Important to note is that the space in our working memory is limited, many researchers put it at between 4 or 7 items. Oliver Caviglioli has graciously sketched a wonderful poster that show this process. From https://www.olicav.com/#/diagrams/ A child who is not secure in multiplication is likely to use so much of their working memory on solving the multiplication part of the question that all the other steps, as we saw in the model earlier, are forgotten. 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 Next, I would call upon all pupils to solve the multiplication, again showing me on their fingers or mini-whiteboards to ensure participation. Therefore, it is crucial that pupils become fluent in the method. When I say fluent, this is what I mean:

I would then ask: ‘Thumbs up for yes, thumbs down for no. Has the way I have set out the calculation in the column method changed when the multiplier has two digits?” 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. It has been my experience that pupils who are fluent in their multiplication tables have an easier time working with larger numbers, such as 3 or 4 digit by 1-digit multiplication. 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 No matter what pupils’ starting point is, there are still things we can do in the classroom to help them all get to grips with the procedure of long multiplication. As I mentioned earlier, my aim for the first couple of lessons is to build confidence in the method.While one answer is correct, the other three distractors will be carefully planned to show a specific misconception. Finally, I would ask pupils to look at the other worked example on the board and to tell their partner what the final step would be –the addition of the two products. The class would do this with me, showing the answers with their fingers or on mini-whiteboards.

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.” If you need more long multiplication examples, Third Space Learning’s White Rose lesson slides and worksheets for Year 6 Four Operations gives you more opportunities to work through the stages step by step. In the Year 5 objectives for multiplication and division, it states that ‘pupils should be taught to multiply numbers up to 4 digits by a one- or two-digit number using a formal written method, including long multiplication for two-digit numbers.’ 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 easierNow 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. That will leave us with the finished product of: Step 4 – Repeated examples of long multiplication method The last multiplication question would also have a different multiplier than 11 to see if pupils could apply the process when the demand on working memory is greater. How does this help us teach the long multiplication method? Well let’s be clear about something first.

The formal long multiplication method is a step by step method of supporting children to understand conceptually and practically how to multiply one three or four digit number by another two digit number or greater. The long multiplication method step by step 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. 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.’ The other lesson from cognitive science that has impacted my teaching has been the role of cognitive load theory in the classroom. Cognitive load theory attempts to explain why it is that we fail to encode new information from our working memory into our long-term memory.As you go through each example, get the pupils to do more of the explaining, particularly when it comes to the dropping of the zero and reminding one another to add the two products together. If you find children struggling, stop and rehearse this to ensure the correct language is being embedded.

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 The multiplier is how many groups of these you need; how many times you’re going to multiply the multiplicand by. When doing this in lessons, I assign each letter a number so A=1, B=2, etc. which corresponds with the number of fingers I want them to hold up. I then give the command ‘think’. Pupils will think about what the correct answer is. Pupils’ responses to these questions will help plan future interventions. In my experience, I have not come across many pupils whose prior attainment means they cannot set out the column method of multiplication correctly. 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 makes it far more likely that the procedure will be remembered, as pupils can focus all their attention on understanding the procedure and not on the multiplication. Again, I would like to stress that the purpose of this is so pupils can get to grips with the procedure so it can be internalised. Step 1 – Establishing prior multiplication knowledge It is worth repeating again that the main aims for the first lesson are to build pupil confidence and begin to learn this method of multiplication.