Next, I would call upon all pupils to solve the multiplication, again showing me on their fingers or mini-whiteboards to ensure participation. This significantly reduces the cognitive load on and helps free up all their working memory to learn the procedure of long multiplication. Of course, these pupils will still have to learn their multiplication facts but this just helps break down those barriers and helps them become successful. Now we are onto the new piece of information we want pupils to learn, so I would slow down and explain what is happening here, using this moment again to reinforce place value.

In this step, pupils will be called on to give answers and the whole class can mark as they hear the answer. If some of them disagree with an answer we can discuss it as a class until the correct answer is found. Step 8 – Diagnostic questions

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This makes sense as if they are fluent in these areas, they are effectively reducing what their working memory needs to attend to. Assuming fluency in these two things, what they need to learn is reduced from 16 to 4-6 things. As this happens, I would be circulating the room to gauge how pupils are doing – not only on the questions from this lesson but previous content too. Pupils are free to skip over questions that they are not sure of. Step 7 – Shared marking The rest of this article explains how to teach long multiplication to develop a conceptual understanding, which will have the biggest impact for your class. It includes links to multiplication worksheetsto provide you with lots of practice. How cognitive science has affected my teaching of long multiplication

During this next part of the lesson, I would show an example of the type of question they would be expected to answer by the end of the unit – in this case, it would be a 4 by 2-digit multiplication with any digit using the long multiplication method. This is an important point for teachers to recognise: it’s not that one child has an innate ability to do long multiplication and one child does not. It’s that one child has simply retained the crucial knowledge needed to be successful and therefore can make the connection to prior knowledge to drastically reduce what they need to actively work out. Slightly more manageable as an option for birders is the retro-looking Celestron Up Close G2 10-30x50 binocular, though it’s still heavy compared with what we have here due to that extra zoom power and larger objective lens. If weight is an issue, a zoom monocular is another alternative. Here Nikon’s arch-rival Canon provides one in its PowerShot Zoom Monocular, on which a minimum 100mm focus setting is adjustable to a 800mm equivalent. It can even capture stills and videos to microSD card too, though requires a battery to power it. I would then show them another example. This time, the example would be with 11 as the multiplier – this would be on the same slide as the previous example. The second digit is in the tens place so it is worth 10. This means we have 10 multiplied by 3. To show that we are multiplying by 10, we can place a zero in the ones place to act as a place holder.”This nicely sets out a progression model for teachers once the class are comfortable with multiplying 3 or 4-digit numbers by a 1-digit number. Long multiplication questions in SATs My next instruction to the class would be: ‘For the starter, we looked at examples where the multiplier was a one-digit number. That number would be in the ‘ones’ place value. So with the number that is in the ‘ones’ in this 2-digit number, we do exactly the same.’ Two lessons from cognitive science have massively changed the way I approach teaching the long multiplication method. 1. Long and short term memory To ensure everyone is participating, I would ask them to show me, using fingers or mini-whiteboards, the answer to the multiplication questions – not because I think they don’t know it but to keep their working memory firmly on the maths at hand.

I would then provide two long multiplication questions that I would ask pupils to complete independently. During this time, I will observe and support as required. How does this help us teach the long multiplication method? Well let’s be clear about something first. Fluency is the process of retrieving information from out of long-term memory with no effort on our working memory, freeing up valuable space in our working memory to give attention to other things.’ Read more: Fluency, Reasoning and Problem Solving What is the long multiplication method?Not sure if your pupils are ready to jump into long multiplication? Grid method multiplication is a great ‘stepping stone’ to the column method. Long multiplication in the national curriculum That’s a total of 16 steps that children need to become fluent in to get to the final answer. Bearing in mind the limits of our working memory, this is a lot to take on and can quite easily overwhelm it. This will prevent this information from being encoded.

You may also like: 35 times tables games suitable for home and school – choose one or two each week for home learning if your pupils still need to build consistency. Read more: Commutative property of multiplication How to make long multiplication easier When revising for SATs, you may want to interleave long multiplicationproblems with long division problems to further reinforce the relationship between the two. The step-by-step process to solve the problem is the same as the example above but we have dramatically cut down the strain on working memory. If a child is not secure in their multiplication facts, then you need to stage an intervention to get them up to speed. Contrary to popular opinion, learning multiplication facts is important, and while you may be able to teach times tables for instant recall at earlier ages, by upper KS2 it’s very difficult to find the time. As their confidence grows and the process is embedded further, the multiplier can be changed and reasoning and problem solving questions can be introduced and answered with greater independence. Long multiplication examples

Therefore, it is crucial that pupils become fluent in the method. When I say fluent, this is what I mean: Happy that pupils are able to copy the process and understand it, I would now provide a long multiplication worksheet for them to complete. In the Year 6 objectives for multiplication and division, it says that, ‘pupils should be multiply multi-digit numbers up to 4 digits by a two-digit whole number using the formal written method of long multiplication.’