Lesson video

Hello, everybody.

Great to see you once again on Oak National Academy.

Thank you for joining me, Mr. Ward, for this lesson on short division, as we continue your unit on multiplication and division.

Now, I hope you're well, wherever you are in the country and that you have all the things that you need for today's lesson.

I'm really excited and eager to get started, 'cause there's lots to cover, you can imagine.

So if you're free of distraction, and you've got a quiet space where you can focus on your learning, I think you're just about ready, and so am I.

So, let's make it start then, shall we? But before we make a start on the main learning, it is, of course, time for the mathematical joke of the day to put a smile on your face.

This one's been making me chuckle for at least three days, so it must be pretty good, eh? I hope you enjoy it too.

Why do fractions do badly in maths tests? Because they are sometimes two tenths! Hands up if you thought that was quite funny.

Yes, I did, and I hope you enjoyed it too.

However, if maths jokes isn't your thing, but maths learning is, well this is pretty the lesson for you.

Just a little overview of how the lesson looks today.

We're going to start by introducing short division as a method for sharing.

Then you're going to have a go in a talk task independently, sharing a number out using the correct short division method.

Then we're going to look at it a little bit differently and introduce division as a way of grouping.

And then, once we've demonstrated different examples of short division, of concretely, pictorially and abstractly, it will be over to you to see if you can implement that method and complete a series of independent calculations.

And then, as always, at the end of an Oak National Academy lesson, we ask that you have a go at the quiz to see how much of that learning has been embedded from today and how confident you are in the concepts moving forward.

It's important to get the most out of our learning by having the correct equipment to aid us.

So as always, I ask you to have something like a pencil or a pen to record your work and your jottings, you're going to need a ruler, and you're going to need some paper.

It could be squared, lined, blank, or just something to write down on.

But if you have got a book from school, that's even better, fantastic, the rubber that you can see on your screen is optional, and actually, drawing a line neatly through your mistakes demonstrates your learning, 'cause you are showing where you went wrong, how you identified it as being wrong, and then you can make the appropriate corrections and that, at the end of the day, is what maths learning is all about.

So if you haven't got the correct equipment right now, you don't feel you can start the lesson yet, please pause the video, go and get whatever you need, get yourself ready.

And then when you are ready to begin the lesson and focus on the next half an hour, then you may resume the video.

See you in a few moments.

It's important that we're firing on all cylinders for our mathematical learning, so I've got a warm-up based on division to get you ready for the lesson.

Look at the screen, you'll see there are six number sentences with missing values.

Can you find the missing values to complete the number sentence and make them accurate? Pause the video if you need a little bit of extra time.

Spend a few moments now.

What are the missing values to make those number sentences accurate? Right, let's see how you got on, hopefully you found those numbers.

24 divided by six equaled four, and therefore, 240 divided by six equals 40, 'cause one of the parts has become 10 times greater.

240 divided by 60 equals four, because you know 24 divided by six equals four.

24 divided by four equals six.

One of the parts has become greater again, so 240 divided by four will make 60, and 240 divided by 40 equals six.

I hope that was fine, that it all makes sense, and you can see how understanding our knowledge of how a number can get greater by 10, 100 or 1000, or we can divide by 10, 100 and 1000.

I hope by understanding that knowledge, you find a task like this relatively straightforward.

We will start today by introducing the concept of division as sharing.

Take a moment to read the question on your screen.

As you will have identified, the problem requires us to share 645 amongst three groups or categories.

We need to identify how many gold medals there are, but it also says equal number of bronze, silver, and gold, so we will have this equal amount.

I've represented this problem as a bar model on your screen.

You will see the bar is split into three equal parts, and we're going to share 645 amongst those three parts.

Of course, whenever we do a calculation, it's very important to estimate first, and we're going to do so.

I'm going to write it down.

However, this is me demonstrating what estimations are going through my head, because it's a mental strategy.

I know that three lots of two make six.

So, theoretically, three lots of 200 make 600, because it's 100 times greater.

However, I'm still 45 short, which is quite a lot in the context of this question.

Can I get closer with an estimate that I could do mentally? Well, I know that three lots of 21 make 63.

So, therefore, three lots of 210 make 630.

That brings me closer to 645.

I also know that three lots of 22 is 66, so three lots of 220 is 660.

As you see by the number line in front of you, 645 sits between those two estimates, so either one would be an appropriate estimate and something we can do quickly.

Now, I know that I'm quite comfortable with my seven times table, so I know that three lots of seven make 21, so I'm quite comfortable using 21, so I would've chosen three lots of 210 to make 630.

With an estimate done, we're going to do the formal method division now.

I'm going to introduce three words that you may or may not have heard.

And these are words that we use when we use division.

You've got the dividend, which is the amount that's to be divided, the divisor, which is a number in which we're going to divide the dividend into.

And the quotient is the result of a dividend being divided by the divisor.

That's a bit of a tongue twister, some of those words, but we're going to use this slide regularly.

You're going to see these vocabulary words being used on a regular basis in today's lessons, so hopefully it will help to embed that and it become more familiar with you.

So, one more time, the dividend is the amount that is going to be divided, and in this context, it's 645.

The divisor is a number we're going to divide the dividend into.

On this example, it's three.

And the quotient will be the result.

The answer we get when we divide 645 by three.

I'm going to represent using place value counters, the stages of short division.

I'm also setting out short division on the square grid to show you each step by step.

And this is how it should look on your paper or maths books.

So the first thing we're going to look at is how many threes or how can I share 600 in amongst the three groups? Well I know, that three lots of two makes six, so I can share six into three and give 200 per group.

And I write the two on my calculation on the line.

There's no regrouping.

Now, if we going to look at the tens column, I've got 40, four tens.

I can share four tens out amongst three groups by giving one 10, to each, but I've got a that 10 leftover, which I'm going to regroup into the ones columns to create 15.

I put a one to represent the fact that I have been able to share out one of three tens and I've got one 10 of leftover we get regrouped into the ones column.

You can see by the small one I've written on my formal calculation.

Up on here, I share five or 15 ones amongst three.

Yes I can.

I can share 15 ones amongst three groups and give each group five equal ones.

And I show that by writing the five in my formal work algorithm, I have no leftover and it goes perfectly.

So my answer is 215 and you can see I've completed my bar model to demonstrate that each part as an equal part of 215, I've also completed my abstract calculation to show you the dividend was 645, it was divided by the divisor three, and that gave me the quotient of 215.

We'll have another go.

Feel free to listen or to go along with me as we go stage by stage.

If you want to jot down as we go, please take a moment to read the question on your screen.

So our question here is to try and divide 8,572 amongst or share that amongst four groups.

So I've demonstrated with another bar model to show that problem.

That you can see that we are sharing 8,572 amongst four equal parts.

First of all we want to estimate.

I know four lots of two is eight, so four lots of 2000 will be 8,000 because one of the parts is a thousand times greater.

However, I still have 572 short on my estimation.

So why was 8000? It's a good estimate.

I think with my knowledge, I can get a little bit closer.

I know that for lots of 21 is 84, therefore four lots of 2,100 is 8,400.

I also know that four lots 22 is 88.

So four lots of 2200 would be 8,800.

Now, as you can see on one number line, I fill that four lots of 2100, is closer to the final dividend.

So I'm going to use that as my estimate.

Now we're going to try and work it out.

Again, the dividend is 8,572.

Now are we going to divide that by the divisor, which is four.

And that's going to help us work out the quotient, which will be the result of the dividend being divided by the divisor.

Okay, we set out our algorithm formally on our page, and we start off in the thousands column now.

I need to share 8,000 into four parts.

I can do that because I know that two lots of four make eight, therefore four lots of 2000 will make 8,000.

So each part would have 2000.

There's no regrouping.

I write my two to represent that, I move on to the hundred column.

This time we're looking at how we can share 500 amongst four parts.

I know that each part will have 100 and I'll have a 100 leftover, which we'll then regroup into the tens column to create 17 tens and not seven tens.

I show that by writing the one to demonstrate that is 100.

I can share 500 amongst four once, and that little one to represent the remaining 100 which I've regrouped into the tens column.

We're next going to try and share 17 tens amongst four parts or four groups.

Again, I know that four lots of four make 16 so I can share 17 tens into four parts, and give four tens to each part.

But that leaves there'll be one remaining 10.

I'm going to regroup that into my ones column to create 12 ones now.

And I'm going to write on my algorithm four, to represent the fact that there were four tens for each part, and I'm going to write a little one to represent the remaining 10, which I've regrouped into the ones column.

So the last stage of our algorithm is to share 12 ones amongst the four groups.

But I know three lots of four makes 12, so therefore I can give three ones to each of the parts or the groups.

And that'll leave me with a final answer of 2,143.

Just checking I've got all the stages for my written algorithm.

I'm absolutely very happy with that.

If you ever want to check to make sure you've got it right, you can always use your inverse so I could multiply 2,143 by four, which would give me the answer of 8,572.

So once again, I'm demonstrating that one of my parts is 2,143.

So four lots of 2,143 would give me 8,572.

The dividend was 8,572, and it was divided by the divisor, which was four.

And it gave us a quotient of 2,143.

Time for today's talk task part of the lesson.

Just to remind you that talk task normally take place in school in pairs, small groups, or in the whole class.

And it's an opportunity to not only complete independent tasks, but to talk about the work as we're going through it.

We share our ideas, our methods, and to use the vocabulary that we're introducing.

If you haven been working on your own, not to worry, you can still complete the task independently and just reflect on the information being shared.

But if you have got anyone close by that you can talk about the maths with, as you're going through the task, please do, because it's a wonderful opportunity to really use that mathematical vocabulary, become very confident in the work that we're doing.

Given to your talk task today you can complete short division form of sharing.

Complete the calculations using the short division method shown.

If you have place value counters you can use them to help demonstrate, but not to worry if you haven't, you can just jot in some drawings if you want to reinforce your understanding.

Try to explain each step of the method, including estimation.

Now you can still do this if you're on your own.

I just want you to talk about each step you're doing, so you are absolutely sure about the method of short division.

Don't forget to estimate, please It's a really good skill to develop to help your mental calculations.

Try and include and use the key vocabulary words that we've learned today.

I've put the three main words that we've introduced on the screen to help with this task.

The full calculation in total.

Pause video now, spend as long as you need on this task and then resume the video when you're willing to share your answers and to move on into the next stage of today's lesson.

Speak to you in a few minutes.

Everybody we'll just quickly share our answers.

I hope that you were either able to talk about your maths, or if you're working on your own you were able to systematically go through stage by stage and try to include some of the key vocabulary.

So as you can see there are your four answers and how we would line them up in a formal way in our columns with the correct regrouping.

You'll notice were no remainders in our division today.

We're going to look at remainders in lesson 14 of the unit multiplication division.

We're now moving into the developing our learning section of the lesson.

We're going to continue to use formal short division and the algorithm and the way we record it will look the same.

However, some of the language I use, and a few of the representations may look slightly different.

And that's because we're going to introduce the concept of grouping with our division, as opposed to sharing.

Get a moment to read the question on your screen.

Hopefully you've identified that we're going to try and work out, how many groups of eight exist within 256.

Once again, I've demonstrated with a bar model the question.

The whole it's 256, and we're going to try and find out how many groups of eight exists.

So therefore I've represented that by showing eight equal parts.

There's another way we use a bar model it looks slightly different and probably very new to you.

And I'm going to introduce you to this concept within the lesson, so don't worry if it's absolutely new and you're not quite sure what that looks like.

But I'm going to use my knowledge of partitioning to help.

I know that I can break 256 into 240 and 16.

So therefore I'm going to have two parts of my bar model that's going to allow me to do some of my both my mental algorithms, but double check while I do my formal.

First of all, because we're doing a calculation let's do an estimate first.

Now I know with my prior knowledge, It's three lots of eight makes 24, therefore eight lots of 30 we'll make 240, because one of those factors is now 10 times greater, so will the product.

And as you can see on the number line, eight lots of 30 is 240.

Now another estimation could have been eight lots of four, cause I know that eight lots of four is 32, so eight lots of 40 would be through the 320.

However 240 is much closer to the actual dividend that we've got.

So I think eight lots of 30 is a very appropriate estimation to make.

The reminder of the vocabulary.

The dividend for this question is 256.

The divisor is eight.

Now we're going to divide the dividend by the divisor to give us the quotient, which will be the result of the calculation.

So we're going to try and find out how many stacks of hurdles are there within 256.

First of all I'm going to start in the hundreds column.

I want to know how many groups of 800 exists within 200.

Well the answer to that, is nothing.

There's nothing.

You cannot do eight into two or 800 into 200.

Oh I don't need to write zero, all on my screen now I'm going to do another colour.

And the reason I'm doing another colour is I want to represent the fact that no, there's nothing there.

And sometimes people feel comfortable writing the zero, is not a error, but we don't need the zero there because it's not a place holder.

So you will see, as I go through the slides that zero will disappear because actually it doesn't need to be there.

What I do need to do, however, is regroup that 200 into the tens column and that now creates 25 tens.

So the next stage, once I've regrouped correctly is to identify how many groups of 80 exist in 250.

Or rather how many groups of eight tens exist in 25 tens.

I found that I can have three grouped of 80 or three groups of eight tens exist within 25 tens.

So I've write my three on my algorithm, but I had a spare 10 leftover, and I'm going to regroup that into the ones column.

And that creates 16 ones.

So now I'm going to try and find out how many groups of eight ones exist within 16 ones.

The answer is two groups of eight ones exist within 16 ones exactly.

There are two equal parts, or two equal groups of eight.

Just to show it how that looks on a bar model.

I know 30 lots of eight goes into 240, and I know that two lots of eight exist within 16.

So within 256, there are 32 groups of eight the dividend is two, five, six.

256.

The divisor was eight.

When we divided the dividend by the divisor, we got the quotient of 32.

The result of the calculation.

Take a moment to read the question on your screen.

Hopefully you've been able to identify as a bar model would indicate that we need to identify, how many equal groups of six people exist within 1,854, as demonstrated by the whole and the equal parts of the bar.

Of course we're calculating so we're going to estimate first with number facts we might already know.

If we know six lots of three makes 18, we will therefore know that six lots of 300 makes 1,800 because one of the factors is a 100 times greater, therefore the product will be 100 times greater.

And as you can see on the number line, our estimation of six lots of 300 being 1800 or 1,800 is a very appropriate estimation to make and bring this fairly close to the dividend of 1,854 on this occasion.

The key vocabulary again, no harm in hearing it once again so that you can familiar with it.

The dividend for this question is 1,854.

That means the amount that's going to be divided by the divisor which is six.

Once the dividend is divided by the divisor, that will give us a quotient.

The result of the calculation.

This will tell us how many equal groups of six people exist within 1,854.

Again, I'm going to record my formal method of short division and the algorithm stage by stage.

I'm also going to demonstrate it with place value counters to show what's happening at each stage.

The first thing that I need to find out is in the thousands column.

How many groups of 6,000 exists within 1000? The answer to that is zero of course.

However, unlike previously in the lesson, I'm not going to put the zero, If you remember, the zero would not act as a place holder, it doesn't need to be there, so I'm not going to record it.

I'm also going to do something, little bit cheeky.

I'm not going to regroup the one into the hundreds column.

Now, technically I am regrouping it, but I'm not going to write it because it's less efficient for me, saves me time.

So I'm now going to look at that sum and look at the 18 as 18 hundreds.

So I have regrouped the thousands into the hundreds column.

I'm looking at 18 hundreds.

So my question now is, how many groups of 600 exists within 1800? The answer to that, is three groups of 600.

There's no regrouping, so we move on to the tens column.

How many groups of 60 existing in 50? Or rather how many groups of six tens, exist within five tens? The answer to that is zero.

I do have to write the zero now because that is acting as a place holder.

I'm also going to regroup the five tens, which were left over, to create 54 ones.

The final stage of my calculation is to identify how many groups of six exists within 54.

This is where your mental arithmetic and timetable knowledge comes in to fruition.

I know that nine lots of six makes 54, therefore there are nine groups of six that exist within 54 ones.

There were no remainders.

There were exactly 309 groups of six in 1,854.

So to recollect, we can complete our written calculation.

The dividend 1854 was divided by the divisor of six.

And that gave us the quotient of 309.

After all of those demonstrations and examples.

I think you should be pretty confident now and have a good go yourself and completing some short division independently.

So I'm going to pass over responsibility to you and let you have a go in the independent task.

This is all about the short division method in which we have been showing today.

I'd like you to create a map story for a word problem for each calculation.

Then you need to estimate the answer first to check that it is reasonable.

And then finally you need to calculate using the short division methods shown today.

As you can see, there are six calculations I'd you like to have a go at, plus the key vocabulary that we introduced earlier in the lesson.

Pause the video now, for as long as you need, If still a bit unsure about the method of short division, feel free to re-watch parts of the video, become a bit more comfortable and confident in the process.

Good luck with the task take as long as you need.

And then when you're ready to share your answers, briefly resume the video, and we'll see how you got on.

Enjoy the task everybody.

Speak to you very soon.

All right everyone I just check how you got on.

I hope you found that task enjoyable and you were able to be quite efficient with it.

We'll just share the, accurate answers, the calculations.

I hope you came up with a useful word problem, that was good in context that allowed you to kind of work it through.

And I hope that your estimations are based on, the right number facts that you already have.

So for instance the first one, I know that three lots of three makes nine.

So therefore three lots of 3000, it would make 9,000.

I think that would be a good estimate to have.

Just check your totals at the end of the calculations on the six that are in front of you.

If you have made any misconceptions you might need to just go back and have a little look through your method, your columns, to see where you went wrong.

Did you not quite divide accurately enough? Or did you regroup incorrectly and carry too many or too little over into the next column? If you've got them all right, or you got most of them right, Or you at least feel confident in using the method then, excellent.

That's really good news to hear.

And I hope that from now on, you're going to find the process of short division, quite a, relatively straight forward method to introduce into your maths.

And so we're almost at the end of today's lesson, of course it's quiz time as always.

If you've been on Oak National Academy before, you know it's coming.

But actually it's a really good way just to double check how confident you are and to double check the key concepts that we have taught during the lesson.

Taking away from today's lesson I just want you to remember the three keywords that we introduced at the start of the lesson, dividend, divisor, and quotient to represent a division calculation.

So find that quiz now, have a go at it.

Good luck.

Read the question very carefully.

And then please come back for the last few messages at the end of today's lesson.

Speak to you very soon.

And as mentioned, we would love to see some of the work and jokes that are being produced out across the country here at Oak National Academy.

So if you would like to share your work or share your mathematic jokes with us here at Oak National Academy, please ask your parent or carer to share it on Twitter tagging @OakNational and #LearnwithOak.

Right everybody, that brings us to the end of today's lesson.

And thank you once again for your hard work and focus.

Blimey, where does the time go? Now I hope you found it useful to see the method of short division you've been shown, alongside the pictorial and concrete representations.

And remember across this unit, we have shared a wide variety of strategies both formal and mental, that you can use to help calculate flexibly and confidently on faith for a wide variety of calculations and problems associated multiplication and division.

Now there are more lessons to learn on the unit multiplication and division, and I hope that you will join me again soon here on Oak National Academy.

But for the meantime, have a great rest of the day.

And I'll speak to you very very soon.

From me Mr. Ward, have a great day.

Thank you for your help.