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 solving division problems involving sharing, sometimes with remainders.

I wonder if you can spot when there's going to be a remainder.

Can you use your times table facts? Times table facts are really useful when we're doing division, so have yours at your fingertips ready to use today.

There are three key words in our lesson, sharing, division, and remainder.

They may well be words you're familiar with, but let's just rehearse them and remind ourselves what they mean.

I'll take my turn, then it'll be your turn.

My turn, sharing.

Your turn.

My turn, division.

Your turn.

My turn, remainder.

Your turn.

Well done.

You may have considered different ways of thinking about division, but we are going to be thinking about sharing today.

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

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

Division is splitting into equal parts or groups.

We are splitting into equal parts today and working out using our multiplication knowledge and our skip counting, working out how many are in each part.

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

The dividend is the number we start with, our whole, and the divisor is the number we are dividing by.

So today, it's the number of groups we are making.

There are two parts to our lesson.

In the first part, we're going to be solving division problems with no remainder.

And in the second part, we're gonna be thinking about remainders.

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

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

Jun and Sofia are helping on the cake stall at the Summer Fayre.

Jun says, "We divide the cakes and cookies equally between the bags and boxes so that each customer receives the same number." Really good idea, Jun.

So, we've got cookies in a bag, we've got cakes in boxes, and we've got chocolate cakes in boxes as well.

Jun has 24 cookies to share equally between six bags.

How many cookies will there be in each bag? Jun says, "Let's think about the equation we will write to represent this." We could just share out those cookies, couldn't we? But what's it going to look like when we represent it as an equation? Sofia says, "We know sharing is a type of division so we can write a division equation." 24 is our whole, it's our dividend, and we are dividing by six because we are dividing our cookies between six bags, and we want to make sure there's the same number in each bag or we want to find out how many there are going to be in each bag.

So, 24 divided between six.

And as Sofia says, we are dividing between six bags.

So, the divisor, the number we're dividing by, is six.

Jun says, "We will share out one group of six at a time so that we can use our multiplication facts.

We could also write a multiplication equation." 24 is equal to six times, hmm.

How many groups of six are we going to be able to make? Each group of six means one cookie in a bag.

24 is equal to six groups of, hmm.

That's what we are thinking about today.

The total number of cookies we have to share is 24.

So, that's the dividend in our division and it's also the product of our multiplication.

So, the product of our multiplication when we write it as a division becomes the dividend, the whole in our division.

And six is one of our factors, and it's the dividend, it's the number of groups or bags we're sharing between.

And the unknown is the size of the group or the number of cookies in each bag.

So, let's have a look.

There are six bags.

So, every time we put one cookie in a bag, we are taking out one group of six to share out.

We need to find out how many groups of six are in 24.

So, there's our 24, and there are our six bags.

And our bar model has six parts and they need to be equal.

One cookie each, that's six, one group of six.

Two cookies each, that's two groups of six, that's 12.

Three cookies in each bag, that's three groups of six, that's 18 cookies used.

And four, four cookies in each bag, four groups of six, that's 24.

Did you know your times table fact for that? Six times four is equal to 24.

So, there are four cookies in each bag.

We took out four groups of six, and the number of groups we take out is how many cookies are in each bag.

So, there are four cookies in each bag, 24 is equal to six times four.

And 24 divided by six is equal to four.

24 divided between six bags means four cookies in each bag.

Time to check your understanding.

Can you write a division and a multiplication equation to represent this problem? Then draw a bar model to help you solve it.

Sofia has 28 cookies, and she decides to divide them between four bags.

Pause the video, have a go at writing the division and the multiplication, and see if you can use a bar model to help you.

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

How did you get on? So, this time, we had 28 cookies in total, that was our whole, so that's our dividend, the number we are dividing.

We had four bags, so we're dividing between four.

So, four is our dividend.

We can also think as a multiplication because we want to know how many groups of four are we going to take out before we've run outta cookies.

And the number of groups we take out will be the number of cookies in each bag.

So, 28 is equal to four times something.

And here's our bar model, 28 divided into four equal groups.

We know there are four groups, we dunno how many are in each group at the moment.

Although, how's your four times table? Have you worked it out yet? So, one group of four means one cookie each.

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

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

Four groups of four, that's 16, that's four cookies each.

Five groups of four, that's 20 cookies used, that's five cookies each.

Six groups of four is 24, that's six cookies each.

And seven groups of four, that's 28, that's seven cookies each.

Once shared out, there are four bags of seven cookies.

Seven cookies in each bag.

28 is equal to four times seven.

So, 28 divided between four will be equal to seven.

Jun is selling cakes.

He has 30 cakes and he's dividing them between six boxes.

Let's look at what's actually happening here.

He says, "I am dividing between six boxes, so the divisor is six." We can visualise each group of cakes Jun takes to share on a number line.

He's got 30, and he's dividing them between six boxes.

So, our bar model represents the whole of 30 and the six boxes.

We need to know how many cakes will be in each box.

So, he's dividing by six, so he's going to take out six cakes at a time.

He says, "I take six cakes and put one in each box, that's six.

Two cakes in each box, that's 12, two groups of six.

Three cakes in each box is 18, three groups of six is 18.

Four cakes in each box is 24, four groups of six is 24.

And five cakes in each box is 35 groups of six is equal to 30." So, he's shared out all 30 cakes.

He was able to take five groups of six cakes, so that means five in each box.

30 is equal to six times five.

So, 30 divided between six is equal to five.

There'll be five cakes in each box.

Sofia says, "The number line shows us what is happening.

It actually shows five groups of six being taken to share." Five groups of six is equal to 30.

But the bar model now shows the end result, six boxes of five cakes.

So, six times five is equal to 30, but which factor we use? We've got six times five is equal to 30, and five times six is equal to 30.

Jun says, "It doesn't matter! Here, six represents the number of groups and five represents the size of each group." So, we've got five six times or six groups of five.

As long as we know what each number in our equation represents, we can use either to help us to solve the problem.

We know that multiplication is commutative, so the order doesn't matter.

But we do need to know what each number represents.

We were dividing between six boxes.

So, six was our number of groups, we knew that.

What we didn't know was how many were going to be in each group, and that's our five.

So, five is the size of the group, six is the number of groups.

Time for you to do some practise.

Can you draw a bar model to represent each problem then write a division equation and use your multiplication facts to solve it.

Show your thinking on a number line.

So in A, Jun shares 36 cakes between nine boxes.

How many cakes are in each box? When you're writing your multiplication, think carefully.

What is it that you know and what is it that you're trying to work out? What do the numbers represent? In B, Sofia divides 42 biscuits equally between seven bags.

How many biscuits does she put in each bag? And in C, Alex divides 56 sweets between eight packets.

How many sweets are in each packet? I have a feeling that C uses my favourite times table fact.

Hmm, I wonder what that is.

Pause the video, have a go at representing those problems and solving them.

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

How did you get on? So in A, Jun shares 36 cakes between nine boxes.

So, we're 36 and we're dividing it by nine.

36 is our whole, our divisor is nine because there are nine boxes.

What we don't know is how many cakes will be in each box.

So, one lot of nine, that's one cake in each box.

Two lots of nine, that's two cakes in each box, that's 18 cakes used.

Three lots of nine is 27, that's three cakes in each box.

And four groups of nine is 36, that's four cakes in each box.

We were able to take out four groups of nine from 36.

So, that means four cakes in each box.

And our multiplication fact is nine times four or four times nine.

We knew that we had nine boxes, we needed to know how many cakes were in each box.

So, 36 is equal to four times nine.

Nine was our number of boxes, so four represents the number of cakes in each box.

In B, Sofia divides 42 biscuits equally between seven bags.

How many biscuits does she put in each bag? So, 42 is our whole, it's our dividend.

And it's 42 that we are dividing between seven bags, so our divisor is seven.

We are making seven groups, we want to know how many are in each bag.

So, if we take out one group of seven, that's one in each bag.

Two groups of seven, that's two in each bag.

Three groups of seven, that's three in each bag.

Four groups of seven with four in each bag.

Five groups of seven, five in each bag.

Six groups of seven, six in each bag.

And six groups of seven is equal to 42.

So, we've taken out six groups of seven, so there are six biscuits in each bag.

So, our multiplication fact, seven times what is equal to 42.

Seven times six.

Seven is the number of bags.

So, we've got seven and we've got six cookies in each bag, so six groups of seven or seven times six is equal to 42.

And in C, Alex divides 56 sweets between eight packets.

So, what's our whole this time? Our dividend is 56 and our divisor is eight.

We are dividing by eight because we've got eight packets.

We want to know how many sweets are in each packet.

So, 56 divided into eight equal groups.

And there our bar model shows that 56, we've got our eight groups waiting, we need to know how many are in each group.

One lots of eight, that's one in each packet.

Two lots of eight, two in each packet.

Three lots of eight, that's 24, that's three in each packet.

Four eights of 32, that's four in each packet.

Five eights of 40, that's five in each packet.

Six eights of 48, that's six in each packet.

Seven times eight is 56, there are seven in each packet.

So, we know that 56 is equal to eight times seven.

So, if we've got eight bags, then there will be seven sweets in each packet.

There we go.

And seven times eight is 56, is my favourite times table fact.

And on into the second part of our lesson, we are going to solve division problems with the remainder this time.

So, most of the cookies have been sold.

Sofia has 27 cookies left to share equally between six bags.

Is 27 in the six times table? It isn't, is it? It's an odd number, and we know that all multiples of six are even.

Ah, Jun spotted it too.

"27 is not a multiple of six, so there will be a remainder.

My equations," he says, "will look a bit different." Sofia says, "We are dividing between six bags, so the divisor is six." But we know we're going to have a remainder as part of our answer.

27 divided between six is going to be equal to something remainder something.

She says, "We can use our multiplication facts for the six times table." What do you know about the six times table? Can you think of a multiple of six that's close to 27 but less than 27? So, 27 is equal to something times six plus our remainder, or six times something plus our remainder.

Jun says, "I will use my multiplication facts to predict the answer, and then I'll check it by dividing the cookies between the bags." Sofia says, "We know that four times six is equal to 24, so we can share out four groups of six." We know that we are looking for six equal groups, and each time we share out six, that's one in each group.

So, that's four times six.

So, four times six is equal to 24, but we had 27 cookies.

So, how many cookies left over? Well, 24 plus three is equal to 27.

So, there will be three cookies left over, so there'll be a remainder of three.

There they are on the number line.

So, 27 divided into six groups means four in each group and a remainder of three.

Let's check.

There's our 27 in our bar model.

And Jun says, "I can take out four groups of six to share out." One group of six, one cookie in each bag.

Two groups of six, two in each bag.

Three groups of six, three in each bag.

Four groups of six, four in each bag.

And there are three cookies left over.

So, there are four cookies in each bag and there's a remainder of three.

So, we can make six bags with four cookies in each bag, and then remainder of three cookies.

"I was right!" says Jun.

Time to check your understanding.

Can you use your multiplication facts to predict the answer to the following problem? And then we'll check it together using the cookies.

Jun has 32 cookies, and he divides them between five bags.

How many cookies will be in each bag? So, think about an equation, a bar model, maybe thinking about your number line to support your counting.

See if you can work out the answer.

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

How did you get on? So, we've got 32 cookies in whole and we're dividing by five because there are five bags, that's our divisor.

Now, we know that 32 is not in the five times table, so there will be a remainder.

Five times six is equal to 30.

So, we can predict that there will be six cookies in each of the five bags, and 32 is two more than 30, so there'll be a remainder of two.

Let's check.

We know that six groups of five is 30, so we can share out six groups of five.

So, one group of five, one cookie in each bag.

Two groups of five for two in each bag.

Three groups of five for three in each bag.

Four groups of five for four in each bag.

Five groups of five for five in each bag.

Six groups of five is equal to 30.

So, that's six cookies in each bag.

But we had 32 cookies.

So, there are two cookies left over.

So, there are six groups of five in 32 and two leftover.

So, we can say that there are six cookies in each bag and a remainder of two cookies.

32 divided between five is equal to six, remainder two.

So, now let's check using those cookies.

32 divided between five bags.

So, we can take out six groups of five to share out.

One group of five, two groups of five, three groups of five, four groups of five, five groups of five, six groups of five, that's 30 cookies.

Six groups of five, and there are two left over.

So, there are six cookies in each bag, and there's a remainder of two.

This time, Sofia is selling drinks.

She has 37 drinks and she's dividing them between 12 trays.

She uses her multiplication facts to help her find out how many drinks to put on each tray.

So, 37 drinks and 12 trays.

So, the bar model shows us that there are 37 drinks and we want 12 trays, but we know there's going to be some leftover because 37 is not in the 12 times table.

So, if she puts one drink on each tray, she's used 12 drinks.

If she puts two drinks on each tray, that's 24 drinks.

If she puts three drinks on each tray, that's 36 drinks.

So, she's put three drinks on each tray, but there's one drink leftover.

She's used 36 drinks, but she had 37 to start with.

So, there's one leftover.

37 divided between 12 is equal to three remainder one.

There'll be three drinks on each tray and one drink leftover.

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

Can you draw a bar model to represent each problem? Then write a division equation and use your multiplication facts to solve it.

Show your thinking on a number line.

So in A, Jun shares 39 cakes between nine boxes.

How many cakes are in each box? In B, Sofia divides 45 biscuits equally between seven bags.

How many biscuits does she put in each bag? And in C, Alex divides 58 sweets between eight packets.

How many sweets are in each packet? Draw a bar model, write a division equation and use your multiplication facts to solve these problems. You might need to use a number line to show your thinking as well.

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

How did you get on? In A, Jun shares 39 cakes between nine boxes.

How many cakes are in each box? So, we've got 39 as our whole, and our divisor is nine because we are dividing by nine.

Now, 39 is not in the nine times table, so we will have a remainder.

Let's think about using our knowledge of our nine times table.

So, one group of nine is nine, that's one in each box.

Two groups of nine are 18, that's two in each box.

Three groups of nine are 27, that's three in each box.

Four groups of nine is 36, that's four in each box.

I can't make another group of nine, can I? So, I can put four cakes in each box and I'll have a remainder of three cakes.

So, 39 divided by nine is equal to four remainder three.

There are four cakes in each box and three leftover.

In B, Sofia divides 45 biscuits equally between seven bags.

How many biscuits does she put in each bag? So, 45 is our whole, the number we are dividing, and we're dividing it by seven.

Seven is our divisor, the number we're dividing by.

And in our bar model, we've got seven parts and apart for the remainder, because we know that 45 is not in the seven times table.

So, let's have a look.

One group of seven, that's seven, one in each bag.

Two groups of seven is 14, two in each bag.

Three groups of seven is 21, three in each bag.

Four groups of seven is 28, four in each bag.

Five groups of seven is 35, five in each bag.

Six groups of seven is 42, six biscuits in each bag.

I can't make another group of seven, I've used 42 biscuits already.

So, I can put six biscuits in each bag, and then there will be three biscuits left over.

So, 45 divided between seven is six remainder three, there are six biscuits in each bag and three leftover.

And in C, Alex divides 58 sweets between eight packets.

How many sweets are in each packet? So, we've got 58 as our whole, and our divisor is eight, we're dividing by eight.

What do you know about the eight times table? It's my favourite times table fact, again, I think there's going to be seven sweets in each packet and some left over.

Let's have a look.

One group of eight is eight, that's one in each packet.

Two eights of 16, that's two in each packet.

Three eights of 24, that's three in each packet.

Four eights of 32, that's four in each packet.

Five eights of 40, that's five in each packet.

Six eights of 48, that's six in each packet.

And seven times eight is 56, that's seven in each packet and two leftover.

So, in our eight packets, we can put seven sweets in each and there will be two leftover.

58 divided by eight is equal to seven remainder two.

Well done if you've got all those right.

I wonder which was your favourite representation or way of thinking.

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

We've been solving division problems involving sharing, including those with remainders.

What have we learned about? We've learned that objects can be divided equally between groups, sometimes with a remainder.

When we divide equally between groups, it's called sharing.

So, we know how many groups we're making and we're working out the number in each group.

We can use multiplication and addition equations or division equations to represent sharing with a remainder.

And we can use multiplication facts to solve sharing problems. We just need to know in our multiplication what represents the number of groups and what represents the number in each group.

Thank you for all your hard work in this lesson and I hope I get to work with you again soon.

Bye-bye.