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 deciding what to do with the answer to a division calculation to solve a problem.

Now you may think that once you've got the answer to a calculation, you've solved the problem.

But with division, we have to think really carefully about what the question is asking us and what the answer is telling us.

So let's make a start and solve some problems. We've got 2 key words in our lesson today.

They are quotient and remainder.

So let's practise saying them.

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

So my turn, quotient, your turn.

My turn, remainder, your turn.

Well done.

They're words connected to division, you may have come across them before.

Let's just check what they mean 'cause they're going to be really important in our lesson.

The quotient is the result after a division has taken place, it's sort of the answer, and a remainder is the amount left over after a division, when the dividend does not exactly divide by the divisors.

So 2 words to look out for and use in our lesson today.

And there are 2 parts to our lesson.

In the first part, we're going to think about rounding the quotient, hmm.

So we're going to think about doing some rounding.

You may have done some rounding before in other maths lessons.

We're going to think about what rounding means when we're rounding the quotient, the answer of a division.

And in the second part, we're going to think about problems and we're going to think about whether we need to round up or down.

So let's make a start on part one.

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

The children are packing fruit for the school picnic.

That sounds like fun.

They have 35 apples and they must be packed into boxes of 4.

And we can see there one box of 4 apples ready for us, so 35 apples.

How many boxes will they have and how many apples will there be left over? Sofia says, "I will write an equation to represent this." What equation do you think she's going to write? Remember, we have 35 apples and we were packing them into boxes of 4.

Ah, that's right, it's a division equation, isn't it? We've got 35 apples and we're dividing them into groups of 4.

Can you think about what the answer will be to this? What will our quotient be the result where we've divided? Will there be a remainder? There will, won't there, because 35 is not an even number and we know that all multiples of 4 are even numbers.

So we can use our times table facts to help us here.

We know that 8 times 4 is equal to 32, but 32 leaves us with 3 more apples, we can't make another group of 4.

So 35 is equal to 8 times 4 plus 3.

So the quotient when we divide is 8 remainder 3, and we write that remainder 3 as R3, R for remainder.

This means there will be 8 boxes of apples with 4 apples in each box and 3 apples left over.

Let's think about what each numeral in the equation represents.

So what did the 35 represent? Well, that represents the whole group of 35 apples, and you might have heard that called the dividend.

What does the 4 represent? Well, the 4 represents the number of apples to be put into each box, and you might have heard that called the divisors, the number we are dividing by.

What about the 8? The 8 represents the number of boxes of apples that can be made, the number of full boxes, the number of groups of 4.

And what about that 3? Well, the 3 represents the number of apples that are left over without a box, so they can't make a full box of 4.

So there's a remainder of 3 apples.

In this problem, it asked us how many apples were left over, so the remainder was recorded to answer the problem.

However, in some division problems, there's no need to record the remainder when solving the problem.

Let's look at an example.

So we've still got 35 apples and we are dividing by 4.

So the solution to our equation is 8 remainder 3.

Let's look at a different problem though.

There are 35 apples and they must be packed into boxes of 4.

How many full boxes can be made? Hmm, do you see what's happened here? So we can show this on a number line.

8 times 4 is equal to 32.

That's 8 full boxes of apples, 8 boxes with 4 apples in each box.

The leftover apples are not in a full box, there's only 3.

Sofia says, "For this problem, I only need to count full boxes, so I don't need to include a box for the 3 leftover apples.

I don't need to record the remainder this time." There were 8 full boxes of apples, that's the answer that solves our problem.

So in division, the result of the equation is not always the same as the answer to the problem.

The result of our equation was 8 remainder 3.

For the first problem, yes, the answer was 8 full boxes and 3 apples left over.

In the last problem we solved, we ignored the remainder because the leftover apples were not in a full box, and the question asked us about full boxes.

Sofia thinks of a question that will change the problem slightly.

Oh, go on Sofia.

Sofia needs to collect enough boxes to store all of the apples.

How many boxes will she have to collect? Oh, that's a bit different, isn't it? We were asked about full boxes in the remainder, then we were asked just about the full boxes, now Sofia needs boxes to store all the apples.

Our division equation is still the same.

35 apples divided into groups of 4 and our answer is 8 remainder 3, 8 groups of 4 and 3 left over.

She says, "The equation is the same as for the last problem.

So will I answer the problem in the same way," she says? What do you think? Jun says, "This time, we must find out how many boxes are needed for all the apples including the remainder." Ah, that's different, isn't it? It's not full boxes this time, it's boxes for all the apples.

"The leftover apples need a box," she says, "So 9 boxes are needed." We'll need another box for those 3 apples.

So we've got 8 full boxes, but we need to round up and get another box for the 3 remaining apples.

This time we rounded the quotient, the result of our division up to 9 because we needed an extra group to include the remainder.

Let's have a look at another one.

Although we don't have a worded problem here, we can work out the possible answers to a division problem if we have the equation to represent it, let's try.

So we've got 62 divided by 7 is equal to 8 remainder 6.

How can we work this out? What multiplication fact helps us? Well, 7 times 8 is equal to 56, and then we've got 6 more to make up our 62.

So there are 8 groups of 7 and 6 left over.

We dunno what these are groups of, we don't have a problem here.

The quotient is 8 whole groups and a remainder of 6.

But this result may not give the exact answer when a division problem is asked.

We may have to ignore the remainder so the answer would be 8 like when we had to answer the question about how many full boxes of apples.

Or we may need another group to include the remainder.

So then the answer would be 9.

Like when we had to have boxes for all the apples, we had to add an extra box for the remainder.

In a division problem represented by this equation, the answer may be 8 or 9.

Sofia writes this equation to represent a division problem.

Which of the following would be possible answers to a division problem? Look at the answers A, B, and C and decide which could be possible answers to this division.

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

How did you get on? What did you think? Well, 9 could be the answer, couldn't it? The problem may only ask about complete groups made so the remainder would have to be ignored, the whole number part of the quotient is 9, so this would be the answer.

Could there be any other answers? Ah yes, the problem may require that the remainder is included in a new group.

So an extra group would be needed.

Instead of 9, the answer would be 10.

We would round the answer up to the next whole number.

We would round up the whole number parts of our quotient to include an extra group so that the remainder could be included.

Well done if you've got both of those and were able to explain why.

And it's time for you to do some practise, you are going to solve each equation, we've got some divisions there, and then you're going to adapt the results to show the different possible answers that may be reached in a division problem.

So what would the answer be if you were ignoring the remainder, and what would the answer be if you were including the remainder? And you're going to solve the equations first.

Pause the video, have a go.

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

How did you get on? So here are the answers.

We have 34 divided by 4.

So if we think about our grouping, 34 divided into groups of 4, we know that 8 4s are 32 and there'll be a remainder of 2.

So 8 remainder 2.

If we were ignoring the remainder, so thinking about maybe full boxes of apples, the answer would be 8.

If we were including the remainder and thinking about how many boxes would we need for all the apples, I'm thinking about apples again here, then our answer would be 9.

What about B, 55 divided by 6, hmm.

6 times 9 is equal to 54 and there'd be a remainder of one, so 9 remainder one.

If we ignored the remainder, the answer would be 9, and if we needed to include the remainder, the answer would be 10.

75 divided by 9, the answer is 8, remainder 3, 9 times 8 is 72 plus 3.

Again, ignoring the remainder, we'd just take the whole number part of our quotient 8, ad if we needed to include the remainder, we'd have to round it up to 9.

59 divided by 8.

Well, 7 8s are 56 plus 3, so 7 remainder 3.

So ignoring the remainder, we'd have an answer of 7, and including it, we'd have 8.

43 divided by 7.

Well, 6 times 7 is 42.

So 6 remainder one.

Ignoring the remainder, we'd have an answer of 6, including the remainder, we'd have an answer of 7.

And 129 divided by 12.

Oh well, 10 times 12 is equal to 120 and there's 9 remaining, so 10 remainder 9.

Ignoring the remainder, we'd have an answer of 10, including it, we'd have an answer of 11.

We'd have to round our whole number up from 10 and some more to 11.

And on into the second part of our lesson.

This time we're going to be thinking about that idea of rounding up and down.

So let's look at a problem represented by this equation and decide whether to ignore or include the remainder.

We've got 62 divided by 7 and it's 8 remainder 6.

7 times 8 is equal to 56, plus 6 more equals 62.

So we can make 8 groups of 7 and have a remainder of 6.

So let's have a look at this.

There are 62 children at the school picnic.

Each picnic table on the field seats 7 children.

How many tables are needed so that all the children can sit down? Ah, there's a clue there, all the children.

Hmm, what do you think Sofia says, "We must look at the number of groups and decide if we need an extra group to include the remainder or not." So we know that we can make 8 groups of 7, but there will be 6 children left over.

Jun says, "In the problem, all the children must be seated.

So we need an extra group for the 6 children left over." So how many tables will they need? Ah, that's right, we must include the remainder and roundup.

9 tables are needed to seat all of the children.

So we need an extra table for the 6 children.

So we'll need 9 tables.

Here's a different problem.

I wonder if we'll still need to include the remainder to answer this problem, let's have a look.

There are 62 children at the school picnic.

Each picnic table on the field seats 7 children.

How many tables would be full if all the children sat down at a table? Ah, now that's different, isn't it? First of all, we needed to seat all the children, now we're talking about full tables.

Sofia says again, "We must look at the number of groups and decide if we need an extra group to include the remainder or not." Do you think we'll need to this time? "In the problem, it asks how many tables are full," says Jun, "So we don't need an extra group for the 6 children left over." They don't make a full table, do they? So this time we can ignore the remainder.

There are 8 tables that are full.

Time to check your understanding.

Look at each problem and decide if the remainder should be ignored or included to answer it.

Then write the equation and solve each problem.

So first of all, at the picnic, the teacher puts out blankets for the 67 children to sit on.

8 children can fit on each blanket.

How many blankets are needed for all the children to sit down? And the second problem, at the picnic, the teacher puts out blankets for the 67 children to sit on, again, 8 children can fit on each blanket.

How many blankets are full? So decide what we would need to do with the remainder in each of these problems and then write the equation and solve it.

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

How did you get on? So this problem asks how many blankets are needed for all the children to sit down? So our division is 67 divided by 8.

Well, 8 times 8 is 64 plus another 3, so the answer to our division equation is 8 remainder 3.

But this time we need blankets for all the children, so the 3 leftover children must sit down.

So we need to make an extra group to include the remainder, so that means an extra blanket, so 9 blankets are needed.

What about the other problem? So this problem asks us how many blankets are full.

So we don't need an extra group for the remainder.

We can ignore the remainder, 8 blankets are full.

I'm sure the other children are sitting down as well but we are just asked about the full blankets this time.

Well done if you've got those right.

Let's consider a problem where we share out instead of grouping.

We've been doing lots of grouping in our thinking about division so far, let's do some sharing.

Sofia buys some strawberries for the school picnic.

Ooh, lovely.

When she counts them, there are 58 strawberries.

She shares them equally between her 7 friends.

How many whole strawberries do they each receive? She says, "I will write an equation to represent this." Can you think what the equation is that she's going to write? You might want to have a think before Sofia writes it down.

That's right, 58 divided by 7, this time we are sharing between 7.

So 58 divided between 7.

We know we're making 7 groups of strawberries, we don't know how many strawberries will be in each group, but our division, we can think about in the same way.

We know that 7 times 8 is equal to 56, and 56 plus 2 is equal to 58.

So she can give each of her friends 8 remainder 2.

Hmm, that doesn't sound quite right.

Let's have a think about the problem.

Jun says, "8 groups of 7 strawberries can be shared out.

So for each group of strawberries we share out, the children get one each.

So that's 8 strawberries each and there are 2 left over.

In the problem, it asks how many strawberries each child receives." So the answer is 8 with a remainder of 2.

How does that work? Well, we can't share out the leftover whole strawberries equally.

So this time, we can ignore the remainder.

To answer the question, each child receives 8 whole strawberries.

We can cut strawberries up, didn't we? But the question asked about whole strawberries.

So they receive 8 whole strawberries each and there are 2 leftover, I wonder if Sofia could eat those or maybe she'd give one to Jun.

Time to check your understanding.

Sofia has 29 stickers and she divides them equally between her 5 friends, she's going to share them out.

How many stickers does each friend receive? Is it 6, 5 or 4? Pause the video, have a go, ad when you're ready for the answer and some feedback, press play.

What did you think, 6, 5 or 4? It's 5, isn't it? She's got 5 friends and they're sharing 29 stickers.

5 times 5 is equal to 25 and there'll be 4 left over.

So 29 divided between 5 means they get 5 each.

We can make 5 groups of 5 stickers, so they each get 5 and there are 4 stickers left over.

We certainly don't want to cut up stickers, do we? That wouldn't make any sense.

So this time we can ignore the remainder and each child gets 5 stickers.

The children are giving out drinks at the picnic.

Each bottle of water can fill 11 glasses.

So imagine a bottle of water, nice big bottle of water and it fills 11 glasses.

How many bottles are needed to fill 67 glasses? Hmm, can you think what the equation's going to look like? "I'll write an equation," she says, "I'm sharing out 11 between 67." Is that right, 11 divided by 67? Hmm, I'm not sure about that, but are you? Jun says, "That can't be right.

We have to fill 67 glasses.

This is the whole amount.

Each bottle holds 11 glasses.

So we can think of these as groups of 11." Ah, that's good thinking, Jun.

So we are thinking about how many groups of 11 do we need to make the 67.

Ah, so that's our equation, well corrected, Sofia.

67 divided into groups of 11 and that will tell us how many bottles we need.

There are 67 glasses to fill.

Oh my goodness, that's a lot of glasses, isn't it? Each bottle will fill one group of 11 glasses.

So we must group the glasses into groups of 11.

So there we are, we've grouped them into groups of 11.

But we've got one leftover, haven't we? 67 divided by 11.

How many groups can we make? Well, there are 6 groups of 11.

6 times 11 is 66 and one more.

So we'll need 6 bottles remainder 1, that remainder one is one glass, isn't it? We can make 6 lots of 11 and there's one glass left over.

So we will need either 6 or 7 bottles.

We can only fill 66 glasses from 6 bottles, so we must need 7 bottles.

We'll have some spare water in case anybody wants another glass.

The children need 6 mini buses to take them and their friends to the picnic.

Each minibus can carry 12 children.

Jun says, "One minibus carries 12 children.

6 times 12 is equal to 72.

So there must be 72 children going to the picnic." Do you agree, is he right? Sofia says, "I respectfully challenge you." That's a very nice way of putting it.

I'm not sure Sofia agrees.

"There cannot be more than 72 children, but there could be fewer than 72 children." That's interesting, Sofia, can you tell us a bit more? She says, "5 times 12 is equal to 60, that would be 5 minibuses." She says, "So if 6 minibuses are needed, there must be more than 60 children going to the picnic." Ah, good thinking, Sofia, she's thinking about remainders, isn't she? Jun says, "I've spotted my mistake.

6 mini buses could carry any number of children from 61 to 72." "That's right," says Sofia, "There could be 72 children, but there could also be between 61 and 72 children." It's useful to think about that, isn't it? Thinking about the remainder the other way.

We don't know what the remainder might be this time.

All we know is that they need more than 5 buses, but they might not fill 6 buses.

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

You are going to decide whether to ignore or include the remainder to answer these problems. So in A, there are 43 children in the playground, 6 children can sit on each bench.

How many benches will be full if all the children sit down and you've got the division there? And in B, there are 43 children in the playground, 6 children can sit on each bench.

How many benches will be needed so all of the children can sit down and we've given you the divisions there.

In C, in an art lesson, 50 children need a piece of card.

It comes in packs of 8 pieces.

How many packs of card are needed for all the children to have a piece of card? And in D, in an art lesson, 50 pieces of card are divided equally between 8 tables.

How many pieces of card will each table receive? So have a think about those questions.

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

How did you get on? So let's look at A and B.

Did you see that there was something similar? They have the same equation, didn't they? So in A, there are 43 children in the playground.

6 children can sit on each bench.

How many benches will be full if all the children sit down? So 43 divided into groups of 6.

Well, 6 times 7 is 42 plus another one makes 43.

So we must look at the number of groups and decide if we need an extra group to include the remainder or if we can ignore the remainder.

The problem asks us how many benches will be full? The bench for the one child left over will not be full.

So we can ignore the remainder this time.

I'm sure that child is still sitting down, but we are talking about full benches, so our answer is 7 full benches.

What about the second question? It was the same sort of scenario or the same story, but it said how many benches will be needed so all of the children can sit down.

It's the same equation, but again, we need to decide if we can include the remainder or ignore the remainder.

This time we're asked how many benches are needed so all of the children can sit down.

So an extra bench is needed for the one child left over.

So we need an extra group to include the remainder.

So 8 benches will be needed in B to seat all of the children.

So in C and D, we were thinking about an art lesson.

In C, 50 children need a piece of card and it comes in packs of 8 pieces.

How many packs are needed for all of the children to have a piece of card? So we're thinking about 50 divided into groups of 8 or 50 divided by 8.

Well, 8 times 6 is 48 plus 2 is 50.

So the answer to our division is 6 remainder 2.

But we need to look at the number of groups and consider if we need an extra group to include the remainder or if we can ignore the remainder.

The problem asks us how many packs are needed so all the children can have a piece of card.

An extra pack is needed for the 2 leftover children.

So we need an extra group to include the remainder.

So 7 packs of card are needed to give all the children a piece of card.

And in D, again, we've got 50 pieces of card this time and they're equally divided between 8 tables.

So we're sharing the card out between 8 tables.

How many pieces of card will each table receive? So again, this time we're sharing 50 between 8, but we're still thinking about groups of 8, 'cause each group of 8 means one piece of card.

So 50 divided by 8 is still 6 remainder 2.

So we can take out 6 groups of 8.

So each table will get 6 pieces and there'll be 2 pieces of card left over.

So again, we are looking at the number of groups to decide if we need an extra group to include the remainder.

This problem asks us how many pieces of card each table will receive when it's divided equally.

The 2 leftover pieces of card will not be shared between the tables or we could cut it up, but that wouldn't be a whole piece of card, would it? So this time we can ignore the remainder.

Each table will receive 6 pieces of card.

I hope you were able to look at those problems and decide whether to include or ignore the remainder.

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

We've been deciding what to do with the answer to a division calculation.

So when we've been solving division problems, we've seen that sometimes the remainder is recorded as the number left over and sometimes that's part of the problem.

Sometimes the remainder can be ignored.

If we are asked about full groups or complete things, then often the remainder can be ignored.

But sometimes an extra group is made to include the remainder.

So looking out for things where it says, "For all the apples to be put in a box, for all the children to be able to sit down," then we have to do what we call rounding up and we add an extra group to include the remainder.

I hope you've enjoyed exploring what to do with remainders and how to give accurate answers to division problems. Thank you for all your hard work, and I hope I get to work with you again soon.

Bye-bye.