaching that might have meant I could ‘just do it’. If you can ‘just do’ 37+8 it might not be obvious what you are doing but I definitely “fold” the numbers round multiples of 10 when I do mental maths so I use number bonds to 10 all the time. It’s also not uncommon for people to do it that way of a session I went to on maths metacognition is at all representative.

@ghgn - also assuming your not being facetious; for37 +98 I’d do 8+7= 15 , as described above 8+2=10 5 left, then add 30 and 90, 9+1= 10, 2 left over =12 put the zero back = 120 add 15. = 135. It’s quite laboured when you right it out but I obv do that very quick in my head.

The oneness of one is a good way of think about it. I get that obviously there will be outliers that will take till senior school to get it. I was just asking about an average group of kids, that's all

My youngest who is 7 had number sense (never heard that term before this thread) at 3 she is an absolute whizz at maths though and just scored off the charts in our national tests. However my eldest was 7 before she would have even got the basics of take 1 away from 150. She would have been overwhelmed by the size of he number despite the rudimentary maths.

Pingu I am not familiar with what kids learn at Primary level hence my questions.
Even with instant recall, you still need to do so many calculations because you use number bond up to 10.

Imagine that you know number bond up to 18 then 7+8 = 15 carry 1 over. Since you know number bond up to 18, 3+9=12 with 1 carry over that makes 13. When adding 2 numbers, the carry over is at most 1 so not too difficult.

Do all kids in primary school get taught the method that you described?