When do kids typically grasp number sense?

[RoboJesus]

Is it before starting school or because of starting school?

The Y1 programme of study requires children to be taught number bonds to twenty ...so by age six.

"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" I would say a small number of children start school with a good sense of number, others without any number sense and some with basic number sense. Average is probably the ability to recite number names in order and with some understanding of more and less when there is an obvious difference in quantity (by that I mean a group of three compared to a group of ten or more. They might struggle with a group of five compared to a group of six). Ive met many children entering reception who can't match objects to numbers and certainly couldn't combine groups of objects (to add) and count accurately.

That’s why I said knowing the sum of all pairs of single digit numbers can be useful. You can work it out quickly by bridging through the ten if you have instantaneous recall of the number bonds to 10.

To take 7+8 - if you know you need to add 3 to 7 to get to 10 and you know that 8 can be partitioned into 3 and 5, then your calculation is essentially 10+5. You can apply that strategy to much larger or smaller numbers too.

In terms of adding 98, I wouldn’t do that by partitioning. 98 is essentially 100-2. It’s much easier to calculate by adding 100, then subtracting 2.

www.pbs.org/parents/education/math/milestones/preschool-kindergarten/

I found this site really useful.

@Rafals, in my view number bonds are a red herring... Even more so, most likely you can skip all the maths you do in YR and Y1 and do that in the first couple of weeks of Y2 without issues. YR kids are simply too young to deal with numbers. If I correctly remember, Piaget claims that kids over 5 can understand numbers, not before, so how can you get a child to understand 2+3?
Said that, kids do understand quantities, so you can have them do 150-1 no bother. I had my youngest who, aged less than 6, worked out 1000 - 501 simply by looking at a picture of bookshelves - see my previous post - and counting in her head (and my jaw dropped because I didn't think she could do it).

I would say that introducing numbers to YR kids is like teaching them the alphabet - Anathema to those who do ;)
Just like you introduce sounds and build up from there, the same should happen with numbers. You introduce quantities (raws of balls in 2x5 groups, just like in the post that mrz linked) and help them develop mental maths. Anything else, even though it is in the curriculum, simply risks to make everybody's life a misery and create kids who "don't get numbers" :D

Rafal that’s why I asked in my original post why not number bond up to 18 because the sum of a pair of single digits could be anything from 0 to 18.
I am not a big fan of little tricks like add 100 then minus 2. Kids learn tricks and then extrapolate to other concepts and get things completely wrong. It also means their brain is busy recalling numerous tricks to see if they can be applied instead of just going ahead and carry out the calculation in an automatic process. Anyway, this has gone too far from the original thread.

Number sense isn't an all or nothing thing is it? I think the maths they do in R and yr1 is very much geared towards them developing number sense. Lots of hands on, visual, counting things and rearranging them and 10-frames and numberlines. My kids already having a reasonable amount of intuition about numbers and place value were not impressed at all, DD just finished yr1 currently says she hates maths (while reading maths books and requesting maths games at home...!)

GHGN I think if you have a good feel for numbers, tricks are handy and easy to intuit if the child doesn't just see them without telling anyway. From what I gather for the weaker students it can be better to just choose one method and stick to it.

PS if anyone has a child lacking number sense, Dragonbox Numbers is a great little app.

I’m sort of agreeing with you on the number bonds to 18. I’m just not sold on the point of learning all of them.

I agree, catkind, it’s not so much a trick as what children or adults with a good sense of number do automatically. It wouldn’t take them any more than a few seconds to pick the method and calculate the answer. It would probably be weaker children that would use a different method.

I think the last Framework (which was generally awful) had a bit of a scattergun approach to mental methods leading to children being slightly familiar with lots of methods but not necessarily mastering them to automaticity.

https://thirdspacelearning.com/blog/maths-tricks-bad-habits-we-teach-pupils/?utmsq=fpe4legeqq&utmsource=Twitter&utmmedium=social&utmcampaign=thirdspacetweet&utm_content=New+blog+post

@Norestformrz, thanks for the great link which I have been digesting for a few days now (I know I live a SAD life). I wonder, do you have another link where they elaborate a bit further on the 2/3:1/4 example? I have been going over it, but keep getting into knots in the end, and would not be able to explain it nor would I be confident to conclude that you always flip the second fraction and multiply the two. Thanks.

This is easier to follow.

So perhaps you can have your graphic representation and then move to a more practical approach.

I always thought "number sense" is something that some children has it without being taught, or some get it if they are taught, or some really struggle with.
Op's dc is profoundly gifted, he/she must have it already, so don't know what she wants to know from this thread.

DS is nearly 8 and pretty good at maths - he has a good 'sense' of how the basic operations work, and gets place value, so he is pretty strong at mental arithmetics.
At age 4, before starting school, he could count (objects or actions such as steps) beyond 100, and recite numbers as far as you like to go, and match quantities to numerals. Find one more or one less, and because finding two less is just finding one less and then one less again, finding 2 less as well. But he didn't have much of a 'sense' of quantities and numbers, e.g. he didn't 'get' that 6 can be split into 4 and 2.

Some of the 'techniques' he has been taught at school have been more of a distraction than anything else, and all the memorisation (number bonds, times tables) - though easy for him - has taken away from developing more of a 'sense' of numbers and quantities. By instantly being able to say that 4x5 is 20, he doesn't get to practise his 'sense' of the four sets of five that are in 20. Since memorising his tables, when asked a multiplication question within the 1x1 - 12x12 range, it is the language/word/memory part of his brain that kicks in, rather than the maths/numbers/reasoning part. It is only when multiplying beyond 12x12 that he applies his 'sense' of multiplication and numbers. And therefore he stopped practising/firming his 'sense' for eg. the four groups of five that are in 20.
Similarly with number bonds, as he has always found memorisation easy and fun, he memorised number bonds to 10 at a young age. And because he 'gets' addition, has always been able to apply them too. But has stopped developing his 'sense' for how the numbers up to 10 fit together - too early IMO.

DD in contrast, is four now, and has a much greater 'sense' of numbers/quantities than DS had at that age. She will randomly (e.g. whilst cycling to nursery) announce that e.g. 7 can be made up of 3 and 4, or that 6 can be made up of 2 and 2 and 2. She claims she can count to 100 but in reality will stumble around 29 or 39, and confuses 12 with 20, but I would say her number sense is vastly better than DS' was at that age.

There are clearly multiple aspects to 'number sense' and sometimes you will develop the 'sense' after the technique/memorisation by lots of applying it, other times the 'trick' or technique will distract from the 'sense'.