Resourceaholic: Easy Multiples

In 2018 I made a decision to produce a series of short posts about strategies or methods that instructors could possibly not have seen right before. When I share these posts, I am well conscious that there will be lots of folks who currently know the issue I’m blogging about, but I figured that it is really continue to value sharing even if it is only new to a handful of people. My very first write-up in this series was about using vectors for enlargements and my next post was about factorising by inspection. I then got seriously active composing my book, and failed to include to this blog post sequence for 4 several years! Oops. So nowadays I am relaunching the series with a extremely straightforward small ‘trick’ (not a trick at all, just maths).

My Calendar year 6 daughter has just lately learnt long division. To be crystal clear on what I am referring to, extended division looks like this:

While ‘short division’ seems to be like this (this is in some cases colloquially referred to as a ‘bus cease method’):

The only big difference in between the two techniques is that in limited division we operate out the remainders in our head and jot them down in the dividend, but in very long division we do the job out the remainders on paper in a far more structured format. If your divisor is larger than twelve (for case in point if you are dividing by 28) then it may possibly be tricky to operate out remainders in your head, so that is usually when the long division structure could be desired. But they are effectively the same approach, just with a a little bit various structure for processing the calculations.

It was humorous to see my daughter understanding prolonged division as it’s a thing that I actually never ever teach in secondary college. I was pleased with myself for remembering how it performs. For several pupils it exists in Calendar year 6 alone, under no circumstances to be found once more. A regular Critical Phase 2 SATs problem could look like this:

But a thing like this is extremely unlikely to appear up at GCSE. Students do at times have to do divisions by hand in their non-calculator GCSE examination (an example is demonstrated under, from the Foundation tier), but I imagine most learners would opt for to use short division.

Some individuals argue that the extended division algorithm is applied yet again when students learn algebraic division in Yr 12. This may well have been the situation ten yrs in the past, but I assume that most(?) A amount teachers now want far more intuitive strategies of polynomial division, like the factor technique shown below for case in point. 

So for the most portion, extended division resides exclusively in Yr 6. And my daughter, who is in the ‘middle’ group for maths, was coping great with it, but she advised me that she finds it tough to create out the multiples at the commence. For example when she’s dividing by 28, she’s been informed to start off by creating out some multiples of 28. She finds this time-consuming, a bit tough, and somewhat uninteresting.

But don’t stress, due to the fact you can find a definitely easy way to generate out the multiples of 28. My colleague Sian showed me this – she picked it up a few years back from her daughter’s 12 months 6 trainer. I confirmed my daughter, who beloved it – she was then able to master long division as she’d located a way round the challenging bit.

To quickly and effortlessly generate out the multiples of 28, just publish the multiples of 20 and the multiples of 8 and incorporate them alongside one another:

As extended as the baby understands their common occasions tables relatively properly, listing the two sets of multiples is uncomplicated. And the addition is very easy also, as they are often incorporating to a various of 10.

Here is an additional case in point: multiples of 17.

This may now be actually broadly made use of by Year 6 academics. But in scenario anyone hadn’t thought about this tremendous very simple way of listing multiples, I assumed it value sharing in this article. As I have constantly explained, even if it just aids 1 human being then it is really value taking the time to create about it.