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While one answer is correct, the other three distractors will be carefully planned to show a specific misconception. 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 So far everything that has happened before is not new to us. Now we have a brand new step. To understand what happens we need to activate our knowledge of place value. The first digit in the multiplier is in the ones and it is worth one. Two lessons from cognitive science have massively changed the way I approach teaching the long multiplication method. 1. Long and short term memory 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.

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.’ That will leave us with the finished product of: Step 4 – Repeated examples of long multiplication method In the maths national curriculum for England, the formal long multiplication method is mentioned in both in Year 5 and Year 6. 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.Long multiplication is a written multiplication method used when multiplying two or three digit numbers by another number of two or more digits. It is often referred to as column multiplication. 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. 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. An example of the one I would use in this lesson is below. Long multiplication diagnostic question example

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.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 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. 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? Here is the long multiplication method broken down step by step using the second example from the national curriculum appendix: How to do long multiplication step by step Example: 124 x 26 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.

From the model, we can see that the person uses their attention to take things from the environment into the working memory. The person then attempts to encode this information into their long-term memory, but some information may be forgotten for a myriad of reasons. 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 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. 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.The appendix at the end of the year group objectives gives us an insight into what this looks like: How does this help us teach the long multiplication method? Well let’s be clear about something first. But this is missing out a crucial stage of learning – moving from a procedural to a conceptual understanding of what’s going on.