Lesson video

Hi, everyone.

It's Mr. Whitehead here and ready for your math lesson.

I need to put out a disclaimer before we start.

In this lesson, we will be talking about pizza.

Fortunately for me, I've just eaten.

So I'm not too worried about feeling hungry, partway through the lesson.

However, if any of you haven't eaten recently, it could be that hunger is on it's way.

Before we get started, please can you check that you are able to give me your full attention for the next 20 minutes.

If you are in a room full of distractions, then you need to move.

Press pause, find yourself somewhere quiet, where you can work and focus and press play again as soon as you are ready.

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

We're going to start off with a division with remainders activity, before outcomes to pizza for some sharing.

We're going to then make some connections within fractions and division.

lead you set for your independent task to end the lesson.

Things are going to need, pen or pencil, some paper, something to write on a book.

If you've got one from the school and a ruler.

Press pause, go and collect those items and come back as soon as you are ready to start.

Here we go then.

A start activity looking at division with remainders.

I've given you almost the complete equations, alongside some images.

I would like you to explain which number is missing and how the image is help you to find it.

Press pause.

Come back when you're ready to take a look.

How did you get on? Hold up your paper.

Let me see what you've written.

I see numbers.

I see sentences.

Good explaining how the images match and helped you looking good paper down.

Let's check them.

So in this first image, I can see three groups.

So I have divided by three, in each group there are four, we had a remainder of two.

We couldn't share equally those final two within the three groups that we were sharing between.

Next.

Okay I can see groups of 10 and I've got a remainder of three, but five groups, five, lots of 10, 50 and the remainder of 53 divided by three.

Sorry, divided by five.

The last image I can see two groups.

Each group has four.

There's a remainder of three.

There were two groups.

Two is the missing part of your questions.

Good start.

There'll be connections throughout this lesson between fractions and division.

Let's start off then with pizza.

There it is three different pizzas.

When I say different, there are three pizzas, actually they look like they've got similar toppings on each.

Let's not talk too much about toppings.

I didn't think I'd feel hungry, but if I start talking too much about my favourite pizza, then I certainly will be.

So let's leave it there.

There's some pizza.

How many pieces are there? Absolutely there are three and we are sharing between four, three divided by four.

How much piece will they get each? I said fractions and division, there'll be connections okay.

So I'm thinking at first three pizzas four people, there's not enough pizza, but of course there is, we can divide and split that piece of between them.

So thinking about that, then we've got three pizzas, we've got four people, each pizza shared between four people.

So for each pizza, each person will have 1/4 of each pizza each.

Looking there across there's three pizzas, how much pizza would they have each? 3/4, look you can see it.

Each of them has 1/4, three times, 3/4.

Thinking about how that looks.

Three divided by four equals 3/4.

What do you notice about those parts of the equation? Yeah, three and a four, three and a four, three divided by four is equal to 3/4.

Let's see what this means in terms of division and how we can actually record as a decimal as well.

So three divided by four.

If you want to pause and have a go at this do, come back when you're ready to follow along with the lesson, otherwise stay with me and do it at the same time.

So be ready to be recording on your paper.

Three divided by four, three, three ones divided by four.

So normally, here we're asking how many groups of four can we make from three ones, we would leave it as a remainder.

But we know the solution is 3/4.

We can continue dividing into our decimal places so that we haven't just got a remainder three.

So that would mean those three ones, we're going to exchange for 30 tenths.

Watch.

There goes one of them.

Now I'm with two to exchange for 10 tenths, another one for another 10 tenths.

And the third one for our third group of 10 tenths, 30 tenths.

Now we're asking how many groups of four can we make from 30 tenths? Or we can make how many? Absolutely as they go, we do have some left, but we have made seven groups of four using 28 of the tenths with 2/10 left.

But once again, we can exchange for hundredths, 20/100, 1/10, 10/100.

The second 10th, another 10/100, 20/100.

How many groups of four? They go back, it's a bit too soon.

How many groups of four can we make from 20/100? How many fours and 20.

We can make five groups of four using those 20/100.

0.

75.

But of course, 3/4 as a decimal 0.

75.

Three divided by four is equal to 0.

75.

Look at those connections coming through, between three divided by four and 3/4 and 0.

75.

There is another connection.

3/4 is equal to three divided by four, 3/4 is 0.

75, three divided by four is 0.

75.

0.

75 is equal to 0.

75.

So many connections from that pizza sharing problem.

I'm wondering if those same connections exist for when we're sharing a different number of pizzas between a different number of people.

Here's another one.

How much pizza each? One pizza, three friends, one pizza three friends, how much would they have each one divided by three.

One pizza divided by three, 1/3 of a pizza each.

One divided by three is equal to 1/3.

That connection between the numbers, is there again.

One divided by three is equal to 1/3.

Let's try it out again with a division, one divided by three.

How many groups of three can we make from one one? We can't make any so let's exchange one one for 10 tenths.

How many groups of three can we make from 10 tenths? three six nine, we can make or let me show you them first here they are.

We can make from those 10 tenths, three groups of three with 1/10 remaining.

Then we can exchange for 10/100.

How many groups of three can we make from 10/100? Three six nine, three groups of three with 1/100 remaining.

Okay let's exchange 1/100 for 10/1000.

How many groups of three can we make from 10/1000? Three six nine, hang on a minute.

Three groups of three from 10/1000 with one remaining, so we could exchange that 1/1000 for 10 of the next smallest decimal place.

I imagine and actually I think I'm right in predicting that this just would not stop there will always be one remaining that we can exchange for another 10.

This is an example division where it makes sense to stop at some point.

And there are different rules for how many decimal places you would show in your solution.

When it comes to 1/3 we typically would say that, that is equal to 0.

333 you might then say recurring, which means it's going to continue forever.

And we stopped up to three decimal places.

So 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.

Another connection 1/3 is equal to one divided by three they're the same thing.

The solution to the problem 1/3, the question to the problem one divided by three, one divided by three means 1/3.

When we think about how we record fractions, the numerator, the vinculum, the denominator, one divided by three.

I'm curious to know we've only looked at those two examples.

but in your independent task, there are some more common fractions I'd like you to investigate.

Are those same connections appearing for the other common fractions that I have left for you to look at? Come back when you're ready to share.

How did you get on? So I left you with these pizza problems. Number one, one divided by two, 1/2.

Number two, one divided by five, 1/5.

Number three, one divided by four, 1/4.

And number four, one divided by 10, 1/10.

Did those connections come through? I'm just making a prediction right now based on the numbers, one divided by two, 1/2 each.

One divided by two means 1/2.

Let's have a look.

So the divisions are going to help us to connect to give us that proof.

How many groups of two can we make from one one? So we exchange, how many groups of two can we make from 10 tenths? It's 0.

5, one divided by two, 0.

5.

1/2 equal to 0.

5.

Next, can't make any groups of five from one one.

So we exchange the 10 tenths, how many groups of five from 10 tenths? Two groups of five from 10 tenths.

0.

2, 2/10 equal to 1/5, one divided by five.

this is really exciting.

Next, groups of four from one one, how about from 10 tenths? We could make two groups with how many remaining? 2/10, let's exchange them for 20/100.

How many groups of four can we make? Five, four fives, 20, we can make five groups of four from 20, 0.

25 but of course one divided by four, 1/4 equal to 0.

25.

Final one, how many groups of 10 can we make from one? What if we exchange them for 10 tenths? How many groups of one can we make from 10 tenths? How many groups of 10 sorry, can we make from 10 tenths? One group of 10, 0.

1, 1/10.

The connections are there 1/2 is equal to one divided by two, is equal to 0.

5, 1/5.

One divided by five, 0.

2, 1/10, one divided by 10, 0.

1, 1/4.

One divided by four 0.

25.

Fractions and division are connected.

The fraction 1/2 means one divided by two equal to 0.

5 its equal to 1/2.

1/2 is the question, one divided by two and the solution 1/2, 0.

5.

Or I don't know about you but my mind is being blown slightly, by these fantastic connections.

I hope you enjoyed this session, and connecting fractions with division and going really deeply using your short division and exchanging into the decimal places, to help you with that.

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

So raise your hands, did you finish the lesson feeling hungry? I thought you might I can only apologise but good news is the lesson is finished.

You've earned a well deserved break.

And perhaps a snack from the kitchen.

Be sure to check with the parent or carer first though.

I've really enjoyed this lesson and working with you.

I look forward to more maths lessons very soon.

Until then look after yourselves, bye.