Lesson video

Hello, I'm Miss Miah, and I'm so excited to be a part of your learning journey today.

I hope you enjoy this lesson as much as I do.

Today you'll be learning how to divide a two-digit by a one-digit number using partitioning and representations with no remainders.

Here are the keywords that you will be using today in this lesson, and I'd like you to repeat them after me: Dividend, divisor, partial quotient, partition, quotient, good job.

Now, don't worry if you've not come across these words before.

We will be using them, and the sooner you learn what they mean, the better, because then it will really help you with your mathematical thinking and will also help you to reason further.

I'll now explain to you what these words mean.

So the dividend is the amount that you want to divide up.

So in this question, we've got 6 divided by 3 is equal to 2.

So because 6 is the number that we are wanting to divide up, that is known as the dividend.

Now a divisor is the number that we are actually dividing by.

So in this case, that's 3.

A partial quotient is seen when the dividend is partitioned.

So partial quotients here are 2 tens and one one.

You don't need to worry about this now because we will be looking at this as the lesson progresses.

We definitely have come across partitioning.

So partition means splitting a number into parts.

So you've got an example there.

A quotient is the result after division has taken place.

It is the whole number part.

So 2 is our quotient.

Now, when I was in school, we just said, oh, 6 divided by 3, the answer is 2, but I want you to get used to saying quotient instead because that is the correct mathematical term, and we want to speak like mathematicians.

So this lesson is a three part lesson.

We're going to start off by understanding partial quotients.

Now when it comes to dividing, it's so important that we know how to divide.

It is a skill for life.

When you grow up, you may need to spit the bills, that involves dividing.

You may need to know what the halfway point is between two locations, that involves dividing.

So what we are going to do is really build on our understanding of division to then help us tackle more complex division questions later on.

Let's get it right now In this lesson you'll meet Andeep and Izzy.

So 6 glow sticks are shared equally between three children.

How many glow sticks does each child get? So we've got our six glow sticks here and we've got three children.

Now what we are going to do is skip in threes because our divisor is three.

This will help us to divide far more quickly rather than sharing one glow stick out at a time, that's quite time consuming.

So one three is one each, that's three.

Two threes is two each, that's six.

So that means 6 divided by 3 is 2.

6 divided between 3 is equal to 2 each, which means each child will get two sticks.

You skip count in threes because the divisor is three.

This makes dividing smaller dividends easier.

Back to you, Andeep is working out 10 divided by 5.

He can skip count in? Pause the video here to select your answer.

How did you do? He can skip count in fives.

So if you've got C, you are correct, and this is because the divisor is five.

63 glow sticks are shared equally between three children.

How many glow sticks does each child get? So what division equation is needed? Let's begin by highlighting the key parts.

So 63, now we're sharing, which means out of the four operations of addition, subtraction, multiplication, and division, we are picking division, and we're sharing that between three children.

So that means our division equation is 63 divided by 3.

The dividend represents the number that we want to divide up.

So that, in this case, is 63.

The divisor represents the number that we are dividing by.

So in this case that is 3, and the quotient represents the result after the division has taken place, and that is what we're solving.

So here, I've got my glow sticks.

One bundle represents 10 glow sticks and then we've got three singular glow sticks at the end as well.

So altogether, we've got 63, and we're sharing that between three children.

We will start off by skip counting in threes.

So three tens is 1 ten each, that's 30.

Six tens is 2 tens each, that's 60.

6 tens divided between 3 is equal to 2 tens each.

One 3 is 1 each, that's 3.

3 divided by 1 is equal to 3, 3 divided between 1 is equal to 3 each.

So you can also show your calculation like this.

We have partitioned our tens and our ones, we can divide each part to get the partial quotients.

So here we can see that after dividing our tens, we've got two tens as a partial quotient, and after dividing our ones, we've got one one as our partial quotient.

So what you do after you've got your partial quotients, is that you add them together to get to your quotient.

So ultimately, you are adding two tens and one one which gives you 21.

6 tens and 3 ones divided by 3 is equal to 2 tens and one one.

So that means each child gets 21 glow sticks.

Now this jotting represents our understanding of partitioning in division.

I know some of you may have a different way of jotting it down, but this would be a very clear way of jotting down your thinking to work out this division equation.

Back to you, I'd like you to label the diagram.

You can pause the video here.

So how did you do? The 2 tens and one one are our partial quotients and our quotient is 21.

Back to you again, which is the correct division equation for this word problem: 88 glow sticks are shared equally between four children.

How many glow sticks does each child get? You can pause the video here.

So how did you do? You should have got B as your answer because 88 is our dividend and the key word here is sharing, so we are dividing, and that too between four children.

So that means our divisors is four.

So 88 divided by 4 is the correct equation.

Onto the main task.

For question one, you're going to be labelling the diagrams. For question two, you're going to use the diagram to fill in the gaps.

You can pause the video here.

Off you go, good luck.

So how did you do? So for the first question, this is what you should have got.

You can pause the video here to check your work.

Once you've done that, click play so we can carry on.

So for question two, let's have a look at this more closely.

So we've got 99 glow sticks altogether.

Now, what we have to do is fill in the gaps.

So 3 tens are 1 ten each, that's 30.

9 tens are 3 tens each, that's 90.

9 tens divided by three is equal to 3 tens.

Now if you didn't know that, forget about the tens, try and think about what you do know.

So you do know that 9 divided by 3 is 3, so that means 9 tens divided by 3 is 3 tens.

Now we're going to move on to our ones.

So 3 ones are one one each, that's 3.

9 ones are three ones each, that's nine.

So 9 ones divided by 3 is equal to 3 ones.

Now if we have a look at our jottings, we've got 9 tens divided by 3, which is equal to 3 tens.

9 ones divided by 3 is equal to 3 ones.

And then when we add our partial quotients, we should have got 33.

Let's move on to our second lesson cycle, and that is to identify multiples using the part whole model.

Now this part is super important because by identifying our multiples within our dividend, we will be able to make our division equation so much more efficient to calculate.

So 63 glow sticks are shared equally between three children.

How many glow sticks does each child get? Now you're probably wondering, "Miss Mia, we've already covered this question, why are we doing it again?" This time, I'd like you to show you a different strategy that you can use that I think you may find super effective, and it's a very good tool to have in your toolkit as a mathematician because it may come in handy.

So watch this.

Sometimes partitioning the dividend can help us to solve division problems mentally, and some of you probably do this in your head, and you don't even realise you're doing it.

This is a good way to record it.

So there are so many ways that you can partition 63.

For example, like this, or like this, or like this.

However, it's up to us to decide which way of partitioning the dividend is helpful for the calculation.

So Izzy's saying she's going to be using her times tables facts to also help her.

So first we're going to partition the dividend into tens and ones.

So here we've got 60 and 3.

Then you're going to divide each part by the divisor.

So we're going to start off with 60.

Izzy knows that 3 groups of 2 is 6.

So 6 divided into 3 groups is 2, which also means 3 groups of 2 tens is 6 tens.

So 6 tens divided into 3 groups is 2 tens.

Now we're going to move on to our ones.

So Izzy knows that anything divided itself is one.

So 3 divided by 3 is 1.

Then you add your partial quotients to find the answer.

So in this case it's 20 + 1, which is 21, the quotient is 21.

And if we were to represent this using the place value counters, this is what it would look like.

So we're going to skip count in threes.

I know that 3 groups of 2 tens is 6 tens.

So 6 tens divided into 3 groups is 2 tens, and this can be arranged in a multiplication equation, which is the inverse of division.

3 multiplied by 20 is 60, so 60 divided by 3 is 20.

This can also be written as 6 tens divided by 3 is equal to 2 tens.

Then we move on to dividing our ones by three.

So I know that 3 groups of 3 ones is one one.

So 3 ones divided into 3 groups is one one, which can also be represented like this.

So to check, we can do 3 multiplied by 1, which is 3.

So 3 divided by 3 is equal to 1.

Now we have to add our partial quotients.

So that means 2 tens add one one is the same as 21, our quotient is 21.

So each child gets 21 glow sticks.

Back to you.

Andeep is calculating 38 divided by 2.

Select the part whole model for his calculation.

Can you think of other ways to partition 38? You can pause the video here, and when you're ready, just click play.

So how did you do? C is the correct answer.

38 can be partitioned into 3 tens and 8 ones.

Other examples may have included 20 and 18, 28 and 10, 14 and 24, and we'll talk more about why some parts are better to use than others when it comes to dividing.

Now let us try using Andeep's part whole model to help us divide, okay.

So Andeep's got 63, he's partitioned 63 into 59 and 4.

Izzy's saying she's going to use her times table's facts again to help her.

Oh, hang on a minute, this is hard.

Usually, we partition two digit numbers to make them easier to work with.

This part whole model shows parts that are 59 and 4.

It is really difficult to divide these numbers by three as neither of these parts are multiples of three.

However, this particular part whole model is helpful because 30 and 33 are multiples of 3.

I know that 30 is a multiple of 3 because 3 groups of 1 ten is 3 tens.

So 3 multiplied by 10 is 30.

So 30 divided by 3 is 10.

33 is also a multiple of 3 because 3 groups of 1 ten add 3 groups of one one is 33, so 3 tens and 3 ones divided into 3 groups is 1 ten and one one.

In other words, 3 multiplied by 11 is 33, 33 divided by 3 is equal to 11, which can also be written like this, and I'll let you have a look at that.

Now out of these part whole models, what is most helpful is that the parts that you've got have to be a multiple where possible off the divisors because this will be incredibly helpful when you are dividing the parts by your divisor.

Back to you.

Andeep has partitioned 38 into the options below.

Which is least helpful in dividing by 2? Pause the video here.

So how did you do? You should have got A, as neither part is divisible by 2, and we know that because both numbers are odd and we are dividing by two.

Moving on, Izzy is calculating 70 divided by 5.

She partitions her dividend in the following ways.

So there's three ways there, A, B, and C.

I'll let you have a look at that.

So which part whole model will be most efficient to use? I'd like you to explain your thinking to your partner.

So there is no right or wrong answer because all parts are divisible by 5.

Some of you may have also thought actually there are more ways that you can partition 70 to help you further with dividing by 5.

Some of you may have thought of 4 parts for 70.

As long as your parts are multiples of the divisor.

Izzy and Andeep are working out 64 divided by 4, work out the division using both ways of partitioning.

What do you notice, and what advice would you give to make it easier? Well, Andeep's method is more difficult because the parts are not divisible by 4.

So what Andeep should try and do is partition his dividend into multiples of 4.

Now when I say "Partitioning your dividend into multiples of 4," the best thing to do is think about the greatest multiple of four that you know within the dividend.

So in this case, what I'm thinking about is my 4 times tables.

I know that 4 multiplied by 12 is 48, so 48 is one of my parts.

The remaining part will be 16, which I also know is a multiple of 4.

So that's actually worked out pretty well.

Right, onto your task for this lesson cycle.

For question one, you're going to complete the calculations shown on the screen.

One part whole model has been filled out for you.

What I'd like you to do is show your working underneath the part whole model.

For question two, I'd like you to decide which way of partitioning the dividend is most helpful and least helpful for the calculation, 88 divided by 4, and I'd like you to also write down why.

I'd like you to also think about any other helpful ways to partition the dividend.

For question three, you're going to use the partitioning method to help you solve the problems. So 3a: There are 95 marbles shared between five children.

How many marbles will each child get? For 3b, 51 sweets are shared between three children.

How many sweets does each child get? You can pause the video here.

Off you go, good luck.

So how did you do? For question one, you should have got your quotient as 15 for the first question.

For the second question, you should have got 18.

And for the third question, you should have got 17.

Now, for the last question, you could have partitioned 68 in many ways as long as your parts were multiples of the divisor.

You can pause the video here to mark your work.

For question two, A, C, and D are the most helpful ways of partitioning as they easily allow you to divide by 4.

Whereas B was the least helpful because none of the parts were divisible by 4.

And do remember, when dividing by 4, you half and half again.

So your parts should have been an even number and should have been multiples of four.

Other examples that you could have had where the examples shown on the screen as long as your parts were multiples of four and added up to a whole of 88.

Question 3a, your quotient should have been 19, so each child would've got 19 marbles each.

Let's look at 3b more closely.

So there were 51 sweets which were to be shared between three children.

Now here our parts are 30 and 21, which are both multiples of three.

You could have also had 36 and 15, or any other multiples as parts which when added together, give you 51.

You then would've had to divide each part by three, and in doing so you would've got 17 as your quotient, meaning that each child will get 70 marbles each.

On to our final lesson cycle: Dividing using partitioning.

Well done, you've been so good so far, let's go.

So 96 marbles are shared equally between three children.

How many marbles does each child get? So what division equation do you think is needed to calculate this equation? So 96 divided by 3 is our division equation.

We can use our place value counters here and we're going to skip count in threes because that is our divisor.

So 3 tens is 1 each, that's 30.

And let's keep going.

9 tens is 3 tens each, that's 90.

So 9 tens divided by 3 is 3 tens.

3 ones is one one each, that's 3.

And 6 ones is 2 ones each, that's 6.

So 6 ones divided by 3 is 2 ones.

So this can also be written like this.

So once we've partitioned our tens and ones and divided both by three, that gives us our partial quotients of 3 tens and 2 ones, which we now need to add together, which gives us 32 as our quotient, each child will get 32 marbles.

Back to you.

Choose the correct informal written method for this equation: 84 divided by two.

Explain why the others are incorrect to your partner.

Pause the video here.

Okay, so how did you do? Well, C is correct.

A is incorrect because it's been partitioned incorrectly.

And B, we've got incorrect place value.

So 8 tens divided by 2 is not 4 ones, it should be 4 tens.

I love problem solving questions like this, so let's get started.

It may seem complex, but all we have to do is break it down.

A square has a total perimeter of 92 centimetres.

What is the length of one side? What division equation is needed for this question? Well, let's begin by highlighting the key parts.

92 is the dividend as that is the total perimeter.

As a square has four equal sides and you are calculating one side, the divisors is 4.

Begin by partitioning the dividend into tens and ones.

90 and 2 are not multiples of 4.

However, 80 and 12 are multiples of 4.

So let's write that down.

So 92 can be written as equal to 8 tens and 12 ones.

Next, divide your tens by 4.

So 8 tens divided by 4 is 2 tens.

12 ones divided by 4 is 3 ones.

And now we're going to add our partial quotients.

So 2 tens add 3 ones is 23, so that means 92 divided by 4 is 23.

The length of one side is 23 centimetres, and don't forget to write in your units.

Back to you, you're going to fill in the gaps, you can pause the video here.

How did you do? So 6 tens divided by 3, you should have got 2 tens, and then 6 ones divided by 3 is equal to 2 ones.

I'd like you to fill in the gaps again.

You can pause the video here.

So how did you do? You should have got 13 as your quotient.

Well done if you got that.

On to the main task.

For question one, you're going to fill in the gaps.

For question two, you're going to use partitioning or an informal written method to solve these problems. 2a: A regular pentagon has a total perimeter of 55 centimetres.

What is the length of one side? 2b: The total perimeter of three triangles is 99 centimetres.

What is the length of one side? You can pause the video here, off you go.

So how did you do? This is what you should have got.

You can pause the video here to mark your work.

If you've got all of those correct, good job, let's move on to the problem solving questions.

Right, for 2a, let's have a look at this together: A regular Pentagon has a total perimeter of 55 centimetres.

So we need to figure out what the length of one side is.

So 55 is our dividend because that's how much we need to divide up.

Now, there's five sides in a Pentagon, so that must be our divisor, and we know that that's the divisor because we need to find the length of one side.

So that means we can start off by dividing our tens by five.

5 tens divided by 5 is 1 ten.

Now we can move on to our ones.

5 ones divided by 5 is one one.

So 55 divided by 5 is 11, which means that the quotient is 11 centimetres.

Some of you may have also been able to calculate that mentally, that's absolutely fine as well because you would've used your table facts to know that 55 divided by 5 is 11, or 11 multiplied by five is 55, which is the inverse.

For 2b, the total perimeter of three triangles is 99 centimetres.

Now we need to find out what the length of one side of one triangle is.

So before we even find out the length of one side, so there were a couple of ways that we could have calculated this.

But in this example, what we've done is figure out the perimeter for one triangle first.

So we know that the total perimeter is 99, that is our dividend, our divisors is 3.

So 9 tens divided by 3 gives us 3 tens.

9 ones divided by 3 gives us 3 ones.

So that means 99 divided by 3 is 33, which means the total perimeter of one triangle is 33 centimetres.

Now to find out the length of one side of that one triangle, we now have a dividend of 33 and our divisor is still three.

So 3 tens divided by 3 is 1 ten.

3 ones divided by 3 is one one.

So 33 divided by 3 is 11, which means our quotient is 11 centimetres and the length of one side is 11 centimetres.

If you got that correct, good job, well done, give yourself a tick.

Let's summarise our learning for today.

So you divided a two-digit by a one-digit number using partitioning and representations, no remainders.

You can use skip counting, the language of unitization, and place value to divide a two-digit by one-digit number.

You can effectively partition numbers to help you solve division equations with no remainders.

You can also use the informal written methods to solve division problems, which include no remainders as well.

Well done for getting through to the end of this lesson.

I really enjoy teaching it to you, and I hope to see you in the next one.