Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson on representing the 5 times table and linking it to the 10 times table.

So, are you ready to do some counting in fives and tens and explore how the 5 and 10 times table are related to each other, are you? Excellent.

Let's make a start.

So, in this lesson, we're going to be using our knowledge of the 2, 5 and 10 times tables to solve problems. Are you good at skip counting in 2s, 5s and 10s? I hope so.

Well, let's see if we can develop that into our knowledge of the 2, 5 and 10 times tables and use it to solve some problems. Are you ready? Let's make a start.

We've only got one keyword in our lesson today and that's commutative.

Are you ready? I'll take my turn.

And then it'll be your turn to practise it.

So my turn.

Commutative.

Your turn.

Well done.

Not the easiest word to say, is it? And we're going to be exploring what commutative means when we're thinking about our multiplications in this lesson.

There are two parts to our lesson today.

In the first part, we're going to be using the 2, 5, and 10 times table facts.

And in the second part, we're going to be solving problems using commutativity.

Another way of saying that word that we had as our keyword, commutative and commutativity.

So, let's make a start on part one.

And we've got Aisha, Laura, and Jun helping us with our learning today.

Aisha and Laura and Jun are playing the Bean Bag game.

For this game, they have to score all their bean bags in the same zone.

So you can see we've got a green zone with 10 points.

Outside that is a zone for 5 points.

And on the outside ring, we score 2 points, but they've got to have all their bean bags in the same zone in order to score.

And whoever scores the most points is the winner.

Aisha has a go first.

She's got two bean bags.

Where do you think they're going to land? (gasps) Well done, Aisha.

She's got both her bean bags in the green zone scoring 10.

So she's got 10 plus 10, and that's 20 points.

So Aisha scored 20 points.

Instead of using addition, you can use multiplication to find the total.

Can you think what the multiplication would look like? 10 plus 10 is the same as saying 2 groups of 10, and that's 2 times 10.

And we can use the multiplication sign.

2 times 10 is the same as 10 plus 10.

Aisha says, "It's quicker and easier to use multiplication to calculate the score." So we're going to focus on that as we go through the rest of our lesson.

Now, it's Laura's turn.

I wonder where Laura's bean bags are going to land.

Ah, where did Laura's bean bags land? Well, she scored both her bean bags in the 5-point zone.

So she gets 2 lots of 5, 2 times 5.

And 2 times 5 is equal to 10.

That's the same as saying 2 groups of 5.

So Laura scored 10 points.

How many points did Jun score? You're going to fill in the stem sentences and work out how many points he scored.

You watch where his bean bags go.

Pause the video.

Work out how many points Jun scored.

And when you're ready for some feedback, press play.

What did you find out? Oh, Jun got both of his bean bags in the 2-point zone.

So 2 groups of 2 is equal to 4.

So Jun scored 4 points.

Can you think how that would look as an addition and a multiplication? Aisha has another go.

She throws an extra bean bag.

How many points did she score? So look where her three bean bags landed.

Well, they all landed in the 2-point zone, didn't they? So that's the same as saying 3 groups of 2.

So she scored 6 points, and we can record that as a multiplication.

Three times 2 is equal to 6.

3 groups of 2 is equal to 6.

And we could count.

2, 4, 6.

3 groups of 2 is equal to 6.

Laura has another go and throws 4 bean bags.

Look where her first 3 have landed.

I wonder if her last one's going to go into the same zone.

It has! Look at that.

All 4 in the 10-point zone.

How many points did she score? Well, that's the same as saying 4 groups of 10.

4 bean bags in the 10-point zone.

So Laura scored 40 points.

What will that look like as a multiplication? That's right.

4 groups of 10.

We can write 4 times 10, and 4 times 10 is equal to 40.

10, 20, 30, 40.

Jun's thrown 6 bean bags and they've all landed in the same point scoring zone.

How many points did Jun score? Can you complete the multiplication equation and the stem sentence? Pause the video.

Have a go.

And when you're ready for some feedback, press play.

Jun did very well, didn't he? But where did his bean bags land? They all landed in the 5-point zone.

So he scored 6 lots of 5 points.

6 times 5 is equal to 30.

So Jun scored 30 points.

If we count up in 5 six times, 5, 10, 15, 20, 25, 30, 6 groups of 5 is equal to 30.

So Jun scored 30 points.

For round two, Aisha scored 10 points.

In what ways might she have scored this if the bean bags had landed in the same zone each time? So, how could she have made up a score of 10 points? He might want to have a think about this before Aisha shows her thinking.

So, she may have scored 2 lots of 5 points.

We know that 2 times 5 is equal to 10.

How else could she have done it? She could have scored 5 lots of 2 points.

5 times 2 is equal to 10.

Can you think of one other way she could have done it? Yes, she could have had 1 lot of 10 points.

1 times 10 is equal to 10 as well.

Aisha says the total score or product is 10.

So my factors when multiplied together must be equal to 10.

So we had 2 times 5, 5 times 2, and 1 times 10.

For round two, Aisha and Laura both scored 20 points.

They both used a different number of bean bags.

Aisha says I used 4 bean bags and scored all of them in the same point zone.

Laura says I used 2 bean bags and scored all of them in the same point zone.

I wonder where their bean bags landed.

So, what zones did Aisha and Laura score in? So Aisha scored 20 points and she threw 4 bean bags.

So 4 times something is equal to 20.

The total points is 20.

That's the product.

Aisha had 4 bean bags and that's one factor.

You need to find the other missing factor, which is the zone that Aisha scored in.

So we know that the zones are 2, 5, and 10 points.

So we could use trial and improvement to find out which zones Aisha scored in.

Let's see what that looks like.

So, if she had all her bean bags in the 10-point zone, she'd have scored 10 times 4 points.

Well, 10 times 4 is equal to 40.

10, 20, 30, 40.

So that's not right, is it? So 4 times 10 was too big a score.

So she needed to score in a lower point scoring zone.

So what about if all her bean bags landed in the 2 zone? What's 4 times 2? Well, 4 times 2 is equal to 8, isn't it? 2, 4, 6, 8.

4 twos are equal to 8.

So that's not enough.

She scored 20 points.

So where must her bean bags have landed? That's right.

They must have landed in the 5-point zone.

4 times 5 is equal to 20.

5, 10, 15, 20.

4 fives are equal to 20.

Aisha scored all her bean bags in zone 5 for 5 points.

So what zone did Laura score in? She threw 2 bean bags and she had a score of 20.

So the total points is 20.

That's the product.

Laura had 2 bean bags.

That's one factor.

So the missing factor is the zone in which Laura scored, where her bean bags landed.

So we know the zones are 2, 5, and 10 again.

So we could use trial and improvement, but can you think of a way to do it? How Laura says, "There's an easier way.

If I know 2 groups of 10 are 20, then I know that 2 times 10 is equal to 20.

So I scored both my bean bags in zone 10." And Laura says, "I used half the number of bean bags Aisha used so I would've scored in the zone that was double Aisha's." Ah, that's interesting, isn't it? Aisha had 4 groups of 5 bean bags.

Laura had the same score, but she only had 2 bean bags so each bean bag had to score twice as many.

So she needed 2 bean bags in the 10-point zone, and that's what she got.

Laura scored all her bean bags in zone 10.

Time to check your understanding.

The total points is 30.

Aisha scored this in the same zone using three bean bags.

So what zone did Aisha score in? Pause the video.

Have a go.

And when you're ready for the answer and some feedback, press play.

How did you get on? So she used three bean bags and they all landed in the same zone, and she scored 30 points.

Ah, well 3 groups of 10 are equal to 30.

So Aisha scored all her bean bags in zone 10.

3 times 10 is equal to 30.

Time for you to do some practise.

Aisha, Jun, and Laura continue to play the game.

Use what you know about the 2, 5, and 10 times tables to answer these questions.

So in A, Aisha scores three bean bags in the 5 zone.

How many points did she score altogether? For B, Laura scores 12 bean bags in the 2-point zone.

How many points did she score altogether? That's a lot of bean bags to land in the 2-point zone, isn't it? And in C, Jun scored 40 points using 4 bean bags.

What zone did he score all of his bean bags in? In D, Aisha scored 90 points using 9 bean bags.

What zone did Aisha score all her bean bags in? Where did they land on the target? And in E, Laura and Aisha both score 30 points.

Aisha used 6 bean bags and Laura used 3 bean bags.

Which zone did both Aisha and Laura throw their bean bags in? And for F, Jun scored 20 points.

How many ways could he have scored this? Pause the video.

Have a go.

And when you're ready for some feedback and answers, press play.

How did you get on? So, for A, Aisha scores 3 bean bags in the 5-point zone.

How many did she score? Well, that's 3 times 5.

So Aisha scored 15 points altogether.

In B, Laura scores 12 bean bags in the 2-point zone.

How many points did she score altogether? We know that 12 lots of 2 are equal to 24.

So Laura scored 24 points altogether.

I wonder if you counted up in twos 12 times.

In C, Jun scored 40 points using 4 bean bags.

What zone did he score all his bean bags in? Well, we know that 4 times 10 is equal to 40.

So Jun scored in zone 10.

4 times 10 is equal to 40, and that's his points.

So for D, Aisha scored 90 points using 9 bean bags.

What zone did Aisha score all her bean bags in? Well, it must have been the 10, mustn't it? 9 times 10 is equal to 90.

So Aisha scored in zone 10.

And in E, Laura and Aisha both score 30 points.

Aisha used 6 bean bags and Laura used 3 bean bags.

So which zone did Aisha and Laura throw their bean bags in? So we had to find out 6 times something is equal to 30 and 3 times something is equal to 30.

So with 6 bean bags, Aisha must have scored in the 5 zone because 6 groups of 5 is equal to 30.

And Laura must have scored in zone 10.

3 times 10 is equal to 30.

And for F, Jun scored 20 points.

How many ways could he have scored this? Well, he could have had 2 bean bags in the 10-point zone, 2 times 10 is equal to 20.

He could have had 4 bean bags in the 5-point zone.

4 times 5 is equal to 20.

Or he could have had 10 bean bags in the 2-point zone.

10 times 2 is equal to 20.

Well done if you worked out all those different ways that Jun could have scored 20 points.

And on into the second part of our lesson.

We're going to be solving problems using commutativity.

I wonder if you can remember what that word means.

So you can use factors from the times tables to help you to solve problems. Let's have a look at this problem.

There are 2 plates of sweets.

Each plate holds 7 sweets.

How many sweets are there altogether? Well there's 2 groups of 7.

2 times 7.

But Aisha says, "I don't know my 7 times table yet.

How can I work this out?" Well, you can think about 2 times 7 in another way.

So this picture shows 2 groups of 7.

And there we've represented it with counters as well.

Each counter represents one of the sweets.

We've got 2 groups of 7 sweets, but you can also think of 7 groups of 2.

So there are the same number of dots, but this time we've arranged them in groups of 2.

Now, we do know our 2 times table, don't we? Aisha says, "I can use the 2 times table to solve this.

7 twos are equal to 14.

" 7 groups of 2 are equal to 14.

So 7 groups of 2 are equal to 14, then 2 groups of 7 are also equal to 14.

We have the same number of counters.

We were just thinking about grouping them in a different way.

There are 14 sweets altogether.

Let's look at the equation more closely.

So, the 2 represents the number of plates.

It's the number of groups.

And the 7 represents the number of sweets on each plate.

And 14 is the product.

That's how many sweets there are altogether.

So in our original problem, the 2 represents the number of plates and the 7 represents the number of sweets.

But Aisha says, "To use my 2 times table, I thought about the problem in a different way." Multiplication is commutative.

Do you remember? That means that we can change the order of the factors and the product stays the same.

So you could think of 7 groups of 2, which is equal to 2 groups of 7.

2 times 7 is equal to 7 times 2.

And there are 2 equations that are the same.

2 times 7 is equal to 7 times 2.

14 is the product of both and that's how many sweets there are altogether.

So once we know that one factor is 2 and the other factor is 7, we can change the order of them so that it means that we can use a times table fact that we know.

We might not know 2 groups of 7, but we do know 7 groups of 2.

We could use our skip counting in twos if we needed to to find that out.

So, over to you to check your understanding.

In this problem, what does the 2 represent? And what does the 8 represent? Pause the video.

Complete the stem sentences.

And when you're ready for some feedback, press play.

How did you get on? Did you spot that in this problem? The 2 represents the number of plates and the 8 represents the number of sweets on each plate.

2 multiplied by 8.

2 groups of 8 sweets.

Carry on with this check.

If you don't yet know your 8 times table, how else could you think about the numbers in the multiplication? So, can we complete the equation and the stem sentence, 2 times 8 is equal to and 2 groups of 8 is the same as, hmm, groups of, hmm.

Pause the video.

Have a go.

And when you're ready for some feedback, press play.

How did you get on? Did you realise that because multiplication is commutative, we can swap the order of the factors and the product stays the same? So 2 times 8 is equal to 8 times 2.

2 groups of 8 is the same as 8 groups of 2.

Let's have a look at another problem.

The plates show 5 groups of 7 sweets.

And there's our array showing the same.

Can you see 5 groups of 7 sweets? 5 times 7 is equal to our total number of sweets.

5 groups of 7 is equal to 7 groups of 5.

So you can use your 5 times table.

Multiplication is commutative.

Let's watch the array change.

We've got 5 groups of 7.

And now, we've got 7 groups of 5.

It's the same number of counters.

We can just think about dividing them up in a different way.

5 groups of 7 is equal to 7 groups of 5.

And we know that 7 lots of 5 is 35.

We could skip count in fives 7 times and we would get to a total of 35.

Time to check your understanding again.

How many sweets are there altogether? What does the 2 represent? And what does the 6 represent? And which times table can you use to solve the problem? Pause the video.

Have a go.

And when you're ready for the answer and some feedback, press play.

How did you get on? Well, did you spot that this time the 2 represents the number of sweets and the 6 represents the number of plates? So we have got 6 groups of 2.

6 times 2.

Aisha says, "I can use the 2 times table.

6 groups of 2 is equal to 12." In the other problems, we've had to think about it the other way around, but this time we can use our 2 times table straight away.

6 times 2 is equal to 12.

So in this problem, there are 10 plates of apples.

Each plate has 6 apples.

How many apples are there altogether? Well, this is 10 groups of 6 and that's equal to our total number of apples.

But if we can't skip counting sixes, we can use commutativity.

You know that 10 groups of 6 is the same as 6 groups of 10, so we can skip count in 10s.

Commutativity means that we can change the order of the factors and the product remains the same.

So rather than thinking about 10 groups of 6, we can think about 6 groups of 10, and that is equal to 60.

So there are 60 apples altogether.

Time to check your understanding.

What does the 4 represent? And what does the 10 represent in each of these two problems? Pause the video.

Have a look and complete those stem sentences.

And when you're ready for some feedback, press play.

How did you get on? So, in the first problem, the 4 represents the number of sweets and the 10 represents the number of plates.

And in the second representation, the 10 represents the number of sweets and the 4 represents the number of plates.

How many sweets have we got altogether? We know that multiplication is commutative.

The factors 4 and 10 can represent 10 groups of 4 or 4 groups of 10.

And they are equal.

10 times 4 is equal to 4 times 10.

Time for you to have a go and do some practise.

In question one, you're going to use what you know about commutativity and the 2, 5, and 10 times table and answer the questions below.

So A, there are 2 plates of apples.

Each plate has 6 apples on.

How many apples are there altogether.

Remember to use your knowledge of counting in twos in the 2 times table.

In B, there are 5 plates of muffins.

Each plate has 7 muffins on.

How many muffins are there altogether? In C, there are 10 bowls of apples, and each bowl contains 9 apples.

How many apples are there altogether? And indeed there are 10 pizzas.

Each pizza is made up of 12 slices.

How many pizza slices are there altogether? Pause the video.

Have a go at solving the problems. And when you're ready for the answers and some feedback, press play.

How did you get on? So in A, there were 2 plates of apples and each plate had 6 apples on it.

So 2 groups of 6.

Well, we know that's equal to 6 times 2, and we know that 6 groups of 2 is equal to 12.

So there are 12 apples altogether and you could skip count in twos.

In B, there are 5 plates of muffins and each plate has 7 muffins on it.

5 groups of 7 is equal to 7 groups of 5.

So you can use your 5 times table.

7 groups of 5 is equal to 35.

So there were 35 muffins altogether.

In C, there are 10 bowls of apples.

Each bowl contains 9 apples.

So how many apples are there altogether? Well, there are 10 groups of 9, but we know that that is equal to 9 groups of 10.

So there are 90 apples altogether.

9 groups of 10 is equal to 90.

And indeed there are 10 pizzas.

Each pizza is made up of 12 slices.

How many pizza slices are there altogether? So that's 10 groups of 12, which is equal to 12 groups of 10 and that's equal to 120.

There are 120 pizza slices altogether.

That would feed a lot of people, wouldn't it? And we've come to the end of our lesson.

We've been using our knowledge of the 2, 5, and 10 times tables to solve problems. We can use our knowledge of those times tables to help us to solve problems. And we know that multiplication is commutative so we can swap the factors and use our known facts to solve problems. Thank you for all your hard work and your mathematical thinking today, and I hope I get to work with you again soon.

Bye-Bye.