Lesson video

Sorry.

I've been trying to keep up with my eight glasses of water a day.

Two litres of water a day, I've been told, you're meant to have to keep your body healthy, and your mind healthy and focused.

And these math lessons are so important to be focused on that I'm doing all I can to keep my water up, to keep my focus level up, my attention, to make these lessons are good as they can be.

Do you manage to keep up with your daily intake of water? Do you know how much you're meant to have a day? Could be something to have a chat with an adult at home about if you are not sure.

Right, I've had my water.

Although, I certainly haven't had eight glasses just yet.

I'm ready for the math lesson to start.

Are you? Can you make sure that you are in a space that's free of distractions, a space where you'll be able to give me your attention for the next 20 minutes or so as we move forward with our maths learning.

Press pause if you need to make any changes, and then play again when you're ready to start.

In this lesson, we will be using the formal written method for short division.

We'll start off with a grouping activity.

I'll show you some number and you're going to have a go at grouping them in a way of your choice.

Then we will spend some time looking at how we can estimate quotients to division calculations, before we work through some short division.

That will leave you ready to practise those skills, estimating and short division, in the independent task.

The things you'll need: pen or pencil, a ruler, and some paper, a pad, or a book to write onto.

Press pause if you need to go collect anything.

Otherwise, let's get started.

So here are your numbers.

I would like you to group them into categories of your choice, and you must be able to explain the reasons behind the categorization, the titles of the groups that you created.

Press pause and go and have a go at organising these numbers into different groups.

So how did you get on? Hold up your paper, let me see the groups that you've chosen.

How many groups have you managed? Uh, okay.

Two groups, three, four groups.

Interesting.

Can I show you the groups that I chose? I wonder if you can challenge yourselves to working out the titles for my groups.

What was I thinking about? Here we go.

I used a group of three numbers.

Another three.

Two.

And two.

But what was my thinking? Look at each group.

You're looking at each column.

What's the same about the numbers in the column? There's a property.

There's something about them that's shared.

What do you think about the first group? They're square numbers.

Well done.

The next one.

Very good, multiple of six.

They're all in the six times table.

Next, multiples of five? That they are, I agree, but that's not the thinking I had.

Here, it's a little bit more creative.

They are one more than a multiple of seven.

What does that mean? One more, ah, one more than 14, one more than 49, one more than a multiple of seven.

How about the remaining two? Very good.

Prime numbers.

They only have factors of one and themselves.

Moving on, let's think about divisions.

Let's get out head in the division game.

Look at the equation.

There are some words underneath.

Each number has a name.

Which names match the numbers? 23 is the dividend.

Hmm.

Which is the quotient? Three.

And so the divisor is eight.

Let's get these two moved into the right places.

Dividend, divisor, quotient.

Really helpful language to have for when you're talking about division, and you're naming the numbers in the equation.

We can be more technical as we use these words to name the numbers that we're talking about.

Here's a problem for us.

Let's have a read.

In 2017, Oak Travel booked holidays for 2387 customers to Costa Rica.

Due to volcanic eruptions, there were seven times fewer bookings the following year.

How many holidays to Costa Rica were booked in 2018, 2018? Press pause.

Have a go at answering the questions.

What do you know? And what do you not know? And possibly start thinking about any knowledge or skills that you could use to solve the problem.

So what do you know? Anything else? And what do you not know? Good.

So we know how many holidays were booked in the 2017.

We know that there were seven times fewer the next year.

But we don't know how many there were in that year, in 2018.

I'd like you to pause again and have a go at drawing a bar model to represent the maths within the problem.

Represent what you know.

Show what you do not know.

And then, I think, it will be really clear what maths is needed, what knowledge and skills you have already that will help you solve the problem.

Press pause.

Come back when you're ready.

Show me your bar models.

Hold up your paper.

Keep it steady.

I can't have it if it's flapping.

I won't be able to see or read it.

Thank you.

Really good.

Compare your bar models now to mine.

So we're thinking, what do we know? We know how many holidays there were in 2017.

And we know that the following year, there we how many times? Seven times fewer, seven times fewer.

But how many is that? Looking at the bar model, is the maths coming through? Are the skills being connected? What's going to help us here? Excellent.

We're dividing 2387 by seven, into seven equal groups.

But how can we do that? So division strategies that we've gone over, we could factors, we could multiples, we could use related facts, we could use equivalent division, when we're working mentally.

But will any of those apply here? What do you think? Press pause.

Take a moment to think about it.

So will any of these work? Division using factors? Well, seven is a prime number, so we can't change seven into factors of seven.

It's just one and seven.

That's not going to help, that's the same as dividing by seven.

Using multiples? I could start counting in sevens, I could start counting in 70s, it's going to take me a while though.

Perhaps not so efficient.

Related facts? There aren't any that are calling out to me.

Any related facts that can help? Not clear.

How about an equivalent division? No.

There's not an equivalent division to help us here.

So what do we do? The answer is short division, written division, a formal method, because the mental approaches are not appropriate here.

The numbers that we're using are not appropriate for a mental strategy, so we use a written method.

Before we do, let's have a think about estimation.

These four children have some ideas for how you could estimate the size of the quotient.

Press pause.

Have a look at what they're thinking.

See which ones you agree would help you to estimate the size of the quotient.

So what do you think? Is it going to helpful to round to 2400 and divide by seven? Counting 70s? I'm thinking a combination of these two children's thinking.

We're going to use some related facts.

So we're dividing by seven, and we've got to 2387.

Well, 21 is seven lots of three.

But I've got 2300, so we need to make this 21 bigger.

210, well, that's seven 30s.

Still, I need an estimate that's going to help me with 2387.

2100, much closer.

That's seven lots of 300.

So the quotient is going to be bigger than 300, because 2387 is larger than 2100.

And it's going to be smaller than 400, because 2800 is larger than 2387.

So my quotient is going to be between 300 and 400.

Why don't you press pause? Have a go at using the approach to estimate the size of the quotients for the three divisions underneath my video.

Press pause now.

How did you get on? Were you able to estimate using that approach? Hold up your paper.

Let me have a look.

Good effort.

Well done.

So estimates, then, for the first one, 13.

13, 26, 39.

13 300 times is 3900.

So my quotient's going to bigger than 300, 13, 26, 39, 52, it's going to be smaller than 400.

13 400s is 5200.

And 4056 is between 3900 and 5200.

So the quotient is going to between 400, sorry, between 300 and 400.

Next one.

So this is going to be between 80 and 90.

96.

12 eights, 96.

12 80s, 960.

12 nines, 108.

12 90s, 1080.

My quotient will be between 80 and 90, because my dividend is between 960 and 1080.

Last one, it's going to be between 130 and 140, because seven 13s, seven 12s, 84, seven 13s, 91.

Seven 130s, 910.

Seven 13s, 91, seven 14s, 98.

Seven 140s, 980.

945 is between 910 and 980, so my quotient is going to be between 130 and 140.

How did you find that? Challenging? It is, isn't it? It's all about making connections between multiplication and division, the parts of each equation, and some known facts as well.

Something maybe for some more practise.

And if you're finding it challenge, sorry, if you're finding it challenging, brilliant, because that means there's some learning happening.

Let's have a look now, then, at the short division.

We've estimated that the quotient will be 300 and 400.

So let's now divide.

See what you can see.

Good.

There's our dividend: 2387.

And I'm going to show you the short division alongside it.

2387 divided by seven.

So we're starting off by asking, from our 2000s, how many groups of seven we can make? We can't make any.

We can't make any groups of seven.

So we're going to exchange.

Did you see it happen? Two thousands we're going to exchange for hundreds, we've now got 20 hundreds.

We've now actually got 23 hundreds.

And we can start to make groups of seven from 23, counting in sevens.

Seven, 14, 21.

We made three groups of seven from 23, with how many left? We have two left.

Now, again, that two is going to be exchanged.

Did you see? The two hundreds we're going to exchange for 20 tens.

How many 10s do we now have? 28 tens.

How many groups of seven can we make from 28 tens? Seven, 14, 21, 28.

Four groups of seven.

That was really fast.

Let me go back.

Four groups of seven we've made from 28 tens.

We've just got our seven ones left.

How many groups of seven can we make from our seven ones? One group of seven.

So we've completed the division using short division.

We've divided by seven.

I'm just going to go back to how the number was at the beginning.

And just watch again as we exchange, because we can't make groups of seven from two thousands, but we can make groups of seven from 23 hundreds.

We will have three of them with two hundreds to exchange for 20 tens.

And did you notice, on my grid, the pink two that appeared? Watch again.

Look at the pink two appear, because we're exchanging from hundreds to tens.

We've got 28 tens.

Sevens from 28 tens, groups of seven, we can make four of them, leaving us, then, with our one group of seven from seven ones, 341.

Going back to the original problem, how many holidays to Costa Rica were booked in 2018? Only 341 compared to 2387 the year before.

That's quite a drop.

Seven times smaller, in fact.

I'd like you to pause now, so that you can have a go at solving some short division independently.

If you need to rewatch any of this lesson, or have a look at parts of it again, please do.

But come back and see once you've been able to achieve, independently, your task.

See you shortly.

Let's take a look.

Hold your paper up.

Show me your estimates, show me your found quotients, and your short division for getting there.

Looking good, everyone.

Let's work through, then.

So my estimates was a quotient between 130 and 140, 135, and between 300 and 400, 312.

Pause on this page if you need to, because you're still checking your short divisions.

Otherwise, he's number three.

A quotient between 80 and 90 is my estimate, 87.

And between 700 and 800, 792.

So, again, pause if you're still checking.

Question five, an estimated quotient between 100 and 200, 165.

So the final part was to reflect on whether any of these could be solved mentally.

I wonder if any of those questions you thought could be.

Hold up a number of fingers to indicate a question number that you think could be solved mentally.

Okay, most of you thinking these would be through a written approach.

And it's by looking at the questions, looking at the numbers, that you would decide on whether you're going to work mentally or using a written method.

Final question before I leave you, how else could I check if this is correct, that 5544 divided by seven is 791? How could I check? We could compare to our estimate, or we could use the inverse 791 multiplied by seven, and we would see if that equals 5544.

If you would like to share any of your learning from this lesson with Oak National, please ask a parent or carer to share your work on Twitter, tagging @OakNational, and #LearnwithOak.

Well done, everyone.

Your learning was absolutely fantastic today.

I'm really proud of all of you for your participation and engagement, and the learning that you have shown.

A well deserved break awaits, I think, for you and for me before any of the learning that you have lined up for the rest of the day continues.

I'm going to go and get myself another glass of water, I think.

Keep the water levels topped up as much as possible.

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

Look after yourselves, and bye for now.