Let's see what you have learnt today about 'fact families'

The inverse of division is

If you know that 3 x 6 = 18 this can help solve

Which number is missing from this this fact family 21, 7 and ....?

What fact family could this bead string represent?

This array shows 3 x 5 = 15 and ...

Using the inverse operation to find missing numbers

﻿Hello everyone, I'm Miss Brinkworth. I'm going to be going through this multiplication math lesson with you today. So we have a look at the learning objective together. So what we're going to be focusing on is recalling multiplication and division facts. That means we're going to use some of the multiplication facts that we've become quite confident with and we're going to use those in different contexts, and we're going to practise recalling them quickly and recognising when we apply a particular factor at a certain type of question. So if we have a look at our lesson agenda, today, we are starting with arrays. That's a really, always a really good place to start when we are looking at multiplication. There are probably ways that you're used to looking at multiplications, a lovely way of representing them making it really clear what we're talking about when we're talking about multiplication. We're then going to talk about applying our known facts to find missing numbers, and that's not just at the end of an equation, that's not just after the equal sign, that could be at any point in the question. we're going to have a good look of spotting mistakes, which is a really, really good skill to have 'cause hopefully if you can spot other people's mistakes, you can support your own. And then we're going to have a go at some independent work where you get to practise your new skills and then an exit quiz to see how well today's learning has gone in. So all you're going to need is a pen or pencil, some paper, and a fantastic can do attitude. So pause the video here if you need to and go and get what you need. Wonderful, lovely to have you back. So let's get started on our Maths tight then. So here's a nice warm up for you. It's a machine, you have to start with any number you like. So I am going to, for example, start with two. You can then, times it by two times, times it by two and times it by two for the yellow, and then you do the blue, what the blue tells you to do, and then you do what the pink tells you to do at the bottom. Have a look at what number you end up with in the last yellow, blue and pink box, and have a think about why that's happened. Wonderful, well, let's have a look then. You might not have chosen two, but you will hopefully have found the same pattern I have found. So let's just look at what happens to my two. Two times by two is four and four times by two is eight, and eight times five to 16. If I then go to the blue part, two times by floor is eight and eight times two to 16. I'm sure you guess what's going to happen here. Two times eight is 16. Now, why do you think that's happened? Well, that's because these different processes, the yellow process, the blue process and the pink process have all taken me to the same answer because actually they're doing the same thing. Timesing by two, three times, we'll add timesing by four and then two and then timesing by eight will get me exactly the same answer. You know, that two, four, and eight have a very close relationship. They're the double of each other, and so this hopefully draws out some of those known facts that you have. You know that 16, eight, two, four, these appear in all of those times tables. And so what we're going to be looking at today is applying what you already know to new situations and really looking at how a question is, how we work out what the question is asking us to do. So let's move on. Like I mentioned, we're going to start by looking at arrays. So which two multiplication and division facts can we find from this array? All we have to do is count, so we can see that there are five across the top and so one of the numbers we're going for using it's five, and we've also got two down the side. So we need to think about what number we might be talking about when we've got five and two. Where does your mind go when you hear the numbers five and two? what is their relationship? What is the missing number? We know that we need three numbers in our multiplication and our division numbers, our division calculations normally, we have two parts in a whole and they just swapped places for our multiplication and our division questions. Let me show you what I mean. So for this one, for example, we've got five and two, five times two makes 10. We can swap those rounds because we know that we can do multiplication in any order, so we can do two times five is 10. For those two multiplication questions we've been given the parts, and then the answer is the whole for multiplication. You're given parts and how many are in each part, and you're asked, so how many have I got altogether? If I have five groups of two, how many have I got altogether? If I have two groups of five, how many have I got altogether? If you look at those division questions there, they're different because you start with the whole and you're asked, what if you split it up, what will you get? So we can have 10 divided by two is five and 10 divided by five is two. So if I've got 10 and I share it between five people, what part of 10 will each of those people get? Well, they'll get two. And if I've got 10 and I share it with two people, or I share 10 into two groups, how much would there be in each group? There will be five. So this you can see, it's just the one factor really. Five times by two is 10, we can use it in lots and lots of different contexts to help us with lots and lots of different kinds of questions. So here are those facts again. And can you see, I've picked them out in different colours so you can see it's just the three numbers that we use here. It's just five, two and 10. And those three numbers have a close relationship, they come up in the same times, tables as each other, and they allow us to pull out these multiplication and division facts. So let's move on. Which these is incorrect and how do you know? Pause the video for a moment and see if you can work out, which one does this array not show? Well, really well done if you could say that this question here, this calculation is not correct. If we look at it, you should see straight away that that calculation does not look correct. What is it about that calculation that doesn't look correct? Well, it's a division question but it doesn't have the whole, the larger number at the start of the question. The question is saying four divided by 12, four split between 12. Well, that doesn't sound right, does it? It's not that we can't do that but it would give us a decimal answer and it would give us an answer smaller than one, because if we've got four and we're trying to split it between 12, we haven't got, we haven't got a whole number to go around. So hopefully you can see that that was the incorrect question and well done if you got that right, but these are mistakes that people make when they're applying their times table knowledge to division questions. You cannot just put the numbers in whatever order you want. You have to think carefully about what division is all about, and it's about a whole being shared equally. So that question must be wrong because the whole is not at the start of the division question. Well done, if you could see that. Okay, so if we move on, let's have a think about which of these are true and which are false. They all have that multiplication and division relationship, and we can use our multiplication knowledge to help us with all of these questions. So the first question says 21 divided by seven is three. So to check that I would think to myself, is seven times by three 21? Is 21 and the seven times table and in the three times table? It is, so that one's correct. What about four times by three is 12, four times by three as 12, I could check in that four, eight, 12, there are three fours in 12, or I could check in my threes as well, three six, nine, 12, four threes to 12. So that one looks correct as well. What about this next one? Five divided by three is 15. Well, I know that five, three and 15 do have that relationship, but these numbers are the wrong way around. That whole, that 15, that largest number must be at the start of a division question. We must start with the big number if we're going to split it up into smaller parts, so that one's wrong. Looking at the last question as well, that one's also wrong. Can you think why? 27 times by three is nine? What is it about that question that should tell you straight away it's not right? Well, numbers get greater when we multiply them. We take a number and we make it bigger by two or three or four or five, but 27 hasn't got bigger in this question. So although again, three, nine and 27 do have that relationship, somebody here has them in the wrong order. So just be careful about that type of thing. When you're using your multiplication knowledge, you do need to think carefully about the order of the numbers come in. So your turn then. Pause the video here and have a think about which of these questions is true, which one shows the correct relationship, think carefully about parts and wholes and how those are used in division and multiplication. Some of them are wrong. See if you can find them. How did you get them? Should we have a look? Well, 30 divided by 10 is three. If I have 30 and I share it into 10 groups, well, each group gets three, that one's correct. That is the relationship between 30, 10 and three. 30 is the bigger number, the whole and it's come at the start of the division question. So we can see that that one's correct. 16 times by four is four. That one's not quite right, is it? We know that four times four makes 16, but that whole for a multiplication question, the 16 we would expect to be at the end of the question. So that one's not right. 15 divided by three is five, are five threes 15? Let me check three, six, nine, 12, 15. Yes, that one's correct. And 20 times by four is five. Four times five is 20, but it seems again that someone's got the wrong order for those ones. So well done if you could see that those questions were incorrect, really, really great. Okay, let's move on. Here are our fact families and so this is what we've been doing all the way through. We've been thinking about these three numbers where they have a strong relationship. What do you think the missing number might be on this pyramid? What do you think the number of relationship might be between 10 and 15, which is the missing number? Well, it could be two because two times five is, two times five is 10, but actually we've got 50 here. We've got 10 times five gives 50. So well done, if you could see that. And here are the facts that we can get from those three numbers. So we've got our two division questions and our two multiplication questions, and you can see that they use just those three numbers. Just those three numbers, which have that, they're in that fact family. Here's another one for you then, your turn. See if you can find the missing number and can you find the four facts to multiplication and two division facts from that fact family? Well done, not too difficult I hope. Hopefully you can see that 10 times nine is 90, and then these are the four facts that we can get from that two division and two multiplication. Okay, how can we solve these then? Some of these questions might look a bit unusual to you because the answer, the traditional sort of answer is there after the equal sign, we've got those numbers. But what we need to do is use what we know about fact families, use what we know about our times tables and think about what the missing number is. What has happened to nine, if I've got 90? What is the missing number? What times table am I looking for? 9 times something gives me 90. How many nines are there in 90? Well, I can see that that's my 10 times table. And well done if you could spot that too. Okay, 50 divided by something gives me five. So again, this is my 10 times table when nine got 10 times bigger. If these got 10 times smaller to go to five. So hopefully you could see that relationship of your 10 times table. Nine times 10 is 90, five times 10 is 50, and so the inverse of that is 50 divided by 10 gives me five. What about this on then? What's happened to 55 if I've ended up with 11? It's got smaller I can see it's a division question, but I need to think about what the question was. I could think of it as 11 times by something gives me 55. Well, what am I 11 times table? What have I done to 11 to get 55 at the start there? Well, well done if you can see that that's five. That's your five times table. And for the last one, something divided by four gives me nine. So I could take those two numbers and do the inverse, nine times four. What a nine fours or four nines if you prefer saying it that way, well done if you can see that that's 36. So what we're doing here is we're using the facts that you're comfortable with, the times tables that you've had a lot of practise with, and we've got the missing numbers in slightly different places. But it's just about pulling through that knowledge, those fact families where you have the three numbers. Where does your mind go when you see nine and 90? What's relationship between nine and 90, that sounds like the 10 times table, doesn't it? So it's about applying what you know in new context. Your turn then. Pause the video here and see if you can find out the missing numbers. Well done if you got these right, let's have a look at the answers. So five times five is 25, 40 divided by four is 10, 33 divided by three is 11, and something divided by four gives me four. Well, four times by four, I often for a mistake with this one, I often think of four times four as 12. I don't know why, I just always make that mistake. So what I do is I think, don't make the mistake you normally make most frequent. Four times four isn't 12, four times four is 16. Well done if you've got all of those right. Okay, so time now for you to pause the video and have a go at your independent task on your own, come back together when you're ready and we'll go through the answers. Okay, let's see how you got. So here you need to work out what the missing numbers are. So the numbers across the top and down the side, on the left hand side are the ones that you're multiplying by to the numbers in the middle. So you need to think what am I multiplying by? What if I multiplied two by to get 14? What does 14 appear in my two times table? Well, I know that my missing number there must be seven, two lots of seven or 14. Okay, what's next then? Moving along, I've got 10 and 60. If I line those up, what's the missing number for 10 and 60? What have I done to 10 if I've got 60? What if I times it by? Well, I've times it by six, haven't I? If you decided to add these in in a different order, that's absolutely fine. This is just the order that I decided to do with it in. I then came down the side and I thought what's missing there. I've got nine and 36. What number does your mind go to when you think about nine and 36? What have I done to nine to get me to 36. I've times it by four. Well done, if you've got all of those right because they're the ones that allow you to then just multiply for the rest. So those were the hardest ones to find 'cause you had to sort of work backwards. When you have to find those missing numbers. So you really, really well done if you found all three of those. Now your task is quite easy as long as you know your times tables to fill in the rest of them. So we've just got six times two is 12, nine times two is 18 and three times two is six. For your fours, four times seven is 28, four times six is 24. and then we've got our tens, 70, 90 and 30, and our fives which you can see, a 1/2 your five timetable will be 1/2 your 10 times table because five is half of 10. So 35 is 1/2 of 70 and 30 is 1/2 of 60, for example. Really, really well done if you got all of those right. That shows a real confidence in those times tables. Okay, let's have a look at the last one then. So some of these are incorrect and hopefully you could find which ones were incorrect. So we've got these ones here where, although they've got the sort of right idea in that they've got those three numbers that do have a close relationship, they've got them in the wrong order in either a division or multiplication question. And one of the normally happens there is because someone hasn't understood what multiplication and division are all about, about that relationship between the parts and the whole. So well done if you could use all that with division, you're starting with the whole, you're starting with the big group and you're sharing it out. With multiplication, you're starting with the parts and you're being asked, what is the whole? So if you see a division question where maybe the biggest number isn't at the start, that's a good clue. But actually with 50 divided by five, your clues should be five times five isn't 50. It's not five, five and 50 in that fact family. So well done if you could correct it. I got 50 divided by five is 10, but you could have changed it in a different way, that's absolutely fine. As long as you've written a correct sum using those types of numbers, I'm happy. Okay again, four divided by four is not 12, but if you wanted, you could have four divided by four is one or 12 divided by four is three. That's again, can you see that I've put in the one that I normally make a mistake on. So well done if you got that one right. And then nine divided by three is 27. We can see that that one's wrong because the whole number, the 27 is at the end. So if we wanted to division question, we can need to move that 27 to the start. 27 divided by three is nine. Obviously you could have 27 divided by nine is three. So that come at the end. Again, we haven't got the whole at the beginning of the question, is going to be very hard to share four sweets amongst 12 people. So we could change that question around and we could do 12 divided by three and get the answer four. Well done everybody, I would love to see your work from today's lesson. If you'd like to, please ask a parent or carer to show your work on Instagram, Facebook or Twitter, tagging @OakNational and #LearnwithOak. But finally, before you go, at least have a go about knowledge quiz. It's just five questions just to see how well today's learning's gone in. Really well done everybody, have a great day, bye bye.

Let's see what you have learnt today about recalling key facts

4 x 4 =

7 ÷ 3 = 21

10 x ? = 90

Which of these does this array NOT show?

I have 36 sweets to share equally between 4 children. How many sweets will each child get?

Recalling multiplication and division facts

In this lesson, we will consolidate our knowledge of multiplication and divison and apply our new strategies to further problems including incomplete multiplication tables and 'spot the error' activities.

Maths

Y3 Maths

Key Stage 2

Year 3

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 factors and products to solve division problems

Consolidating multiplication and division knowledge (Part 1)

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?

6 is a factor of 24

27 glue-sticks were shared equally between 3 classes. How many glue-sticks did each class 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:Recalling multiplication and division facts

Core Content

Multiplication and division: