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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. 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. 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.
To do that, I ensure that our first multiplier is 11. By making the second factors 11, all that is required here is to multiply by one. I have yet to come across a child, even those who may struggle with their multiplication, who doesn’t know the 1 times table. See also: Lowest common multiple, Highest common factor& What is a multiple Next, I would call upon all pupils to solve the multiplication, again showing me on their fingers or mini-whiteboards to ensure participation. 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. 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?” I would then hope to see all thumbs down. If a child has put their thumbs up, I would engage in a whole-class dialogue to see why this is the case and refer to the example that is on the board. Step 3 – Setting out the long multiplication method
The first has been understanding that we have a long-term memory that is near limitless in the information that it can store; and working memory, where we make our conscious thoughts.
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. 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. 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.”Happy that pupils are able to copy the process and understand it, I would now provide a long multiplication worksheet for them to complete. 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? 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.
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. 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 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 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.
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. The appendix at the end of the year group objectives gives us an insight into what this looks like: 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. 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
In Year 5 and Year 6 at primary school, long multiplication means multiplying a number that is at least three digits by one that is two digits or more. 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. 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.’ 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.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. 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 To differentiate the work sheet would only lead to an increase in the attainment gap. The differentiation will come from additional instruction that I may give during this time.
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