Lesson video

Hello, my name is Mrs. Hopper and I'm really looking forward to working with you in this lesson on representing the five 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 five 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 explaining what each factor represents in a multiplication story, when one of the factors is one.

So let's have a look, see what we're going to be thinking about today.

We've got two keywords, we've got factor and product.

So I'll take my turn to say the word and then it'll be your turn.

So my turn: factor.

Your turn.

My turn: product.

Your turn.

I hope you're quite familiar with those words now.

Factor is that we multiply together to get a product when we are thinking about multiplication.

So there are two parts to our lesson today.

In the first part we're going to be thinking about one as a factor, and in the second part we're going to be solving some word problems. So let's make a start on part one of our lesson.

And we've got Aisha and Laura working with us today.

So we're thinking about multiplying by one.

So we've got four times one here, four groups of one, and we've got four altogether.

And Aisha says, "When one is a factor, the product is equal to the other factor." Let's have a look at that.

Four times one is equal to four.

One is a factor and the product is equal to four, our other factor.

4 x 1 = 4.

You can represent multiples of one in different ways.

So we've got four groups of one here, 4 x 1 = 4.

And four times one can represent four groups of one.

And there are our four ones.

Oh, and we've got four intriguing-looking things.

But Aisha says, "Remember, multiplication is commutative.

The factor pairs are four and one.

Each of these shows four groups of one.

I can see four groups of one Jellyblobs." That's what they are.

Those are multicoloured rainbow Jellyblobs.

But there's four groups of one of them.

But we could also look at it in a different way.

What can you see on the other side of the screen? Aisha says, "Now I can see one group of four Jellyblobs." One times four can represent one group of four.

We know that multiplication is commutative, we can change the order of the factors and the product remains the same.

So four times one is equal to one times four.

What can you see now? What's the equation? Can you see? Oh, there's one extra Jellyblob.

That means there are five groups of one Jellyblob.

Aisha says, "I can see more Jellyblobs." So we've got five groups of one, 5 x 1 = 5.

What's changed and what's the same? So we've got five groups of one, five groups of one, and five groups of one Jellyblob.

Let's have a look on the other side.

We're thinking about one group of five.

So now our five counters are all in one group.

We've got one counter representing five, one group of five.

And our Jellyblobs have all clustered together to be one group of five.

And Aisha says, "I've grouped the Jellyblobs in two ways." The group size and the groupings are different.

We've got five groups of one on one side and one group of five on the other.

What's changed and what's stayed the same? Well, here we've got five groups of one, 5 x 1 = 5.

And on the other side we've got one group of five.

1 x 5 = 5.

Time to check your understanding.

10 x 1 = 10.

Can you represent this in two different ways and show it using counters? Remember we can change the order of the factors, but the product will stay the same.

So can you think about 10 times one in two different ways? Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So 10 times one can represent 10 groups of one, but one times 10 can represent one group of 10, or 10 one time.

So you can see we've got 10 individual groups of one counter and then one group of 10 counters.

We've got 10 counters each worth one, and we've got one counter worth 10.

Aisha now represents groups using coins.

So she's thinking about one times five.

So there's one group of five, and she can represent that with one group of five.

1 x 5 = 5.

She says, "I know that a 5 pence coin can represent five groups of one pennies." And a 5 pence coin is equal to one group of five and has a value of 5 pence.

It's five one time.

How else can we think about this? Well, we've got five times one, five groups of one, but we can also have one five times.

So one times five is equal to five.

And Aisha says, "I know that five 1 p coins can represent the amount 5 p.

So we can replace our one value counters for 1 p coins Five 1 pence coins is equal to 5 pence and has a value of 5 pence.

It's one five times.

1 x 5.

So, over to you to check your understanding.

Which groupings of coins show 10 p altogether? Is it A, B, or C? Pause the video, have a go, and when you're ready for some feedback, press play.

What did you think? Well B and C both show 10 p.

Two times five is equal to 10, and one times 10 is equal to 10 p.

So we've got two groups of 5 p and one group of 10 p.

Why wasn't A equal to it? That's right, we've only got eight 1 pence coins.

We'd need ten 1 pence coins to be the same as one 10 pence coin.

So A is not equal to 10 pence.

Time for you to do some practise.

You are going to need a set of cards from one to 12.

You are going to pick a card and multiply it by one, and you're going to draw two representations to show the equation.

So Aisha and Laura are showing you how to play the game.

They picked a three card.

Laura says, "I can represent 3 x 1 = 3 one three times.

I can use counters." So she's got three counters, three groups of one counter.

Aisha says, "I can represent 1 x 3 as one group of three.

I can use counters too." But she's put all her counters together in one group.

So you are going to pick a card, you are going to use that as one of your factors.

And the other factor is one, create a multiplication and represent it in two ways.

Think about all the ways you could describe it and think about commutativity, that the order of the factors can change but the product stays the same.

Pause the video, have a go, and when you're ready for some feedback, press play.

How did you get on? So they pick the card five.

And Laura says, "I can represent 5 x 1 = 5 as one five times." So she's got five groups of one counter.

And Aisha says, "I can represent 1 x 5 as one group of five." So she's got her five counters all in one group.

I wonder how you got on, what numbers did you choose? Did you represent them in a similar way with counters? I hope you had fun.

And on into the second part of our lesson, we're going to be solving word problems. Aisha has two coins of the same value.

Which amount to 10 p.

Laura has one coin but the same total amount of money as Aisha.

What could Laura's coin be? So Aisha's got two coins and Laura's got one coin, but they've got the same amount of money.

So what could the coins be? There are two groups of 5 p.

You know two times five is equal to 10 p.

So Aisha maybe could have two groups of 5 p.

And there they are.

What would Laura have then? Ah, well you also know that one times 10 is equal to 10.

So Laura has one 10 p coin.

So Aisha had two 5 pence coins that have a total value of 10 pence and Laura has one 10 pence coin, 1 x 10 = 10.

So she has a value of 10 pence as well.

They have the same amount of money but their coins look different.

Now Aisha has 10 coins of the same value and Laura has one coin.

Both have the same amount of money.

What could the coins be? What do you think? Well Aisha could have 10 groups of 1 p, 'cause we know that 10 times one is equal to 10 p.

And there are her ten 1 pennies.

So what must Laura have? Well we know that one times 10 p is also equal to 10 p.

So Laura has one 10 p coin.

So there we are, 10 ones are the same as one 10.

10 times one is equal to one times 10.

Time to check your understanding.

Aisha has five coins of the same value and Laura has one coin.

They have the same amount of money.

What could the coins be? Pause the video, have a think, and when you're ready for some feedback, press play.

What did you think? Well, Aisha could have five 1 pence coins, which is equal to 5 p, 5 x 1 = 5.

And Laura could have one 5 pence coin.

1 x 5 = 5.

Five times one is equal to one times five.

Five 1 pence coins is equal to one 5 pence coin.

Well done if you worked that out.

There are other ways they could have solved this, but not with one as a factor.

This one we had 5 x 1 and 1 x 5.

Aisha has 10 coins and Laura has one coin.

Andeep says, "Aisha has more money because she has more coins than Laura." But Jun says, "They might both have the same amount." Who's right? Well, Jun is correct.

Even though Aisha has more coins, the value of Laura's coin could be equal to Aisha's 10 coins.

Aisha might have more money, so Andeep might be correct, but it's not definitely so.

They could have the same amount of money.

Let's explore if they did.

So for example, ten 1 p coins is equal to one 10 p coin.

So Aisha could have ten 1 p coins and Laura could have one 10 p coin.

So it's not always the person with the most coins that has the most money.

Time to check your understanding.

Who has more money? Aisha says, "I have two 5 p coins.

Laura says, "I have one 10 p coin.

And Andeep says, "I have two 5 p coins.

So who has more money? Pause the video, see if you can work it out, and when you're ready for the answer and some feedback, press play.

What did you think? Well, they were all the same, weren't they? Aisha, Laura and Andeep all have the same amount of money.

They have 10 p.

Two 5 p coins is equal to 10 p, one 10 p coin is equal to 10 p and five 2 p coins is equal to 10 p.

So they all have the same amount of money.

Time for you to do some practise now.

You are going to gather a set of 1 p, 2 p, 5 p, and 10 p coins and use them to help you to answer the questions below and use your knowledge of one as a factor.

So in question one, Aisha has two coins of the same value and Laura has one coin.

Both have the same amount of money.

What could the coins be? In two, Aisha now has five coins of the same value and Laura still has one coin.

Both have the same amount of money.

What could the coins be? And in C, Laura has 10 coins of the same value and Aisha has one coin.

Both have the same amount of money.

What could the coins be? Pause the video, have a go, and when you're ready for some answers and feedback, press play.

How did you get on? So in question one, Aisha has two coins of the same value and Laura has one coin.

Both have the same amount of money.

What could the coins be? So Aisha could have two one penny coins, two times 1 p is equal to 2 p.

And Laura could have one 2 p coin.

One times 2 p is equal to 2 p as well.

Aisha could have two 5 p coins.

Two times 5 p is equal to 10 p.

So Laura could have one 10 p coin.

One times 10 is also equal to 10.

In two, Aisha had five coins of the same value and Laura had one coin.

Both have the same amount of money.

So Aisha could have five one penny coins, five times 1 p is equal to 5 p.

And Laura could have one 5 p coin.

One times 5 p is equal to 5 p.

Aisha could have five 2 p coins.

Five times two is equal to 10 p.

So Laura could have a 10 p coin.

One times 10 p is equal to 10 p.

Why couldn't Aisha have five 5 penny coins? What would five 5 penny coins be worth? They'd be worth 25 p, wouldn't they? There isn't a 25 pence coin, so no, that wouldn't work.

There's no 25 pence coin.

And in question three, Laura has 10 coins of the same value and Aisha has one coin.

So what could the coins be? Well, Laura could have ten 1 penny coins, 10 times 1 p is equal to 10 p and Aisha could have a 10 p coin.

One times 10 p is also equal to 10 p.

Well done if you found all those possible answers.

And we've come to the end of our lesson.

We've been explaining what each factor represents in a multiplication story when one of the factors is one.

We understand that when there are two factors and one factor is equal to one, then the product is equal to the other factor because we've only got one group of it.

And we can use this knowledge to solve problems, including thinking about the values of different coins.

Thank you for all your hard work today.

I hope you've enjoyed the lesson and I hope I get to work with you again soon.

Bye-bye.