Help! Long Multiplication

So it turns out that I’m not 100% sure how to do long multiplication. I really should be, you probably are. Please help.

I want to make a resource that will support children doing long multiplication so but first I want to make sure I’ve got my method straight. Here’s the issue: when you are multiplying by the tens value in a 2-digit number, where are you supposed to position the digit being carried? Here, I’ve done 80×3=240 and have put down 40. Where should the 2 hundreds go?

multiplication-which

A shows where the 2 hundreds will be added to (but it could make the calculation messy). B shows the 2 above the hundreds column, the column that it will be added to (but two places along from the 3 we’ve just multiplied by). puts the 2 above the next number to be multiplied, but in the same column as the 4 tens.

The example on the national curriculum (below) somewhat ducks the issue in that there are no carries from the 20, and the examples in the mark scheme for the 2016 SATS don’t show the position of carried digits.
nc-multiplication

I inferred from this it’s up to schools to decide which way is best. Is there a ‘right’ way? What do you do? I’d love to know. Just to repeat, this isn’t me trying to make a point, rather I’m in the process of designing a resource that will model this calculation process, but I want to do it right. I’d love to know what you think, or from any ‘higher power’ if they can give a definitive stance.

All input welcome!

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8 thoughts on “Help! Long Multiplication”

  1. I teach A but some pupils do B or C depending on what their parents were taught. If the carry over is in smaller writing I think A reminds pupils that they need to add that amount when carrying out the addition stage.

  2. Our calc policy (Sense of Number) uses the image in A. the posters we use have each column and the number that is exchanged and regrouped in the same colour as its original column.

    The children cope with it ok.

    Donna

    ________________________________

  3. We teach to leave a space ( or row of squares ) underneath the x26 then draw your line, the carry then goes above this space, makes sense as it is not left out when adding it on. We also multiply by then tens first to coincide with the teachings of add the largest number first, this can also eliminate the forgetfulness of placing the zero since it’s easier to forget if you have multiplied by the units first. So with all these logical methods you would think the lessons go pretty smoothly? Nah, not on your nelly! 👩

  4. A is the closest to what I do personally and also how I teach it. I would put the 2 down ‘below’ the second row of answers, not up under the 8.

  5. I teach A but written below the tens multiplication line. Maybe you need option buttons to click on for your schools preferred method.

  6. Hi Gareth we had this discussion about 18 months ago in my school and although myself and the DH were taught C we decided to go with A because we felt that it gets too crowded doing C if you were calculating HTU x HTU and had to carry for the tens and hundreds. I advise the children to put a line through the carried digit once added to ensure it doesn’t get used in the final addition. I am one of the Cohort 2 Mastery specialists for London North East Maths Hub and am attending my second NCETM training residential a week tomorrow so will ask Debbie Morgan or Pete Griffin of the NCETM their views . I’ll let you know.
    Regards
    Ian Connor

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