Lesson video

Hi everyone, it's Mr. Whitehead here and ready for your maths lesson.

I don't know if you noticed, but this is lesson 15 of 15.

Perhaps this is your first lesson with me.

Perhaps you have been here for all 15.

For those of you that have been here for longer than one session, and in fact, if you are here for the first one today, there is a celebration in order.

Now, unfortunately we can't celebrate together in person but I have brought some pizza to the party.

Well, maybe I am over egging that a little bit.

I don't have any pizza to bring to the party but I've got pizza in the maths lesson.

We will be looking at it briefly as part of our focus on fractions and division.

So when you see that pizza that's my way of celebrating with you reaching lesson 15 of 15.

Before we get going with that, can you check that you are in a quiet space, distraction free and able to focus.

If you're not yet able to do those things, press pause, go and find somewhere where you can do those things and play again as soon as you're ready.

In this lesson, we will be solving problems involving fractions and division.

We're going to start off with a division activity involving some remainders before the pizza comes out, and we use that to make some connections between fractions and division.

It will leave you ready to tackle the independent task at the end of the lesson.

Things you're going to need, pen or pencil, a ruler, some paper, a pad or a book from school if you've been provided one.

Pause, please go and collect those items and then come back when you're ready to start.

Great, let's get going.

Here are three images, and three equations with some of the parts hidden.

Use the images to explain which numbers are missing.

Press pause, have a go at this then come back when you're ready.

How did you do? Can I have a look? Hold up your paper.

Do we have any written explanations to go alongside the numbers? Yes, I can see some, looking good.

Okay, paper down.

Let's have a check.

So the first missing number, well, it's the whole, it's what we had before we started to share it.

So that will be three groups of four plus two, 14.

Next, hmm, 50 that's the whole group divided into groups between five, divided between five.

How many in each of the groups? 10, 10 remainder three.

Final one, 11 divided by something is equal to two.

So, we've got two groups remainder three, ah, 11 shared equally into groups of four.

11 divided by four equal to two remainder three.

Before we bring out the pizza, I want to recap on the parts of a fraction and what they are called.

Notice the order in which they appear.

I've started with the line followed by the four and then the one.

That's really important when it comes to fractions and their meaning.

The way I've ordered how that's been written matches the meaning of the parts of the fraction and fractions as a whole.

Let's check on what I mean by that through some questions.

What is this line called and why do we need it? What is this number called? Why do we need it? What is this number called and why do we need it? So take a moment if you need to, and otherwise starts telling me the pink question.

What do we call that part of the fraction? It is the vinculum.

My turn, your turn, vinculum.

Vinculum, well done.

Why do we need it? Brilliant, it shows us what we are looking at is a fraction.

How about the green question? What do we call that number? Good, say it again.

The denominator, why do we need it? It tells us the total number of equal parts.

The whole might be a shape, quantity, a number.

The denominator tells us how many equal parts that thing has been divided into.

How about the purple question? What do we call it? The numerator, say that again.

Good, why do we need it? Super, it tells us the number of equal parts highlighted, the number of equal parts that we're talking about.

Okay, let's make some connections now.

How much pizza, here is the pizza ready for us to celebrate.

How much pizza would each of these children get? Three pizzas divided by four, hmm.

Three pizzas divided by four.

It doesn't feel right to me but actually the image of the pizza is helping.

I know that I don't need to give each of these children the whole pizza each.

They can have parts of a pizza.

Fine, then how much do they get? Three pizzas, four children, they're going to get 1/4 of the pizza.

1/4 of each pizza each.

So how many quarters do they get all together? Each child gets 3/4 of a pizza.

So three divided by four is equal to 3/4.

Let's have a look at how we can represent that question using decimals.

We might already know in fact you should know the decimal equivalent to 3/4.

What is it? 0.

75, let me show you where that comes from.

Three divided by four.

How many groups of four can we make from three ones? We can't, so we exchange three ones for 30 tenths.

Watch how it happens.

10, 20, 30 tenths.

How many groups of four can we make now? We can make seven groups of four using 28 of the tenths but we will have two tenths remaining.

So let's exchanged them for hundredths.

How many hundreds will we exchange two tenths for? 20 hundredths, watch them as they go.

10, 20 hundredths.

How many groups of four can we make from 20 hundredths? We can make five groups of four, 0.

75.

Just what we knew, but confirmed with some short division.

So 3/4 is equal to 0.

75.

Yeah, we know that and we proved it with the division.

Three divided by four is equal to 0.

75.

And 3/4 is equal to three divided by four.

The problem, three divided by four and the solution 3/4, they're the same thing.

We could represent the division as 3/4 because 3/4 means three divided by four.

Let's see if that works for some other fractions.

One pizza divided by three friends.

If 3/4, sorry, if three divided by four is equal to 3/4.

One divided by three should be 1/3.

And it is, one pizza divided by three, 1/3 each.

Wow, these connections, I'm really liking.

Checking with some division.

1/3, one divided by three is equal to 1/3, but as a division, as a decimal from the division, one divided by three.

How many groups of three can we make from one, one? So let's exchange for 10 tenths.

How many groups of three can we make from 10 tenths? Three, using nine of them with one left to exchange for hundredths, for 10 hundredths.

How many groups of three can we make from 10 hundredths? Three groups with one hundredth remaining.

Let's exchange it.

For how many thousandths? For 10 thousandths.

How many groups of three can we make from 10 thousandths? We can make three with one remaining.

Now look at the size of that decimal.

Look how many places we've used.

We've used three, typically with division and exchanging through the decimal place, you'll stop after a certain number of decimal places.

In this occasion we're stopping at three.

And it's important to, because looking at what's been happening so far, we would continue with this for eternity.

There will always be one of the place you're in remaining to exchange for 10 of the next.

So we stop.

1/3 is equal to 0.

333.

One divided by three is equal to 1/3.

1/3 is equal to 0.

333.

One divided by three is equal to 0.

333.

And the final connection.

1/3 is equal to one divided by three.

They're the same thing.

The fraction 1/3 means one divided by three, and it works for these other common fractions as well.

1/2, 1/5, 1/10, 1/4.

Fractions and division are closely connected.

A fraction can be the solution to a division, and it can be the division.

1/2 is one divided by two, and one divided by two is equal to 1/2.

Wow, let's see how this connects.

So let me give you a chance to practise independently.

Have a go with this problem.

How much pizza will they get each? Six pizzas, five friends.

How much will they get each? Have a go.

How did you get on? So, six pizzas, I'm going to represent just one of the pizzas and the five friends.

How much of one piece will they get each? 1/5, one pizza divided into five equal parts, 1/5.

But there are six pizzas.

So each child will get 1/5 of each of the pizzas.

Each of the six pizzas.

How many fifths? 6/5, let's check how that works with some division.

How many groups of five can we make from six ones? One, with how many remaining? One, let's exchange it for some tenths.

How many groups of five can we make from 10 tenths? Two, 1.

2, one and 2/10.

2/10 is equal to 1/5.

Six divided by five, one and 1/5.

6/5 is one and 1/5.

Six divided by five is equal to 6/5.

The connection is there.

Try it with these two.

Press pause and have a go.

Say what you think that the equation will be based on the connections between fractions and division, and the decimals that you find through your short division.

Come back when you're ready.

How did you do? Did the connections continue? Fantastic, hold up your paper.

Let me see.

Oh, looking good everyone.

Look at all of those connections between fractions and division.

Fantastic, paper down.

Take a look.

First one, five pizzas divided by three friends.

What will the fraction equation be? 5/3, let's see how these connections come through.

So five divided by three is the same as 5/3.

5/3 is the same as five divided by three.

5/3 means five divided by three.

Five divided by three, one and 2/3.

5/3 is improper as it makes number one and 2/3.

Each child gets one pizza and 2/3 of a pizza.

The division should have shown you that five divided by three is equal to 1.

666 and we stop on that third decimal place.

Second one, five pizzas divided by four.

What will the fraction equation be? 5/4, 5/4 means five divided by four.

So as a mixed number, how much pizza do they get each? One whole pizza and 1/4.

What's that going to be as a decimal? We could just use what we know about the decimal equivalent to 1/4, 0.

25.

Let's confirm it through the short division.

1.

25, of course.

One pizza and 1/4.

Five divided by four is equal to 1.

25.

Those connections that run through division.

Sorry, a fraction as the question as the division and a fraction as the question.

If we know the fraction then we know the division and we know the equation.

I'd like you to pause now and to have a go at solving the task that I've left for you independently.

Come back when you're ready to check your solutions.

How did you do? Hold up your paper.

Let me have a look.

Oh, I can see drawings.

I can see writing.

Oh, look at those stories.

And most importantly, I can see the maths, the connections, the fractions, the decimals, the division, brilliant work.

I'm just going to show you for those two expressions what the equations would look like so you can check those off.

Seven divided by three, 7/3.

Two and 1/3.

Seven divided by three with short division, stopping after the third decimal place, 2.

333.

So seven divided by three is the same as 7/3.

7/3 is the same as seven divided by three.

And do you have your own story to match to that expression.

As for 11 divided by five.

We know that the fraction question is going to be 11/5.

That's an improper fraction as a mixed number two and 1/5.

We could use two and 1/5 to find the decimal, and using our understanding of equivalent, two and 1/5, two and 2/10, 2.

2.

And the short division is that just to confirm it, 2.

2 so 11 divided by five is the same as 11/5.

11/5 means 11 divided by five and it means 11/5.

I hope you enjoyed that session and that your mind isn't too blown by those connections between fractions and division, decimals and division, and the questions.

So many connections across all of those, but really really powerful ones to know and be able to use and understand.

If you would like to share any of your learning from this session with Oak National, please ask your parents or carer to share your work on Twitter tagging @OakNational and using the hashtag LearnwithOak.

So I said at the beginning that that was lesson 15 of 15.

And for some of you, a celebration is in order.

That's those of you that have been here for many of those sessions.

If today was your first, you of course have been very welcome as well, and join in the celebration, why not? I've really enjoyed this sequence of sessions with you and I hope that you have as well.

Thank you so much for your participation throughout, your contributions, your calling out and showing me all of that fantastic learning.

I've had a wonderful, wonderful time.

All that's left to say is, look after yourselves and enjoy any of the learning that you have lined up for the rest of the day, bye.