Lesson video

Hi everyone, it's Mr. Whitehead.

I'm here and ready for your maths lesson.

I'm in a quiet space, my television is off, my phone is switched off, there aren't any distractions around me.

Can you say the same? It's really important now to pause, take yourself off to a quiet space, where you are able to focus on yourself and your learning for the next 20 minutes.

Press pause, then come back once you're ready to start.

in this lesson, we will be interpreting remainders from division calculations, using the context of a problem, to help us make those decisions.

So using the problem to tell us what to do with the remainder.

We're going to start off with a number line activity, then we'll spend some time exploring a problem, responding to a problem, and I will leave you to have a go at applying your skills independently, to end the lesson.

Things that you're going to need, pen or pencil, some paper, a pad or book and a ruler.

Press pause, collect the items, come back and we'll start.

Okay, here's your number line activity, to start the lesson.

You can see six arrows, you can see a number line divided into a number of equal parts, a different number of equal parts, depending on which parts of the number line you're looking at.

So spend some time really interpreting those equal spaces and what's each division must be worth.

Notice the start point and the end point of the number line as well.

Press pause, make a note of what numbers the arrows are pointing to, come back when you're ready to check.

Should we have a look? Hold up your paper let me see how you got on.

Keep your papers still, I can't read it when it's moving.

And there we go.

Looking good, fantastic, I can see some of you have tried to represent the number line.

Note we've a quite so many equal parts, but you've really made a good effort at positioning those numbers in roughly, in approximately the right location.

Others have made a list of numbers.

Let's see if we've got them right, working across the bottom, we should have 5,500.

Each of those longer divisions increase by 500 each time, whereas the shorter divisions are increasing by 250, the shortest by 50.

So here we've got 6850, 9050 and working along the top, 6250, 8500 and 9990.

Oops! did I say that right? Should we try again? You tell me what it is.

That's better 9,900, thank you.

Let's have a look at this problem, give it a read with me.

A local school is planning an end of year trip.

The children have voted to go skiing, but that will cost, wow, £654 per person.

A trip to Cornwall will cost eight times less than this.

How much is the trip to Cornwall per person? Press pause, have a go at answering those questions for me.

What do you know? What do you not know? And are there any connections coming through to knowledge and skills that you have, which will help you to solve the problem? Press pause now, how did you get on? Tell me something you know, from reading the problem.

Is there anything else you know? Okay, and what do you not know? Fantastic, so let's see, we know that they want to go skiing and the cost of that, £654 per person.

Alternatively, a trip to Cornwall will cost eight times less.

What we don't know, how much that trip to Cornwall will cost per person.

Let's now turn this information into a bar model.

Press pause and to have a go at representing the problem, using a bar model.

And once you have, what connections are coming through? What can you see in the bar model, that's helping you to identify the knowledge and skills that you need, to be able to solve the problem? Press pause.

So can you hold up your paper? Let me take a look at your bar models, looking good, fantastic, some slight variations I can see.

So compare your bar model now to mine and see what's the same, what's different, and whether or not it matters with identifying the maths that we need to solve the problem.

So I went for this, I'm representing the whole cost of, the skiing trip, £654, that's the cost per person.

So I represented that as a whole.

And now within that, I'm representing the trip to Cornwall, is costing eight times less than the cost of the skiing trip.

But what I don't know is how much that trip to Cornwall will be.

I do know it's eight times less than 654.

Okay, so what about those connections? What are you going to use to solve the problem? What do you think? Tell me.

Oh, I can hear some division expressions.

You can find the quotient, okay.

Someone's talking about subtraction.

We could, oh, could we? Do we know what to subtract? Not here.

If we knew the cost already of what one of those parts was representing, then we could have some repeated subtraction.

But a division, dividing into eight equal parts, 654, it will tell us then the cost of the trip to Cornwall.

I'd like us to have a go at solving this problem using short division.

So we're not thinking about any mental strategies at this point.

I want us to use short division.

And it's quite likely that you would have picked short division anyway.

When you've seen this problem, some of you may have gone for a mental strategy, but short division please.

If you'd like to pause now and work ahead, I'd like the short division methods, perhaps some drawings of place value counters, then come back when you're ready to work through it with me.

If not, work through with me at the same time, let's go, start with an estimate.

What would you estimate the size of the quotient to be? I can see some nice.

Look at that 654, 64, 640, is eight lots of 80, eight, eight, 64, 880, 640.

So I'm estimating the quotient to be around 80.

Let's represent 654 with counters and we've got it recorded already.

654 divided by eight for my short division method.

Let's start then.

So how many groups of eight can we make from six hundreds? We can't make any.

So we're going to exchange six hundreds for 60 more tens.

Now we can ask, how many groups of eight can we make from 65 tens? We can eight, 16, 24, 32, 40, 48, 56, 64, eight groups of eight, we can make from 65 tens.

We've used 64 tens, there's one 10 remaining.

We're going to exchange that one 10, for 10 ones.

How many ones do we now have? 14 ones.

How many groups of eight can we make from 14 ones? We can make one group of eight.

How many remaining? Six.

So we've solved the problem.

81, remainder six.

Is that what you got? Okay, let's take that back to the problem.

So we were working out each of those parts, one of those parts, in fact, 81 remainder six, £81 remainder six.

Wait, that doesn't sound right.

Say that again, £81 remainder six.

How much is this trip to Cornwall per person? £81 remainder six.

We need to do something different with the remainder.

We have some options.

We can represent a remainder as it is, as a fraction, as a decimal, or we can work to the next whole number, or the previous whole number, so £81 or £82.

What's going to be appropriate here? What do you think? Okay, let's try it, let's try some.

Let's try just representing as a fraction.

Remainder six, the group size, we were trying to create, eight, well done.

We were creating groups of eight.

We couldn't make a whole group of eight.

We've only got six parts, six of those eights, 6/8, 81 and 6/8, let's see how that works.

£81 and 6/8.

That doesn't sound right either, 6/8 of a pound.

It's not been appropriate to represent the remainder as a fraction in this problem, we're working with money.

Let's try it as a decimal then.

So our remainder of 6/1, let's continue to exchange our ones for tenths, six ones, 60/10.

20, 30, 40, 50, 60/10.

How many groups of eight can we make from 60/10? We can use 56 of them, to create seven groups.

56/10, let's throw that down.

56/10, used to make seven groups of eight with four tenths remaining.

Continue to exchange, 4/10 for 40/100, watch as they appear, 10, 20, 30, 40/100.

How many groups of eight can we make from 40/100? We can make five, eight, 16, 24, 32, 40.

40/100 into five groups of eight.

So let's have a look now at how this works, back with our problem.

81 remainder six, 81.

75, £81, 75, that sounds better.

So how much is the cost of the trip to Cornwall per person? £81, 75.

So for this problem, it was most appropriate to interpret the remainder as a decimal, because the context of the problem told us to do that.

The context of the problem was money.

So it was most appropriate to represent the remainder, using decimals so that we've got an amount of money, come the end of the problem.

It's time for you to have a go at solving some problems independently.

Let's compare, shall we? Hold your paper up for me, so I can take a look.

Let me see all of the questions, so I can see some bar models, fantastic.

I can see a short division and I can see what you've been doing with the remainder.

Perfect, let's take a look.

So this first one, you can see the bar model.

We're working out essentially 1/6 of 495.

We're dividing by six, we're working with money.

So it's most appropriate to represent the remainder as a decimal form.

We had 5/10 in the remainder, 5/10 of a pound, 50/100 of a pound, £82, 50.

We could have thoughts of the remainder as 3/6, if we did, because it is, it is 3/6.

It's 1/2 a pound, but it's pounds that we're working in, that's why we finished off with decimals, instead of the remainder of 3/6.

And certainly not just a remainder of three.

Second question.

So we're working in a measurement here in length and metres.

We've represented the decimal or the remainder as a decimal, 131.

25 metres, as a fraction, that was going to be 1/4.

So if 525 and 1/4 metres, that would have worked as well.

So we could have represented as either there.

The third one, we had a remainder of six.

We were looking at how many packs we could create, packs of eight from 798 suites.

Here, this is an example of where we either round the whole part of the quotient to the next whole number, or keep it as it is.

We can make 99 packs.

We've got a remainder of six suites that couldn't fill a pack.

So we can't answer 99 million to six pack or 99 and 6/8 of a pack.

How many full packs? Is what the question was asking us.

We can make 99 full packs.

Thank you for joining me for this lesson.

There's a lot of learning that you could share with Oak National, if you'd like to.

Please make sure you ask your parents or carer though, and they can help you to share your learning on Twitter, tagging @OakNational and #LearnwithOak.

That was a fantastic lesson.

Thank you so much for your participation and your engagement from start to finish.

You should be really, really proud of all you've achieved, over the last 20 minutes.

Whatever you have lined up for the rest of the day.

I hope that you enjoy it and that you show that same level of engagement and participation in that as well.

I look forward to seeing you again soon for some more maths.

Until then, look after yourselves and I hope see you soon.

Bye.