Lesson video

Hi everybody, I'm Miss Brinkworth.

I'm going to be going through this math lesson with you today, which is all about helping you with your multiplication questions.

So if we look at our learning objective for today, we're going to be using arrays, and these are going to help us with our three and four times tables.

Those are two times tables, which are really important to get very confident with at this stage in your education, they're going to help you move on to your bigger times tables.

They're going to help you with your division questions.

And I promise you that if you can get really good at your times tables, it will help you through all of your math.

So let's have a look at what today's agenda has got for us.

So we're going to practise creating arrays, and those are ways of drawing out multiplication to make them a bit clearer to us.

We're then going to relate those arrays to other representations, so other ways of drawing out multiplication problems. Then you're going to have a go at using some arrays to answer calculations, and you'll have that independent work to apply that knowledge, and an exit quiz to see how well you got on with today's learning.

So, you don't need much for today's lesson, but do pause the video here if you need to go and get a pen or pencil, and some paper.

Come back with that really happy, sunny disposition.

Okay, here's a warm up for you then.

So we've got some statements here.

Pause the video and just decide whether they are always, sometimes, or never true.

Shall we see how you did? So the first one says a number in the two times table will also be in the four times table.

Is that always, sometimes, or never true? Well, that's an interesting question, because some of the numbers in the two times table do appear in the four times table.

So it's sometimes true.

So eight is in the twos and the fours, but six is just in the twos.

So that statement is sometimes true, What about the next one then? A number with a three in it is always a multiple of three.

Well again, that's sometimes true.

Numbers like 30 have got a three in them and go in the three times table.

But then there's 13, that's got a three in it, but it's not in the three times table.

So when you're looking at these statements, it's really good to think of a few different examples, just to check, because if you only think of one and you think, "Hmm, a number with three in it is a multiple of three," well three is a multiple of three, and 30 is a multiple of three, and 33 is a multiple of three, they must all be.

But keep trying, and look for a few more.

Try and see if you're completely right, cause that statement is only sometimes true.

Okay, what about the next statement then? You can do multiplication in any order and get the same answer.

That is always true.

So 3 times 4, and 4 times 3, will always give you the same answer, which is 12.

Okay, repeated addition can represent the same thing as multiplication.

Again, that's always true.

So we can have 2 add 2 add 2, or we can have 3 times 2, they represent the same thing.

Well done if you could see that everybody.

So we've got warmed up from multiplication now.

So let's move on to arrays.

So, if you haven't had to write arrays before, I'm sure you've seen them before.

They look like this.

And it's a way of representing multiplication.

Sometimes there's a fear when we're going through our multiplication that we're talking about two times this and eight times that, but actually, we've forgotten what multiplication is all about.

Multiplication is about equal groups.

That's it.

And arrays show that really clearly for us.

Can you see that we have rows, and we have columns, and they are in equal groups.

So when we multiply equal groups, we have more than one equal group.

We're doing multiplication.

It's as simple as that.

So what multiplication is being shown with this array? Well, all we need to do is count how many columns we've got, how many rows we've got, and then we'll work out what multiplication is being shown.

So, if we count these, we've got one, two, three, four, five, six, seven columns.

We've got seven dots going across the top, seven.

So we're talking about our sevens.

How many groups of seven have I got? Well, I've got three.

I've got three rows of seven.

So I've got 7 times 3, or 3 times 7.

It's going to give me the same answer.

Do you know it? 3 times 7? I could count all my dots to work it out.

Or hopefully I know my three times tables, and I know that three sevens are 21.

So this is what we're talking about when we're talking about arrays.

Rather than showing multiplication as a calculation, as numbers, we are showing it in a series of dots.

And that's what we're doing with today's lesson to help us clearly understand what multiplication is really all about.

So should we have another go? Here is a multiplication.

Can you see which one is being shown? I've got four and I've got three.

It could also be shown like this.

This is a part-whole model, and it makes it really clear to us what we're talking about, when we're talking about multiplication, We're talking about having four groups of three, three and three, and three, and three.

Three, four times.

Four equal groups, and in each group there are three.

That gives us 12.

These are all different representations, pitches, and ways of saying exactly the same thing.

If I have four lots of three, I have 12.

If I have three lots of four, I have 12.

Okay, so here's that same array again, showing four threes, three fours.

And here's a way of showing you that it can be four threes.

So all I've done is pick it up.

It's got exactly the same number of dots on it, but it's a slightly different multiplication.

Instead of 3 times 4, I've got 4 times 3, but you can see it's exactly the same array.

It's got the same number of dots.

It gets me the same answer.

Okay.

Here's another array.

It's in the four times table.

Can you have a go at telling me what this array shows? It's in the four times table.

Four times what? And what is the answer? Well done if you could count and see that it's 4 times 5, and well done again if you know your four times table well enough to know that 4 times 5 is 20.

Okay, not going to give you any clues this time, pause the video and have a go at working out what this array is showing.

Well done again if you could see we're still talking about our four times table.

Four times, and what have we got down the side? We've got seven.

4 times 7 this time is 28.

It's two bigger than our last question, two lots of four bigger than our last question.

We had 4 times 5 is 20.

So if I add four and four again to 20, I get 28, which gives me 7 times 4.

Okay, what about drawing arrays then? I've been drawing them all up for you up to this point.

Drawing them is really simple.

We just think about what our question is, and we draw out the right number of rows and columns.

So here's my drawing of an array.

What was my question do you think? How many rows and columns have I got? Well, I've done three rows, sorry, three columns, and three rows.

So I've got 3 times 3 is 9.

Okay, here's a question for old time's sake.

Pause the video and have a go at just drawing your own array.

It doesn't need to be perfect.

We're just talking about circles in rows and columns.

Well done for having a go everybody.

Let's see if yours looks like mine.

So, we've got four across the top, and then we need to do six rows of those, six lots of four.

Six lots of four.

If you work this the other way round that's okay.

You might really have done 6 times 4, but we know that you'll get the same answer.

And the answer is, 24.

So that was one in between the two we just looked at.

We looked at 20 and 28, 5 times 4, and 7 times 4.

Now we've got one in the middle, 6 times 4, 24.

Okay, here's how arrays might move on to other representations.

So, here's a picture of some sheep, and they've all got four legs.

They've all got all their legs.

So there's some sheep in a field with four legs.

How many legs are there in total? How are we going to work that out? We need to count the sheep, don't we? Just like we counted our rows on our array, we can count the sheep.

How many sheep are there? One, two, three, four, five, six, seven, eight, nine.

Nine sheep.

They've got four legs each.

So what might that question look like? What multiplication question is that? 9 times 4.

Do you know 9 times 4? I wonder if you might know 10 times 4.

10 times 4 is 40, so 40 takeaway four to get me to the one before.

40 takeaway four, well I can use my number bonds.

I know that 10 takeaway four is six.

So 40 takeaway four is 36.

Here's another question for you.

Eight customers buy three cartons of milk each.

How many cartons were sold altogether? I've even been nice enough to give you the sum.

Draw an array if you'd like to, or a different representation to help you answer that question.

Let's see how you got on.

Well, 8 times 3 is 24, and well done as well if you drew a picture.

You could draw an array, or you could draw lots of cartons of milk.

It's all representing multiplication and really making sure you understand what multiplication is all about.

Those little groups of cartons of milk are one customer.

One customer bought three cartons of milk.

So there were eight customers.

So I've had to draw that out eight times.

And if I count all those cartons of milk, I'll get my answer 24.

Okay, time to pause the video and have a go at that independent task.

Let's see how you did everybody.

So, this is an array, and you need to write in what it is it's showing you.

So hopefully you can see that we've got three rows and eight columns.

3 times 8 is 24.

If you've got any of these the other way around, that's absolutely fine.

Okay, so 8 times 3 is also completely the right answer.

So, the next one, four and six is 24.

Oh, we've got the same fact there.

That's an important one to remember.

Okay.

3 times 9.

What's 3 times 9? You've got the array there to help you.

3 times 9 is 27.

9, 18, 27.

If you want to count it in your nine times tables rather than your threes, that's absolutely fine.

Okay, here's one of those questions.

Again, we've got an animal with four legs.

There are six cows in a field.

They've all got their four legs.

So what's the question? And what's the answer? So if there are six cows and they've all got four legs, we're talking about 6 times 4, and well done if you know that answer is 24.

The final question was just making sure you understand what arrays do represent, and what they don't represent.

So one of these arrays does not represent 7 times 3.

Which one is it? Well done if you could see it's that middle one that hasn't got seven rows.

Okay, I'd love to see your work, So if you'd like to share it, please ask a parent or carer to share your work on Instagram, Facebook, or Twitter, tagging @OakNational and #LearnwithOak.

But, before you go, please do complete the final knowledge quiz and see how well you got on with today's learning.

Great work everybody, well done.

Bye bye.