Lesson video

Hello, everybody Great to see you again here on Oak National Academy.

My name's Mr. Ward, and you can see, as always I'm in a really good mood.

The sun is shining and we're about to do some mathematical learning.

So that really has put me in the best mood possible.

Now, today we're going to continue our unit on multiplication division by looking how we can calculate flexibly.

Which will mean sharing a range of different strategies to give you the freedom and the option, to decide which is the most efficient certainly to use in the context of the question.

Now as always, to make sure that you are ready to get the most out of your learning, to try to be free of distraction if you can; try and find a nice quiet space to do your work, make sure you've got all the equipment that you need when you are happy with everything you've got and you're ready to make a start, stop; continue with the video, and let's get into our main learning.

See you in a few moments.

Great news, everybody, I know you thought we might run out of time, but of course, there is always time for the mathematical joke of the day.

I thought we're going to miss it then.

This was an absolute Corker.

I hope you like it, fingers crossed.

Why were the school pupils deeply suspicious of their maths teachers during their recent statistics lesson? They were convinced they were plotting things.

And if that doesn't get you in the mood for mathematical learning, then nothing works, I'm afraid.

As you can see, we've got a busy lesson today.

We're going to introduce estimating calculations and on new learning, then you're going to have a go at that and talk task.

We're going to develop our learning further by looking at strategy of rounding and adjusting the numbers to help with our calculations.

And then the handed tasks will be about you having a bit of choice, it's flexibility to different strategies that we've looked at.

You have a choice; which one's the most efficient for you to use in the calculation, and then, of course, as always at the end of an Oak National Academy lesson, you get to have a go at the quiz to see how confident you are familiar with the content we've taught to date.

Every lesson you will be asked to make sure you got the right equipment so you need something to record on; paper,or it could be grid paper, lined paper, blank paper, back of cereal box.

Anything you could just jot down on really.

A ruler and a pencil, rubber is optional.

If you've got none of these equipment or you haven't got what you need, pause the video, go get anything you need.

Use a loo, if you need to, I'd like you to be ready to go through the entire lesson when you're ready to start and prepared, So get what you need, and then resume the video.

We'll starts off with a bit of a lateral thinking warm up.

On the screen you will see an image.

I want to know how many counters are there? And how did you work it out? How many counters all there on the screen.

And how did you work it out? Take a few moments, pause the video if you need to And then prepare to either feedback your own ideas with somebody you're working with, or if you're on your own, I will share some of the ideas.

I want you to reflect on what you're doing.

I'll see in a couple of moments, bye for now.

Right, let's see how you got on everybody, very quickly, then the correct amount of counters was actually 49.

Now I'm curious as to know how people work with counting the counters.

Now, assuming you might literally try to count them individually, but I find it very difficult to do if not an efficient method it takes a long time and I have to wear my glasses on, I can't really pick them out; I keep forgetting where I'm starting.

So the clue is actually in the outside space and in the middle, you can see this one here that goes the longest one is worth nine, nine counters.

And it's also nine across, so that tells me it was nine down and nine across, that there's actually a cube that we can try, And we could times nine itself, nine times nine.

So there was actually a square.

I say, cube but it's not 3D, it's 2D.

It's a square, a square of nine times nine, which is 81.

So if all the counters were filled in, it would be 81, but then you could see in each corner, There were four corners, where some counters look like it could have been removed.

So we count the ones that aren't there.

Four, five, six, seven, eight.

You can see there's four, lots of eight, which is 32.

So 81, take away the 32 counters that are missing leaves you with 49 different counters.

Okay, let's get into the main learning today.

We're going to start by looking at estimation in our calculations.

Now what I mean by the word estimation, Hopefully that's not a new word to you.

We've looked at it in other units and other concepts, However, just to remind you, the estimation is about using the mathematical knowledge in front of you to make a reasoned approximation of the answer it's essentially an informed guess but it's not a guess.

I think it's unfair to use the word guessing because you're not guessing, you're basing on knowledge you have and deriving facts that you know.

So you're actually basing your approximation on mathematical reasoning.

So let's have a go, in front of us, as you can see, I've got a number line that I've marked in three places.

Now, how would you estimate that answer? Take a moment.

what would you do if you want to quickly estimate that question? Well, hopefully you would have identified that it's closer to 200 than any of the multiple, and it's close to 200, then multiple attempts.

We couldn't move it to 90 for instance.

And as you can see, it's three possible answers down there, but I think some of them are wrong.

So 500 videos, a 100 x 5, it's nearer to 200 and a 100, so that wouldn't help.

And 750 is 150 x 5, but it's nearer to 200 than it is 150 That's not going to help.

However, it is closer to 200, and 200 lots of five is a thousand.

Now, how do I know that? Two, lots of five, how am I confident? Well, I know two, lots of 5 makes, 10 and 200 is a hundred times greater than two.

So because one of the parts is a hundred times greater.

Our answer is going to be a hundred times greater.

So no longer is two times five 10, because 200, is 100 times greater than 10 is 100 times greater and becomes a thousand.

So that's how we would have got our answer, using a derived factor of 2 x 5 and 20 x 5 and 200 x 5.

How about this one? How would you estimate this? Think about multiples.

How would you estimate this question? Think a moment, hopefully you would have identified it as being very close to the multiple of a hundred or 500.

Now we know that five lots of five make, well, five divided by five, sorry, would be one and 50, which is 10 times greater, divided by five would be 10.

So if we got 500, which is 100 times greater than 5 500 divided by five would give us a hundred.

So we can do our inverse to know that 5 lots of 100 would make 500.

So I think that's a very good approximation.

You can see here's an example of five lots of nine, but that wouldn't be close, not for us I don't think, because we know five lots of nine makes 45 for five lots of 90 makes 450, and that would be too far away from our final answer, I think.

But to multiplication, How about you do this sum? How might you estimate this one? Well, hopefully you see the 78 is close to the multiple 10 of 80.

So 80 lost of 12, well 80 lots of 12 sounds quite difficult, but let's think about our timetable knowledge.

We know that eight lots at 12 is 96.

And because 80 is 10 times greater than eight, 960 is 10 times greater than 96.

So 80 times 12 would be an appropriate estimation that we can use with derived number facts.

And we would be very comfortable in using that as our estimation.

Division; how about you divide this number? How might you divide this number? How would you estimate it? Well, the derive facts I know is that 354, although, it's closer to them, a multiple of 350, I actually want to try and get it to a multiple of six.

Now I know that through 36 divided by six or six times or 6 x 6 makes 36, so 36 divided by six is six because I know my timetable it's six lots of six makes 36 in inverse.

So if 36 divided by six, makes six then 360 divided by six, because it's 10 times greater, will give me the answer of 60, because that's also 10 times greater.

So I'm going to estimate by rounding to 360 divided by six, which will give me an estimated answer of 60.

Now that we quickly look I estimation, and we've looked at what would we do by using multiples, appropriate multiples, composites, multiples tens.

Sometimes these multiples a hundred, Sometimes it's a multiples of one of the parts, Like it was in the case of the six, 360 divided by six, because 36 divided by six.

You are now going to have a go at talk task.

Now, if you are working on your own, that's absolutely fine.

You can have a go at the task independently, and you'd be ready to kind of feedback and check your answers.

If you're lucky enough to be working in a group or pair, or have something close by to talk about your maths with, try and get them over and have this discussion as you're completing your task.

Your talk task is this; he's placed multiples of a hundred onto the number line, to explain your estimate of each calculation.

So you need to estimate each question, then try and work it out, what would your estimation be? You won't need too long for this, I don't think, So give yourself a maximum of five minutes, Pause the video, come back when you're ready to resume and share your video.

I've given you some number lines that you could print off, or you could replicate, if you want some assistance with that, Remember the strategy reviews.

And if you need to go back over the original slides again, to watch some of the demonstrations, please do.

Best of luck, speak to you very soon.

Let's just briefly check our answers on estimating calculations.

The first one, the derived fact, is two lots of 7 makes 14, Therefore I know that as one of the parts of the a hundred times greater, therefore my product will be a hundred times greater, So 200 times seven is 1,400.

I know for the second one, that eight lots of four makes 32, as the whole is 320 is 10 times greater than 32, therefore my answer or one of my parts is going to be 10 times greater.

So three 20 divided by four gives us 80.

And finally I've rounded 295 to 300, the closest multiple of a hundred, and also the closest multiple with 10.

And I know that through lots of nine makes 27, And because one of those parts is a hundred times greater than three, my product will be a hundred times greater.

So three lots of the nine, 27, therefore 32 x 9 is 2,700.

Fantastic, really quick, so far, really good job on estimation.

Now I'm going to remember estimating for every sum that you do, every calculation you do, cause it's really useful for a mental strategy.

So even if I don't mention the use of estimation, I would recommend, highly recommend that you do so on every question.

We're going to look at the idea of rounding and adjusting.

No Rounding and adjusting How can we use our estimate to calculate? Well, we said that we rounded down, so the 200 times five, and that gave us an estimated answer of a thousand.

How could I find the actual answer and accurately calculate? Well, I know that there was five.

I ran it up by adding five didn't I? Five to 200 so five lots of five makes 25.

So I can take that 25 away from the estimated answer a thousand.

Let's get you to show you another strategy of using area models.

Every one of the fantastic, we're just going to drop this box down to show you two boxes to show what I mean.

So the first box was our area model, and we knew that we had, when we estimated, 200 times five didn't we? The Aboriginal sum was 195.

So we estimated five lots of 200 makes a thousand.

That was what I estimated, However, what I actually ended up doing was to help with my estimation, I added five didn't I? But actually here, I ended up having five too much, So I need to subtract from 1,000, 5 lots of five, which is 25; so five lots of five.

Now, I took five away, I added five to 200.

So then that becomes 195 and actually 25 away from a thousand leads me 975 because 5 lots of 195 is 975 and that's my answer.

And that's how I've used an area model to demonstrate my estimated answer, but also the part I have to subtract from the estimated to get my actual calculation.

So let's return to the question we estimate early on, 490 divided by five, now at the times, remember, we round it up to the nearest multiple of a hundred, because it's a multiple five.

And we knew that five divided by five is one, and 50 divided by five makes 10.

So therefore, 500 would be a hundred times greater.

The answer would be a hundred times greater, 500 divided by five was a hundred.

That was estimated answer.

We can see that on a number line, that we did follow up to a hundred, but then we've got a jump back and we've got to jump back 10 because actually we added 10 didn't we? We added 10 and we then had to divide that by five.

So I divide 10 by five and that takes you two, so I jumped back two spots and that leaves me on 98.

It's just so quickly going to show you an area mode again, it's a great strategy to demonstrate what's kind of your thinking in your head, okay? So again, agreed that it was 490 divided by five, was a calculation.

We rounded 500 to help with our estimation.

So essentially I've got 500 here.

How many fives do I go going 500? but it went one hundred times, but that was an estimated answer.

So I actually want to find my actual answer, and I'm going to use an area model again.

Now I ended up adding 10.

So actually there's ten too much in this, So actually what I'm going to do is I'm going to put my 10 here, five here, How many fines going to 10? Well, two.

And so I have to take two away from my estimated answer, 100 to leave me with 98.

And that is the equivalent of 490 divided by five, because five lots of 90 make 490, 5 goes into 490 98 times, and 98 plus two was the same as estimate answer 490 plus 10.

Right, now I've done a few examples of grounding, and adjusting to calculate accurately, Why don't you have a go? I'd like you to spend a couple of moments on this calculation, adjust and round it to be able to estimate it, then considering using a number line to show your steps and an area model to demonstrate your mental strategy, and solve the calculation, okay? So pause the video , then a couple of minutes, jotting down on your paper or books, thinking about your answer, and then we'll go through the steps, one by one.

Speak to very soon, right, okay.

Hopefully you came up with this, 118 x six.

What derived fact helps me? My six times table.

I know that six goes into 12 ,two, or I'm sorry, it's a multiple, but I also have 12 lots of six is 72.

So I round into 120, 12 times 6 is 72.

So therefore 10 times greater, So that's 720.

That's my estimated answer.

So my number line, I could show my estimated answer of 120 times six is 720, but I added two didn't I? I added that two to make 120.

So actually there's two lots of six.

They have to take away from that answer, estimated answer, to give the actual answer of 708.

And you can see that with our calculation on the board.

And we can also show that with an area model, It's nice and simple.

So again, I've got my six and we're multiplying by, well we said, 120, which was here, but actually, we also had the our So 600, 120, which was our estimated answer of 720.

However, we added two didn't we? So we've got our two here to six lots of two is 12, take 12 from 720 and I'm left with eight.

So I'm going to put that in here as my estimated answers, in brackets so you know the difference.

So six plus six is 12, I took that away because of the value of those two plus two or six is 12 and therefore I took them away from 720, and I'm left with 708; You can see that's my amp.

I'm going to ask you now to have a go at this on your question on your page; 236 divided by four, what you're going to do now is estimate and use an area model to demonstrate it.

So if you've got a piece of paper and you can jot down and follow me as I go through this.

The first thing we do is estimate.

So I'm going to estimate 236.

And now I know that from a four time table, that four goes into 24, six times.

So therefore, because one of those parts is 10 times greater, 240 divided by four must be 60.

Some estimate the answer is 60.

Now I'm going to do the bottom one to show what I did here.

Now, in my estimated answer is 240 here, my estimate is 60.

How many fours going to 240? However, I had to add a 4, So one of my values or four is here.

So actually I had to add a four.

So to get my estimated answer.

So that's when, in there once, I'm going to take that one value away from the 60, and that's going to mean that actually, take the four way, my actual answer is 59, because 60 is 59 plus one.

So my answer is 59.

So after all of those examples that we've shared together, and the modelling that's taken place, and now I'm going to hand over responsibility to you.

And have you asked you to have a go at an independent task to try and use some of those strategies we've just discussed.

Now, if at any stage you get a bit confused and you need to go back over the video, feel free to do so we can go and find the relevant content that you need to double check the strategies that you are using.

Your task as you can see on the screen is this: You are going to use a round and adjust strategy to calculate the following sums. I'd like you to demonstrate the strategy using area models with an example on your screen.

And perhaps you'd like to use a blank number line also to help.

There were six sums in total, and here are some number lines you could print off, or you could replicate if you needed to.

Pause the video now, spend as long as you need on this task, And when you are finished and you're confident about your answers, We can feedback and have a look and see how accurate you were.

Good luck with the task, and I'll speak to you all very soon, enjoy.

Welcome back everybody, how did you get on? Did you enjoy the task and were you able to use those different strategies that we have been discussing today? Just roughly the first three questions to estimate you would have probably rounded the first one to the nearest multiple 10, because 12 times four we know is 48.

So the estimation was 480, the actual calculation was 476.

The next two, you would probably round to the nearest multiple of a hundred.

So 400 times five is 2000, because we know four times five is 20, And calculation, The calculation was 1,990.

Number three, again, we've rounded to the nearest multiple of a hundred, which is 300.

We know that three lots of seven is 21, therefore that's a hundred times greater for the estimation.

And the accurate calculation was 2065.

The division questions, well, we know that 48, by the way, 86, so we probably would have rounded to the nearest, what we would have rounded to 480, because that is a multiple of eight.

So 48 divided by eight was six.

Therefore it's a 10 times greater.

One of the parts is 10 times greater, The product will be, or the answer, not product, sorry, that's wrong, the total will be, the other factor will be 10 times greater.

So it was 60.

The actual calculation was 58, 888 While we ran into the nearest multiple of a hundred, because that's also a multiple of three.

We know that nine divided by three is three.

So therefore one of the factors there, or one of the parts is going to be a hundred times greater 900.

So therefore the answer is going to be a hundred times greater, 300, the actual calculation was 296.

And the final one that 1,770 divided by six, or we rounded that again to 1,800, because that is a multiple of six, that is the hole.

And if you see that 18 times greater than the 18, is 1,800.

So therefore one of the other parts is going to be a hundred times greater, So three becomes 300.

And that's why I estimated answer the calculation was 295.

Well done everybody for completing that task.

I hope you enjoyed it.

For anyone who does not want to finish now And what's the continue with their learning, They're super keen and they're really enjoying the lesson, which fingers crossed, I hope you are, You can have a go at today's challenge slide, which is flexibility fun.

I won't read this script, but I'd like you to pause the video, read the information your screen, take as long as you need for the task And it challenged slides are often a great opportunity to continue talking and discussions about maths.

If you've got somebody nearby to share your ideas with.

Please do.

Now we're almost at the end of today's lesson, which leads only the quiz for you to do, which is what we do every time we have a National Oak Academy lesson.

So read the questions very carefully, try to remember the key vocabulary and the ideas of strategies we talk today and take your time.

And when you finish the quiz and you're pretty confident in what you've done, come back to finish the lesson officially.

See you all very, very soon.

Good luck in the course guide.

Well, I did as I mentioned at the start of the lesson and I do on every lesson that we have, we would love to see your work.

And there is an opportunity for you to share your work and your mathematical jokes with us here at Oak national Academy.

If you would like to do this, please ask your parent and carer to share your work on Twitter, tagging at national and #learnwithoak I'm sure today's lesson you've got some fantastic area models that you are proud of, and I would love to see your work and your efforts from today's lesson.

Okay, Everybody that does bring us to the end of today's lesson and what a super job you did, big thumbs up and thank you once again for your dedication and your effort.

Now, after all that modelling and all of those strategies, I need a break.

So I'm going to go outside and get some summer air, which is why I've got these Uber cool glasses on.

I know he didn't have to say it.

They are pretty spectacular.

I think you probably deserve a little break as well for after all that learning.

However, I do hope to see you again soon here on Oak National Academy, have a great rest of the day, and I hope to see you soon.

So for me, Mr. Ward, bye for now.