Teachers how do you like Y2 children to work out number bonds -20?

[MrsHeffley]

Dd needs work on these but I've no idea how to get her to work out the more tricky ones eg 15-9. They don't seem to be allowed number lines so I'm stumped.Dd says she's allowed to use her fingers but that seems clumsy and open to errors.

TIA

People get into an awful tangle over basic maths so forgive me if I digress to begin with. The calculation 15 - 9 can be viewed in lots of ways. The two main ideas are subtraction (taking away) and difference (adding on). Using subtraction you could count back in 1s along a number line, do 15 take 5 (to get to 10) then take 4 more, or 15 take 10 then add 1 back on. All of these lead to the correct answer, and none is right or wrong, but they are all the concept of getting smaller. This should be introduced in reception as, for example, I have 15 cows in a field and the farmer takes 9 cows out (using toys). How many cows are left? Alternatively, using the concept of inverse (and therefore difference) you could start at 9 and add on until you get to 15 (either in 1s, or add 1 to get to 10 then add 5 more). In reception this is introduced as I have this stick of multilink cubes with 9 and this one with 15. How many more are in the longer stick? (The numbers are a little awkward for reception, but you get the idea.) Children often find one method that works for them and stick with it, even if it is not very efficient. This causes them terrible problems later. In my school, we discovered that the children who tended to plateau were those without secure concept of difference and those who could not use inverse, both concepts usually introduced formally around Y2. Once we tackled that explicitly, the progress was remarkable.
Going back to the original calcualtion (15 - 9), for efficiency, I would want children to know that as 9 + 6 = 15, the answer is 6. If they are needing to work it out, either by counting on or back, they need to learn the basic facts. The classic example given to older children is 101 - 99. Hopefully it takes you about 1 second to count on; if you are still relying on counting back, you will be there a long time!
Number bonds are like the phonics of maths. If you are having to 'sound out' each calculation, you will never become fluent. Some children pick up reading without needing phonics, but most need to learn the structure and will then fly. Similarly in maths, some children see the relationships automatically, but most need to be drilled in the basics in order to be fluent in more complicated calculations. Therefore, to go back to the original post, ultimately, your child needs to know the facts so that they are not working it out each time. That boils down to drilling. Flash cards, computer programs, quick quiz........... As I say at school, I can teach the concept, but I cannot teach the fluency. That needs daily practice at the individual level. Out of interest, we do not give any maths homework at all at my school other than to say, learn and reinforce the basic facts (we give an indication of the appropriate level for the age and ability). The parents hate it ("We want sums, we want sums."), but cannot complain too much as our outcomes and progress in terms of SATs are astronomical for children of all abilities!
I hope this makes sense. Looking back, I fear I have tried to include too much. It's much easier to do at parent maths evenings when I can see from the looks on faces if I need to go over it it again!

That is really,really helpful.Many thanks.Sorry to ask for more but what basic facts would you get me to learn and reinforce with dd(Y2) regularly?

I still use the 'old' National Numeracy Strategy (NNS). You can find a copy here:
www.edu.dudley.gov.uk/numeracy/Primary/NNSoldfwrk/NNSoldfrmwrk.htm
If you look under the Key Objectives, that would give an indication of what children should know by the end of the year in order to access what is being covered in the subsequent year. They seem easy, but if your child knows them (as opposed to is able to work them out) the rest of the primary maths curriuclum is simple to teach.
A word of warning: Know by heart all addition and subtraction facts for each number to at least 10 means including knowing 6 + 3 = 9, 3 + 6 = 9, 9 - 6 = 3, 9 - 3 = 6 with instant recall, not just the pairs of numbers which total 10. I would learn pairs to 4, 5, 10, 6, 8, 7, 9 in that order before moving on. Once you know 6 + 3 = 9, don't forget that you can quickly learn 16 + 3 = 19, 26 + 3 = 29 (use a hundred square to help that concept), and, at a later date, 60 + 30 = 90. Then, pairs to exactly 20 (applying knowledge for pairs to exactly 10) before 11, 12 and so on. Pairs to up to 20 are absolutely key to the whole number framework and you cannot do too much repetition of these.
(For the purists, yes, the expectations have been upped slightly with newer guidance, but the 'old' framework still works for me. I find the new guidance leaps around too much before making sure that concepts are secure.)
Hope this helps.

Hi there, number bonds are much talked about at school, but very little comes home to support them. In fact most parents don't seem to know what they are let alone how to help their child.

In my experience as a parent they are something that you must slowly and steadily work on at home, because there are so many combinations it actually takes longer to learn than the tables. If your child learns them well, avoiding counting on fingers (which might take a little longer) they will find addition and subtraction in year 3 much easier. There's no rush, its all down to developing mental maths skills and practice.

Every day choose a number and get them to write down all the different pairings that make that particular number. e.g. 6 = 1+5, 2+4, 3+3, 4+2, 5+1. Once they can do up to the number 30 it's fair to say they have cracked it.
The beauty is that once they are in the practice of doing it like this, number comprehension comes automatically. Alternatively challenge your child verbally by saying things like 'what number does 9 need to make 15?', doing it like this makes it more practical to do on the go and in casual conversation.

Small bite-size chunks like this make it really easy to do and your child soon understands that they can get off and play when they've finished.

Thankyou Small and 11 that's really helpful.

Let me know if it's any good, thanks and good luck!

A fun game to play involves (in school) small cubes but could involve sweets at home. Take (eg)10 cubes. You and your child have a cup/yoghurt pot/beaker each. Shake the cubes and scatter them on the floor. Each player scoops up as many as possible and calls out "I have (eg)4 so you have (eg)6." etc. A simpler version is for you to scatter (eg)8 cubes and cover a few. Your child has to guess how many you have (eg s/he can see 5 so you must have 3).
Another way is to put a number of buttons on some string and then hide some. Your child will need to use number bonds to wrok out what is hidden.
Alternatively, put some peg on a coat hanger and slide some out of sight.
(There are hundreds of ways we do this in my school - I should write a book!)

Actually there are only 40? number bonds your child needs to learn

1+1
2 +2
3+3
4+4
5 +5
2+1
2+3
1+9
2+8
3+7

4+6
4+2
4+3
7+2
5+2
8+2
6+2
9+2
5+3
6+3

6+6
7+7
8+8
9+9
4+7
4+8
4+9
3+8
3+9
5+4

5+6
6+7
8+7
8+9
5+7
5+8
5+9
6+8
6+9
7+9

Granted but it's a lot of information, then there are the reversals, then understanding how to use the same information to work out the inverse operations and all at such at young age. And if like at my childrens school tables are introduced in year two, many kids never get to consolidate the basics and therefore develop insecurities about maths and education.

Bonds aren't like the tables in as much as they don't come in a tidy learning package and so it takes longer to feel confident with numbers - which is absolutely fine if a school can communicate teaching methods with parents to support at home every now and again.

Why do they need to learn the reversals separately

We teach
1+1
2 +2
3+3
4+4
5 +5
2+1
2+3
in reception

1+9
2+8
3+7

4+6
4+2
4+3
7+2
5+2
8+2
6+2
9+2
5+3
6+3

6+6
7+7
8+8
9+9 in Y1

and
4+7
4+8
4+9
3+8
3+9
5+4

5+6
6+7
8+7
8+9
5+7
5+8
5+9
6+8
6+9
7+9
in Y2

by the end of Y2 children are expected to have instant recall of all and know that it doesn't matter which order the numbers are the answer is the same plus the inverse operation

Not saying that reversals should be learnt seperately but cognitively at that age it's a lot to take in. Bonds and tables are fundamently huge to primary maths and often introduced too early and rushed through to tick curriculum boxes or satisfy ofsted, especially when at the same time reception classes are expected to grasp phonics, reading, writing...whoaa, there's just too much going on and too much pressure.

Most parents really want to support their children, but where do you start and where do you focus your attention, especially when teaching methods have changed so much in recent years.

In the constant panic to raise levels of education, broaden the curriculum, the point is lost and so too are many children.

If a teacher at my child's school said this is the target, it would freak me out, because I know that trying to take in all of the above is way beyond the cognitive ability of my child, besides the fact that rote methods need constant reinforcing if premature. But also if child starts to feel confused or is lagging behind from an early age their academic confidence is shattered.

Get the timing right and hit the critical ages and all it'll take is a couple of recitals, consequently processing is much deeper.

If you look at countries where education systems work they are based on a slower introduction, more play, keeping abilities within the class much tighter and hitting the critically cognitive ages. The result of which is more efficient learning processes.

This is so addictive, (am new to mumsnet) thankyou for sparring with me, are you a teacher?

Day off msnet tomorrow - I volunteer at my kids school on Thursdays supporting year three's with number bonds, and year fives with tables. I can't tell you how lovely it is to see their excitement when they 'get' the numbers after years of feeling really confused.

First term we are learning double 1 double 2 and double 3 (over 13 weeks) hardly worth freaking out ....

Too much too soon...especially when there are seven years at primary school to get it right, why rush?

I think we'll probably have to agree to disagree on this topic, have a good weekend :)

3 facts in 13 weeks (really only two and most children know 1+1 long before reception) too much too soon most MN parents would say too little

Do primary teachers mind if children use a different method of working which is correct? I once asked a primary school teacher friend why she taught her pupils her way of working (which I thought would be problematic if you had more numbers). I won't elaborate on it (unless anyone wants me to!) but needless to say both hers and mine technically give you the right answer, though I've never seen anyone beyond GCSE use that method. She looked a bit hurt and puzzled, and replied that the school was using that method across the board and they couldn't teach mine. We're still v v good friends but haven't discussed maths since, lol.

OK, over to the KS1 and EYFS teachers......thanks!

I don't care how children reach the correct answer but we do have a calculation policy which says how calculations should be set down in books.

Hi,

Thanks small SchoolPrimaryTeacher, 11PlusParent and MRZ for all your input. You encompass all the arguments that I am having with my DH!
This was very reassuring in an indirect way...

We are raising our DD bicultural and bilingual. She temporarily goes to school in France (Year 2 equiv-CP) ; our home is in London. My DH does the Bond papers in order to keep up with her English (should we decide to get into an English school later on). We found the UK more focused on mental arithmetic in the early years whereas , here, they are more focused on logic and mental reasoning (geometrical shapes, spatial awareness etc..). Each to their own I expect; it is the end result which counts.

The most interesting argument we have is with which way around to count and with which way around to learn tables.

It seems that in the UK one learns the following way; much more logical according to DH. Indeed, in the UK, one. starts with numbers 1, 2, 3 in left hand column then add or multiply with the same number ie 1 or 2 .
www.brobstsystems.com/kids/addchart.htm
www.brobstsystems.com/kids/mulchart.htm

In France they learn the following way; much more logical to me!!!!! (but DH mental arithmetic is miles better than mine!!)
rainbowresource.com/pictures/026354/ab82baae3a3382427dbf13ff
rainbowresource.com/pictures/039827/ab82baae3a3382427dbf13ff

Reading all the arguments, DH will stick to his way and I will stick to my way. I am sure that our DD will find which way will work out the best for her.

Thanks
Y.

If it's so easy why are so many kids leaving school with poor maths skills?

Why do I find myself supporting kids who at the age of 8 haven't secured bonds or year sixes who still don't know their tables. And that's in a school that sits above the national average.

I absolutely agree they are easy concepts, but my point is that the critical ages are being missed and therefore learning efficiency is compromised. But also classes are so stretched in ability between lowest achieving and highest performing because learning is rushed. This makes a class more difficult to teach on so many levels.

I think with the benefit of modern teaching theory, psychology of learning and some traditional methods it's possible to get the formula right without having to change methods with every wind change.

Google-CEO said in the Autumn that the UK no-longer nurtures polymaths - it's true. If teaching nurtured Literacy and numercy at a pace that works, it's possible to be good at both, then perhaps more children would leave school with wider opportunities.

Maths is the confidence, literacy is the gateway...

because they aren't being taught early enough
If you want to wait until they are seven to begin they have lots to learn quickly rather than spread out over a long period

yvette37 we use www.andrelleducation.co.uk/shop/by-type/books/big-maths-learn-its-jingles/ to teach number facts and teach
2+2 = 4
2+3 = 5
2+ 4 = 6
2+5 = 7
2+6= 8
2+7 =9
2+8 =10
2+9 =11

(we don't bother learning 2+0 or 2+1 for instant recall as they are v simple)

Thanks for that. what do you mean by 'we'? your school? I will look your link up. It is good to have different materials.

It seems that different schools use different material and different methods of teaching..
I lived in Surrey for decades and dealt with Tiffins, Kingston grammar and Daneshill Prep; they all differed in their methods of teaching and they were all very good. We now live in Central London and again different schools and different methods.

Could also be an age thing. My DH is in his forties, ex-grammar school, and he learnt with numbers 1, 2, 3 in left hand column then add or multiply with the same number ie 1 or 2. So did his father and many of my friends who are in their forties/fifties bracket + etc... DH never learnt 2+6, 2+ 8 etc..; think it illogical.

Frankly, it does not matter -the end result matters-check out the PISA International Results. Finland and NZ seem to get it right!!!
Y

I mean my school and the many schools that use the same system

No Finland doesn't include children with SEN in their reported PISA results (can't comment on NZ) whereas the UK does so not comparable data.

I go by the PISA tables which are international and cannot be dismissed. Canada is doing well too so does Singapore etc but then all data is subjective and open to interpretation ... Best to be open minded in my view...

Thanks mrz!!