Lesson video

Hi, everyone, welcome to your maths lesson for today.

If you can't remember, my name's Mrs. Harris.

I was with you in your last lesson, and I gave you a little bit of a challenge, something to do in between last lesson and this lesson.

Let's see how you got on with it.

Ah, yes, this was our problem yesterday that I left you with, and you had to represent this sentence with pictures, maybe a bar model, but most importantly, you had to write the equations.

Let me just read the sentence to you.

The product of 7 and 2 is 14.

Go on, say it with me.

The product of 7 and 2 is 14.

What's the product? Yeah, it's 14.

What are my two factors? Yeah, seven and two.

I had a go at this as well, and I look around my house to see what things I could find that come in twos, 'cause two is a factor, and that I had seven lots of.

Well, I had seven lots of eyes in my house, and eyes come in pairs, come in twos.

One lot of two, two lots of two, three lots of two, ooh, they're mine, four lots of two, five lots of two, six lots of two, seven lots of two.

Seven is a factor.

Two is a factor.

And the product is 14.

Did you notice not all the eyes there are human? My cat and dog are there as well.

I also used some Numicon, with my product being 14 and my 7 groups of 2.

It looks a bit like a bar model, doesn't it? I found some shoes.

They come in twos.

They come in pairs.

And I knew two was a factor, and I found seven lots of them.

So here I have the product of 7 and 2 as 14, just like the sentence.

I drew a bar model with my 14 as the product and my seven lots of twos underneath.

My two lots, my factors, seven and two.

Do you remember last time, we also used counters? And the counters were blank, so I used them again, and I gave them all the value of two.

2, 4, 6, 8, 19, 12, 14.

So even though they didn't have any value written on them, we've given them a value, and that value was two.

But I'm missing something that's really important.

I'm missing them equations.

Here's my first one with my factor, factor, product.

And then I've got one with my product, factor, factor.

7 times 2 equals 14.

The product of 14 is equal to 7 times 2.

Wow, what a lot of representations I got from just one sentence.

I'd love to see how you got on.

Maybe you can get your grownups to share some of your pictures with us.

Oh, more shoes.

Looks like a shoe shop.

People buy shoes in pairs, don't they? In twos.

And her are our shoes in pairs, in groups of twos.

I wonder if we could pretend that people are coming to buy the shoes and they take a pair at a time.

I think to do this, we're going to need to count back in twos.

I know you're really good at counting forwards in twos, so let's just practise our counting backwards in twos quickly.

Let's start at six because we've got six shoes altogether.

Six, four, two, zero.

Do it with me.

Six, four, two, zero.

Let's do it quicker.

Six, four, two, zero.

Your turn now.

Brilliant.

Well, if I circle this six, we've got all the information we need to write our first multiplication expression.

We've got the product, six.

We've got our factors, three and two.

Do you think you could have a quick go at writing the equation for me? Fantastic.

Let me show you what I got.

I got three times two equals six.

Three from the number of groups, two from the number in each group, and six because six is the product of three times two.

We have six shoes altogether.

But someone's going to come and take a pair of shoes.

Hopefully they'll buy them, not take them.

So our six goes to four.

A pair of our shoes go away, and we need to write the new expression.

Don't forget your product and your factors, and have a go yourself.

This is what I wrote.

I've got my factors.

I've got two lots of two, two groups of two.

And I've got my product, all the shoes I've got together, as being four.

But then someone comes to buy some more shoes.

And now our product is just two.

We've got one group of two.

So we know our factors, and we know our product.

Can you write me the equation? Wow, that was quick.

I wrote one times four.

Not one times four.

I wrote one times two equals two.

Factor, factor, product.

But then someone's going to come and buy that lovely purply pink pair of shoes, and I'll have zero shoes left in the shop.

But I can still write a multiplication equation for this.

Just have a little go.

Okay, let me give you a hand.

We know that the product is zero.

We've got zero shoes.

In fact, we've got zero groups.

So we know one of the factors, zero.

We know the product, zero.

But we're missing the other factor.

What were our groups of? Yes, I know they were shoes.

How many shoes in a group? Two, so we've got our factors, zero and two.

We've got zero groups of two.

And the product of zero times two is zero.

So this is what I wrote.

Zero times two equals zero.

Well done if you got that.

If you didn't, just have a look at where you think I got these numbers from.

But don't worry, we'll do some more work on this.

This is my two p purse.

I only keep two p coins in here.

In here, can you see? I have five of them.

I have five two p coins in my purse.

Hmm.

I've got five of them, and they're two pence coins.

My factors must be, yeah, five and two.

Five because there are five groups of two.

And the two because each of our groups is worth two.

So my expression has factor times factor, five times two, but I want to make it into an equation.

I want to know the product.

So I'm going to put equals.

What is five lots of two? 2, 4, 6, 8, 10.

Maybe you just knew.

Our product is 10.

Oh, I've only got four two pence coins in this two p purse, so I have four as a factor and two as a factor.

I wonder what my product is.

Oh, my product is eight.

How did you know that? That's right, because four times two is eight.

We could count in twos, but maybe you just knew.

I could say the product is equal to factor times factor.

Eight is equal to four times two.

You're getting really good at this.

This time, my two p coins, they look like the spots on a die, don't they? Does that make it easy to see how many I have? That's right, I have three groups of two.

Now, before I talk you through this one, I'd like you to have a go at writing what you think the equation will be.

And does it matter where my equals sign go or which side my product is? No, it doesn't matter.

As long as they're on side of the equals sign and the product is on the other, I know our equation will work.

So give it a go.

You might want to pause the video while you think about the factors and the product.

Okay, so I had one of my factors of three 'cause I have three groups.

I had one of my factors as two because each of my group is worth two.

And I had my product as six.

I wrote my product here, but you could've written your product over here.

You could've written six is equal to three times two.

You could've written product, factor, factor, and both are right.

Oh.

Another one of my two p coins is gone.

Wonder if my purse has got a hole in.

This time, well, I'm not going to tell you the factors.

And I'm not going to tell you the product.

Can you write me the equation? Well done.

Did you notice both our factors are actually the same? We've got two groups of two.

Two groups of two is equal to four.

Two, four, factor, factor, product.

Go on, just put your finger on the product.

Okay, put your finger on the factor that represents the number of groups.

This one isn't.

So that must mean that this factor represents the value of each group.

Fantastic, you're working really hard today.

Well done.

Oh, definitely got a hole in my purse.

So how many groups do I have? Yeah, I've got one group.

What is the value of my group, though? Yeah, it's two p.

I know it's a two pence coin, and I've got a clue: it's my two p purse.

So what is my product? Wow, you knew that without even writing the equation.

But you know what I'm going to ask you to do now.

Could you write the equation for me? Fantastic.

One times two is equal to two.

This is one of my factors, and this is one of my factors.

Oh, but this product, it's the same as this factor.

Oh, that's because I've only got one group of it.

That's actually quite interesting.

Wonder if you spotted it as well.

Oh, look, my two p purse is empty.

How many groups do I have? I've got no groups.

I've got zero groups of two.

I know that my group would have a value of two because I only put two pence coins in here.

I wonder what my product would be and how I would write an equation to show this.

Can you pause the video and just have a little go yourself? Okay, so my first number is the number of groups.

This factor represents the number of groups, and I have zero groups.

This number, the number two, is a factor, and it would represent the value of each group in my purse.

We know it's my two p purse, so it has a value of two.

But I'm just wondering, what would the product be? Zero times two equals.

Something is the product of zero times two.

How much money have I got altogether? What's that? My product is zero, even though I've got a factor of two.

Oh, yes, because I've got zero groups of two, so my product has to be zero.

I've got no money left.

I've got a little matching job for you to do now.

And I would like you to match these pictures to these equations.

Going to give you a little bit of time to do it yourself, and then we'll go through them together, so you might want to pause the video now.

Okay, let's take the video, the pictures one at a time.

Let's start with the coins.

Did you notice how many coins there are? That's right, there's five.

So five is a factor.

And then we know the value of a two pence coin is the same as having two one pennies, and so it has a value of two.

So now I know both of my factors, five and two.

Now, I probably could match it to my equation now, but I just want to make sure that I know the product's right.

So 2, 4, 6, 8, 10.

Fantastic, I know what equation that one is.

Can you point to it? Yeah, it's 5 times 2 equals 10.

Factor, factor, product.

Okay, let's look at the bicycles next.

Oh, do you know what I noticed first? I noticed the value of each group.

I can see the value of this group is two.

And then it was really easy to see the product of this group, the number of wheels altogether.

It was six.

I could've counted them in ones, but I know that I'm working in twos and that it's more efficient.

So I counted to myself, two, four, six.

And I noticed how many groups of two there was 'cause I need that last factor.

One group of two, two groups of two, three groups of two.

So I've got my factors, three and two.

And I've got my product, six.

That gives me all the information I need to match it to my equations.

Are you pointing to the right one for me? Fantastic.

Now, I think I probably know which equation matches this picture 'cause I've only got one left.

But I also know that my teachers like convincing.

So can you convince me that this picture goes with this equation? How would you do that? Ah, so you'd tell me that once again, like in our other pictures, our factor is two 'cause shoes come in pairs, and pairs means two.

And then you'd tell me how many pairs of shoes I've got to find my other factor.

One pair of shoes, two pairs of shoes, three pairs of shoes, four pairs of shoes, five pairs of shoe, six pairs of shoes, seven pairs of shoes, eight pairs of shoes.

Ooh, that's both of my factors, eight and two.

It's definitely looking like it's going to match that equation at the top, but I'm just going to count in twos to check that the product is actually 16.

2, 4, 6, 8, 10, 12, 14, 16.

It does match.

Well done if you got all them right, but also thanks for working through them with me.

This time, I have the equations, but I don't have any pictures to go with them, so that's one thing you're going to need to do.

But just have a look at my question.

Which of these does not represent groups of two? Let me say it again.

Which of these does not represent groups of two? I think you're going to want to pause the video now and draw some pictures to prove your ideas.

Think very carefully about the products and the factors, and then we'll go through them together.

Okay, so we had the question, "Which of these does not represent groups of two?" And the first one I want to look at is three times two equals six.

So we have how many groups? That's right, three.

And what is in those groups? Two.

Shall we draw it? Okay, so here's one group, here's the other group, and here's the third group.

And in my groups, I have.

I have two apples in each one because my groups are of two.

And the product is six.

So does that one match a group of two? Yeah, it does, so it's not the one we're looking for.

We're still on the same question.

Which of these does not represent groups of two? But this time, we're looking at eight is the product of four times two.

What's different this time? Oh, yes, the product has been put here at the start of our equation.

But we're okay with it.

So this time, I have groups of two.

Ah, it does represent a group of two.

And I have four of them.

So this time, I could draw four bikes.

Not very good at drawing bikes, but I know they represent bikes.

And it does show groups of two.

I could even draw it as a bar model as well.

I could have my product of eight.

I've drawn that first because it comes first in my equation.

I'll draw my bar underneath the same size.

And then I'll draw my four groups.

And in each group, I've got two.

And some sunshine.

Still on the same question.

We're looking at the third equation now, where we have 4 times 3 equals 12.

And we're still thinking, which of these does not represent groups of two? So how many groups do we have? We have four groups.

Going to try our bumper cars.

There's its flag.

And in each group, we have three.

One, two, three, one, two, three, one, two, three, one, two, three.

Oh.

This does not represent a group of two.

It represents groups of three.

I think this one is our odd one out because it does not represent a group of three.

This is the last one in our problem, isn't it? And we were trying to find out which of these does not represent a group of two? I've got zero times two equals two.

Oh, how many groups do we have? We have zero groups.

And how many in each group? Well, in each group there's two, but there's zero of them.

Can we draw it? We can't draw it because there are no groups.

But if we could, we'd draw a group of two.

So this equation, it does represent groups of two, but there are just no groups of two.

Thank you for joining me today.

You worked really really hard, and I just have a little practise activity for you to have a go at before you join us next time.

Now, Iniko, he started drawing some pairs of mittens to match this equation, but he hasn't quite finished it.

What do we know by looking at the equation? We know the product, and we know the two factors.

What does he already have in his pictures? He already has some groups of two.

He's joined his mittens up with some string.

I remember my mum doing that when I was little.

Ah, he's drawn six mittens but not six groups of mittens, so he doesn't have the right product.

I'd like you to finish the drawing.

Have a go, and share it with us before next time.

Bye!.