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.

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.” Once they have noticed that there is a double digit number as the multiplier, I would then solve this silently at a normal pace – the reason for this is to show how effortless it can be and to give them the confidence that this is something that they do not need to struggle with.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 Diagnostic questions and diagnostic assessment in general is an incredibly effective way to gauge pupils’ understanding of a concept. They work by posing a question and giving 4 possible answers. That will leave us with the finished product of: Step 4 – Repeated examples of long multiplication method

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. 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. Where possible, make the content relatable to what has been taught; for example, as I have taught multiplication, I would have some division questions from the previous year’s objectives in there to reinforce that division is the inverse of multiplication. 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 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.

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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.’ 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.

Hopefully the gradual progressive structure of the lesson – or it may be two or three, depending on your class – shows how the long multiplication method can be taught with confidence and learnt by most Year 5s and Year 6s.My outcome for the first lesson or two will be to give my pupils confidence in learning the method. Only then will we move on to the rest. How to teach the long multiplication method Essential precursor multiplication knowledge 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.

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/ 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. 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 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

In the maths national curriculum for England, the formal long multiplication method is mentioned in both in Year 5 and Year 6. In previous blogs, I have mentioned being aware of learning vs performing and this is no different. Despite hearing pupils give really articulate answers during step 2 or getting both questions right in step 3, I am still very much aware that although these pupils are performing well, nothing has changed in their long-term memory as they are merely repeating what has been shown to them. 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 multiplier is how many groups of these you need; how many times you’re going to multiply the multiplicand by.