# Using efficient written methods to subtract &#163;.p Y4/5/6

Discussion in 'Mathematics' started by elizabeth1972, Jan 14, 2012.

1. ### elizabeth1972

I've also posted this on the primary forum...<table cellpadding="0" cellspacing="0"><tr><td class="post">I teach Y4/5/6 for maths, with abilities ranging from 2c to 5b.
I'm planning for next week and I'm going round in circles with maths! I'm on the second week of A2, but we only have 2 weeks this half term for it.
Last week, we looked at decimal numbers: place value, positioning on number lines, rounding and counting in decimal steps to create/continue sequences.
This week, we really need to work on written methods for + and -
On Monday, LA will use an expanded written column method to add pairs of three-digit numbers; MA will begin with expanded column method and then progress to the compact column method to add pairs of three-digit and four-digit numbers. HA will use the compact column method to add numbers with 1,2 and 3 decimal places.
So far so good!
On Tuesday, we really need to move on to subtraction using a written method. Only the HA are really very secure with this, so we'll do 1 day on whole numbers and then, if getting more secure, 1 day on &pound;.p
My question is, which written method is most appropriate as a starting point? Everybody (including me, if I'm perfectly honest) seems to find the counting up column method quite confusing, but the LA, especially the LA Y4s, won't get compact decomposition.
I'm tearing my hair out here! Any ideas?
By the way, we don't have a school calculation policy.
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2. ### elizabeth1972

I've also posted this on the primary forum...<table cellpadding="0" cellspacing="0"><tr><td class="post">I teach Y4/5/6 for maths, with abilities ranging from 2c to 5b.
I'm planning for next week and I'm going round in circles with maths! I'm on the second week of A2, but we only have 2 weeks this half term for it.
Last week, we looked at decimal numbers: place value, positioning on number lines, rounding and counting in decimal steps to create/continue sequences.
This week, we really need to work on written methods for + and -
On Monday, LA will use an expanded written column method to add pairs of three-digit numbers; MA will begin with expanded column method and then progress to the compact column method to add pairs of three-digit and four-digit numbers. HA will use the compact column method to add numbers with 1,2 and 3 decimal places.
So far so good!
On Tuesday, we really need to move on to subtraction using a written method. Only the HA are really very secure with this, so we'll do 1 day on whole numbers and then, if getting more secure, 1 day on &pound;.p
My question is, which written method is most appropriate as a starting point? Everybody (including me, if I'm perfectly honest) seems to find the counting up column method quite confusing, but the LA, especially the LA Y4s, won't get compact decomposition.
I'm tearing my hair out here! Any ideas?
By the way, we don't have a school calculation policy.
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3. ### robyn147

Why are 2C doing expanded written column method? Oh - and then the next day doing a written method for subtraction.
Sorry - but they are 2C - 3C for a reason. Concentrate on informal methods, practical investigations, number lines. Then at least they might understand it. This kind of sums up what's wrong with maths - well education in general - progress, progress, moving on, moving on. Give them a chance to understand it using informal methods. If you think they won't get it, then they won't get it.
Sorry - I'm not having a go but it does make me despair.
Your higher ability children will probably be okay with expanded decomposition. That at least leads to the idea of taking 10 / 100 from the other numbers. Some will argue that you should teach the method straightaway without worrying about why it works.
Speak to your maths co-ordinator. You should have a policy for school calculations.

4. ### robyn147

Why - why can't they have a chance to consolidate what they learnt on Monday?

5. ### elizabeth1972

Because of constant pressure from the HT to get everyone using written methods as early as possible. Some of these children are Y5 and can't reliably use a written method for + or -. Now, I know that this is because of a lack of consolidation through practical methods previously, and some rather large gaps in knowledge and understanding, but they are part of the HT's "monitoring" group and he expects to see written methods.
It makes me despair too. I'm simply trying to do what I have been told to do, and teach a wide ability- and age-range to the best of my ability. I know you are not having a go, I don't agree with what I am being asked to do either... but believe me, life is not worth living at school if we don't do as directed.
Our maths co-ordinator is the HT, who is next to useless at giving help and rather good at giving orders. We don't have a calculation policy because we "use the National Strategies" (his words, not mine).
I desparately need to get these children progressing, but if I'm told to use written calculation methods, then I'm afraid that's what I have to do.

6. ### elizabeth1972

Because I've been given two weeks to teach A2, and we never even got onto multiplication and division last time...
Pressure from above again I'm afraid.
Honestly, I could sit and sob... I'm just trying to do the right thing and get all my children progressing, but I also have to do as I am told, however ridiculous it might sometimes seem to me.

7. ### robyn147

Sorry - it must be difficult for you. I understand all about pressure but the children need to work at the level they can access the work at.
My experience of working 1-1 with children from Y3 to Y6 at level 2 to 5 for the last 3 years has really opened my eyes to what children get and don't get.
At Level 2, change or "how much more money do I need" (which is the basic reason for subtraction) is best done with a numberline starting with pence and not even going into pounds and pence. At Level 2, some children still don't recognise pounds and pence. A numberline is really effective. I've even found with Level 3 children that they prefer a numberline.
How comfortable are they with column subtraction without going into decimals? If they can do that method, complete with "borrowing" (and I know there is another word for it" , then really the decimal should cause no issues. if not,then get them to learn this method. Arguments reign over whether to just teach the method and tell them what to do if they have to borrow - or whether to do the expanded method.
I've seen children make all sorts of mistakes with this method - especially for say &pound;500 - &pound;88 where the 0's get complicated. But you can learn it with lots of practise - if you are allowed to practise.
I just really hate all this accelerated progress - children need to learn at their speed and have time to consolidate. I see it in my tutees who can not keep up and "don't get it" - not your fault but I would not want to work in a school with a head like that.
Take care

8. ### elizabeth1972

Ok, I have 4 maths lessons next week. I'll focus on + and - and not try and squeeze in x and division (goodness only knows when we'll ever get round to those, but I'll worry about that another time).
That means I can do two days each on + and -. One day of teaching/practice and one day of teaching/consolidation. Lots of consolidation through M/O starters in the next couple of weeks to secure.
I'm OK with addition - ENLs, progressing on to ENLS alongside expanded written, progressing on to compact written method. I agree, if secure with the written method, it should only be a small step to then apply the same written method to decimal numbers. Will use this as an extension for some, and keep for future use for the rest.
Subtraction - ENLs for less able. They can all reliably use counters to subtract U from TU and TU from TU, so it's now a case of getting that written down on a number line.
For the middle and more able, are you suggesting ignoring the rather confusing expanded written method of finding the difference by counting up and move directly onto the compact method? Place value is generally quite secure from my middle ability upwards.
Again for subtraction, one day of teaching/practice and one day of teaching/consolidation, with plenty of opportunities to revisit through M/Os in the next couple of weeks?
I do appreciate your help. I've spent all day planning today, and expect to be doing the same tomorrow.
I hate all this accelerated progress too, and we've even been told by advisors that our targets and expectations are too aspirational, but for the moment, I just have to do as I'm told, I'm afraid. I dream of working in a school where you can respond to children's learning needs and teach accordingly!

9. ### robyn147

If you read these forums regularly, you'll see a wide range of opinions on teaching written methods.
In theory - the compact written method is not complicated to learn - just as long as you can do the complicated ones. But should you use a compact written method to do &pound;500 - &pound;88 when mentally it's not hard to work out.
I have never taught "counting up" as a written method. I have however taught a numberline method as an encouragement to lead to mental counting up.
I tutor 1-1, do private tutoring and occasional supply work. I work in a school and I can see the pressure teachers are under. I hate the lack of control there is over lessons, the diktats from above and over high expectations and over ambitious targets.
There are schools out there that aren't like your school.
Hope things improve
Robyn

10. ### elizabeth1972

Thank you for your patience and understanding, Robyn.
Plenty to think about to try to ensure that everyone, at every ability level, properly grasps what they are doing.
I think I might just call it a day and have another bash tomorrow with a clear head!
I know there are different school out there.... I'm constantly looking, but the job situation is just so dire at the moment in my area. Hard though it may be at my place, at least I have a job! There are still many from my cohort of trainees who qualified in 2010 who haven't.