Let's see what you have learnt about factors and products

A product is

A factor is

6 is a factor of 24

21 is the product of 7 and 4

Which of these is NOT a factor of 20?

Using factors and products to solve division problems

﻿Hello mathematicians, my name is Miss Brinkworth. I'm going to be going through this lesson with you today, which is a consolidation lesson which means we're going to be looking at a lot of the learning you've already done on multiplication and division. And we're going to be pulling it together and having a bit of practise today. So hopefully today's lesson won't include too much new learning, but will be a chance for you to revise some of the things that you're hopefully feeling quite confident on. But feel free to spend longer on parts of the lesson that you feel like you need a little bit more help on. So let's get started by looking at the agenda. We're going to be focusing quite a lot on our three and four times tables today. We are then going to have a think about how we represent those differently with arrays and bar models and how those are tools that can help us work out the answer to questions. We're going to have a go at looking at some of those ideas of commutativity which is that multiplication can be done in either order, and that inverse operation so that relationship between multiplication and division. And then finally, you will have a chance to do independent work and have a knowledge... an exit quiz at the end just to see how much of this is revision for you. Okay, so all you need is pen or pencil, paper, and a big smile. So take as long as you need to get your equipment and come back when you're ready. Welcome back. Let's get started. Okay, so here is your warm up. All you need to do is answer these questions. Some of them have got the information missing within the calculation. So for some of those, you need to work out what are those fact families? What is the relationship between those numbers to find that Missing calculation. So take as long as you need and come back for the answer shortly. Well done. Let's see how you got on. Don't worry if you made some mistakes, but do have a think about the questions that you've got wrong because maybe there's a times table there Or maybe that's going to highlight a question that you're not feeling quite so confident with and that should give you the opportunity to just maybe practise those. There were times tables that we all find a little trickier than others. And certain questions even within times tables that we are confident with, there are some that are easier than others. So if there are some that you're getting wrong, just take that as an opportunity to practise ones that maybe you're not feeling quite so confident about. So, two times something equals 12. What does two times something equal 12. Well, hopefully you can see that the missing number there is six, two times six is 12. Something times by six is 18. Or you could use the last question to help you because 12 add six is 18. And if two sixes were 12, then it must be three sixes are 18. Five times five, five lots of five are 25, and 10 needs to be times by eight to get 80. Four times by six, twenty four. And three times by seven is 21. Nine times by two is 18. Four times by 11 is 44. Really, really well done. If you've got all of those right. You're feeling very confident with your times tables, which is wonderful. Now, the rest of the questions, move on to division questions. But, hopefully, if you got these right, you were utilising, you were using all of your times table knowledge to help you. We've just switch the question around a little. So for 40 divided by 10. Again, we're looking at that relationship. What is the relationship between 40 and 10? You can see it as what have I done to 10 to get 40? What happens if I make 40 ten times smaller? What number is missing If I think about 40 in the 10 times table? well, it's four times by 10 is 40. So 40 divided by 10 is four. 14 divided by seven... sorry divided by two is seven. 12 divided by four is three, and 16 divided by eight is two. 10 divided by two... ten divided by five is two, Nine divided by three is three. 30 divided by 10 is three, and 32 divided by four is eight. If you've got all of those, right, that is a fantastic start to the lesson. And hopefully, lots of what we go through now will just be revision. If you've got quite a lot of those wrong, or if you missed a lot out, or if you found them very hard, today's lesson is going to really help you. So let's get going. So, here's our three times table. You can see from that bead string at the bottom, that what we do is we go in jumps of three. And I've given you the first part of your three times table there three, six, nine, 12, 15 takes us up to five times three. What patterns do you notice when you look at that first part of your three times table? Obviously, we're adding three each time. But have you noticed that your three times table goes, even odd, even odd. So, three is odd and six is even and nine is odd and 12 is even. There are patterns that come up in all of our times tables and if we recognise those it can make it easier to work out. So if 15 is an odd number the next answer must be even. So if I got an odd number, that would be a way of working out that I was wrong. So six times three is 18 and seven times three is 21. For some reason, I always remembered seven times three, I don't know if I think of it as three times seven, but that's one that always sticks with me. And that allows me to think about the other ones that fit around it because I always remember seven times three is 21. That helps me with eight times three because I can take 21 and quickly add three on in my head, because 21 add three is easy. It's one add three is four, so 21 add three is 24. I then obviously just need to add another one for my nines. But some people feel quite confident with their nines. So you might want to think about one of the other way around, because we only need to count three of your nines. So you could go nine, 18 ,27 rather than counting nine threes. 10s again, a number that people... timetable that people often feel quite confident with. 10 times three is 30. 11s people usually feel quite confident with as well, they like the pattern of their 11 times table. And that's because 11 times three is 33 and then we just need to add one more three on to get to 36. So there is your three times table all the way up to 12 times three. I bet there are some that you feel very confident with answering straightaway every time and there might be others there, that you maybe don't feel quite so confident with. Often they come around 6, 7, 8, 9. So if you'd like to, please feel confident to pause the video and just have a little practise with those that could mean writing them out, writing them out in different orders, saying them out loud. But if you're ready, we will move on. And the next question is about applying that three times tables. So, here's a question for you. What can you see? How many eggs are there? Well, I'll give you a little clue. Because there are five nests. And there are three eggs in each nest. So pause the video and let me know how many eggs you think that are in total. Let's see how you did. So there were five nests with three eggs in each. So it's five times three. And if know your three times table quite well, you know that five times three is 15. Really, really well done. Okay. So let's move on to our fours. This bead string here this time is going in jumps of four for the start of our four times table. And there again, I've given you the start of the four times table all the way up to six times four. Unlike our threes, all of the answers in our four times table are even. That means they can be evenly split in half. So if you find an odd number when you're answering a four times table question you probably need to have another look at it and check whether you've made a mistake. So we've gone all the way up to 24 there. I know five times four very confidently, and I used that as a bit of an anchor to help me with the others. So for example, if someone asked me what six times four is probably quite quickly in my head, I think about what five times four is. Five times four is 20 and I add another four on. Seven times four. Well, I mentioned just before that I find three times seven, a fact that sticks with me. Three times seven is 21. So I only need to add another seven to 21. One, add seven is eight. So 21 add seven is 28. And that's a way of remembering that one. Eight times four is 32, and nine fours, again some people find their nines quite easy. 9, 18, 27, 36. We then get on to the 10s and the 11s, which a lot of people feel a bit more confident with. 40 and 44. And then for the 12 we just need to add four more on to the 11. So 44 becomes 48. Again have a look at those timetables and think about which ones you feel quite comfortable with and which ones maybe wouldn't be right there as soon as somebody asked you. If you'd like to pause the video and have a go at practising some that you're a little bit less confident with, please do. And like I say that could be just writing them out over and over again, it could be saying them, or it could be asking someone to just just test you quickly. But if you're ready, we can move on to another picture problem. So this is another problem involving our times tables. So something times four. How many groups of four are they there? And what's the answer going to be? Pause the video and see if you can work it out. Okay, so if we count those parts, we've got 1, 2, 3, 4, 5, 6 parts and then each got four in. So the question must be, six times four. What's six times four? Well, I know five times four is 20. I add one more four on, gives me 24. Well done if you got that one right everybody. Okay. We're going to talk a little bit about bar arrays and bar models here because these can really help us remember what we mean by multiplication. So here we have an array and a bar model showing exactly the same thing. The same question. We have groups of three. Can you see that we've got three dots in a row? And then we've got, how many rows? We've got five. So this array is showing three, lots of five or five lots of three, whichever way you want to look at that. What are these arrays showing? I wonder if you can write for me two multiplication questions for each one? Pause the video and have a go at them. Let's see how you got on. So Oh, I said multiplication questions but here there are division questions as well. So don't worry if you didn't find a division question, but let's go through them anyway. It also says four when clearly there's five here so let's go through what it actually says on those arrays. We've got five times three, haven't we? So if you put five times three is 15. Brilliant. If you put three times five is 15. Fantastic. And if for some reason you did a division question even though I didn't ask you to 15 divided by five is three, and 15 divided by three is five. And here are some questions which those do not answer. Okay. So here's another bar model. This time, can you have a go at writing out two multiplication and two division questions that this bar model shows. Okay, let's see how you got them. So we can see that the groups each represent four, how many groups of four are there? There are six. We've got six groups of four, six times by four is 24. 24 divided by six is four. And then we can do those in the other order as well. And if you've got all four of those, that is fantastic work. It shows you really understand what multiplication and division... the relationship between the two. That's wonderful work. Well done. So just to recap, that when we're talking about multiplication, when we have a multiplication question, we've been given the parts, and we're looking for the whole. So if you look at this bar model here, we know that each part has got three in them and we know that there are four parts. So that multiplication will be three times four. We're looking for the whole. Whereas if we have that same bar model, but for a division question, what we're being given at the start is the whole and we're being asked what happens when we split it up? How many parts will there be and how many will there be in each part? So this division question would be 12 divided by four equals three. Okay. Can you have a go at this. Here is a multiplication fact. I'd like you to tell me using that fact, What else... what other facts you can calculate from it? I'm going to come up with some that are probably different to yours. But come up with as many facts as you can using that information. Okay, how did you get on? So here are some of the facts that I came up with. And you can move for an eight round so that its eight times four equals 32 and then you can do the two division from that as well. If you got those three, fantastic. Really, really good work. Especially the division questions, making sure that 32 moves its way to the front of the calculation for a division question. Okay. Then we can think a little bit broader and we might want to think about making one of our numbers 10 times bigger. So if make for 10 times bigger, we've got 40. 40 times by eight is 320. So 32 has also become 10 times bigger. Also these two, we might want to think about the question either side of the one were being asked. So if we know what four times eight is, it's easy for us to work out what five times eight is. And if we know what four times eight is, it might be easy for us to work out what four times nine is. So from one piece of multiplication knowledge, we can pull out a lot of different facts. Okay. Inverse. So here we're talking about the relationship between multiplication and division. So if you see a multiplication question, can you move the numbers around into the right order for a division question? And if you see a division have a go a on multiplication, please. How did you do? Now you might have these in a different order. So you might have six divided by three is two, that's absolutely fine. And you might have... for this one there's only that order, there's only four times four is 16. So it's got to be that one. But this one, as long as you've got 50 at the start, that's fine but you might have 50 divided by five is 10 or you might have 50 divided by 10 is five. And here you might have two times by four is eight which is also fine. Really good work. Okay. Time for you to complete your independent task. So pause the video here and when you're ready, come back for the answers. Okay, welcome back. I hope you enjoyed your independent task. Let's go through the answers together. If four children... all get given six stars for their wonderful math work how many is that in total? Well, it's four times six is 24. Eight groups of three book to go to the cinema, how many go in total? Well, eight times three is 24, as well. So we have two factor pairs of 24 there. 44 seeds are shared equally between 11 pots, how many seeds are put into each pot? There were four. Well done if you've got that one right. Okay. Which of these calculations does this array not show? I think that was quite an easy question, because we've got an addition question there and it's just good to remind ourselves that five add three is not the same as five times by three. Okay. And here again, you've got a division calculation that you need to write for these fact families. So turning multiplication questions into division questions using the same numbers. So those large whole numbers that are the answers in the multiplication need to come to the start for our division questions. So you can have these in slightly different orders as well, you can swap around the last two numbers. So you can have 20 divided by five is four, you can have 20 divided by four is five, and for the others you could move those around as well. Hey, if you'd like to share your work with us today, that would be wonderful. Please ask a parent or carer, to share your work on Instagram, Facebook or Twitter, tagging @OakNational and #LearnwithOak. And just time for a final knowledge quiz before you go just to see how much of that learning is gone in today. Lots and lots to take in there. So well done everybody. Enjoy the rest of your day. Bye bye.

Let's see what you have learnt today about multiplication and division

What calculation could this array show?

What is the inverse calculation for 12 ÷ 2 = 6

What calculation could this bar-model show?

12 x ? = 48

27 glue-sticks were shared equally between 3 classes. How many glue-sticks did each class get?

Consolidating multiplication and division knowledge

In this lesson, we will revisit arrays and bar models as ways of representing multiplication, as well as solving questions involving inverse operations and commutativity.

Maths

Y3 Maths

Key Stage 2

Year 3

Consolidating multiplication and division knowledge (Part 1)

Multiplication and division

Number

THEME

UNIT

Recalling the 3 times table

Recalling the 4 times table

Using arrays to represent the 3 and 4 times tables

Understanding multiplication can be completed in any order

Using bar models to represent known times tables

Understanding that multiplication and division are inverse operations

Using the inverse operation to find missing numbers

Recalling multiplication and division facts

Solving correspondence problems

Using doubles to multiply

Using ten times greater for known times tables

Using bar models to represent word problems

Consolidating multiplication and division knowledge (Part 2)

Which one of these is not a multiple of 3?

What does this array show?

What could be the question this bar model is showing?

The inverse of 3 x 4 =  is

I have 30 sweets to share with my friends. I have 5 friends. How many sweets will each of them get?

To solve 11 x 6 I can use

Which times-table can we double to find our 12s?

Which of these factor pairs makes the product 48?

Lesson overview:Consolidating multiplication and division knowledge (Part 1)

Core Content

Multiplication and division: