Lesson video

Hello, my name's 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.

Remember, the factors are the numbers that we multiply together to make our product.

So are you ready to explore some multiplication stories and think about the factors? Let's get going.

There are two key words in our lesson today.

We've got factor and commutative, so I'll take my turn to say it and then it'll be your turn.

Are you ready? My turn factor, your turn.

My turn, commutative, your turn.

Excellent.

I wonder if you've come across those words before.

I'm sure you have.

We'll be exploring them again in our lesson today.

There are two parts to our lesson.

In the first part, we're going to be writing equations and in the second part, we're going to be interpreting problems. Ooh, we'll get to that.

Find out what interpreting means when we get to part two.

Let's make a start on part one and we've got Aisha and Laura helping us in our lesson today.

How many T-shirts are there? Can you write an equation to represent both pictures? So for the first one we've got 2 x 3 = 6.

Can you see we've got sort of two rows of three T-shirts there, two lots of three? "In 2 x 3 = 6," Aisha says, "the three is the number of T-shirts in each group and there are two groups of three." Can you see sort of two rows of three T-shirts in that first picture? So we can represent that with 2 x 3 = 6.

What about the second one? So all we can write, oh, 3 x 2 = 6.

"In 3 x 2 = 6, the three still represents the number of T-shirts in each group, because we can say it is three, two times." So this time we've got two columns of three T-shirts.

We've got three blue ones and three brown ones.

So we can say it's three groups of two or we can say it is three, two times and we remember that multiplication is commutative, two times three is equal to six and three times two is equal to six, because multiplication is commutative.

That's one of our key words, isn't it? Listen out.

That's going to be really important in our lesson.

How many fingers are there all together? We've got two pictures there.

What do you notice? Can you write an equation to represent both pictures? Well in our first picture, we've got three groups of five fingers.

We've got three hands each with five fingers on or four fingers and a thumb if we're being really precise, but five on each hand.

So we've got three groups of five.

What about the other picture? What can you see there? Well, we've got five groups of three haven't we? Each hand is holding up three fingers this time and we've got five groups of them, but remember, multiplication is commutative, so the product will remain the same, 3 x 5 = 15, but five times three is also equal to 15.

There are 15 fingers showing in each picture.

Laura says in 3 x 5, the five is the number of fingers in each group and there are three groups of five.

In 5 x 3, the three represents the number of fingers in each group, because it is five groups of three.

So the job that each factor is doing has changed.

In one picture, three represents the number of groups and in the other picture it represents how many are in each group and in the first picture, the five represents the number in each group and in the second picture, the five represents the number of groups, but the product will be the same.

It's 15.

Multiplication is commutative.

We can change the order of the factors and the product stays the same.

So what's the same and what's different here? What can you see? We've got one 10 pence and ten one pence pieces.

We've got one group of 10.

So that 10 pence represents one group of 10 and we've got 10 groups of one.

Can we represent those with equations, do you think? The value of each coin is different, but the total amount of money is the same.

One, 10 pence is equal to 10, one pences.

One group of 10, one times 10 is equal to 10 or 10 groups of one is equal to 10, 10 times one.

The value of the money is the same.

It may look very different this time, but the value of the money is the same.

Laura says, "I can see one 10 pence coin and ten one pence coins, one times 10 and 10 times one." There are 10 groups of one p coins.

So can you use what you know about commutative to describe the images below? We've got a five pence coin this time and we've got five one pence coins.

So can you describe them and can you represent them with an equation? Pause the video, have a go and when you're ready for the answers and some feedback, press play.

What did you see? Well, there's one five pence coin and there are five one pence coins.

So we can say five times one and one times five.

There are five groups of one p coins and that's equal to five pence and there's one five pence coin and that's equal to five pence as well.

So we can represent that with five times one or one times five, we can change the order of the factors and the product stays the same.

Both of those are worth five p, one five P coin and five one p coins.

Well done if he's spotted that.

Oh, we've got some ice creams here.

If one ice cream costs two Pounds, how much do four ice creams cost? So what's the multiplication equation needed to solve this equation? This time we know what each factor's going to represent, don't we? Let's have a look.

So you know that one ice cream costs two Pounds, that's one factor and there are four ice creams. That's the other factor.

We're trying to work out what the total cost is.

So we've got four groups of two, four ice creams costing two Pounds each, four lots of two Pounds and that's equal to eight Pounds.

So four ice creams will cost eight Pounds altogether.

There are four groups of two Pounds, so we can use our two times table.

Four times two is equal to eight, eight Pounds altogether.

We've got some lollipops here.

They look very bright and colourful.

I wonder if they're multi fruit flavoured lollipops.

What do you think? If one lollipop costs five p, how much does six lollipops cost? Can we write a multiplication equation to represent our problem? Let's have a think.

Well we know one lollipop costs five pence, so that's going to be one of our factors and there are six lollipops, so that's the other factor.

So we've got six lots of five pence, six times five pence is equal to 30 pence.

We know that six fives are equal to 30.

We could skip count five, 10, 15, 20, 25, 30.

Count six lots of five and we've got 30 p.

Six lollipops will cost 30 p altogether.

There are six groups of five p.

Here's another one.

If one eraser costs 10 p, how much do four erasers cost? Again, what's the multiplication equation we need to solve this problem? We know that one eraser costs 10 pence, "That's one factor" says Laura, what's the other factor going to be? That's right.

"There are four erasers.

That's our other factor." So we've got four lots of 10 p, four times 10 is equal to 40.

We know that from our skip counting in tens and our 10 times table.

So four erasers will cost 40 p altogether.

It's time to check your understanding now.

What's the multiplication equation needed to solve this problem? If one eraser costs 10 p, how much do five erases cost? 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 you know that one eraser costs 10 pence and that's one factor and how many erases were there? That's right, there are five and that's the other factor.

So we've got to work out what five lots of 10 pence are.

So five times 10 and that's equal to 50.

So five erasers will cost 50 p altogether and now it's time for you to do some practise.

In question one, you're going to solve the word problems below using your knowledge of the two, five and 10 times tables and you're going to solve the equations.

So in A, if one ice cream cost two Pounds, how much does six ice creams cost? And we've given you the six as one of the factors there.

In B, if one T-shirt costs 10 Pounds and Ms. Hopkins buys five, how much will she spend altogether? Can you work out which are the factors that you've got to multiply together to find out how much Ms. Hopkins spends? And in C there are five boxes of three apples.

How many apples are there all together? In D, a baker bakes 10 pastries every hour.

He baked 80 pastries, how many hours did he bake for? And in E, Aisha scored five points in every round of her game, she scored 60 points.

How many rounds of the game did she play? 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 question one said if one ice cream costs two Pounds, how much does six ice creams cost? Well that's six lots of two Pounds.

So six times two is equal to 12.

So the ice creams cost 12 Pounds.

In B, if one T-shirt costs 10 Pounds and Ms. Hopkins buys five of them, how much will she spend altogether? So she spent five lots of 10 Pounds, five times 10 is equal to 50, so she spent 50 Pounds and in C there are five boxes of three apples.

How many apples are there all together? So there are five lots of three apples, five times three is equal to 15.

Five, three times we could think about to use our five times table.

So there'll be 15 apples all together and in D, a baker bakes 10 pastries every hour.

He baked 80 pastries.

How many hours did he bake for? So we had a missing number here.

So we know he baked 80 pastries altogether and we know that one of our factors was 10.

So 10 times what is equal to 80? Well it's 10 times eight isn't it? Eight tens are 80.

So he must have baked for eight hours.

We could have skipped counted in tens.

10 pastries is one hour, 20 pastries, two hours and so on all the way up to 80 pastries and that would've been eight counts of 10, so eight hours and in E Aisha scored five points for every round she played in her game, she scored 60 points.

How many rounds did she play? Again, we know that five is one of our factors, but this time 60 is our product.

60 is the total, our whole amount.

So how many groups of five are there in 60? Well we can count up to 60 in fives and we'd count 12 lots of five, so Aisha played 12 rounds.

12 times five is equal to 60.

Well done if you've got all of those right and on into part two of our lesson.

This time we're going to be interpreting problems. So we're gonna be thinking about problems and working out what they mean and how we can represent them.

So what's the same and what's different? We've got two times six is equal to 12 and six times two is equal to 12.

What do you notice? Well we can see that the factor pairs, two and six and the product are the same.

So two times six is equal to 12 and six times two is equal to 12, but what's different is the order of the factors, we've changed them around, but we know that multiplication is commutative, so we can change the order of the factors and the product stays the same and Laura's pointing out, "This is the law of commutative and it can help us to solve problems." Because we know the two times table, we can use six times two to work out two lots of six, because we know that we can change the order of the factors.

So if we don't know what two sixes are, we do know what six lots of two are and that's equal to 12.

So we can identify the factors even when we are not using our two, five and 10 times tables.

So let's have a look at these cakes and the candles.

How many candles are there altogether? There are two groups of six candles and we're going to think about this using multiplication.

The two represents the number of cakes, that's one of our factors and the six represents the number of candles in each cake.

So we've got two times six, two groups of six and we know from the previous slide that, that's equal to 12.

There are six candles, two times, six times two and now we can use our two times table, can't we? Six times two is equal to 12.

We could represent this using repeated addition.

Six plus six is equal to 12, but it's much quicker to solve this using multiplication.

If we know that six twos are 12, then that's an easy way, an efficient way of solving our problem.

So we're really thinking about multiplication today.

How many candles are there altogether here? Well there are four groups of three candles.

So we can say that four times three is equal to 12.

We know that there are 12 altogether.

We could represent it as repeated addition, but we are thinking about multiplication today, but that is the same.

Three plus three plus three plus three is the same as four, lots of three.

The four represents the number of cakes and the three represents the number of candles in each cake.

There are three candles, four times, so we know we can represent the multiplication as three times four and we can think about that as three candles, four times.

Time to check your understanding.

How many candles are there all together? Can you complete the stem sentences and the equations to represent that, thinking about commutativity, thinking about changing the order of the factors and what the factors represent? 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 there were six groups of three candles? We've got six cakes, with three candles on each cake.

So we can say six times three and it's equal to 18.

We can also say there are three candles, six times.

So we could record our multiplication as three times six is equal to 18, because we know that multiplication is commutative, we can change the order of the factors and the product stays the same.

So six times three is equal to three times six and they're both equal to 18.

There are some sweets in boxes.

So what situations can the equation represent? We've got three times four is equal to 12 and Laura says we can represent this in two ways, because multiplication is commutative.

She says the three could represent the number of boxes.

So if the three represents the number of boxes, what must the four represent? Ah, and the four could represent the number of sweets in each box.

So we've got three groups of four, three times four is equal to 12, but the four could also represent the number of boxes.

So if the four represents the number of boxes, what must the three represent? That's right, the three could represent the number of sweets, so four times three is equal to 12.

We've still got 12 sweets, but our factors have swapped their jobs.

In one equation, the three represents the number of boxes and in the other one it represents the number of sweets, but because we know multiplication is commutative, the product stays the same.

Let's have a look at another situation.

We've got two times 8 is equal to 16 and again Laura says we can represent this in two ways, because multiplication is commutative.

Let's have a look.

So the two could represent the number of boxes.

So the eight would represent the number of sweets in each box, two groups of eight and that equals 16, two times eight, but the eight could represent the number of boxes, couldn't it? And then the two would represent the number of sweets in each box.

So we'd have eight times two and we've still got 16 sweets, because multiplication is commutative.

We can change the order of the factors and the factors can change their jobs, can't they? The factor pairs and the product are the same, the order is different.

Multiplication is commutative.

Over to you, using the counters, what situations can the equation represent? You might want to think about sweets and boxes again.

So you've got four times two is equal to eight.

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

How did you get on? Did you draw something that looked a bit like this? So we could represent this in two ways because we know that multiplication is commutative.

So this first way, the two could represent the number boxes, if you were thinking about the sweets again or the number of groups and the four could represent the number of counters in each box or the sweets in each box.

So that's representing two groups of four, two times four is equal to eight and what about the second way? Well the four could also represent the number of boxes.

So we've got four boxes or four groups this time and the two represents the number in each box or the number of counters or the number of sweets.

So here we've got four times two, four groups of two.

I hope you were successful with that.

Time for you to do some practise now.

Now in question one, you are thinking about how many candles there are all together.

So we've told you there are two groups of three candles and there are three candles two times.

Can you write the equations that go with those images? So you've got two groups of three candles and you've got three groups of hmm candles on the other side.

Can you fill in the blanks in those stem sentences and in the equations and think about what's the same and what's different.

In question two, you've got lots of fingers there, haven't you? So you've got fingers that are just five fingers and where we've got them joining at the thumbs, we've got 10 fingers there.

So have a think about what those pictures are showing you.

Fill in the gaps in the stem sentences and the equations as well and finally, there are some cakes in boxes.

What situations could the equations represent? So can you think of two different ways to draw cakes in boxes to represent six times four is equal to 24 and in B, three times seven is equal to 21.

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

How did you get on? So in one, we had two groups of three candles.

Two times three is equal to six or there are three candles, two times, three times two is equal to six and in the other picture we had three groups of two candles.

Three times two is equal to six or there are two candles, three times.

Two times three is equal to six.

Did you notice that the factor pairs and the product are the same? We've got three and two as our factors and six is our product, but the groupings are different and the order of the factors changes, but we know that because multiplication is commutative, we can change the order of the factors, but the product stays the same and in two, we had six groups of five fingers to begin with.

Six times five is equal to 30 or there are five fingers, six times, five times six is equal to 30 and in the other picture we had three groups of 10 fingers.

Three times 10 is equal to 30 or there are 10 fingers, three times, 10 times three is equal to 30.

Did you spot that? Because we'd put the hands together, we had half the number of groups, because we had double the number of fingers and for question three, you were looking at the different ways that we could interpret six times four in A.

So we could say that the six represented the number of groups and the four represented how many were in each group.

So we've got six boxes with four cakes in each box or the four could represent the number of boxes and the six could represent the number of cakes.

So here we've got four groups of six, four times six, but we know that there are 24 cakes in total both times and for B you had three times seven is equal to 21.

So the seven could have represented the number of boxes and the three could have represented the number of cakes.

So in the first image we've got seven groups of three and that's 21 cakes altogether and then on the right hand side of our screen, the three could have represented the number of boxes and the seven would've been how many cakes were in each box.

So three times seven is equal to 21.

I hope you found all those different ways of representing the cakes in the boxes and we've come to the end of our lesson.

We've been explaining what each factor represents in a multiplication story.

We understand that in a multiplication, one factor represents the group size and one factor represents the number of groups and by identifying the group size and the number of groups in the multiplication story, we can solve the problem and we can record it with an equation.

Well done.

You've worked really hard today.

Thank you very much for all your mathematical thinking and I hope I get to work with you again soon.

Bye-Bye.