tell me how i should explain this to ds's year 2 teacher

[witchwithallthetrimmings]

DS got really really angry and frustrated with his maths homework last week, to the extent that he put his head inside the sofa and refused to talk to me. All it was, was using a number line to add and substract 2 digit numbers. Now ds has worked out himself how do to this in his head so it is not the maths that is the problem but he cant get the number line to look neat and clear (think he is also confused as i would by the idea that you go in the same direction when taking away as you do by addding). I asked his teacher whether he could show his work like this instead
35-23
23= 20+3
35+20=55
55+3=58
she said no as he needs to work on his presentation, but it is the same steps ffs. If i make ds do the number line now (i understand he might need to do it later) we will turn something that is a lovely game for him into something that is at best a chore and at worst a source of stress for everybody.

Can't he just count on/back the tens then units via the numberline. He has to learn to show his working as well as doing sums in his head but frankly your working does n't look right either !

Tell her you will work on developing mathematical concepts and understanding at home, and that she can work on his presentation at school.
Point out that he is frustrated and distressed by his homework and he is 6, so that you will work with her over the year to help him see homework as useful and fun rather than upsetting and bewildering. You will talk about numberlines, but perhaps a TA could put in some support in school too.
If she's reasonable, she will listen.
If not, draw the numberline for him and tell her you are scaffolding his learning.

Well, yes. You have added rather than subtracted in your OP.
That might be part of the confusion.

was doing it rather quick and meant to put a plus rather than minus in the top line, thanks you two

12345678910

If you are doing 5-3 how is that going the same way as doing 5+3?

Draw the basic number line and, if possible ask your son to fill in the numbers, if not, get him to tell you what the numbers should be and then write them in yourself. Then just add a note to let the teacher know what you have done, I often have homework handed in with "scribed by Mum" written on it.

FAB i know but he is told to do a jump to the right for the 10s and then another jump for the units even if you are taking away

I would be happy to draw it for him but how is this working on his presentation, surely writing down the sums all in a line and with the numbers all the same size would be of more help?

Just to check - I presume that you write 35-23 as a mistake, meaning 35+23, as the working that you have shown is for the addition calculation? If you really did mean the subtraction calculation, then your reasoning doesn't work!

In your position, I would draw the numberline for your son (as in draw the initial line), then 'scribe' the jumps in for him (or he can write the numbers and you can draw the jumps / vice versa, depending on which bit he is finding it hardest to get neat).

I would then put on his homework: X told me what to do, I scribed it for him.

Tbh, as his teacher I would want to know about his reasoning, not about the presentation of the numberline. As long as it was readable, went from left to right (as in smaller numbers at the left hand end) and his jumps were labelled legibly, I'd be happy.

About 'going in the same direction for subtraction as for adding', I presume you mean counting on to find the difference between two numbers which are reasonably close together? The reason for teaching it is that 'counting back' for subtraction is inefficient when the numbers are close together (imagine calculation 2285 - 2278 - 'counting back' means taking away thousands, then hundreds, then tens, then units, whereas 'counting up to find the difference' means counting up 2 to get to 80, then 5 more to get to 8.

Are you sure he hasn't misunderstood ?!

I'm more bothered by the fact he's unhappy and stressed about homework and he's only Y2. That's the bit I'd be working on.

no he hasn't, the teacher has sent examples, we have

83-23

83 [semi circle with -20 on the top] 63 [semi circle with -3 on the top] 60

i can see the logic on doing it this way because it show the steps but it is not really a number line is it?

Yes, that's exactly what it is! It's a blank number line and used in a HUGE number of schools to show the steps in the calculations. The child is expected to develop towards drawing a line, adding the figures and the jumps.

DWTR this is what i am most worried about and so was keen to co-ordinate with his teacher so that he could do something he got pleasure from (that taught/reinforced the same skills) that somthing that made him sad

Sounds like a plan to me OP, pop in and have a chat with her about her number lines and perhaps you can work together to make them less threatening.

My Y6 use them a lot, it's a useful strategy. But not if you are too scared, bewildered and resentful to learn how they work.

www.topmarks.co.uk/Flash.aspx?f=Subtractdifference shows subtraction by finding the difference
What your son is currently doing is subtraction by counting back!

DWRT can you tell me what they are a useful strategy for (it might motivate ds to learn them) at the moment i think he sees it as a far more cumbersome way of doing what he does already (i.e. partition the number into 10s and units) and add them separetely

Bigger numbers, adding and subtracting decimals, crossing number boundaries. The possibilities are endless as they say.

We also use them for multiplication and division, they are the starting point for aa four operations and are a really useful visual representation of each.

thanks DWRT but why is doing it with a semi-circle easier or more intuitive
so why is

35.5 semi ciricle with +0.1 on the top
better than
35.5+0.1

he is already adding 3 and 4 digit numbers in his head so has a really good grasp of place value (is this the right term)

aah thanks snowball, can you give me a link to how they can help with division. I think if ds sees what the point is he will be more keen to do it

The teacher clearly wants your child to learn to use a blank numberline. That is the 'Learning Objective'. Children learn many methods to do maths now. It's not just knowing that 35+23=58, it's about understanding why it is, and having a range of tools to work it out.

The business with 'semi-circles' makes perfect sense if you do them on an real blank numberline. This doc might help ... www.leics.gov.uk/using_empty_number_lines.doc

Division is simply repeated subtraction, so on a number line 85 divided by 6 would have jumps of 6 backwards along the line until you get as close as possible to the zero, the number of jumps shows the answer, the difference between the last jump and the zero is the remainder! ( or jumps forwards towards the target, depending on which way round you do it!)

Some children DO go straight to partitioning ( adding the place value holders)when adding but this method is much more difficult when subtracting but as number lines are multi functional they ARE definitely encouraged!

The way I talk about methods such as using blank number lines for children who mentally partition (or partitioning for children who mentally or in writing use number lines as a preferred strategy) when I am teaching them is to say that every real mathematician has a 'toolbox' of methods. What I am teaching them is a new tool to put in their toolbox (I even have a very impressive-looking wrench as a visual prompt!). If they learn this new tool well, then they will have it on hand when they really need it in the future.

It does seem to get over the initial reluctance of 'but I already have a method for doing this', and if you can find something that your son can't already do with his mental method (e.g. subtraction of large numbers or division with remainders or whatever - for my Year 1 or 2 DS it was subtracting decimals when it involved bridging over a whole number) then you can give him a reason for learning it, practising first on things he can check using his current method, then on the thing he would like to do next.

Does the start and end of the semi-circle indicate tens/units columns ?

ie 83-23 the 8 less the 2, then the 3 less 3 ?

If so this technique may help him build into more complex calculations.

Is your boy actually quite good at maths ? If so he may find it terribly hard to have one way of doing something and then have to learn a different way to perform the same calculation.
If this is what is making him frustrated it is essential that he does learn multiple ways of calculating the same figures - he needs that flexibility of mind to take maths further, shouldn't become a point of contention with school.

I had a similar thing to you op when my son could work it out in his head and so he didn't see the point of number lines. However he is now in y3 and as the sums and maths problems get harder he sees their usefullness. As pp said they are a useful tool that grows with them.
Also I struggled to understand them myself but found it very useful when the school did a short maths evening to explain some of the teaching methods to the parents!