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.

In this lesson, you will divide a three digit by a one digit number using partitioning and representations, and this, time there will be instance of one regrouping happening.

The keywords are now on your screen.

I would like you to repeat these after me.

Remainder.

Partitioning.

Regroup, regrouping.

Good job.

Let's move on.

A remainder is an amount left over after division.

It happens when the first number does not divide exactly by the other.

Partition means splitting a number into parts.

So here, you've got an example there on the screen.

The process of unitizing and exchanging between place value is known as regrouping.

For example, 10 ones can be regrouped for one 10.

One 10 can be regrouped for 10 ones.

So, for this first part of our lesson cycle, we're going to be understanding division, especially when there's one instance of regrouping.

And in this lesson, you will meet Andeep and Izzy.

Now, you may have seen this.

So in this example, 72 marbles were shared equally between three children.

How many marbles would have each child got? We can see that three tens is one 10 each, that's 36 tens is two tens each, that's 60, there is one 10 left over, so seven tens divided by three is two, remainder of one 10.

Today, you will explore what to do when you come across a three-digit dividend that also requires regrouping.

Let's begin.

423 grammes of cat food is to be divided equally between three cats.

How much cat food would each cat get? So the division equation that we are solving is 423 divided by three, and we can represent that using our place value counters.

We're dividing equally between three cats.

We're going to begin by dividing the hundreds, and we're going to skip count in three, because that's our divisor.

Three hundreds is 100 each.

That's 300.

There is 100 left over, so that means four hundreds divided by 3 is equal to one remainder 100.

Four hundreds divided between three is equal to 100 each with a remainder of 100.

So, what we need to do now, and this part is absolutely critical, is we need to regroup that 100 for 10 tens in order to continue dividing.

So here we are.

So twos tens and 10 tens is equal to 12 tens.

Then, we divide our tens, So three tens is one each, that's three, six tens is two each, that's 6, nine tens is three each, that's nine, and lastly, 12 tens is four each, that's 12.

So, 12 tens divided between three is equal to four tens each.

Now, we move on to dividing our ones.

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

So, what do you notice? There are three partial quotients, and even though we had to regroup, there is no remainder.

So that means each cat gets 141 grammes of food.

Another way we can record this is through jottings.

So, three hundreds is divided by three is 100, 12 tens divided three is four tens, three ones divided by three is one one, we add our partial quotient, we've got three there, so 100, add four tens, add one one, is 141.

Over to you, I'd like you to fill in the blanks.

You can pause the video here.

So how did you do? You should have got two hundreds are equal to 20 tens.

20 tens, add four tens is equal to 24 tens.

Let's move on.

705 litres of honey needs to be divided equally between five barrels.

How much litres of honey will be in each barrel? So our division equation is 705 divided by five.

So we can represent this using our place value counters.

I've got seven one hundreds and five ones, no tens.

So we're going to begin by dividing the hundreds and we're going to skip count in fives.

So five is 100 each, that's 500.

There is 200 left over, 700 divided by five is equal to one, remainder two hundreds.

Seven hundreds divided between five is equal to 100 each with a remainder of two hundreds.

What you do now is regroup two hundreds for 20 tens.

Now we're going to divide our tens.

Five tens is one 10 each, which is 50.

10 tens is two tens each, that's 100.

15 tens is three tens each, that's 150, and 20 tens is four tens each, that's 200.

So 20 tens divided between five is equal to four tens each.

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

Five ones is one one each, that's five.

So when we've added our partial quotient, we end up with a quotient of 141.

If we were to jot this, we could record it like this, so five hundreds divided by five is equal to 100, 20 tens divided by five is four tens, and five ones divided by five is one one, so each barrel will contain 141 litres of honey.

141 litres is our quotient.

Back to you.

I'd like you to fill in the blanks.

You can pause the video here.

So how did you do? 24 tens divided by six is equal to four tens.

Andeep and Izzy are discussing how to tell if you have to regroup.

"I can tell straight away if we have to regroup." "How?" "If the number of hundreds in the dividend is not a multiple of a divisor, we must regroup." Do you agree? I'd like you to explain your thinking to your partner.

For example, 300 divided by three, so three hundreds is a multiple of three, we do not need to regroup.

Now let's have a look at 400.

So four hundreds is not a multiple of three.

We do need to regroup.

Six hundreds is a multiple of three.

We do not need to regroup.

And you can see that two groups of three hundreds make 600.

Back to you.

Your divisor is five.

Which numbers will result in regrouping? You can pause the video here.

So how did you do? You should have got B, and that's because six hundreds divided by five is equal to one, remainder 100.

So that will require regrouping.

You should have also got C, seven hundreds divided by five is equal to one, remainder two hundreds.

Onto your task.

For question one, you need to tick the equations that will require regrouping from the hundreds to the tens, and you've got nine division equations here.

I'd also like you to write down what you notice.

You can pause the video here.

Off you go.

So how did you do? So you should have ticked C, E, H, and I, and the way I would've tackled this question is by looking at my hundreds spot, whether it is a multiple of the divisor.

So for example, C, the hundreds digit is seven, and I know seven is not a multiple of three so we're going to have to regroup.

The closest multiple of three to seven is six.

And then, say, for example, if I looked at E as well, I know that eight is not a multiple of three, but nine is.

For that question, we would also have to regroup.

So what you should have noticed is that if the number of hundreds in the dividend is not a multiple of the divisor, we must regroup.

Let's move on to the second part of our lesson cycle.

You're now going to divide using partitioning, and it's going to include one instance of regrouping.

Now, there are many ways to record and solve division equations.

You may have seen some of the informal strategies below.

So here we've got jottings.

Again, more jottings.

Put the part-whole model here to show the partitioning strategy of division.

Now, these are known as informal methods and you can use any of these to help you when dividing, but it's all about picking the right strategy at the right time to help you with the efficiency.

Good mathematicians are efficient.

So a local bakery is having a grand opening.

It has a total of 423 slices of cake, which are packed in boxes of three.

How many boxes will be ready for the bakeries grand opening? So I want you to think about what division equation is needed to solve this problem.

Well, if we look carefully, 423 would be our dividend and our divisor is three.

The dividend is 423 because that is the amount we are dividing up, and the divisors is three because that is the amount we are dividing by.

The quotient is unknown.

That is what we are calculating.

Over to you.

I'd like you to fill in the blanks.

You can pause the video here.

So how did you do? The dividend is 855 because this is the amount we are dividing up.

The divisor is five.

This is the amount we are dividing by.

Now, an example question that you could have had is that 855 cakes are packed into boxes of five.

How many boxes will there be in total? Let's move on.

So Andeep is solving 423 divided by three.

This is his method, so he's used the part-whole model there and he's got some jottings underneath.

This is Izzy's method, so she's used an informal written method to solve this question.

Which method do you prefer and why? Sometimes the part-whole model is more efficient because it makes the process of regrouping easier as we can choose the multiples that are divisible by the divisor.

So for example, in Andeep's method, look for the highest multiple of three that he can think of, and in this case, he's chosen 300, then he's regrouped the 100 from 400 into the tens, and he's got 120, or in other words, 12 tens and then the remaining three ones.

And actually, I would probably prefer Andeep's method because then I know that all my parts are divisible by three.

All I have to do now is divide each part by three, which for me, is efficient.

Let's move on.

A large box of crayons contains six smaller packs.

What is the division equation needed to solve this problem? How else can we represent this problem? Andy wants to find out what the mass of one smaller pack of crayons is.

So what is the division equation needed to solve this problem, and how else can we represent this problem? He says that the total mass of the large box is 726 grammes, so if that's the case, the division equation would be 726, which is the dividend, divided by six, which is the divisor.

So our division equation is 726 divided by six.

So the dividend is 726, that is what we're dividing by, and the divisors is six because we need to calculate the total mass of one pack.

The quotient is unknown.

That is what we are calculating.

So a way to represent this is using a bar model.

So if 726 is our whole, we don't know what the value of each pack is, so we can draw a model like this.

So what advice would you give to Andeep? Have a look at his part-whole model.

Andeep should partition his parts into multiples off the divisor, and we can see that he's partitioned into 700, 20, and six.

700 is not a multiple of six, neither is 20, so in order to make that division equation easier for him, he needs to find multiples of six within 726.

This would be much better for him.

So now our part-whole model shows 600, 120, and six.

Six hundreds divided by six is equal to 100, 12 tens divided by six is two tens, and six ones divided by six is one one.

Now we have to add our three partial quotients, which gives us 121 as our quotient, which means one pack of crayons weighs 121 grammes.

So now it's my turn.

I will be dividing 513 by three.

So let's begin.

I've decided to partition 513 into 300, 210, and three.

All of these parts are multiples of three, so that should make my division easier.

I will start off by dividing my 300.

So three hundreds divided by three is 100.

21 tens divided by three is seven tens.

And lastly, three ones divided by three is one one.

Now we need to add our partial quotients.

So 100, add seven tens, add one one is 171.

Over to you.

You're going to be divided 728 by four.

You can pause the video here.

So how did you do? You may have partitioned 728 in different ways, as long as there are multiples of four.

So in this example, 728 has been partitioned into 400, 320, and eight.

So four hundreds divided by four is equal to 100.

32 tens divided by four is eight tens.

And lastly, eight ones divided by four is two ones, and then we add our partial quotient to get 182.

If you've got 182, well done.

Good job.

Right, over to you.

I'd like you to fill in the gaps.

You can pause the video here.

So how did you do? You should have got nine hundreds divided by six is equal to 100, remainder three hundreds.

Now three hundreds can then be regrouped as 30 tens.

30 tens, add six tens is equal to 36 tens.

Then we continue dividing our 36 tens by our divisor of six, which is equal to six tens.

Moving on to our ones, six ones divided by six is one one.

966 divided by six is 161.

161 is our quotient.

Onto our task.

For question one, you're going to solve the following questions and you're going to record your calculations using the partitioning strategy.

You've got one A, which is 847 divided by seven, B, 968 divided by eight, and C, 786 divided by six.

For question two, you're going to be solving the worded problems using an informal method.

855 pencils are divided equally between five classes.

How many pencils does each class get? For 2B, 576 gaming cards are shared equally between three friends.

How many cards does each child get? You can pause the video here, have a go.

Good luck.

How did you do? So this is what you should have got.

So for A and B, your quotient should have been 121.

And then for C, your quotient should have been 131.

If you got all three of those correct, good job, give yourself a tick.

So for 2A, each class would've got 171 pencils, and for 2B, each friend would've got 192 cards.

If you've got both of those questions correct, you can give yourself a tick.

Well done.

You've made it to the end of the lesson.

Let's summarise our learning for today.

So you can now divide a three digit by a one digit number using partitioning and representations, including one instance of regrouping.

You understand that partitioning the dividend into tens and ones helps when dividing a three digit by a one digit number.

You understand that if the dividend is not a multiple of the divisor, there will be a remainder.

And lastly, you understand that if the remainder is a number of tens, you can regroup the tens for ones and then you can continue to divide to get your quotient.

Well done for making it to the end of this lesson.

I hope you really enjoyed it, and I look forward to seeing you in the next one.