Lesson video

Hello and welcome my name's Miss Thomas.

I'll be going through the lesson with you.

Hope you're good and you've had a good day so far, I certainly have.

So, this today this lesson, we're going to be going through the short division algorithms. I hope you're ready for some exciting maths ahead.

Let's get started.

Here we have a problem, I'll read this out loud, follow along with me.

Maple syrup is stored in barrels that have a capacity of three litres.

How many barrels can be filled with 9,636 litres of syrup? The first question says, "What is known? What is unknown?" Pause the video and decide what you know and what you don't know.

Welcome back.

You might have saw and realised that we know that there's a capacity of three litres in a barrel.

But we don't know how many barrels that can be filled, if we've got 9,636 litres of syrup.

The next question is, "How might you solve this problem/" Pause video and decide.

Welcome back.

So I've got an area model here to represent our problem.

So our whole is 9,636, and we need to share it equally by three because it can hold a capacity of three litres each barrel.

What we don't know is how many barrels we can fill.

So our equation is going to be 9,636 divided by three.

Before we solve our equation, I want to go through three new star words.

The first word is, my turn, dividend.

Your turn.

Dividend is the number being divided.

The next word, my turn, divisor.

Your turn.

Devisor is the number that dividend is being divided by.

The final word, my turn, quotient.

Your turn.

Quotient means the result.

So let's go through our equations.

So, we've got 9,636 divided by three is equal to, and we don't know what it's equal to yet.

So the dividend, the number being divided is 9,636.

And the divisor, the number the dividend is being divided by, is three.

And the quotient, the result, we don't know it yet, but here will be our quotient when we find out.

So let's get solving.

I've got a place value chart here, and I've got on the next side of my screen, I've got the written method for short multiplication.

As you can see, I've labelled my numbers with dividend, divisor, and quotient.

So here, the divisor is three.

So I'm going to be dividing 9,636 by three.

Let's add the dividend to our place value chart.

So I've got nine thousands, six hundreds, three tens, and six ones.

The divisor is three, so I'm dividing by three.

So I'm grouping my counters into groups of three.

How many groups of three in 9,000? So how many groups of three thousands in nine thousands? I can have one group of three thousands, two groups of three thousands, three groups of three thousands in nine thousands.

So I'm going to add that to my short multiplication method.

Next, let's go to the hundreds.

How many groups of three hundreds in six hundreds? I've got one group of three hundreds, two groups of three hundreds.

So I can have two groups of three hundreds in six hundreds.

Next, I'm going to my tens and my divisor is three, so I'm dividing by three, I'm going to have equal groups of three.

So I've got three tens there.

How many groups of three tens in three tens? There's one group of three tens in three tens.

So I'll add that to my written method.

And finally, how many groups of three ones in six ones? I can have one group three ones, two groups of three ones.

So in six ones, I can have two groups of three ones.

And I've added that into my short division method.

So, now we know that 9,636 divided by three is equal to 3,212.

Pause the video and can you explain, looking at my counters, 9,636 divided by three is equal to 3,212? Pause the video and explain out loud to your screen.

Welcome back, great explaining.

Let's see what we've got next.

So now we're at the let's explore task.

Solve the following equations using the short division algorithm to practise.

So we've got number one, 8,426 divided by two.

You've got three new star words, dividend, divisor, and quotient.

When you add your values to your short division algorithm, see if you can use the new star words.

Pause the video to begin your let's explore task.

Welcome back.

Let's go through the answers.

Well done, if you've managed to use your star words when adding the values to the short division method.

So here we've got 8,426 divided by two.

Our divisor is two, so we're going to be dividing the dividend by two.

So let's add those, my dividend and my divisor, to my short multiplication algorithm.

Next, let's add the numbers to our place value chart.

So we always start with the greatest number in division.

So we've got eight thousands, four hundreds, two tens, and six ones.

If my divisors two, what am I going to be grouping my values into? Call your answer out.

Great! The divisor is two, so I'm dividing by two.

So, I'm grouping my counters into groups of two.

Let's get started.

We start with the greatest number and we're grouping into two.

So how many groups of two thousands in eight thousands? Call out your answer.

Fantastic.

Let's see so, we've got one group of two thousands, two groups of two thousands, three groups of two thousands, four groups of two thousands.

So I know that there are four groups of two thousands in eight thousands.

Fantastic.

Let's go to the hundreds column.

How many groups of two hundreds in four hundreds? Call out your answer.

Fantastic.

There are two groups of two hundreds in four hundreds.

And we can use our derived facts.

We know that two times two is four, and 400 is a hundred times greater than four, so our answer will be a hundred times greater.

It will be 200.

Next, let's go to our tens.

How many groups of two tens in two tens? Call out your answer.

Fantastic.

There is one group of two tens in two tens.

So you can add that into our short division algorithm.

Next, let's take a look at the ones.

How many groups of ones are there? How many groups of two ones, sorry, are there in six ones? Call out your answer.

Great.

There's one group of two ones, two groups of two ones, and three groups of two ones.

How did you use your known multiplication facts to answer that? Call out your answer.

Great.

We know that two times three is equal to six.

So, we know that six divided by two is equal to three.

8,426 divided by two is equal to 4,213.

Our quotient is 4,213.

There are many other methods you could use as well when dividing 8,426 by two.

Many of them more efficient for this particular problem than short division.

But we're going to explore it because it will become more useful with some of the problems we face later in the lesson.

Next, let's take a look at this problem.

Tickets to a fairground ride are only sold in groups of three.

84 people have been on the ride, how many tickets have been sold? So, what I do know is that tickets are sold in groups of three.

And that 84 people who've been on the ride.

I want to know how many tickets have been sold.

So my equation is going to be 84 divided by three to find out how many tickets have been sold.

So in my tens, I've got my counters, and I've got my written method on the screen.

So in my counters, I've got eight tens, sorry, I've got eight tens and I've got four ones to represent 84.

And my divisor is three, so I'm going to be dividing 84 by three.

So I'm going to be grouping in groups of three.

So let's start with, always start with the greatest number in short division.

Going to be doing it in the written method alongside it too.

So, eight tens grouped into groups of three, I can have one group of three tens and another group of three tens.

But I've got two tens that I cannot group into a group of three.

I can't share eight tens equally by three.

So I need to regroup those two tens into 20 ones.

I'm going to show you what that looks like now in the written method.

So, we know that we can group two groups of three tens in eight tens, but we have a remainder that we need to regroup, of two tens.

And that becomes 20 ones.

So now I will read the two and the four as 24.

If I was to count all of those counters in my ones column, I've got 24 ones.

So out of 24 ones, how many groups of three can I get? I've got one group of three, two groups of three, three groups of three, four groups of three, five groups of three ones, six groups of three ones, eight groups.

So I've got eight groups of three ones, because we know that 24 divided by three; if I think of my multiplication facts, three times eight is 24.

So, 24 divided by three is equal to eight.

And if we counted all of our groups and our ones column, we would have eight groups of three ones.

So, 84 divided by three is equal to 28, our quotient is 28.

Our next problem says, a weekend in a luxury tree house in the forest costs 879 pounds per tree house.

The standard tree house costs three times less.

How much does the standard tree house cost? Your questions are, what is known and what is unknown? Pause the video and decide.

Welcome back.

You might have realised that we know that a luxury tree house costs 879 pounds per tree house.

And a standard tree house costs three times less.

What we don't know is how much the standard tree house costs.

So my second question is, represent the problem using an area model.

Pause the video and have a go at drawing an area model using your pencil, paper and a ruler.

Pause video now.

Welcome back.

So here, I've got an area model where the whole is 879, and we need to divide it by three to find the other part.

So, the equation is 879 divided by three to find how much a standard tree house costs, because it's three times less than the luxury tree house.

Pause the video now to practise solving 879 divided by three using the short division method.

Okay, so I've drawn my bus stop shape ready for my short division calculation.

So my divisor is three, so I'm going to be dividing by three.

And my dividend, the number that we're dividing up, is 879.

So, 879 is going to be shared into groups of three.

So how many groups of three in 800? Hm.

Well, I can use my known facts.

I want to get as close as I can to 800, but I already think, "Well, I know that eight isn't in the three times table, but I do know that six is in the three times table." If I roll my threes, three, six, nine.

Well, nine has gone past eight.

Six though, I can get two groups of three and six.

So if it was 600, it would be a hundred times greater, so I would have 200.

I'd get three groups of 200, but I haven't got to 800, I only got to six hundred.

So I've got a remainder of 200.

So 200 and seven tens will become 27 tens, or 270.

So now if I've got 27 tens, how many groups of three will I get in 27 tens? Well, I know that three multiplied by nine is 27.

So, I will have nine equal groups of three in 27 tens.

Let's move over now to our final column, our one's column.

How many groups of three ones can I have in nine ones? Well, I know that three times three is equal to nine.

So I know that I can have three groups of three ones in nine.

So 879 divided by three is equal to 293.

The quotient is 293.

You're ready for your independent task now.

Solve the expressions using the short division strategy.

Draw an area model for each problem, check using a different strategy for the inverse.

Pause the video to complete your independent task.

Welcome back.

Here are your answers.

Hopefully you've had a time to practise using the short division algorithm with regrouping.

Well done for your hard work.

If you'd like to share your work with the Oak National, please ask your parent or carer.

Tagging at Oak National and hashtag Learn with Oak.

Now the times come to complete your end of lesson quiz.

And that's it for this lesson.

Congratulations, you've come to the end and you've worked so very hard.

Give yourselves a whoosh.

See you next time.