Lesson video

Hello, I'm Miss Mia 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'll be able to divide a three-digit by a one-digit number using partitioning and representations.

There will be no remainders.

These are the key words that you'll be coming across in today's lesson, and I'd like you to repeat them after me.

Dividend, divisor, partial quotient, partition, and quotient.

Well done, let's move on.

The dividend is the amount that you want to divide.

So in this case it's six.

A divisor is the number that we want to divide by, and in this case it's three.

A partial quotient is seen when the dividend is partitioned.

Partition means splitting an object or value down into smaller parts.

And you can see the example on your screen.

A quotient is the result after division has taken place.

So in this case, the quotient is two.

So in this lesson cycle, we are going to be finding the partial quotients when dividing a three-digit by a one-digit number.

You will also meet Andeep and Izzy.

Now you may have seen this.

This is when we were dividing a two-digit by a one-digit number and we used our place value counters to help you.

Today we will be exploring what happens when we divide a three-digit dividend by a one-digit divisor.

Alright, let's begin.

Now, I actually do have a cat at home, and this was a real problem that I had to use the weighing scale to help me with.

The numbers might be a little bit different.

So 363 grammes of cat food is to be divided equally between three cats.

How much cat food would each cat get? So straight away, my division equation would be 363 divided by three, and I can represent this using place value counters.

So we're going to begin by dividing the hundreds.

Just a heads up, we are going to skip count in our divisor.

So three hundreds is 100 each, that's 300.

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

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

Now we're going to divide our ones.

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

So what do you notice? This time there are three partial quotients.

When we were dividing our two-digit dividend by our one-digit divisor, we only had two partial quotients.

But because we are now dividing into a three-digit dividend, we are going to end up with three partial quotients.

So 100 add two tens, add one one is 121.

This can also be represented like this.

So three hundreds divided by three is 100.

Six tens divided by three is two tens, and three ones divided by three is one one.

So that means our quotient is 121.

Each cat will get 121 grammes of food each.

Izzy is working out 424 divided by four.

She can skip count in.

I'd like you to justify your thinking to your partner.

You can pause the video here.

So how did you do? You should have got C as your answer.

This is because the divisor is four, so you'd skip count in fours.

Okay, so 428 books need to be placed equally on two shelves.

How many books would each shelf have? So what division equation is needed? Well, let's look at this in detail.

428 books onto two shelves.

That means our dividend is 428 and our divisor is two.

So that means the dividend represents the amount that we want to divide.

So in this case it's 428.

The divisors represents the number that we are dividing by, and this is two.

Quotient represents the result after the division has taken place.

And that is what we are calculating.

So we will be using our place value counters again to help us with this question.

So here we can see we've got four one hundreds, two tens, and eight ones.

We're going to begin by dividing the hundreds.

And again, we're going to skip count in twos because that is our divisor.

Four hundreds is two hundreds each, that's 400.

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

Two tens is one 10 each, that's 20.

And then lastly, our ones.

Eight ones is four ones each, that's four.

Now the final step is to add our three partial quotients.

So two hundreds, add one 10, add four ones is 214.

This can also be written like this.

So each shelf will have 214 books each.

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

Think about the keywords that we've used in this lesson.

You can pause the video here.

So how did you do? You should have got partial quotients and quotient.

Andeep has solved the equation using a different method.

"I know that dividing by two is the same as halving." A half of four hundreds is two hundreds, half of two tens is one 10, and half of eight ones is four ones.

So that means 200 add 10, add four is 214.

This is a very effective mental strategy.

And then we've got the informal written method to the right.

Which method do you prefer and why? And which method would you have actually used for this equation? So sometimes using our tables facts and mental strategies can be more efficient when dividing, especially when there aren't any instances of regrouping.

Back to you.

Which method would you choose to use for 484 divided by four? And I'd like you to justify your thinking to your partner.

Is it A, a mental strategy, B, an informal written method, or C, a partitioning strategy? You can pause the video here.

So how did you do? Now you could have used any method, but here are some examples that you may have said to your partner.

A, a mental strategy.

I would use this strategy because I just need to halve and half again.

B, an informal written.

Someone might have chosen to use this because they might find that it helps them identify the partial quotients and then add them together.

And C, someone may have used a partitioning strategy because it would make sure that they divide each part.

Let's move on.

Izzy is using a partitioning strategy to help solve the equation 633 divided by three.

So you can see that Izzy's partitioned 633 into 500, 100 and 33.

She needs to divide each part by three now.

"This is hard." What advice would you give to Izzy? Partitioning into multiples of the divisor would help Izzy to divide.

And actually partitioning effectively makes dividing a three-digit by a one-digit number easier.

And what I mean by that is that if you partition into multiples of three, that would make it easier as opposed to just picking any part that when added together, gives you the whole of 633.

Back to you.

Which partitioning would be efficient to solve 448 divided by four? Is it A, B, or C? You can pause the video here and when you're ready, click play.

Let's see how you did.

So C would've been the most efficient because all of the parts are a multiple of the divisor.

Now there are obviously other ways that you could have partitioned 448, but compared to the other ways that they've been partitioned in this example, C would be the most efficient.

Onto the main task.

Question one.

You are going to be matching each division expression with the correct partial quotients.

For question two, you're going to use the partitioning strategy to find the partial quotients and fill in the gaps.

You can pause the video here.

Off you go, good luck.

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

You can pause the video here to check your work.

For question two, this is what you should have got.

So again, you can pause the video here to check your work.

I will be looking at 369 divided by three.

So in this case, 369 has been partitioned into 300, 60, and nine, which are all multiples of the divisor three.

So three hundreds divided by three is equal to 100.

Six tens divided by three is equal to two tens, and nine ones divided by three is equal to three ones, which means your partial quotient are 100, and 20 and three resulting in a quotient of 123.

If you've got all of that correct, good job.

You are on your way to understanding how to divide a three-digit by a one-digit number.

So our second part of this lesson cycle is to divide using partitioning.

Let's begin.

633 marbles are shared equally between three children.

How many marbles does each child get? So what division equation is needed to calculate this equation? So let's highlight the key part.

So we've got 633 as our dividend.

Now we're sharing, which means our operation is to divide, and our divisor is three because that's how many children there are.

So the equation that we're calculating is 633 divided by three.

Now I've got my place value counters here, we are going to skip count in threes.

So six hundreds is two hundreds each.

That's 600, three tens is one 10 each, that's 30.

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

So 633 divided by three is equal to 211.

So that means each child will get 211 marbles each.

This can also be written like this.

Back to you.

Choose the division expression for this written informal method, and I'd like you to justify your thinking to your partner.

You can pause the video here.

So how did you do? You should have got B.

842 is the dividend, two is the divisor, and that's because if we look at our informal written method here, we can see that each part is being divided by two, which means the divisor is two.

Now our dividend has been partitioned into hundreds, tens and ones.

So eight hundreds, add four tens, add two ones is 842, which means 842 is our dividend.

A digital square has a total perimeter of 484 centimetres.

What is the length of one side? So again, I'd like you to think about the division equation that is required for you to answer this question.

So 484 is the dividend as that is the total perimeter.

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

Begin by partitioning the dividend into hundreds, tens and ones.

So here you can see that we've partitioned 484 into hundreds, tens, and ones.

Then you're going to divide your hundreds by four.

So four hundreds divided by four is 100.

Eight tens divided by four is two tens, and then four ones divided by four.

So anything divided by itself is one.

So you end up with one one.

Now you're going to add your partial quotients.

So 100 add two tens, add one one is 121.

So that means 121 is the length of one side.

Don't forget your units.

So it's 121 centimetres.

And you can double check that by multiplying 121 by four, and you should get 484 centimetres altogether.

So 484 is a multiple of four, which means there will be no remainders.

Back to you.

You're going to fill in the gaps to find the length of one side.

You can pause the video here.

Off you go.

So how did you do? So the total perimeter is 636 centimetres.

We're going to start off by dividing our hundreds.

So six hundreds divided by three is two hundreds.

If you didn't know that, think of the facts that you do know.

You know that six divided by three is two.

So six hundreds divided by three is two hundreds.

Then we can move on to our tens.

Three tens divided by three is one 10.

And lastly, our ones.

Six ones divided by three is two ones.

Back to you.

Fill in the gap.

What did you get? If you got 212 centimetres, you are correct, well done.

Let's move on.

Onto the final task.

So Andeep has created a picture of a barn using 2D shapes.

He would like to draw an accurate representation of this, but needs help finding the perimeter.

And he says that, "Finding the length of one side will help me draw the rest of the shape." So what I'd like you to do is using the information in the table that I'll bring up onto the screen in a bit.

I'd like you to help Andeep find the missing lengths.

So here's the image and here's the table.

You can pause the video here.

Off you go, good luck.

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

So the first shape is a pentagon and a pentagon has five sides.

Now, if the total perimeter for pentagon is 555, what you should have got is 111 as your quotient because you would've been calculating 555 divided by five.

Now your next shape is a hexagon, and a hexagon has six sides.

The total perimeter is 666, your divisor is six.

Again, your quotient would've been 111.

Now for the square we've got a total of four sides, and the total perimeter is 844.

So 844 divided by four.

You should have got a quotient of 211.

For the tinier square or the smaller square, the total perimeter was 484.

The number of sides that you had again was four.

So your dividend would've been 484 in your divisor four.

The length of one side that means would've been 121 centimetres.

And lastly, a triangle has three sides, and if the total perimeter is 969, you are dividing 969 by three, and you should have got a quotient of 323 centimetres.

Well done if you got all of that correct, good job.

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

Let's summarise our learning.

So today you divided a three-digit by a one-digit number using partitioning and representations.

This time with no remainders.

You now understand that there will be three partial quotients when dividing a three-digit by a one-digit number.

You can partition the dividend into hundreds, tens, and ones to help you when dividing a three-digit and a one-digit number.

You can use times tables and unitizing to divide the hundreds, tens, and ones by the divisor and place value resources can represent the division and you can use that to help you as well.

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

I really hope you enjoyed it and I can't wait to see you in the next lesson.