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Maths - column subtraction HELP!

Discussion in 'Primary' started by bigbrat, Nov 5, 2015.

  1. bigbrat

    bigbrat New commenter

    I am working with a young man in year 4 who cannot grasp column addition and subtraction if you need to borrow or carry over. He also tries to work left to right even though he is right-handed. I have tried lots of things written and concrete but with no success. I wonder if he has problems retaining the learned info, it's as though it gets lost between his short-term and working memory. I only get to see him for 1 hour a week but his parents are willing to help. Does anyone have any ideas please? Thank you
     
  2. mystery10

    mystery10 Occasional commenter

    Start with addition. What have you tried to teach him, how, and what exactly can he not grasp? Are you able to provide him with homework too? In general, the best thing for parents would be to give them something at the end of your session which shows exactly what you covered and exactly how - and some homework - a tiny bit to do each day which repeats the bit that he really did understand and could do so that he comes back to you not having forgotten it and ready for you to move on.

    What is his understanding of numbers of more than one digit like?

    I would say that to work with a load of pound coins, ten pence coins and single pennies (have loads of them ready) might help you in explaining stuff at the start - exchanging etc.

    It might be that you need to do more work on "place value" in general before being taught column addition is appropriate.

    and what's his addition like by other methods?
     
  3. ALSpence

    ALSpence New commenter

    Certainly sounds like his place value may be the target area. I agree with using money and coins to help get him started. Numicon or the old purple blocks (the name has totally escaped me) may also help make it a bit more "real" for him.
     
  4. bigbrat

    bigbrat New commenter

    Thanks for taking the time to reply. His place value is really good as I started with this as I was working through Springboard maths 3 last year, he had no issues. He does tend to count on with his fingers and his number bonds are ok if you prompt him- he seems to forget them otherwise. I like the idea of going through the work with parents - he could show them what to do! They have been trying to help but they say he forgets what he needs to do going from one room to the next which is why I wondered about his memory, but then it would affect other subjects as well I suppose. I will try the coins as I have been thinking so hard what to do to represent tens and units that the obvious, now you have pointed it out, could work. Thank you so much - watch this space!
     
  5. bigbrat

    bigbrat New commenter

    Thanks for your time. I will try money and then the blocks if the coins don't work. Thanks again, very much appreciated!
     
  6. TEA2111

    TEA2111 Established commenter

    Yes, sounds like a place value issue. Have you shown him the expanded method to show him why and how 'carrying and borrowing' happens? I have had a lot of success when using this method before going into the standard method.
     
  7. snowyhead

    snowyhead Lead commenter

    Good idea @TEA2111. BUT it's not carrying and borrowing (which suggests you return something) the terms that observers prefer (Ofsted etc) and which are technically correct should be 'take'/'adjust' or 'adjustment' and 'recombine'. Sorry to split hairs.;)
     
  8. carriecat10

    carriecat10 Established commenter Community helper

    Have you checked out the resources on the NCETM website? There are a some great articles in the primary magazines. This one https://www.ncetm.org.uk/resources/46918 is about designing learning for subtraction. There are some good video clips too.
     
  9. TEA2111

    TEA2111 Established commenter

    Yip, was just quoting OP.
     
  10. bigbrat

    bigbrat New commenter

    Splitting hairs could be just what is needed - I have noticed that he can be very literal an has been confused over terminology so this could work, thanks.
     
  11. mystery10

    mystery10 Occasional commenter

    And that's where going back to a concrete method where he has some pictures of what he is doing in his head will help - he's not having to add the struggle to remember different people's terminology and ways of presenting the same working.

    With the coins you can do concrete adding or subtraction by drawing some large 100s, 10s and units columns and then getting him to put the numbers you need him to add into the columns using the coins. Let's say that he is adding 39 plus 48 pennies. Put three ten pences in the tens column and 9 pennies in the units column. then write underneath + 48. He then has to add 8 real pennies to the pile in the the units column and 4 real tenpences to the pile in the tnes column.

    He can now see that he has 17 pennies in the units column and 7 ten pences in the tens column.

    But you can point out that he can't write it down this way as you can't have a number bigger than 9 in the units column. But he can change the 17 pennies in the units column into one ten pence and 7 pennies and put the ten pence into the tens column. He then has 8 ten pences in the tens column and 7 pennies in the units column.

    You can then show him how to write this exchanging with the carrying figure or whatever you or his class teacher likes to call it and he can understand that it is the ten pence that was created by ending up with 17 pennies in the units column.

    Hope that makes sense. Similarly, when you move onto subtraction, put the first number into the columns using coins and then write down the number you want him to subtract. He then needs to carry out the instructions by taking coins away. He will see that if he needs to take away more pennies than there are physically in the units column that he needs to take a ten pence piece out of the tens column and change it into ten pennies in the pennies column - and then he can take away the number of penneis he needs to take away. Also, he has one fewer ten pence in the tens column when he tries to take away the right number of tens etc etc.

    You can then extend this using £1 coins.

    It sounds like he is like my daughter - she tries to remember methods and struggles if she has forgotten the method. More time needs spending on repeating and repeating an exercise which gives them the meaning which then leads into the method - and then once this is fully absorbed they can work out the method for themselves if they've forgotten the method.

    Maths should not need too much memory. Fast arithmetic needs memory for the number facts but successful maths does not.
     
    Last edited: Nov 6, 2015
    ALSpence likes this.
  12. bigbrat

    bigbrat New commenter

    Had a quick look over lunch and they look like they will be really helpful - thank you
     
  13. snowyhead

    snowyhead Lead commenter

    Almost forgot: exchanging (instead of 'borrowing')
     
  14. mystery10

    mystery10 Occasional commenter

    Yes, the word borrowing does not have the right meaning for what is taking place mathematically and therefore does not aid the explanation to the child and therefore could unwittingly add some confusion for some children. But there are plenty of other well chosen words that could be used in a good explanation to aid understanding.
     
  15. TP17

    TP17 New commenter

    I have found building up subtraction step by step quite helpful. Maybe try bar modelling or number lines. II also quite like to use the method of partitioning the written subtraction into HTU out to the side or you could try using counters to show what happens when you are exchanging.
     

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