Lesson video

Hello, everybody.

Great to see you once again.

And thank you, if you've decided to keep me company here on Oak National Academy.

It can get awfully lonely on your own.

My name is Mr. Ward, and we're continuing our journey with multiplication and division by focusing on division with remainders today.

Now, wherever you are on the country, I hope you're well, and I hope that you're looking forward to this session, but I just ask that you are free of distraction, that you have a quiet space where you can focus on your work and that you have everything you need for the session.

Ready to go? So am I! Let's get started.

Those familiar with a Mr. Ward lesson here on Oak National Academy will know that before the main math lesson, I like to start off with a math joke that puts a smile on your face.

It definitely puts a smile on my face, 'cause I've been chuckling to myself for many days about this one.

I hope you enjoy it.

Why was the circle crying? Because the maths teacher called it pointless.

If you think you could do better than me, and the bar's not very high if I'm honest, I'll be sharing details at the end of the lesson about how your parents and carers can share your work or mathematical jokes with us here at Oak National Academy, so please keep watching until the end of the video.

If maths jokes, isn't your thing, but mathematical learning is then this is a lesson for you.

So not to worry, no more maths jokes, just lots of fantastic quality maths.

The session is set out in the following sections: We'll introduce the idea of solving problems with remainders.

Then we're going to be a talk.

That's when you have to have a go at independently trying to find remainder problems. Then we're going to develop a log a bit further by introducing short division and remainders.

Then we're going to move on to the independent task of division with remainders which you are going to have a go at and try and complete on your own.

And then, we will conclude the lesson with the Oak National Academy end of lesson quiz, and a challenge slide for those that want to continue their learning today.

Now, there is a previous lesson on the unit of multiplication and division that specifically works on short division and demonstrating the algorithm of using formal short division.

So, although today we will be looking at short division at some point, if you feel unfamiliar and not very confident in using short division as a formal method, I would advise you to go back and watch that video before you complete today's lesson.

It's important that we have the equipment that we need to get the most out of our session today.

You're going to need a pencil or something to record work, a ruler, some paper that could be grid paper, line paper, blank paper or the back of a box or cereal box or something that you can jot down ideas on, and if you've got notebook from school, that's fantastic.

The rubber is optional and actually I encourage pupils to draw a neat line through their work to show that they identify the mistake, and ,actually, they've managed to correct their misconception because they've learned where they went wrong.

That's a really good example of mathematical learning.

If you haven't got any of the things that you need, and you're not quite ready to begin the lesson, pause the video, go and get whatever you need and then press play and resume the video when you are ready to be focused and to begin.

See you in a few moments.

Your first task is to get yourself firing on all cylinders and warmed up to the main content of the lesson.

Today's warmup is based on spotting errors in the two short division algorithms that are represented in front of you.

Pause the video also a few minutes now, try to spot those errors, and try to explain where those errors have occurred.

When you are ready to resume the video and check the answers, press play.

See in a few moments.

So, the two mistakes that I identified, the pupil has not regrouped two into one's column to make 24 ones in the first calculation.

This would change the result, the quotient.

Now, if the word quotient is new to you or unfamiliar, it probably means you have not watched our lesson on short division, the formal methods short division within this unit or multiplication and division, and I strongly recommend that you do.

The second calculation, five does not go into ,in quotes, one, you cannot five into one once.

This would change the result or the quotient, and here's how they should have been correctly, completely represented.

You can see that actually now the correct number of additional tens has been regrouped into the ones.

So, two additional tens to make 24 ones, and that can go in exactly, four can go into 24, six times.

And the second one, we can see that the remainder is shown exactly, because five doesn't go into one at all.

So, we put a zero to show the placeholder and the remainder was one.

I'm moving on to the main content of the lesson by introducing the concept of division with remainders.

You take a moment to read the problem on your page.

So to identify how many buses we are going to need, we can do this problem mentally, because there's quite a small number of people to sort.

Knowing that each bus holds eight, I can make two groups of eight, physically, and that leaves five people left over.

Well, they still need to get on the bus, don't they? So that means the answer to our question, Three buses are needed transport, all 21 people.

And an abstract written algorithm, not that we need to cause we did this mentally, This is what it would look like with the two carried over and the remainder of five.

Now, take a moment to read this question.

Again, we can physically share out the 21 pound and make two groups of eight, because each ticket cost eight pound, and we're left with five pound left over.

Now, I want you to take a few minute on this slide, what's the same and what's different? We had two questions, two word problems, that both gave us the same answer of two remainder five.

Take a minute to discuss this if you're in a group or, on your own, reflect on the information in front of you.

What's the same and what's different? As we've already identified, the answer we got was the same.

The dividend was 21 in both calculations.

The divisor, which was eight, was the same in both calculations, and the quotient of two remainder five was the same for both sums. However, as you will notice, because we were dealing with different context, because the questions were based on different things, one was on money and one was on people and transport, the actual answers to the problems are different.

In the problem about buses, we needed to round up to three buses, because everybody needed to be transported.

So, it was okay that we had a bus that didn't have a full number of eight people, that only had five.

However, in the question about money and buying cinema tickets, unfortunately, if you don't have enough money, you won't be able to buy the tickets you need.

So, not having enough for three tickets, which would be three lots of eight, 24, but only having 21 pound, meant that he could only buy two tickets.

So, on the right hand side for transport, we were able to, in a sense, round up and give an answer of three, whereas in the question about money, we had to round down and only give an answer of two, because there wasn't enough money.

And this is all about the context of the question.

And we're going to be looking at when is it appropriate to use a remainder, when is it appropriate to round up a remainder, and when is it appropriate to round down a remainder.

Now, there's a new problem on your page.

Please spend a moment to read it.

So, we need to organise how many sets of three, how many groups of three, can we make within 35 key chains.

Well, very quickly estimating, I know that three lots of 11 will have derived at least 33.

Therefore, I know that I can have 11 full sets of three key rings.

But that leaves two left over.

Again, that's how it would look in the context of our formal algorithm, 11 remainder 2.

However, would we round up or would we round down this question based on what's asked of us? Unfortunately, we would round down, because we haven't got enough for 12 sets.

You can't have one set of two.

They have to be sold in sets of three.

Therefore, only 11 sets can be made with two spare.

They would have to wait for more key rings to be made in order to be put into a set.

So our answer to the problem is 11 sets.

Can you think of a problem that involves the same calculation, that involves 35 as the divided and three as the divisor, but the remainders can be interpreted differently.

We could round the remainders up, for instance.

Can you think of a problem? Pause the video.

Just think.

What problem could you ask that involved the dividend of 35, the divisor of three, and gave the same quotient, but this time we could round up? Have you got a problem? Here's my example.

Mr. Ward wants to purchase 34 key rings, so every, so I said key rings, key chains, my mistake, so every member of his class has a memento of the Olympic themed maths course.

Key chains are sold in packs of three.

How many packs of key chains does he need to buy? Well in this context, I would have to buy 12 packs, because if I only bought 11 packs, I would only have 33 key chains, and I would not have enough for the 34 that I need.

So, in order to acquire 34 key chains, I have to buy 12 packs of key chains.

So, you see how with the same calculation how I've adapted the problem to require the rounding up of the remainder and not the rounding down.

With that in mind, the idea of taking a calculation and writing slightly different problems to round up or round down and decide which one you would do, you're going to do an independent talk task.

Now, usually talk tasks take place in small groups or pairs or even whole class situations within schools, but of course that's not always possible if you happen to be working on your own.

Not to worry, you can complete this task independently.

Just reflect on the maths that's taken place, and prepare to talk about it either now if someone's close by to try and drag them over and show them what you're learning, or maintain that information at a later date when it's appropriate.

Here's your talk task.

You need to write two problems for both questions which requires the same calculation but will interpret the remainders differently.

The first one has been done for you, but you can rewrite that question to come up with your own if you wanted to.

Once you have written two problems for the same calculation, please solve the equations.

Pause the video for as long as you need on the task and when you're ready to share your work, come back, and I will demonstrate what I came up with for the task.

Speak to you in a few minutes.

Welcome back everybody! Just very quickly, I'm going to share my example.

Hope you came up with some wonderful questions.

Obviously, you can see there's a very Olympic theme for the unit of multiplication and division and we are really focusing on the Olympic language today.

You may have chosen the Olympics, you may have done another context, but that's absolutely fine.

The key, though, is making sure that your problem is allowing you to do the same calculation, but each problem would require you to round down or round up the remainders.

So, the first question I kept as my example.

The apartments in the Olympic village hold six people each.

There are 50, so it's 50 divided by six.

The divided is 50, the divisor is six, the quotient is eight remainder two.

Now, I had to round the remainder up to nine, because you could have two people staying in an apartment.

That's absolutely fine, but we do need nine apartments to make sure that all 50 people are housed.

However, in my second question: Every 100 metre sprint race in the Olympic Games must have eight athletes competing to take place.

So, if I have to have eight athletes to have a race, so I couldn't have a race with only two people.

So, I had to round down to say that only eight races could take place and two people would miss out.

Two athletes would miss out unless six more people were able to join.

And my second calculation, the first one was about rounding the answer up.

In the Olympic Village, the dinner table can hold a maximum of five people for a meal.

How many tables will they need? Well, they will need seven tables to make sure that all 34 athletes can eat.

One of the tables could have four people on it.

My second question was about rounding down my quotient and the remainder.

An official Olympic programme cost five pound.

How many programmes can you buy with 34 pound? Unfortunately, I've got 34 pound not 35 pound.

Five lots of seven makes 35, but I haven't got enough, so I can only buy six programmes that cost five pound each.

That would actually save me four pound and give me four pound to spend on something else, which would be really nice.

Maybe lots and lots of sweets or an apple, depending on how healthy you want to be.

Okay, we're going to continue by developing our learning.

Let me introduce you, or reintroduce you shall I say, the formal method of short division with remainders, but used in the same context of understanding when we need to demonstrate remaining, when we need to round and when we need to round down.

Here's short division remainders.

285 hurdles are stored in stacks of eight.

How many stacks of hurdles are there? So we want to know, really, how many groups of eight we can make within 285.

So, I'm going to set out and record my formal algorithm for short division.

Fell free to go along stage by stage if you do this or to follow the video and then have a go at the independent task using the formal method.

We start off in the hundreds.

How many groups of eight, 800 can I get into 200? Well, zero.

Now, I've got it in a certain colour there.

I want to explain that I've put zero there in a colour because I don't actually need to write zero and I wouldn't normally.

I want to demonstrate that there is nothing there, however that zero is not a placeholder.

It doesn't need to be there.

We can leave that blank, and you will see that I have left it blank for the rest of the calculation.

But I do need to regroup the 200 into the tens, so now we have 28 box of 10.

We're now going to look at the tens.

How many groups of 80 can I get into 280? How many groups of eight tens can I get into 28 tens? I can get three, because I know three lots of eight make 24.

There are three groups of eight tens in 28 tens.

That leaves four tens left over, which I regroup into the ones column to create 45 ones.

So, now I need to know how many groups of eight exist within 45 ones.

There are five groups of eight that make 40, and that leaves five ones left over.

So, I give a remainder of five.

Now, in the context of this question, we can round up.

We can make 36 stacks.

35 complete stacks of eight and one stack of five.

There's no point in leaving five lying around on the floor.

It could be quite dangerous.

So, in the context of this question, it's absolutely appropriate and the right thing to do to round our answer up to 36 to say there will be 36 stacks of hurdles.

Let's look at slightly differently then.

Take a moment to read the question on your screen.

We see now that we're going to try make how many groups of three can we find in 1,450 chains? Remember they are sold in sets of three.

So, we are going to need complete sets of three.

First of all, we're going to estimate, because this is quite a big number.

I think it's going to be important to do so using our mental arithmetic or our prior derived facts.

I know that three lots of five makes 15, therefore three, lots of 500 makes 1,500, because one of the factors is a hundred times greater With the estimation in mind, let's do the formal written algorithm for short division.

This time we're going to start in the thousands column.

How many groups of 3000 exists within 1000? The answer of course zero again, but I'll write the zero in to show you that there's nothing on top of the thousand.

However, you should really leave that blank or you leave that blank, but I do need to regroup the thousand into the hundreds column.

I now have 14 hundreds.

So my second stage of the question is, how many groups of 300 exists within 1400? There are four groups of 300 in 1400, there were 200 remaining.

So I write the four and the 200 remaining I regrouped into the tens column to create 25 tens.

So the next stage of my calculation, of my algorithm is to work out how many groups of three tens exists within 25 tens? How many groups of 30 exists within two 250? The answer is eight! There are eight groups of three tens or eight groups of 30 within 25 tens or 250.

Eight lots of three makes 24.

I have however, one remaining 10.

So, I write my eight on top to show the eight groups of three tens that exist within 25 tens.

And I regroup my remaining 10 into the one's column to create 10 ones.

The final stage is how many groups of three exists within 10 or 10 ones? Well, three lots of three make nine, and I know I have a remaining one.

My answer is 483 remainder one.

The answer to the calculation, the algorithm is 483 remainder one.

However, the answer to my question, is 493.

I need to round down, because I cannot sell or buy a set of one.

The sets come in three key chains.

If I've only got one, I need to wait until two more produced.

So I have to round down and that will be appropriate for this question.

Now I'm going to look at how the problem and the context of the problem can change and be altered to enable us to round the remainder up to 483.

So, the quotient can change.

Here's my example.

I said the key chains are to be sold in sets of three.

On day two of the Olympics, 1,450 key chains were ordered online.

How many sets were sold online on day two? Now the problem's slightly different here because the key chains are being ordered individually.

But in order to get a key chain, you have to buy a set of three.

Therefore, even though 483 complete sets of three exist within 1,450, that also required one extra.

Now in order to get the whole complete 1450, somebody would have to buy a set of three to get that one additional key chain.

Therefore it is appropriate in this question for me to round up and we can say that 494 complete sets of the key chains were sold online on day two of the Olympics to ensure that 1,450 key chains individually were provided to the people that had ordered them online.

We've looked at the use of a division and short division with remainders and where it's appropriate to round up a remainder and where it's appropriate to run down the remainder to a whole number.

Here's your tasks that I'd like you to have a go at independently.

Solve the word problems, interpreting remainders correctly.

And I'd like you to write a word problem for the three calculations presented and sold.

Remember to estimate before each question and use the formal algorithm of short division step by step to ensure that you are accurate in your calculations.

Pause video now.

Go back to the slide that shows the questions and complete the task.

Use as much time as you need, but when you're ready to share your answers and check that you got the correct calculations, please press play and resume the video.

Enjoy the task.

I'll speak to you all in a few minutes time.

Bye for now.

Alright, very briefly here are the answers to the challenge today or to the questions today.

Solving the problems, interpreting remainders.

First one was 226 apartments.

The second one was 105 full boxes of medals.

You have to run down a little bit because it's full boxes.

And question three gave two questions, which allowed you to interpret the remainders and round them down or up.

The first one you had to round up, 'cause we're looking at how many rows, 55.

And then the second one was how many full rows.

So, you couldn't have a row with only a few people on there.

So, therefore you have to run down and say there was only 54 full rows.

And then the answers to our three calculations, whatever maths story you came or whatever word problem, I hope it would appropriate for the question, and it either allowed you to round the answers down or round the answers up where appropriate.

Well, onto another task.

I hope you enjoyed that and you understood both the idea of using remainders, but also being able to demonstrate the formal algorithm of short division.

Those that are not yet ready to end today's lesson and get onto the quiz, there is an extension slide.

Pause the video and take as long as you need for this.

How many different strategies can you use to solve the problem below? Be flexible and consider demonstrating both mental and formal methods.

This is quite a fun task, and it's good to do this either on your own or in your little groups if you can.

Pause the video, spend as long as you need on this, and I think this is a really cool task, so, I look forward to you having to go at this.

Now we're almost at the end of today's lesson, there's only time for you to have a go at the quiz as always as part of an Oak National Academy lesson.

The key reflection I want you to take into the quiz and from today's lesson is to remember that always interpret remainders in the context of the question.

Find the quiz, take your time, read the questions very carefully and fingers crossed, you can do very well and feel confident as you go through the questions.

Good luck everybody and please return to the video and finish with our final few messages at the end of the lesson.

Reminder, as always, we would love to see some of the work or hear some of your mathematical jokes.

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

Alright everybody, that does bring us to the end of today's lesson.

Thank you so much for your hard work and focus.

I hope once you reflect on the lesson that you will take away the key message, which is to make sure you read the question carefully and understand the context of a problem in deciding whether to use remainders, whether to round up or round down where appropriate.

Now I've really enjoyed today's session.

I think we got a lot out of it and I hope you did too.

I look forward to seeing you again here, on Oak National Academy, but if there are other lessons within the unit of multiplication division that you have missed, or you would like to catch up on, some of the key concepts, for instance, or some of the vocabulary that I use that you're a bit unfamiliar with, feel free, please, to find those lessons on Oak National Academy.

I hope you enjoy them too.

But for me, Mr. Ward, in the meantime, I just want to wish you a great rest of the day and I hope to see you soon.

Good luck with the rest of your learning journeys.

Bye for now.