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Year 5 maths- teaching children to borrow for a subtraction sum

Discussion in 'Primary' started by thedancingqueen, May 25, 2011.

  1. It's not my class so I don't blame myself for the fact that the class are so behind. When I started teaching them on placement, place value really confused them and now they seem to understand it much better and with decimals too. They've made quite a bit of progress I think and the class teacher has agreed with me. This is the first time I've taught addition and subtraction but I knew I needed to tackle this because time and time again I see them making errors. Most children in the class can't divide which is another problem. They don't seem to know many strategies, but I do know the school likes the kids to use the number line method so this is what I'll be getting them to do tomorrow, with the exception of one group who are more secure and showed me that they can do it. All of the children seem fine with column addition when adding. I don't know if the children were assessed in September. I was only in for the odd day before christmas and block placement started late March. They might be the middle group in school but most are below average ability or so I've been told. With enough support they seem quite capable and they are making progress. I just hope that soon they can feel confident about tackling subtraction sums. They don't seem very confident when they are using number lines either.
  2. minnieminx

    minnieminx New commenter

    They don't seem behind to me. Most year 5s aren't fully secure with nicking from the next column when subtracting, especially as an abstract concept. Numberline and then expanded counting up would be my choice in year 5, depending on what they had done in year 3/4.

    Dividing, as in chunking/long division, is also a pretty advanced concept and I'd not expect a class of year 5s to be able to do it with any ease. I teach the top half in our school and had year 5 from xmas last year. I introduced it for the first time to them part way through the year. About 2/3 of the group are on target now in year 6 to have just acheived a level 5, so could hardly be described as 'behind'.
  3. Exactly, that's what I thought. It's all very abstract and I've tried to make it more concrete for them by relating it to money, measurements, distances etc but I think it's still a difficult thing for them to grasp. They'll get there, but definitely doing number lines tomorrow.
  4. minnieminx

    minnieminx New commenter

    It is a difficult thing for them to grasp. And remember they don't need to be totally independent, perfect and confident at it by the end of year 5.
  5. I would not be confusing less confident children by teachig addition and subtraction together
    TEach addition then multiplication
    then subtraction and then division

  6. This is obviously too late for today's lesson but might be useful anyway...!
    I am sure the problem described in the original post - children simply finding the difference between the two corresponding digits - is the most common misconception/error made by children when learning column subtraction. There are a few things that I found useful with my low ability Yr 6 set this yr (have also used it in mixed ability Yr 4). Long winded explanation but its great for visual, kinaesthetic AND auditory learners and karma tells me I should take the time to share - I learnt these on here a few years back!

    Use dienes blocks (often purple plastic - 100s = flats, 10s = sticks, units = small blocks) to demonstrate the common misconception. i.e. in 456 - 337, you 'can't take 7 away from 6'. Do this by making 456 using dienes equipment and ask a child to take away 7. They'll realise the answer is not 1 and will probably say they can't do it.
    Write the calculation out as a column:
    (This is also where you could write it out as a previous poster suggested, partitioning hundreds, tens and units:
    400 + 50 + 6
    -300 + 30 + 7
    You could also use blu-tack to stick the dienes to the board in line with their 'columns')
    Ask the children to look at the units column and introduce the rhyme:
    "More on the top, do not stop.
    More on the floor, swap for sure."

    Ask a child to be 'banker' with the dienes equipment. If the children don't already cotton on, model taking one of the tens sticks from the 456 and exchanging it for ten unit blocks. Ask the children to check what you have now: it should be 400 + 40 + 16. You can annotate your calculations on the board as:
    400 + <strike>50</strike> + 16
    -300 + 30 + 7
    or (the formatting works less well here! Imagine the one is much closer to the 6 so it looks like the traditional column method!)
    4 1
    4 <strike>5 </strike>6
    -3 3 7

    Now they can work out the units digit of the answer - 16 - 7 = 9.

    Ask the children to look now at the tens column. Repeat the rhyme again - "More on the top, do not stop..." Referring back to your jottings and the dienes, they can see now they need to calculate 40 - 30 and the rest of this example is quite straightforward.

    Sounds long winded and complicated but it really does work well - have done this with whole class or guided groups (teacher or TA). It also helps later when they start trying things like 2116 - 1877 because it is turning an abstract concept into a practical one. You could also stick to 2-digit calculation for your first demonstration (or two!) with the dienes - 56 - 37. You might need to track down some dienes blocks within your school so that groups of children can use these during the main activity but they love working in pairs/3s and 'playing' at being bankers!

    I agree with the previous poster about sticking to one operation at a time, however once their column addition is secure they can (and arguably should!) check their subtraction with the inverse calculation - an addition. i.e. in the example above, they should add their answer to 337 and check that it adds up to 456. If it does, happy days their subtraction was correct. If not, it's time for some thorough checking.
    I also agree with others that less able children will find number lines easier for counting on - this is especially true for calculating change. The important thing is that we teach a range of methods to give the children confidence and choice about the methods they can use. Having said that, it does depend on your school's calculation policy as some schools do restrict you to either decomposition or the complementary method (counting on).

    As for your group not showing jottings, I have a few like this. Where appropriate, have you tried increasing the level of difficulty for those children - decimals, esp with 'different' place value, such as 123.45 + 6.7 often lead to mental calculation errors. You need to show them some examples where jottings are needed!

    Hope it went well today!
  7. You should speak to the Maths Co-ordinator or the class teacher for the class you are in so that you use the subtraction calculations as agreed in the school's calculation policy.
    This should not be the first time they encounter column subtraction as it should have been taught in Y4. Has the school got a copy of the NNS teaching calculations booklet? (From the NNS was first introduced as that has good egs for various methods.
    Look here http://nationalstrategies.standards.dcsf.gov.uk/node/19205 for egs too - hope the link works.
    A&C Black produce some good activity books for each year group and they include the different calcution methods. Your university library will proably have copies if you can't afford to buy them. I, personally, wouldn't be without mine. They don't just have worksheets but games as well.
  8. I too was taught borrowing. Because we did the method that has completely died out now. We 'borrowed' a ten to help with the units and 'paid back' to the tens digit on the second line.
    Years later I learnt that this works because it is equal addition, thus the difference between the numbers remains the same.
    My terminology for decomposition is 'take a ten' (to help the units) and 'have a hundred' (to help the tens). I will add the 'more on the top . . . ' couplet when next I teach subtraction.
    Incidently, subtracting one unit from the top and bottom number is brilliant for examples such as
    5000 - 473, becoming
    4999 - 472 (a spot of equal subtraction, not dissimilar to my childhood methods) so that the difference is the same but the decomposition is unnecessary.
    I actually prefer the counting on method, but it isn't my school's policy.
    And I use this
    to show decomposition.
  9. I did not say I didnt use the correct terminology or use it in class. I merely pointed out I do not like the term exchanging, as it sounds like you are swapping it for something else entirely, which is not the case. You are swapping it for something that is the same 10 u for 1 ten. I know this does not make sense but i can't really describe what I mean.
    People years ago may have been saying:
    Oh my god I can't believe you are not using the correct term borrowing."
    Maybe in 20 years people will be saying OMG I can't believe you call it exchanging!
    It could be worse - I observed an interviewee teach my class ask for a 'take away' and a 'timesing sum' - she didn't get the job

  10. Is this a maths argument or semantics? How did we all manage to become teachers with all this poor vocabulary coming from our 80's and 90's teachers?
    I have the discussion with my year 5 class why we should not say borrowing and why we should not say add a zero.
    We discuss when you could use 'add a zero' ie when multiplying a whole number by 10 but, not using it for decimals. This really helps. They know when using grid method to multiply two numbers that they can add or remove a zero or multiple zeros for speed - but they have to be comfortable with the idea.
    It's the same with borrowing - borrowing in todays society does not always mean you pay it back!
    I am 29 and I still borrow money off my Dad, he can only wish that he gets it all back!!
    If you have the discussion with the children that the word borrow means you take a 10 and change it to 10 units then the language does not really matter.
    You could say "I am going to 'shh-ting' a ten as long as you explain what shh-ting means.
    I could quite easily argue that many of my children do not understand the term understand the term 'exchange,' it is an expression that is rarely used by my children. I saw a child in my class this week 'borrow' a rubber from a different table. He didn't take it back.
    The only reason I can think of anyone using the word exchange is - taking something back to a shop. Any others?
  11. After doing the reality ( take 4 pencils from 2 etc then use money ) I usually
    • ask them to start at 4 count till you reach 2 (can't so go next column and get a set of 10 and rename.) Now start at 4 count till you reach 12 (you can)
    • OR Write S(mall) or B(ig). If S is at the top then you have to go next column
    I find that this is a topic that requires quite a bit of individual attention to get them to the independent stage but it works for some.
    Hope it helps.
  12. what year group would you do this with?

    I don't get it
  13. veritytrue

    veritytrue New commenter

    What a poor set of excuses for using incorrect terminology.
    Teachers' poor subject knowledge is the reason UK adults' numeracy is in such a parlous state.
  14. Doitforfree

    Doitforfree Star commenter

    I learnt how to 'borrow' (we didn't do paying back but we still called it borrowing) in the infants in the late sixties. And then we practised and practised, and although my junior school was crummy there was still practice of basic adding and subtracting. It doesn't matter a bit what you call it but it does matter that you know how to do it. It doesn't matter if you understand either. if you're clever you'll probably work out for yourself what's happening, and if you're not so clever at least you will have a foolproof method of doing thesum. And it doesn't matter about calling it a sum either!

    My son tutored a year 4 girl in Maths for a while. She was being asked to do normal year 4 things but it seemed to have been overlooked somewhere along the line that her basic grasp of numbers was terrible. Not only could she not do things because they'd been done too quickly and without enough practice but also, as a result, she was convinced that she couldn't do Maths. My son helped her a lot, but ultimately the problem was school, where she was doing different things every few days and she was a child who just needed an awful lot more practice before something was really in her head.


    ROSIEGIRL Lead commenter

    I agree! More time to consolidate the basics!
  16. Milgod

    Milgod Established commenter

    I think some of you get a bit too worked up about using the correct terms. Don't get me wrong, I think in many cases the correct vocab is important (I can't stand it when people call The Netherlands - Holland). I just don't think this is one of those occasions. As long as your class can use the method and understand what they are doing then I don't see the problem.

  17. Doitforfree

    Doitforfree Star commenter

    Holland is a recognised British name for the Netherlands. This is the website of the tourist office of Holland (or the Netherlands).
    But I agree, the right word is not usually the problem. We give all sorts of names to things which are very silly if you think about them but the fact is we don't. It's the name and that's that.
  18. veritytrue

    veritytrue New commenter

    It's in the units column.
  19. CarrieV

    CarrieV Lead commenter

    A sum should only be used in the case of an addition algorithm ( and if I were being pedantic, which obviously I'm not, the sum is the total of an addition algorithm, rather than the algorithm itself, so, in 3+4, 3 and 4 are the addends, 7 is the sum) . I would call subtraction, multiplication and division algorithms "calculations"
  20. Ok thank you. I am secondary trained (not maths) but have done supply in primary, so I' m always trying to learn more.
    From what age would you consider it appropriate to use terms such as "subtraction calculation"? Have you found that using such technical vocab can act as a barrier to somechildren, particularly those who are LA in literacy, accessing what would otherwise be a simple operation? It interests me as someone with TEFL experience, where expressing things in the simplest terms was essential.

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