Long Multiplication and Long Division
So you’ve finally tackled the tables and the children are ready for the hard stuff – long multiplication and long division. I love when I say this on courses as you can hear the loudest groans of all. For some reason, nobody likes long multiplication or long division except me! I love them so much that I have 4 ways to do long multiplication and 2 ways to do long division – (I have a third way to do long division but it is so confusing I won’t burden you or your classes with it here!)
Using an IWB to present information is one of the worst ways to use an Interactive Whiteboard. You don’t even need the IWB to present – a projector will do the trick just as well – simply pre-prepare your slides and off you go. However, sometimes there isn’t really any other way to teach something and long multiplication and long division are two of those times. The only thing the IWB can add to the experience of teaching these topics is a nicer visual representation.
In this article I’m going to show you the four ways I teach long multiplication to the children in my class. Weirdly enough, almost all seem to revert back to the model we are used to, despite two of the methods being much easier.
We’ll start off with the traditional method of doing long multiplication. We’re going to use the interactive whiteboard to model a step-by-step approach, for the inevitable “I’m stuck – where are you stuck – I’m just stuck” dialogue. Using the duplication tool that every software has, we can build up the story of long multiplication simply by copying the previous slide and performing one more step. Let’s see an example: 23 x 47
As you can see, we have changed colours of important pieces of the picture – for example, the zero to show we are multiplying by 40 (not 4). We can now help a child pinpoint the exact stage where they get stuck and we can work with them from there. One might argue that one could do this without an Interactive Whiteboard but, right now in the early days of the IWB, would you get the same motivation from the child?
Moving on to some of the other methods I love. I’m going to show you the easiest way in my opinion to do long multiplication and it’s called the box method. On an IWB, it’s a way of introducing the idea of grids. The screencast below will show you how to set up an interesting looking grid and then we’ll go through 23 x 47. We’ll follow that up with another example and discuss how this can then be used with children interacting.
So, children can choose the variables for the puzzle. This is a nice fun way to do long multiplication and children (especially ones who have had the first method hammered into them) nearly feel hard done by for not seeing this first! Some of them feel too guilty to use this method as if it’s cheating!
Still using the grid, I’m going to show you a third method called Napier’s method. Although this might seem confusing at first, watch the screencast a couple of times and you’ll see that this is a really easy way of solving long multiplication. Using the IWB, again we’re showing how to use grids, but also showing the dotted line, which is a useful tool. This can be used with children in a similar way to the box method and it provides great amazement to everyone who sees it the first time. I remember not trusting it at all the first few times!
The final way I teach long multiplication is the Russian Method, another ingenious way of solving long multiplication problems. It’s also probably the most difficult of the methods. To be honest, there’s no real benefit to doing this on an interactive whiteboard. Instead I’ll just indulge my own geeky leanings and explain how it works in the video cast below.
Funnily enough, unless you happen to love multiplying and dividing by two, this method takes longer than all the rest. I think it’s about time we moved to division!
Long division sends shivers down everyone’s spines because it’s the only part of the primary school maths curriculum where there is really no way of explaining each step in a mathematical way. It’s the only time one has to teach a method to solve the problem without any really good reason behind each step. The IWB doesn’t really offer anything amazing to open up the mysteries behind long division. Like the traditional method of solving long multiplication, we can design any long division puzzle in a step-by-step manner so we can pinpoint the “I’m stuck” moment. A possible fun thing is to make the DMSB (Division, multiplication, subtraction, bring down) order a more graphical experience. For example, one child I had in support loved football so DMSB translated to Does Messi Support Barcelona? So in tribute to that, have a look at the videocast below to see how we spiced up Long Division Messi Style.
For children who just don’t get Long Division and need an easier (but longer) way of doing things, there is a second way of doing it – it’s a variation of the repeated subtraction method that children are introduced to in third and fourth class. Again, the IWB isn’t the greatest tool for showing this, but the added splash of colour might inspire some children to “wanting” to grasp the concept.
So there you have it – the most ineffiective way to use Interactive Whiteboards (apart from showing PowerPoints) – but sometimes I must concede it’s excusable. Perhaps someone a lot more inventive than me will create a really cool interactive way to help children learn the concepts of Long Multiplication and Division without the need for a teacher.