Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson.

Are you ready to do some maths? This lesson comes from the unit "Division with remainders." So we're going to be thinking a bit more about division, how we can represent it, how we can record it, and what it means to have remainders.

So if you're ready to make a start, let's get going.

In this lesson, we're going to be representing and interpreting division by sharing where there is a remainder.

You may have thought about sharing as a grouping way of organising things, but we're going to think about when division is represented by sharing items. So let's have a look at what's in our lesson.

We've got three key words, share, remainder and division.

I'll take my turn and then you can have your turn to practise them.

Are you ready? My turn, share, your turn.

My turn, remainder, your turn.

My turn, division, your turn.

Well done, I'm sure they're words you've used before.

Let's just remind ourselves what they mean 'cause they are going to be useful to us today.

Sharing is when a whole amount is split into equal parts or groups.

We know the total number of objects and we know the number of parts it is split into, but we don't know how many there are in each part.

A remainder is the amount left over after division when the dividend does not exactly divide by the divisor.

The dividend is the whole that we start with and the divisor is the number we're dividing by and division is splitting into equal parts or equal groups.

And today, we're going to be focusing on splitting into equal parts and finding out the value of each part.

There are two parts to our lesson today.

In the first part, we're going to be describing and representing division as sharing.

And in the second part, we're going to be representing division as sharing with remainders.

So let's make a start on part one.

And we've got Jun and Sofia helping us in our lesson today.

Sofia has 12 counters.

She wants to divide them equally between her three friends.

I wonder how many counters they will each receive.

Have you met her friends before? We've got Izzy, Andeep, and Aisha.

Sofia says, "We know that there are two types of division.

Division can be grouping or division can be sharing.

Let's look at an example of each and then we can decide how to solve this problem." We can divide by grouping.

We divide into equal groups, subtracting each group from the whole.

So for example, there are six counters and Sofia gave each of her friends three counters.

How many friends could she give counters to? In this problem, we subtract groups of three from the whole to give three counters to each friend.

So one group of three, two groups of three.

We subtracted two groups of three from six.

So Sofia could give three counters to two of her friends.

There we go, Izzy and Andeep have three counters each.

Six is equal to hmm times three or three times hmm.

Two, six is equal to two times three, two groups of three or three, two times.

And six divided by three is equal to two.

Six divided into groups of three is equal to two groups.

But we can also divide by sharing.

We divide equally between groups by subtracting groups to share out.

So for example, there are six counters and Sofia shared them equally between her friends.

How many counters did they each receive? In this problem, each time we give every friend a counter, we must subtract a group of three 'cause we've got three friends.

So we take away one group of three, that's one counter each.

Another group of three, that's two counters each.

So we subtracted two groups of three from six.

Each of the three friends received two counters.

Six is equal to two times three or three, two times.

Six divided between three is equal to two each.

So this time we divided between the three children and they each got two counters.

Now let's return to the original problem.

Sofia has 12 counters.

She wants to share them equally between her three friends.

I wonder how many counters they will each receive.

Can you see? She says, "I am dividing equally between my friends, so this is a sharing problem." We know how many friends she's dividing between, we don't know how many counters they will each get.

12 is equal to something times three.

And the something this time will be how many counters they get each.

There are three children so I must subtract one group of three to share it out.

So one lot of three, that's one each.

To give them another counter each, I share out another three counters.

Two groups of three, that's two each.

And another one, three groups of three, that's three each.

Four groups of three, that's four each.

So each time she shares, she takes three counters to give them one each.

Each child receives four counters.

12 is equal to four times three.

But instead of saying four groups of three this time, we've got four, three times or three groups of four.

Let's look at this on a bar model.

One group of three, that's three, one each.

Two groups of three, that's six, two each.

Three groups of three, that's nine, three each.

Four groups of three, that's 12, four each.

So the number of groups we make is the same as the number of counters that each child will get.

12 divided between three is equal to four each.

Each child receives four counters.

Time to check your understanding.

Use a set of 12 counters and share them between four people.

Remember to subtract a group of four to share out each time.

Write a multiplication equation and record this as a bar model to help you.

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

How did you get on? So we're thinking 12 is equal to hmm groups of four and 12 is equal to four, hmm times.

So one group of four, that's four, one counter each.

Two groups of four, that's eight, two counters each.

Three groups of four, that's 12, three counters each.

So there were three groups of four.

So that meant that each child gets three counters.

So 12 is equal to three times four and 12 is equal to four groups of three.

So we have four friends, they each get three counters 'cause we were able to make three groups of four from our 12.

And there's our bar model.

12 is equal to four groups of three.

We know sharing is a type of division so we can represent it as a division equation like this.

What do each of the parts mean? Our 12 is the whole, 12 is the dividend, the whole that we're starting with.

We're sharing between three so we need to subtract groups of three to share out.

Three is the divisor.

We're dividing by three.

This time though we're thinking of dividing between three.

We are making three groups and we want to know how many are in each group.

But we can do that by subtracting groups of three and each group of three means one each for the children.

And there are four groups of three in 12.

Four is the quotient, the answer, the result of our division.

Time to check your understanding.

Write a division equation to represent the counters that have been shared out here.

Remember, a group is subtracted to share out between the children.

So think about how many you are sharing between.

Pause the video, have a go.

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

How did you get on? So we had 12 and we were dividing between the four children.

So 12 divided by four.

12 is the dividend, it's the number of counters that we're sharing.

We're sharing between four so we need to subtract groups of four to share out.

Four is the divisor.

So we can make three groups of four.

So each time we take out a group of four, that's one counter for each child.

So three groups means three counters each.

So our quotient is three.

There are three groups of four in 12.

This time Sofia shares eight counters between two friends.

There are two friends.

So each time we give both friends a counter, we will subtract a group of two.

So Izzy and Andeep are sharing the counters.

One each means we subtract one two, so that's two.

Two each means we subtract two twos, so that's four.

Three each means we subtract three twos, that's six.

And four each means we subtract four twos and that's eight.

So can we fill in the stem sentence? Hmm divided between hmm is equal to hmm each.

What did we do? Well, we had eight counters in total and we divided between the two friends.

We could make four groups of two.

Each time we made a group of two, that was one counter each.

So four groups means four each.

Eight divided between two is equal to four each.

When we divide, we subtract equal groups from the whole.

Let's write a division equation and explore this on a number line.

So we're sharing between two so the divisor is two.

Eight divided by two is equal to hmm.

Eight divided between two is equal to hmm.

So we had eight.

We took away our first group of two, that was one each.

Our second group of two, that's two each.

Three groups of two, that's three each.

Four groups of two, that's four each.

We've subtracted four groups of two.

We've got no counters left.

So we've subtracted four groups.

There are four groups of two.

So each of the children receives four counters each.

The number of groups we can make is the number that each child gets.

It's usually easier to count forwards and use your multiplication facts.

So let's look at that same thing counting forwards.

One group of two, we've used two counters.

Two groups of two, we've used four counters.

Three groups of two, we've used six counters.

Four groups of two, we've used all eight counters.

We've made four groups.

The number of groups represents the number that each child gets.

So they each get four counters.

Eight divided between two is equal to four.

Eight is equal to four groups of two, two groups of four.

And this time we are looking at two groups of four that we've made from our eight counters.

Each child gets four.

Time for you to do some practise.

You are going to use counters to divide by sharing.

Write a multiplication equation and show your thinking on a number line and then write a division equation and count back on the number line.

So in A, you're sharing 10 counters between five children, in B, 20 counters between five children, in C, 18 counters between three children and, in D, share 18 counters between six children.

So explore those equations and using your number line to count forwards and backwards.

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

How did you get on? So in A, you are sharing 10 counters between five children.

So we were going to subtract a group of five each time we're dividing by five.

10 divided by five is equal to something but it's 10 divided between five and then 10 is equal to hmm times five.

So we're sharing between five.

So we need to subtract groups of five to share out.

So there's one group of five, that's one each.

Two groups of five, that's all the counters and that's two each.

The children receive two counters each.

10 divided between five is equal to two.

It's usually easier to count forwards to use your multiplication facts.

So let's look at that too.

So one group of five, that's five, one counter each.

Two groups of five is 10, that's 10 counters all used, that's two counters each.

When there's no remainder, we are counting forwards and backwards using our multiples.

But if we think there might be a remainder, it's often easier to count forwards.

10 is equal to two groups of five.

So if we're sharing 10 between five people, we can make two groups of five so that means two each.

In B, we had 20 counters to share between five children.

So again, we're thinking about groups of five.

We're sharing between five.

So we need to subtract groups of five to share out.

One group of five, that's one each, 15 left.

Two groups of five, that's two each, 10 left.

Three groups of five, that's three each, five left.

Four groups of five, we've used all our counters.

So four groups of five means four counters each for the children.

But let's think about that counting forwards 'cause that can be easier.

So one group of five, one each.

Two groups of five, two each.

Three groups of five, three each.

Four groups of five, four each.

20 is equal to four times five.

So you may have noticed that 10 counters divided between five children is equal to two each.

20 is double 10.

So when 20 is divided between five they receive double in number of counters, which is four each.

Can you see there's a two lots of 10 there? And so they've each got two lots of the 10 counters shared out so they've got four each this time.

In C, we had 18 counters shared between three children.

So there are the three children.

We're sharing between three so we need to subtract groups of three to share out.

One group of three.

Two groups of three.

Three groups of three.

Four groups of three.

Five groups of three.

And six groups of three.

And there on our number line, we subtracted a group of three each time.

And when we subtracted six groups of three, we ended on zero on the number line.

So the children received six counters each.

18 divided between three is equal to six each.

Let's think about that counting forwards which can be easier.

So how many groups of three are there in 18? One group of three, one each.

Two groups of three, two each.

Three groups of three, three each.

Four groups of three, four each.

Five groups of three, five each.

Six groups of three, six counters each.

18 is equal to six groups of three.

So the children get six counters each.

So indeed, we've got 18 counters again but we're sharing between six children.

Do you notice something here? We're sharing between six.

So we need to subtract groups of six to share out.

So let's subtract groups of six.

One group of six, that's one each.

Two groups of six, that's two each.

Three groups of six, that's three each.

And that's all our counters, three groups of six.

So 18 divided between six is equal to three.

The children receive three counters each.

But remember we could always count forwards.

So let's have a look at that.

So one group of six is one each, two groups of six is two each, three groups of six is three each and three groups of six is equal to 18.

So 18 is equal to three times six.

So with sharing out between six, and we can do that three times so each child gets three counters.

Did you notice that we have twice the number of children this time? Six is double three.

So if 18 divided by three is equal to six, then 18 divided by six will be equal to three.

We've got twice as many children so they get half the number of counters.

Can you see that? We've halved the number of children.

So they get double the number of counters.

Double the number of children, they get half the number of counters.

I hope you spotted that as well.

And on into the second part of our lesson.

We are representing division as sharing but with remainders this time.

So this time Jun has 14 counters and he wants to share them equally.

Between his three friends.

He says, "I wonder how many counters they'll each receive." So what is it we're dividing by this time? Well, we're dividing by three but 14 is not a multiple of three.

"So I know there will be a remainder," says Jun.

So here are our equations that we can use.

14 is equal to something times three plus our remainder or three times something plus our remainder.

And 14 divided by three will be equal to hmm remainder hmm.

Jun says, "There are three children, so I subtract one group of three to share it out." So one group of three, that's one each.

To give them another counter each, I share out another three counters.

So two groups of three, two counters each.

And we carry on.

Three groups of three is three counters each.

Four groups of three is four counters each.

Can we make another group of three? Hmm.

No.

Each child receives four counters, one for each of the shares of three and there's a remainder of two.

So 14 is equal to four times three plus two or three times four plus two.

And 14 divided between three, shared between three is equal to four remainder two.

They get four counters each and there are two counters remaining.

Let's look at this on a bar model.

So one group of three, that's three, one counter each.

Two groups of three, that's six, two counters each.

Three groups of three, that's nine, three counters each.

Four groups of three, that's 12, four counters each, but with a remainder of two.

So 14 divided between three is equal to four each with a remainder of two.

Each child receives four counters and there are two left over.

Time to check your understanding.

Use a set of 14 counters and share them between four people.

Remember to subtract a group of four to share out each time.

Write a multiplication and a division equation and record it as a bar model to help you.

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

How did you get on? So this time we're thinking about 14 and we're dividing between four.

So we need to make groups of four, our divisor is four.

14 is equal to hmm groups of four plus hmm or four groups of hmm plus hmm.

And 14 divided between four is equal to hmm remainder hmm.

We know that 14 is not in the four times table.

So let's start.

One group of four, that's four, one each.

Two groups of four, that's eight, two each.

Three groups of four, that's 12, three each.

And we've got a remainder of two.

So each child receives three counters and there's a remainder of two.

And we know that because we know that 14 is equal to four times three plus two.

So if we know it's three times four and two more, we know that 14 divided by four will be three each and a two left over.

And our bar model there shows 14 made of four groups of three plus two.

Each child will get three counters and there'll be two left over.

This time, Jun shares 10 counters between four friends.

There are four friends so each time we will give all of the friends a counter, we will subtract a group of four.

Let's have a look.

Well, we also know that 10 is not a multiple of four so there will be a remainder.

So one each means we subtract one four, so that's four.

Two each means two fours, so that's eight out.

Ah, and there's a remainder of two.

So 10 divided between four is equal to two each with a remainder of two.

We know that two times four is equal to eight.

So two groups of four can be made.

So that's two counters each and there'll be a remainder of two.

Let's write the division equation and explore it on a number line.

We're sharing between four children so the divisor is four.

10 divided by four or divided between four is equal to hmm remainder hmm.

So we're starting with 10.

We've subtracted four, that's one group of four, that's one counter each.

Two groups of four, that's two counters each.

And that leaves us with two left over.

10 subtract four subtract four is equal to two.

So 10 divided between four is equal to two remainder two.

The children receive two counters each and there's a remainder of two.

It's usually easier to count forwards, especially when we're dealing with remainders in a way because we can count in our multiples.

So the divisor is four because I'm sharing between four.

So we're subtracting groups of four to share out.

Two times four is equal to eight and I cannot make another group of four from 10 so there'll be a remainder of two.

So we can use our multiplication facts.

One group of four, two groups of four is equal to eight.

And I can't make another group of four because I've only got two left.

So it must be two groups of four, remainder two.

So 10 divided between four is equal to two remainder two.

Sofia has 26 counters and she shares them equally between her three friends.

How many counters do they each receive? The children think they can use their multiplication facts to solve this problem without using the counters.

So we've got 26 divided by three or shared between three is equal to hmm remainder hmm.

How do they know it's a remainder? Oh, well, 26 isn't in the three times table, is it? But we are sharing between three children so the divisor, the number we are dividing by, is three.

Each time we subtract a group of three, the children receive one counter.

We can use our multiplication facts to know how many threes are in 26.

We know that eight times three is equal to 24.

So there are eight groups of three in 24 and two counters left over from the 26.

Nine times three is equal to 27.

That's more counters than we've got though.

So we need to think about the multiple less than our dividend or our number that we're dividing if it's not exact.

So eight times three is equal to 24.

We can see that by counting on our number line.

And we've got two left over.

So we subtract eight groups of three.

So the children receive eight counters each.

There are two counters left over.

So there's a remainder of two.

26 divided by three is equal to eight, remainder two.

And it's time for you to do some practise.

Use counters to divide by sharing, write a multiplication equation and show your thinking on a number line.

And then write a division equation and maybe count back on a number line just to check.

So in A, you're going to share 22 counters between four children.

In B, you're going to share 22 counters between eight children.

Hmm, I wonder if you'll notice something there.

In question two, again, you're going to use multiplication facts to divide by sharing.

Record it as a multiplication equation and a division equation and then draw a number line to prove that you're right.

Maybe counting on this time 'cause we are using our times table facts.

So in A, you're going to share 51 counters between eight children.

And in B, you're going to share 51 counters between four children.

Hmm, will you spot something there, I wonder? Pause the video, have a go at questions one and two.

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

How did you get on? Let's have a look at then.

Share 22 counters between four children.

So we're sharing between four.

So we need to subtract groups of four to share out and it's usually easier to count forwards to use your multiplication facts.

So let's count forwards.

One group of four is four, one each.

Two groups of four is eight, two each.

Three groups of four is 12, three each.

Four groups of four is 16, four each.

Five groups of four is 20, that's five each and a remainder of two.

So 22 is equal to five times four plus two, five groups of four plus two.

22 divided between four is equal to five remainder two.

The children receive five counters each with a remainder of two.

We could also have counted backwards, but this would've been harder because we would not have been able to use our multiplication facts.

So when we know there's a remainder, counting forwards helps us, but we need to know that the remainder is the difference between the multiple that we've got to and our total, our dividend.

In B, we were sharing 22 counters between eight children.

So we need to subtract groups of eight.

So we'll find out how many eights there are in 22.

We're gonna count forwards so we can use our multiples of eight.

One group of eight, that's one counter each.

Two groups of eight is 16, that's two counters each.

And where are we getting to, 22? Ooh, we've got six counters left that we haven't got another whole group of eight, have we? So 22 is equal to two groups of eight plus six, two times eight plus six.

So 22 divided between eight will be equal to two remainder six.

The children will receive two counters each, but there's a remainder of six.

It's a big remainder, isn't it? But we can't make another group of eight, so we can't share them out as whole counters.

We could have counted backwards, but again, because we have a remainder, we wouldn't have been using our multiplication facts.

But there we are on a number line.

If we subtract eight, we get to 14, subtract another eight, we get to six, and that's our remainder, six left.

So for two A, we were sharing 51 counters between eight children.

So we're sharing between eight, so each time we subtract a group of eight, the children receive one counter.

We're going to use our multiplication facts in the eight times table.

We know that six times eight is equal to 48.

That's the biggest multiple of eight we can get without going past 51.

So there must be six groups of eight in 48 and 48, 49, 50, 51, three remaining.

So there are six groups of eight in 48 and three counters left over from the 51, 48 plus three is equal to 51.

So we can make six groups of eight and three left over.

So each of the children receive six counters and there's a remainder of three.

51 is equal to six times eight plus three, 51 divided between eight is equal to six remainder three.

Now we're going to share the 51 counters between four children.

So this time we're going to subtract a group of four and each child will receive one counter.

But again, we're going to use our multiplication facts.

How many fours are there in 51? Well, we know it's not going to be exact because 51 is an odd number and all the multiples of four are even.

If we know our four times table, we know that 12 times four is equal to 48 and that means that there are three more, 48 plus three is equal to 51.

So 51 is equal to 12 times four plus three.

So 51 divided between four must be equal to 12 each and the three remaining.

So the children receive 12 counters each with a remainder of three.

Did you notice that link between A and B here? You may have noticed that four is half of eight.

So if 51 divided by eight is equal to six with a remainder of three, then 51 divided by four must be equal to 12 with a remainder of three.

We've got half as many children so they'll get twice as many counters each.

Well done if you spotted that.

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

We've been representing division by sharing with equations.

What have we been thinking about? Well, we can write a multiplication and addition equation to represent division between groups or sharing.

And we can write a division equation to represent division between groups or sharing.

We can count forwards to find the number of equal groups to be shared out.

And we can also count backwards to find the number of equal groups to be shared out.

It's usually easier to count forwards because we can use our multiplication facts to help us, but we have to be careful that we then have to find the difference between the multiple that we get to and our dividend or our whole if it's not an exact number of times.

Thank you very much for your hard work and exploring division today.

I hope you've enjoyed it and I hope I get to work with you again soon, bye-bye.