This content was created by Rob Langman. This content was uploaded by Rob Langman. This is a YouTube video titled "Greater Depth in Division" (created 2024-04-04) featuring a single presenter, Zoe, delivering an instructional maths lesson aimed at upper Key Stage 2 pupils/teachers. The video works through division problems to develop number sense and fluency: deriving unknown division facts from known multiplication facts (e.g., using 8×6=48 to reason about 96÷8 and 96÷6 via doubling and commutativity) and a two-step word problem about bicycle hire (£2.50 per hour plus a £10 fee) used to highlight order of operations/BIDMAS and the need for brackets. The content is explanatory teaching material focused on reasoning and justification.
Chapters
Hi, I'm Zoe and in this video we're going to look at some problems at greater depth with division. In these, we're hoping that we can see our pupils number sense and the fluency around multiplication and division and knowing about the order of operations. Here's our first problem. We're given a known fact, 8 times 6 is 48. And we're asked to derive unknown facts. 96 divided by 8 and 96 divided by 6. Hopefully their number sense is really strong. We know that 8 times 6 makes 48 can be reversed and we can look at the divisions. So hopefully they will realise that 48 divided by 8 is 6 and 48 divided by 6 is 8. That's the first step. They need to have the fluency to be able to turn these around. Now we're hoping the next thing that they can do is that they can spot that 48 is linked to 96. Hopefully without too much support they can spot its double. So alongside that then we can double the left hand side to be equal to double the right hand side. So 2 lots of 8 times 6 is the same as 2 lots of 48, which gives us our 96. Knowing about the commutativity of multiplication, we can now link these together. So 2 times 8, 16 times 6 must give us 96. And linking the 2 with the 68 times 12 is also 96. By having this fluency, we can now see we've got the answers to our problem. How many eights make 96? 12 of them and how many sixes make 96? That answer there is 16. So again, number sense really important here. They can relate multiplication and division and use known facts for unknown ones. This is a really good practice tool, nice for pupils who aren't working at greater depth to have a real chance to explore this. Our second problem. Again a two step worded problem. We're aiming here at upper key stage two. Bicycle hire costs £2.50 per hour plus a £10 hiring fee. Jo has £20 and says she can work out how many hours she can hire the bike for by using this calculation. Is she right? Explain your answer. Again we're asked to justify explain. Pupils have really got to have a sound understanding now. At first glance, this calculation does not appear wrong. What we're going to do, we're going to take away the £10 hiring fee first of all and then we're going to see how many lots of £2.50 go into what's left. However, this is where the order of operations becomes really crucial. Hopefully pupils are aware of bid mass and the fact that we need to be doing the division first before the subtraction. Again, we can either separate this calculation out, we need to do the first bit 20, take away 10 first and then divide what's left, the 10 pound, by £2.50 to get our four hours, or pupils have to realise that because we want to do our subtraction first, we're going to need to put brackets around there. Hopefully, with their number sense, they'll be able to do this. And these problems are really crucial for that, explaining why they've done it and what it is that's wrong. And there we have some of our problems working at greater depth for division.
