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 using multiplication facts to answer division questions, including those with remainders.

So have you got your multiplication facts ready to go? Let's see what's in this lesson.

So we've got three key words.

We've got grouping, sharing, and remainder.

I'll say them first and then it'll be your turn to practise.

Are you ready? My turn.

Grouping.

Your turn.

My turn.

Sharing.

Your turn.

My turn.

Remainder.

Your turn.

Well done.

I wonder if you've been using those words quite recently.

I hope so.

Let's just remind ourselves what they mean, because they're going to be in use all through our lesson today.

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

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

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's split into, but we don't know how many there are in each group.

And those are the different ways we can think about division.

In one, we know how many are in each group, but we don't know the number of groups, and the other way is where we know how many groups there are, but we don't know how many are in each group, so look out for those two different ways of thinking about division in our lesson today.

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

The dividend is our whole, the number we're starting with, and the number we divide by is the divisor.

There are two parts to our lesson today.

In the first part, we're going to find the largest multiple of a number, and in the second part, we're going to use multiplication facts to solve division questions.

So let's make a start on part one.

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

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

Oh, exciting.

Do you have a Summer Fayre where you are? I wonder, do you have a sweet stall as well? Sometimes we must divide the sweets into equal groups to put in each bag and sometimes we must divide the sweets equally between the bags.

So sometimes we know how many sweets we're putting in a bag, we don't how many bags we need, and sometimes we know how many bags we've got, but we dunno how many sweets are in each group.

Sofia says, "Yes, this is the difference between grouping and sharing." When we're grouping, we know the number of sweets in each group, but we don't know how many groups we can make, and when are sharing, we know how many groups we want to make, but we don't know how many will be in each group.

Jun has 34 lollies and he wants to divide them into groups of four so that each bag has four lollies.

He wonders how many bags he will need.

What sort of division is this? Ah, Jun says, "We are dividing into bags of four, so this is a grouping problem." We're going to make groups of four to put in each bag, but we don't know how many bags we'll need.

Sofia says, "We must subtract groups of four to divide into the bags." Sofia says, "We do not have time to draw a number line, so how can we solve this efficiently?" Let's use our multiplication facts to solve this efficiently.

We must decide which fact to use.

So remember, we had 34 lollies and, "We are dividing into fours, so we must use a fact from our four times table." So here are some four times table facts, but which should we use? "34," that was the number of lollies, "is not a multiple of four," says Jun, "so there will be a remainder." "We need to choose a fact that has a product near to 34." Let's have a look at those times table facts.

Ah, well, 32 and 36 are products in the four times table.

They're both near to 34, aren't they? "8 x 4 = 32 and 9 x 4 = 36, so which fact should we choose to help us?" Remember, we've got 34 lollies.

Nine fours are equal to 36, but we only have 34 lollies, so we must choose the multiplication fact that is less than or equal to 34.

We haven't got one that's equal, have we? So what can we use that's less than? There's 34.

Ah, so 8 x 4 = 32.

We must use this fact, because the product is close to 34, but less than 34.

The largest multiple of four that is less than or equal to 34 is 32.

8 x 4 = 32, and then 34 is two more, so we've got two lollies that won't go into a bag of four.

He says, "I could make eight bags of four lollies with a remainder of two lollies." Let's complete the stem sentence.

The largest multiple of four that is less than or equal to 29 is? Let's think about our four times table.

"Let's find some times table facts with a product close to 29." We've got 7 x 4 = 28 and 8 x 4 = 32, but remember our stem sentence says the largest multiple of four that is less than or equal to 29.

8 x 4 = 32, but it's not less than 29, so that's too much, "So it must be 7 x 4, which is less than 29." So the largest multiple of four that is less than or equal to 29 is 28.

"When we find the largest multiple that is less than or equal to 29, we know we can use this fact," to help us divide.

Time to check your understanding.

Complete the stem sentence, then use it to help you to find the correct times table fact to use.

So the largest multiple of seven that is less than or equal to 58 is? Is it A, B, or C? Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

What do you think? The largest multiple of seven that is less than or equal to 58 is 56 and that is 7 x 8.

7 x 8 = 56, which is less than 58.

And guess what? It's my favourite times table fact again.

Jun wants to complete this sentence.

The largest multiple of four that is less than or equal to 26 is? He says, "I will use a multiplication chart to help me." So he's got some multiplication facts there, hasn't he, for the four times table? Something times four is less than or equal to 26.

That's what he wants to find out.

Ah, he says, "5 x 4 = 20, which is less than 26, so this is definitely correct." What do you think? Yes, Jun is right, but 20 is not the largest multiple of four that is below 26 and that's what's important when we're using division.

5 x 4 = 20, and then there are six more to reach 26, so you could make another group of four out of those six.

So he's right in saying that it is less than 26, but it's not the largest multiple of four that is less than or equal to 26.

Let's have a look.

5 x 4 = 20.

6 x 4 = 24 and that's still less than 26, so the largest multiple is 6 x 4.

Ah yes, says Jun, "It must be 6 x 4.

24 is the largest multiple of four less than or equal to 26." There'd be a remainder of two, wouldn't there? Now, Sofia wants to use the stem sentence to help her to solve the equation.

34/9 is equal to something.

So she's going to fill in the stem sentence.

The largest multiple of, that is less than or equal to, is? What goes in those gaps? Ah, she says, "The divisor is nine." I'm dividing by nine, so I'm looking for a multiple of nine.

So the largest multiple of nine that is less than or equal to 34, that's the dividend, so that's the number we're aiming for, so she needs to find the largest multiple of nine that is less than or equal to 34.

And what is that? She's having a look at the nine times table.

3 x 9 = 27.

4 x 9 = 36.

5 x 9 = 45.

Which one's going to be useful here? That's right.

3 x 9 = 27.

So, "3 x 9 = 27, which is less than 34." So the largest multiple of nine that is less than or equal to 34 is 27 and that's 3 x 9.

3 x 9 = 27 and there's a remainder of seven.

That's right.

So 34 divided by nine will be equal to three remainder seven.

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

Complete each stem sentence, and then use it to decide which times table fact to use if you're solving the following equations.

So A is 4/3.

B, 13/12.

C, 24/12.

D, 25/8.

E, 39/9.

And F, 32/7.

And you can think about grouping perhaps, dividing each into groups of the divisor.

That might help you to think about solving the equation.

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 in A, 4/3, well, they're very close together, aren't they? So four divided into groups of three, the largest multiple of three, that's our divisor, that is less than or equal to four is, well, three.

It's 1 x 3, isn't it? So we'd use the multiplication fact 1 x 3 = 3.

For B, 13/12, so we could think 13 divided into groups of 12.

Again, those numbers are very close together, aren't they? The largest multiple of 12 that is less than or equal to 13 is 12.

It's one times again, isn't it? So the multiplication factor used would be 1 x 12 = 12.

In C, 24/12, 24 divided into groups of 12.

Oh, how many groups of 12? The largest multiple of 12 that is less than or equal to 24 is 24.

2 x 12 = 24, so we would have no remainder for that division.

For D, 25/8, we know there's going to be a remainder here, because all multiples of eight are even numbers.

So what's the largest multiple of eight that is less than or equal to 25? It's 24.

3 x 8 = 24.

Now then, is this a multiple of nine? Well, there's a test of divisibility for nine, isn't there? 3 + 9, so add the digits together.

They equal 12.

That's not a multiple of nine, so no, it's not a multiple of nine.

The largest multiple of nine that is less than or equal to 39 is 36.

4 x 9 = 36.

And 32, that's not a multiple of seven, is it? The largest multiple of seven that is less than or equal to 32 is 28 and the times table fact would be 4 x 7 = 28.

And on into the second part of our lesson, we're going to be using these multiplication facts to solve division questions.

Sofia has 32 pear drops and she wants to divide them equally between six bags.

She wonders how many sweets there will be in each bag.

So are we grouping or sharing here? So we're dividing between six bags.

We know the number of groups.

We don't know how many are in each group.

"So this is a sharing problem," says Sofia.

32 and we want six bags, but 32 is not a multiple of six is it? So there will be a remainder.

So, "We must subtract groups of six to share out into the bags," says Jun.

"I wonder if we can use what we have learned to help us work efficiently." Do you think we need the number line or can we use a multiplication fact? Let's have a go at using our multiplication facts.

We must decide which fact to use.

So we're dividing between six bags, so we must use a fact from our six times table.

Our divisor is six.

So here's our six times table.

Do you remember we had 32 pear drops? "32 is not a multiple of six, so there will be a remainder." But which fact should we use? So, "There are two facts with a product close to 32." 6 x 5 or 5 x 6, 6 x 6.

Which one? We need to use a fact that has a product less than or equal to 32, so which one must it be? Six sixes are equal to 36, but we only have 32 pear drops, so we must choose the multiplication fact that is less than or equal to 32.

6 x 5 is less than or equal to 32, so we must use this fact, and we'll have a remainder of two.

We've got six bags, so we can put five sweets in each bag and there'll be a remainder of two.

So there'd be five in each bag with a remainder of two.

And there's our bar model showing us the six bags with five in each and the remainder of two, giving us our total of 32, our dividend.

Jun wants to divide 29 sweets between six bags.

How many sweets will there be in each bag? He says, "I must find the largest multiple that is less than or equal to 29." The largest multiple of what? Ah, it's six, isn't it? We're dividing between six bags, so our divisor is six, so it's multiples of six we're interested in.

So what's the largest multiple that is less than or equal to 29? That's right.

It's four, isn't it? 6 x 4 = 24 and that's less than 29.

So there's our 29 on our number line.

We've got six groups of four.

So in our six bags, we're gonna have four sweets in each bag and there'll be five left over.

29 is five more than 24.

Sofia says though, "29 is five more than 24, so you can make another group of four." Well, you could make a group of four, but what's Sofia not spotted? Ah, that's right.

Jun says, "Remember, we are dividing between six, so we need a group of six to put another sweet in each bag." We've got four in each bag at the moment, but it's six bags.

Our divisor is six, so we're looking for groups of six.

We'd need another group of six sweets to be able to put one in each bag and we've only got five, so there'll be five remaining.

So 29 sweets divided between six bags will be four sweets in each bag and five sweets remaining.

Time to check your understanding.

37 sweets are divided between seven bags.

How many sweets will there be in each bag? Seven times something is less than or equal to 37.

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

How did you get on? So we can look at the times table facts that have a product close to 37, and remember seven is our divisor, so we're looking at seven times table facts.

Seven times what? Oh, we've got 35 there and 42.

We're looking for less than or equal to 37, so it must be 7 x 5 = 35.

That gives us a product of 35, which is less than 37.

7 x 5 = 35 and we've got a remainder of two.

So we were putting our 37 sweets into seven bags, so there'll be five sweets in each bag with a remainder of two.

The children want to use their multiplication facts to solve this division equation.

Let's help them.

43/7.

Sofia says, "We don't know whether to share or group.

We can't solve it." Is that right? Jun says, "It doesn't matter.

We can use our times tables to solve both.

We must find the largest multiple of seven that we can use." Because we're dividing by seven, that's our divisor, so we can think about 43 divided into groups of seven.

Seven times something is less than or equal to 43.

Sofia says, "6 x 7 = 42 7 x 7 = 49, so the largest multiple that is less than or equal to 43 is 42." 7 x 6, so that means that we must be able to make six groups of seven and there's one remainder.

"43 is one more than 42, so there will be a remainder of one." 43 divided into groups of seven is six remainder one.

We can make six groups of seven and there'll be one remaining.

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

Use what you've learned about finding the largest multiple to fill in the missing numbers.

So you've got some in A, B, C, and D.

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.

So 8 x 2 = 16.

9 x 2 = 18.

17/2, what's that going to be? Well, we can use the multiplication fact 8 x 2 = 16, because 16 is the largest multiple that's less than or equal to 17.

So 17 divided into groups of two will be eight groups of two and one remaining.

In B, we've got 43/5, so we're looking for that nearest multiple that's less than or equal to 43 and we're dividing by five, so it's a multiple of five.

8 x 5 = 40.

9 x 5 = 45.

So we can use 8 x 5 to help us.

43 divided into groups of five will be equal to eight groups and three remaining.

For C, we had 36/11, so we're dividing by 11.

So we're looking for the largest multiple of 11 that is less than or equal to 36.

Well, 3 x 11 is equal to 33 and 4 x 11 is equal to 44.

36 is in between, so it must be 3 x 11.

So 36 divided into groups of 11, we can make three groups of 11 and there will be three left over.

And for D, 30/9, so we're looking for a multiple of nine that's the largest one that is less than or equal to 30.

Well, 3 x 9 = 27.

4 x 9 is too much.

It's equal to 36.

So we can use 3 x 9 to help us.

30/9 will be equal to three and three remaining.

27 + 3 = 30.

Well done if you got those right.

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

We've been using multiplication facts to answer division questions.

What have we been thinking about? Well, we can use multiplication facts to solve division equations and problems. If the question has a remainder, we must find the largest multiple that is less than or equal to the dividend to decide which multiplication factor to use.

And it's a multiple of the divisor that we're looking for, the number we're dividing by.

And when we've found the largest multiple, we must subtract it from the dividend to find the remainder or, if we visualise it on a number line, we can count on from the largest multiple up to the dividend and see what our remainder will be.

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

Bye-bye.