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Grid method vs. traditional long multiplication

Discussion in 'Mathematics' started by BristolLanguages, Mar 31, 2020.

  1. BristolLanguages

    BristolLanguages New commenter

    Buffled parent here. My primary aged daughter could do long multiplication as I taught her at home as part of the curriculum of the distance school in my country. We stopped that this year. Of course, as we never get any homework or get to see the books from primary school I had not idea of what they were learning (that's a different story), but due to the current circumstances, she is getting work from school.

    Imagine my face, I am an old parent... so the grid method looked like out of Mars for me. She explained it to me and I get it, she gets it, and says it's easier. I just don't understand how it is a good idea to regress to the grid method, when you can already do the long multiplication method. Also, what do you do in secondary school, would you expect your students to use long multiplication or you are okay with them spending lots of paper and time doing infinite grids?

    By the way, I am MFL not Maths.
  2. gainly

    gainly Star commenter

    They should be using the traditional method. The Gove reforms, where he wanted to take education back to the 1950's, mean the grid method is no longer an approved method, so I'm not sure why they are being taught it. In KS2 Sats they will get 2 marks if they get the correct answer by any method, but if they get the wrong answer they only get a method mark if they use the traditional method.

    There was a previous thread about this here:

    In secondary school they can use any method.
  3. UKExceED

    UKExceED New commenter

    I would like to point out that the grid method is a crucial step that most children need to use before understanding multiplication with larger numbers, before being herded into the long multiplication methods.

    The previous commenter is not completely correct... yes the children should be able to use long multiplication as per Gove’s ideals for the curriculum by the end of Key Stage 2 assessments, but that does not mean they should not be taught other methods that specifically aid understanding.

    Imagine how many other children haven’t the understanding that 27 x 43 literally can mean 43 + 43 + 43 + ... + 43 twenty seven times, (or 27 lots of 43). Which also means it can be 43 + 43 + 43 + ... + 43 twenty times and then another seven times after that. Without this understanding, most children do not really ‘get’ what the long multiplication method is actually doing. Sure, many of them can ‘do’ it, but the underlying understanding is just not there.

    If your child can ‘do’ both methods (grid and long multiplication) perhaps get them to show you how the part products on the grid method relate to the steps in the long multiplication. If they can explain this, then perhaps they also understand the underlying structure of the long multiplication too. In which case, that’s brilliant, and they’re exactly where they need to be.

    if not, continue asking them to use grid (as her school is advising) and do long multiplication alongside it pointing out how they are the same, and how they are different.

    As for feeling frustrated as a parent (if you do), try not to feel like you are alone in this thought. Grid method was not taught to most of the population, and most of us therefore have that same sinking feeling when seeing it, thinking ‘What is going on here???’ It’s a completely normal and fair reaction when we see something that is effectively alien to us. But trust your children. They can show us how they understand it. Try to have an open mind, and by all means encourage them to relate those methods to all the old ways we were taught, and of course the expected end of key stage methods. The best mathematicians are the ones who can spot the differences and similarities between the methods, and explain exactly what is happening in the processes. The ones who are not the best, definitely need our encouragement and support to reach that place.

    Sadly, many schools have taken the ‘Gove’ way literally and all too often children now can ‘do’ the process but do not have a strong mathematical understanding underpinning it, and this is rather evident when they move on to much more complex maths later on.

    I hope this comment has been useful, and if not I apologise. But this is one maths expert that has spent many years trying to show teachers exactly why children really need this underpinning understanding of the structure in the number system, and sadly have been fighting against the tide as many teachers ‘just want them to get the right answer’, and therefore think 2 marks in the SATs paper is the end aim. I won’t apologise for calling them out on that.
  4. strawbs

    strawbs Established commenter

    In addition to the advice in the post above, the grid method is very useful when they move on to algebraic multiplying out brackets
    I would say from my experience, 5+ years ago vast majority of y7s used grid and had never seen long; now the other way around. I find if they can do long successfully, then great. If they can't however (and largely as mentioned above because they don't actually understand the place value behind the process) then switching to grid can be a good idea.
  5. gainly

    gainly Star commenter

    I imagine many younger teachers would have learnt the grid method when they were at school and may never have used the traditional method. They may well find it difficult to find they are suddenly expected to teach it.
  6. frustum

    frustum Star commenter

    Whether your daughter should have been allowed to ignore the grid method and continue with the standard one depends on whether she had all the understanding she needs, and also on whether she wanted to learn the grid method. (There might be an element of teachers feeling they can't help if they're unfamiliar with the method being used, but (a) she's obviously competent at it, and (b) surely teachers of lower year groups should be aware of the methods used by year 6, and be willing to learn them - they might move to year 6 next year.)

    When I was at primary school, my mum had taught me to subtract by "borrowing and paying back", but by then everyone was using decomposition. My teachers were quite happy to let me continue with the method I was using, but then other kids kept asking me for help when they got stuck, and I didn't understand what they were doing. So in the end I got another brighter kid to teach me decomposition. As I went into teaching, it was not a waste of time, either!

    (I still borrow and pay back when nobody's looking. I also inadvertently did it in front of a top set class once - they asked what I was doing and were fascinated when I explained.)
  7. afterdark

    afterdark Lead commenter

    The problem with most explanations of the grid method, they require an understanding of multiplying out 2 brackets.
    Consider the following example...and ask yourself how many of the steps did you see.

    View attachment 34472

    We miss out lots of step. But that is really the whole point, achieving shortcuts.

    Assume they know absolutely nothing and then be delighted when they do all sorts of stuff. Many times I have paused when hearing some questions but I have learnt to accept that some children arrive in secondary school not knowing why we write 1st and 2nd etc...
  8. briancant

    briancant Occasional commenter

    I like the grid method just because Gove doesn't!
  9. guinnesspuss

    guinnesspuss Star commenter

    I was taught 'borrow and pay back' and my mum taught me decomposition at home. Whilst I thought she was wrong, (obviously when you're that age teachers know all) it came in very useful when as a teacher myself the decomposition method was favoured. And yes, I prefer 'borrow pay back' too.
    frustum likes this.
  10. gainly

    gainly Star commenter

    I just came across this, the late great Tom Lehrer (The Elements, Poisoning Pigeons in the Park) on new methods of subtraction in the 1960's.


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