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 grouping, sometimes with remainders.

I wonder if we'll be able to spot when we're going to have a remainder or not.

Your times tables are gonna be really useful to you, so I hope you've got those ready at your fingertips now.

Let's have a look at what's in this lesson.

We've got four keywords.

We've got grouping, division, divisors, and remainder.

So let's just practise them, then we'll have a look at what they mean.

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

My turn, grouping.

Your turn.

My turn, division.

Your turn.

My turn, divisor.

Your turn.

My turn, remainder.

Your turn.

I'm sure they are words you're familiar with.

You may have used them and heard of them before.

Let's have a look at what they mean 'cause they're going to be really useful in describing our work today.

So grouping is when we divide a number of objects into equal groups.

We know the total number of objects and the number of objects in each group, but we do not know how many equal groups there are.

Division means splitting into equal parts or groups.

The divisors is what we're dividing by.

So that might be today, the number in each group.

And 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 we're going to be thinking about what the divisor is, it's the number we are dividing by.

There are two parts to our lesson today.

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

And in the second part, we're going to be solving division problems with a remainder.

So let's make a start on part one of our lesson.

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

Jun and Sofia are playing with friends, and there, we've got some stick people representing them.

There's Jun on one side and Sofia on the other.

There are 12 children all together and they need to get into teams of four to play their game.

How many teams will they have? So there are 12 children altogether and they need to get into teams of four.

Jun says, "Let's think about the equation we will write to represent this." Sofia says, "The children must be divided into groups of four.

We need to think about how many groups of four there are in 12." Because we've got 12 children altogether.

How many groups of four are there? Jun says, "We can use our multiplication facts to help with this." 12 is equal to hmm times 4.

So 12 is equal to hmm groups of four.

What do you think the missing number's going to be? Or we could say 12 is equal to 4 times something, Four hmm times.

We can skip count on a number line to show our thinking.

Remember we're trying to find out how many groups of 4 there are in 12.

So here's our number line.

Let's count in fours.

Four.

So one team of four is four.

Two teams of four is eight.

Three teams of 4 is 12.

So one times four is four.

That's one team.

Two times four is eight.

That's two teams. And 3 times 4 is 12.

That's three teams. So 12 is equal to three times four.

And because we know that multiplication is commutative, we can also say that 12 is equal to four times three.

So how many teams have we made? Three teams. Jun says, "12 divided into groups of 4 is equal to 3, so we can make three teams of four children." And there you can see them on the number line.

Sofia wonders if she could've written a different equation to represent this.

Can you think of another way to record this? She says, "We know that when we divide a quantity into equal groups, it's called division." Ah, so can we write a division equation? She says, "I think I can write a division equation." Go on, Sofia.

12 divided by four is equal to hmm.

She's written a division equation.

The children were divided into groups of four.

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

12 divided into groups of four, 12 divided by four.

And there's our divisor.

The number we're dividing by.

12 is our whole, the number we started with.

There are 12 children, so this time we're going to subtract groups of four until we reach zero.

So 12 subtract four is equal to eight.

That's one team.

Subtract another four is equal to four.

That's two teams. And subtract another four is equal to zero.

That's three teams. 12 - 4 - 4 - 4.

Three groups of four.

Because we know that three groups of four is equal to 12.

So we subtracted three groups of four.

So 12 divided into groups of four is equal to three groups.

12 divided by four is equal to three.

Time to check your understanding.

Write a multiplication equation to help solve this problem and draw a number line to show your thinking.

There are 15 children in the dinner hall.

Only three children can sit at each table.

How many tables will be full? Pause the video.

Have a go at writing a multiplication equation.

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

How did you get on? So the children must be divided into groups of three.

So we're thinking about groups of three.

We need to think about how many groups of three are in 15.

So 15 is equal to hmm times three.

Or because it's commutative, 15 is equal to three times hmm.

Let's think about skip counting on a number line.

Can we count in threes? So one group of three is three.

That's one table.

Two groups of three is six.

That's two tables.

Three groups of three is nine.

That's three tables.

Four groups of three is 12.

That's four tables.

Five groups of three is 15.

That's five tables.

So 15 is equal to five groups of three, 5 X 3.

And because multiplication is commutative, we can also say 15 is equal to three groups of five.

And we might read that as three, five times.

15 divided into groups of three is equal to five.

So five tables will be full.

Now, part two of the check.

Can you now write a division equation that would help to solve this problem? And you could check it by subtracting, using a number line this time.

So there are still the same number of children, 15 children in the dinner hall and three children can sit at each table.

How many tables will be full? Pause the video, write the division equation, and think about subtracting on a number line.

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

How did you get on? So the children were divided into groups of three.

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

How many altogether? 15, of course.

So there are 15 children.

We must subtract groups of three till we reach zero, but let's have a look at that equation.

15 divided by three, divided into groups of three is equal to hmm.

Let's look at that number line.

So we're going to subtract groups of three until we can't subtract any more groups of three.

15 subtract three is equal to 12.

That's one table.

Subtract another three is equal to nine.

That's two tables.

Another group of three is equal to six.

That's three tables.

Another group of three is equal to three.

That's four tables.

And a final group of three.

We've got to zero.

And we filled five tables again.

So 15 divided into groups of three will give us five groups.

15 and we've subtracted three five times.

Five tables will be full.

15 divided by three is equal to five.

The children solve another problem.

Can you see some cakes here? How many have we got? There are 18 cakes and each plate can hold three cakes.

How many plates are needed to hold all the cakes? We can use counters to represent the cakes 'cause we may not have 18 cakes in the classroom.

So there we go.

Our counters represent our 18 cakes.

Jun says, "We need to find out how many groups of three are in 18." Because we're trying to put the cakes onto plates with three on each plate.

Sofia says, "I can write a multiplication equation to solve this." We want to know how many lots of three are equal to 18.

18 is equal to something multiplied by three or three multiplied by something.

Do you know your three times table? She says, "Or we could write a division equation because we have a divisor of three." We've got 18 cakes and we're dividing them into groups of three.

So 18 divided by three is equal to something.

Jun says, "We can skip count in threes to find out how many plates are needed." Let's have a look.

He says, "Let's count forwards in threes until we reach 18." So one plate of three, that's three.

One plate.

Two plates of three, that's six.

So that's two plates.

Three plates of three is nine of the cakes.

Four plates of three is 12 of the cakes.

Five plates of three is 15 of the cakes.

And six plates of three, that's all 18 cakes.

So 18 is equal to six groups of three.

3 X 6 = 18.

18 divided into groups of three is equal to six.

So six plates are needed for the cakes.

Lots of different ways we can think about it.

We can think about using our multiplication facts.

We could use a number line to support our skip counting.

We can also use our multiplication knowledge.

If six groups of three is equal to 18, then 18 divided into groups of three will be equal to six groups.

But Jun says, "We could also have subtracted groups of three from 18 until we reached zero." So subtract 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.

So we can either skip count upwards in threes or backwards from our total.

So again, we found that when 18 is divided into groups of three, there are six groups.

So six plates were needed for the cakes.

And we can skip count forwards or backwards to find the number of equal groups.

Time for you to do some practise.

Here are three problems. Can you write a multiplication and a division equation to represent each problem? Then solve the problem.

You can use a number line to show your thinking.

I wonder if you'll skip count forwards or backwards.

So in a, Sofia had 25 books.

She could fit five books onto each shelf of her bookshelf.

How many shelves did she fill? In b, Jun had 32 stickers.

He could fit eight on each page of his book.

How many pages did he fill with stickers? And in c, Alex had 28 points left on his computer game.

Each day he bought a coin for seven points.

How many coins could he buy with all of his points? Pause the video, write a multiplication, division equation, and use a number line to solve your problems and show your thinking.

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

How did you get on? So in a, we were thinking about Sofia's 25 books, five on each shelf, how many shelves did she fill? So here are our equations.

25 is equal to something times five.

We know her bookshelves can fit five books.

So we can write that multiplication in two ways.

And we're also thinking that we are dividing into groups of five, so we have a divisor of five.

25 divided by five is equal to something.

The books must be divided into groups of five.

So we could've counted it in fives or used our multiplication facts to help.

If we counted forwards, we'd find that five groups of five is equal to 25.

Or we could've counted backwards, and we'd still have found that five groups of five is equal to 25.

So 25 divided into groups of five is equal to five.

So Sofia filled five bookshelves.

In b, Jun had 32 stickers and he could fit eight on each page of his book.

How many pages did he fill? So we're trying to work out how many groups of eight there are in 32.

32 is hmm times eight or eight times hmm.

And 32 divided into groups of eight is equal to something.

Our divisor is eight.

The stickers must be divided into groups of eight.

So we could've counted in eights or used our multiplication facts to help us.

Do you know your eight times table? Well, if you did, you'd know it was four groups of eight or you might've skip counted on a number line forwards or backwards.

32 is equal to four groups of eight.

So Jun filled four pages.

And we can also say that 32 divided into groups of eight is equal to four.

And in c, Alex had 28 points left on his computer game.

Each day he bought a coin for seven points.

How many coins could he buy with all his points? So we've got 28 points and we're dividing it into groups of seven.

So we need to find out how many groups of seven there are in 28.

So we could've counted in sevens or used our multiplication facts to help us.

Do you know your seven times table? If we counted in sevens forwards or backwards, we know that there are four groups of seven in 28.

28 divided into groups of seven is equal to four.

So Alex would run out of points after four days.

He could buy four coins.

And on into part two of our lesson, this time we're going to be thinking about problems with a remainder.

So they're playing their game again, but this time there are 14 children playing and they need to get into teams of four to play their game.

How many teams will they have? Jun says, "Let's think about the equation we will write to represent this." "The children must still be divided into groups of four," said Sofia.

"We need to think about how many groups of four are in 14." "Ooh," says Jun.

"14 is not a multiple of four." It's not in the four times table, is it? So how can we solve this? 14 is equal to something times four or 14 is equal to four times something.

14 is not a multiple of four.

So we know when we make groups of four that there will be a remainder and we can record it like this.

Ah, that's right.

So we want a number of groups of four and then plus our remainder.

Let's show it on a number line.

So one team of four is four children.

Two teams of four is eight.

Three teams of four is 12.

Can we make another team of four? We've got 14 children.

Now we can't, can we? We haven't got enough children left over to make another team of four.

In fact, we've got two left.

So we've got three groups of four and there are two children left over.

So we have a remainder of two.

And we can see that on the number line, we've got two left, but not enough to make another group of four.

And we can record our remainder by saying 14 is equal to three groups of four plus two or 4 X 3 + 2.

So the children were divided into groups of four, so the divisors is still four if we think about this as a division equation.

14 divided by four is equal to? Hmm.

There's our divisors of four.

"Let's subtract the groups on a number line," says Sofia.

There are 14 children.

We must subtract groups of four until we cannot subtract any more groups of four.

So doing the opposite as we did when we were counting up.

So 14 - 4 = 10.

10 - 4 = 6.

That's two groups we've made.

6 - 4 = 2.

We've made three groups.

And how many have we got left? So 14 - 4 - 4 - 4, subtract our three groups of four is equal to two.

So we subtracted three groups of four, but there was a remainder of two, so we can record it like this.

14 divided into groups of 4 is equal to 3 r 2, and the r stands for remainder.

14 divided into groups of four is equal to three with a remainder of two.

We could make three teams of children with two left over.

Time to check your understanding.

Write a multiplication equation to help solve this problem.

Skip count forwards on a number line to show your thinking.

There are 16 children in the dinner hall.

Only three children can sit at each table.

How many tables will be full? Pause the video.

Have a go at writing your multiplication equation and skip count forwards in a number line to solve the problem.

When you're ready for some feedback, press play.

How did you get on? So this time we had 16 as our whole and it was equal to hmm groups of three plus something.

When we had 15 children, we had full tables, so 16 children means we must have some left over.

So 16 is equal to something times three plus something or three times something plus something.

The children must be divided into groups of three.

So we need to think about how many groups of three there are in 16.

Let's use that number line.

One group of three.

Two groups of three.

Three groups of three.

Four groups of three.

Five groups of three was equal to 15, and we've got one child left over.

So 16 is equal to five groups of three or three times five with one child left over.

Plus one.

16 divided into groups of three is equal to five with a remainder of one.

So five tables will be full and there'll be one child left over.

Now, the same problem, but can you write a division equation to help solve this problem? And use subtraction on a number line to prove you're right.

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 were dividing into groups of three.

So the divisors is three.

16 divided into groups of three is equal to.

Hmm.

So we must subtract groups of three until we cannot subtract anymore.

So there's one group of three.

Two groups of three.

Three groups of three.

Four groups of three.

Five groups of three.

We've only got one left.

We can't make another group of three.

So how many groups of three have we made? Well, we subtracted five groups of three and we had one left.

So five tables will be full and there will be one child left over.

So 16 divided into groups of three is equal to five remainder one.

And we show that by writing r 1, r for remainder.

So we can count forwards or backwards to find out how many equal groups are in a number.

I wonder which way is easier.

So this is showing us that 20 divided into groups of three is equal to six remainder two.

Jun says, "It's usually easier to count forwards because we can use our multiplication facts to help us." Can you see when we count forwards, we're counting in multiples of three.

3, 6, 9, 12, 15, 18, and then two more to get to 20.

If we count backwards, we're not counting in multiples of three, but we land on two and we can see that there aren't any more groups that we can make.

So our remainder is perhaps more obvious if we count backwards.

So the children solve another problem.

There are 20 cakes and each plate can hold 3 cakes.

How many plates are needed to hold all the cakes? Let's represent those cakes as counters again.

And Jun says, "We need to find out how many groups of three there are in 20." Because we need to put three cakes on each plate.

Sofia says, "We can write a multiplication equation." 20 is equal to hmm times three or three times hmm.

"Or we can write a division equation with a divisor of three because we're making groups of three." We're dividing into groups of three.

So 20 divided by three is equal to hmm.

Is this going to have a remainder? "Ah, yes," says Jun.

"20 is not a multiple of three.

It's not in three times table, so I know there will be a remainder.

The equations will change." We'll need a plus something on the end and we'll need an r something, remainder something with the division.

So let's think about counting forwards in threes until we cannot make any more groups of three and then we can find the remainder.

So let's have a look.

One plate of three, three.

Two plates of three, that's six.

Three plates of three, that's nine.

Four plates of three, that's 12.

Five plates of three, that's 15.

Six plates of three, that's 18.

Can I make another group of three? I've only got 20, remember? No, I can't, can I? There are two cakes left over.

So we have a remainder of two.

So our multiplications are 20 = 6 X 3 + 2 or 3 X 6 + 2.

And for our division, 20 divided into groups of three is equal to six remainder two.

But Jun says, "We could also subtract groups of three from 20 until we can't make any more groups." So subtract one group of three, two groups of three, three groups of three, four groups of three, and five groups of three, and six groups of three, and we've landed on two.

We've got two cakes left, haven't we? So 20 subtract the six groups of three is equal to two.

We can't make another group of three.

So we've got six groups of three.

So 20 = 6 X 3 or 3 X 6, but we can't forget that remainder, plus two.

And as a division, 20 divided into groups of three is equal to six remainder two.

But remember, our problem asks us how many plates we needed for all the cakes? So we will need six plates for the groups of three plus another plate.

To put all the cakes on plates, we will need seven plates.

And time for you to do some practise.

Can you write a multiplication and a division equation to represent each problem and then solve the problem? Use a number line to show your thinking.

I wonder if you'll count forwards using the multiples or count backwards because that makes the remainder a bit easier to see.

See which one you find the best.

So in a, Sofia had 27 books.

She could fit five books onto each shelf of her bookshelf.

How many shelves did she fill? In b, Jun had 34 stickers.

He could stick eight on each page of his book.

How many pages did he fill with his stickers? And in c, Alex had 30 points left on his computer game.

Each day, he bought a coin for seven points.

How many coins could he buy with all of his points? Do you notice something similar between these and the problems in A? Hmm.

I wonder.

You might want to look back at your answers for A and see what's happened.

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

How did you get on? So let's look at a.

Sofia had 27 books this time.

She could fit five books onto each shelf of her bookshelf.

How many shelves did she fill? So the books must be divided into groups of five, but 27 is not a multiple of five so there will be a remainder.

So if we write it as a multiplication, 27 is equal to hmm groups of five or five times hmm plus our remainder.

And as a division, 27 divided into groups of five is equal to hmm remainder hmm.

So we can count in fives or use our multiplication facts to help us.

So if we count in fives, we can make five groups of five and then we've got two left over, but we could also have counted backwards.

This time we don't use our multiples of five so the backwards counting is a little bit more challenging.

But again, we'll find five groups of five takes us to two, and we've got a remainder of two.

So 27 divided into groups of five is equal to five.

So Sofia filled five bookshelves and there were two books left over, so our remainder is two.

So in b, Jun had 34 stickers.

He could stick eight on each page of his book.

How many pages did he fill with his stickers? So we're thinking about how many groups of eight there are in 34.

34 must be divided into groups of eight, but 34 is not a multiple of eight, so there will be a remainder.

34 is not in the eight times table.

So we can count in eights or use our multiplication facts to help us.

If we count up, we can see that four groups of eight are equal to 32 and we've got two more.

Or we could've counted backwards.

Again, we're not counting on multiples of eight this time, but we're subtracting eight each time, and we can't subtract any more eights when we get to two.

So again, we can see that remainder of two.

Four groups of eight and a remainder of two.

So 34 divided into groups of eight is equal to four with a remainder of two.

So Jun filled four pages of his book and had two stickers left over.

And for c, Alex had 30 points left on his computer game.

Each day, he bought a coin for seven points.

How many coins could he buy with all of his points? So there are equations.

So the points must be divided into groups of seven, but 30 is not a multiple of seven so there will be a remainder.

We can count in sevens or use our multiplication facts to help us.

30 divided into groups of seven is hmm remainder hmm.

How many groups of seven can we make? So we can count up in sevens or use our known multiplication facts.

You might know that 4 X 7 = 28.

5 X 7 = 35 but that's too many, isn't it? So we've got to think about the known fact that gets us as close to our whole but no bigger.

So 4 X 7 = 28 and we've got two left over.

And we can also see that by counting backwards.

If we take away four groups of seven, we will have two leftover.

30 - 28 = 2.

So 30 divided into groups of seven is equal to four with a remainder of two.

So Alex could buy four coins over four days and he would have two points left over.

Well done if you've got all of those correct.

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

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

What have we been thinking about? Well, we can write a multiplication equation to solve division problems and we can write a division equation to solve division problems as well.

The thinking is the same, but we can record it with a multiplication plus our remainder or a division with that r to represent our remainder.

We can count forwards to find the number of equal groups in a number, and that means we can use our skip counting in our times tables.

But we can also count backwards to find the number of equal groups in a number.

But if there's a remainder, remember we won't be counting in multiples so it makes the subtraction a little bit more challenging.

It's usually easier to count forwards because we can use our multiplication facts to help us.

Thank you for all your hard work.

I hope you've enjoyed exploring divisions with remainders in grouping, and I hope I get to work with you again soon.

Bye-bye.