Let's see what you have learnt about multiplication today

Commutativity means...

4 x 5 has exactly same answer as

48 is the answer to 4 x 12 and

5 x 9 and 9 x 5 =

4 people each buy 8 new pens. How many pens were bought in total?

Understanding multiplication can be completed in any order

﻿Hello everyone, I'm Ms. Brinkworth, I'm going to be doing this math lesson with you today which is all about developing your mathematical knowledge on times tables. So if you look at our learning objectives, what we're going to be doing is using bar models to present times tables that hopefully you're already quite confident with. Bar models are a lovely way of representing times tables, making it really clear in our heads as we move through our maths what times tables are all about and what we mean when we're talking about multiplication. What they represent, and the type of questions they can help us answer. So should we get started? Our agenda for today is that we are going to start by looking at arrays, which are probably the way that you've looked at multiplication questions up to this point. We're then going to connect arrays and bar models because they've got a lot in common. So we'll be really connecting new knowledge to your current knowledge in terms of arrays and bar models today. And, we'll then be practising using bar models to help us answer multiplication questions. They're a tool that are there to help us with our questions. And then towards the end of the lesson, you'll have a chance at independent work because it's all about you embedding your learning, taking as much time as you need to answer those questions, and then there's a quiz at the end which should be a bit of fun and help you see how well today's learning has gone. So, all you need for today's lesson is a pen or a pencil, some paper, that's absolutely crucial, and absolutely crucial as well is a really good attitude because you're going to feel really confident with your times tables by the end of the lesson. So pause the video here and get what you need. Well done everybody, let's get started. So, here's a little warm up for you. Here's a times table fact that I hope you're all quite confident with, It says 3 times 2 is 6. But what other facts can you calculate from this calculation? So what other facts can you come up with? Can you move the numbers around? Can you think about different operations? Let's see how many you can some up with. Now here's the ones I found. You might have other ones, you might have these ones in a slight different order, or you might have come up with completely different one which is fantastic, so let me just go through the ones that I found. So, we can switch around our multiplication because we know that multiplication can be done in any order, so we can have 2 times 3 is 6, we can just switch around the 2 and the 3. We also know, hopefully, that multiplication and division are the inverse, so we can put the whole, the 6, at the beginning of the calculation and turn it into a division question. 6 divided by 3 is 2. Or, you could have has 6 divided by 2 is 3. We could develop that even further and think about our multiples of 10. If I know that 3 times 2 is 6, if I make 3 ten times bigger for 30, my answer will be ten times bigger with 60. Again, we can switch that round and if I make 20 ten times bigger instead, then again my answer will be ten times bigger. I might want to move on to my next number in my 3 times table. So, if I know that 3 times 2 is 6, I just need to add another 3 on to get onto my next multiple of three, which is 9. Or, I might think of it as my 2 times table and move on to the next step in my 2 times table If I know that three 2's is 6, then four 2's are 8. And that's just the start of how you can use one simple multiplication question to help you with a whole range of new scenarios. So that's why it's so important at this stage in your education to start to become really confident with these times tables. Not just so you can reel them off and show off, but so that you can actually use them to help you in lots of questions that are going to come up as you move through school. So, arrays. This is probably how you've seen multiplications represented up to this point. And arrays are really really useful. That's because multiplications are equal groups of a number. So, what is this array showing? Well let's have a look together. We've got two columns, so we could have 2 times by, multiplied by, what? 3. 2 lots of 3, 3 lots of 2. And the answer to that is 6. So this is just a really clear way of showing that simple multiplication fact. 3 times 2 is 6, 3 lots of 2 is 6. So an array is a nice clear way of drawing out that multiplication fact. But today's lesson is all about bar models. So what can you see here is different to that picture on the right there which is a bar model? The only thing that's really different is I've spaced out my array into my groups just to go across now in a bar. So you can still see that I've got three groups of two, I've got two and two and two. And I can see that all together I've got 6. That's about what we're doing today. We're just going to move from arrays to bar models and hopefully you'll see as we go through a few more examples that bar models can be really really useful as we move through into slightly harder multiplication questions. Okay. Shall we have a go with this one? What multiplication do you think this array is showing? Well, we've got 4 equal groups. 1, 2, 3, 4. And in each group, there are three. I've got four equal groups of three. I've got four chunks, four groups, four lots of, four sets, and in each set, I've got three. In each group I've got three. So I've got four lots of three. Do you know what four lots of three are? Four times by three is twelve. So there you can see the array, and then the slightly different one where we stretch it out to make a bar model. Okay, so what's being shown here, then? I've got five equal groups, and in each group I've got three. And I can see that in total, I've got 15. So, the calculation that's being shown here in both the array and then the bar model is 3 times by 5 is 15. Or, 5 times by 3 is 15. Doesn't matter which order we do that in. Okay, here's a array. Can you turn this into a bar model and have a go at writing the question and the answer to what is being shown here? So how many equal groups are there, and what is in each equal group, and what's the answer? Have a go. How did you get on? Well we've got 1, 2, 3 equal groups. 1, 2, 3. And in each group, we've got 3. So the question being asked here is 3 times 3 which is 9. And hopefully you can see that we've got 9 dots. We had 9 dots in our array, and we've got 9 dots in our bar model, we're just laying it out in a slightly different way. 3 times 3 is 9. Okay, as we move on then, we can take the bar model on the next step. So rather than drawing out dots, which, you might have been able to see at this point, can take quite a long time. As we're moving to bar models, it's not necessary to always draw out those dots. If you still find it useful, that's absolutely fine, you can carry on doing that. But if you look at this array, we've got a lot of dots going on here. And as we move through our multiplication knowledge and we start using bigger numbers, there will be lots and lots of dots for us to draw out if we carry on using arrays and bar models in that way. So we can develop our bar models to make them quicker and more efficient, help us answer the questions just as accurately, but more quickly. Now let me show you how we're going to do that. So in each of these rows, there are 10. So I've got two lots of 10. And can you see that if I do a bar model like this, I don't need to draw out all those dots, I don't need to count all the dots, and it's just making it a little bit simpler. If I was going to count twenty dots, or draw out twenty dots, there's quite a lot of room there to make a mistake. I might miss one out or draw one too many, or when I count them I might lose count. Whereas if I draw out my bar model like this, rather than putting 10 dots in each bar, I just write 10, it might be that that's a little bit quicker, a little bit simpler for us. And then I can see that I've got two lots of 10 which is 20. Okay. Now we're going to move on to how we can use bar models when we have a real life word problem to answer. So we're going to look at this question together and we're going to think about what question is being asked. So it says, "Your restaurant has 5 tables of 3 people booked in tonight. How many people are arriving in total?" So hopefully you can see that this is how we might use multiplication in a real life situation. So you've got 5 tables of 3 people each, what does that look like? Well I really like to get that picture in my head when I'm thinking about word problems. So, it's not a very big restaurant, there are only five tables, so maybe it's a lovely cosy restaurant. Maybe it's a special occasion like Mother's Day and there are five groups of people turning up. I can imagine the five different groups turning up at different times, and there's three people in each group. So what does that look like? There's one group. How many groups have I got? Well I've got five groups coming in total, and they've each got three people in, so there's my bar model. Five groups, and three in each group. How much is that in total then? 5 times 3 is 15. I'm going to go back to my question now and just check that that sounds right. I have five tables of three people arriving, five lots of 3. Five groups of 3. Five sets of 3. 5 times 3 is 15. Am I sure 5 times 3 is 15? I could check with my fives, I could do three fives, 5, 10, 15. I feel quite confident with my five times tables so I think that's quite right. Or, if I wanted to really really make sure, I could check my threes as well. I could do five threes, let me just check. 3, 6, 9, 12, 15. Five threes are fifteen. Okay, your turn. Pause the video here. You've got a field with 7 cows in. The cows have 4 legs each. How many legs have you got in total? Hopefully it was clear to you that cows have four legs, they've put that picture in there to help you. So you've got 7 cows and they've each got 4 legs. So you've got 7 groups of 4. 7 groups of 4. There's my bar model with my 7 groups of 4. So my question is 7 times by 4, or I could do 4 times by 7 and get the answer 28. Really really well done if you did that, and especially if you were able to draw out that bar model. And if you bars have got 3 written in it instead of three dots, even better. Really really good work. Okay, time to pause the video and have a go at your independent task. Great, shall we come back together and have a look at the answers? Don't worry if you've got some wrong, this is probably new learning for a lot of you and that is absolutely fine, we all make mistakes. Just have a think about the questions that you got wrong and maybe try and pinpoint the mistake that you've made and have a little bit of a look at those wrong questions because that's where the real learning happens. Okay, so it says to use these arrays to draw out bar models and answer the questions. So, we've got three school bags with five books in each. So, how many is that? If we've got 5 times 3 we've got 15. For question 2, there are three bags each with three sweets in, so I've got three equal groups and in each group is three. So I've got 3 and 3 and 3. 3 add 3 add 3. I've got 9. Really well done if you got those right. This time again, I haven't given you the arrays, but it's for you to decide how you want to represent and how you want to work out these problems. So in the first question it says there are nine rows on a plane, and each row holds four people. Again, I might want to get that picture in my head, see those rows on a plane, equal rows with the same number of people, maybe the people all look a little bit different, but I know that I've got 9 rows and 4 in each row. So I've got 9 times 4 which is 36. And now we've got another kind of real world problem here where maths becomes very useful, a recipe. And it says Nigel needs 4 eggs to make a cake. How many eggs does he need to make 6 cakes? Well he's going to need a bigger number, isn't he? He wants to make six cakes, it must be a special occasion. So he needs 4 eggs for one cake, he needs 4 times 6 to make 6 cakes, so he needs 24 eggs. Really really well done if you got all of those right. On this challenge question then, here is a bar model and it's asking what the question might be. And really well done if you had a go at this. I'm going to give you a few of the answers. Yours might be different, that's absolutely fine. You might have gone for 6 times 4 is 24. What is being shown there on that bar model there is 6 equal groups and each group has got 4, so 6 times 4. Or, maybe you decided to do a division question instead, you used the inverse. You saw that there's 24 in total, it's being divided into 6, 6 equal groups, and in each of those groups there's 4. Really really well done if you saw a division question. Maybe you noticed that some of the bars are red. So you did 4 times 4 is the blue-green bit, and then add 2 times 4 is 24, so you've seen that the bar is split up slightly. Or maybe even a word problem. 6 groups of 4 book to see a film. 2 groups then cancel. How many attended in total? So the whole bar would show the total number of groups who had booked, and then the red would show that some people had cancelled. And it would really explain that word problem quite clearly. I would love to see your work. I would love to see your bar models, your arrays. If you would like to share those with us, please ask a parent or carer to show your work on Instagram, or Facebook, or Twitter, tagging @OakNational and #LearnwithOak. Now it's time to complete that quiz and see how many questions you got right. Really really well done on today's work everybody. Enjoy the rest of your day. Bye bye!

Bar models help us by...

Arrays and bar models can represent the same thing?

This bar model could show...

What could be the question this bar model is showing?

4 x ? = 20 (Use the bar model to help you)

Using bar models to represent known times tables

In this lesson, we will compare arrays and bar models, and use them as ways of visualising multiplication questions. We will use bar models to help us solve multiplication problems.

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 that multiplication and division are inverse operations

Using the inverse operation to find missing numbers

Recalling multiplication and division facts

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?

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:Using bar models to represent known times tables

Core Content

Multiplication and division: