Lesson video

Hi there.

My name is Mr. Taziman, and I'm gonna be teaching you a lesson today from the unit about statistics.

It's a really important unit and one that will help you to understand things around you through number.

Sit comfortably 'cause we're ready to start.

Here's the outcome for the lesson then.

By the end, we want you to be able to say, I can use angles, fractions, and percentages to interpret pie charts.

These are the key words or phrases that you're gonna expect to hear, pie chart and sector.

I'll say them again and I want you to repeat them back to me.

I'll say my turn, say the word, and then I'll say your turn and you can say it back.

Ready? My turn.

Pie chart.

Your turn.

My turn.

Sector.

Your turn.

Here's what those mean.

A pie chart is a circular graph where sectors represent different groups in proportion to each other.

A sector is a part or pie slice part of a pie chart, and you can see the two images that are there to support these definitions.

In the bottom line in particular, you can see the pie chart's been split into two different sectors.

They're unequal in their size.

This is the outline of the lesson then.

We're gonna have an introduction to pie charts to begin with, and then we're gonna think about using angles, fractions, and percentages.

In this lesson, you'll meet Sofia, Izzy, and Jacob.

These three are gonna be discussing some of the maths that we'll be learning about.

What they're gonna say is invaluable because discussion about maths is crucial to help you to understand.

Okay.

Are you ready to start? I know that Sofia, Izzy, and Jacob are so let's go for it.

"Izzy is looking at a pie chart.

What's that, Izzy? What do you think it is? What do you notice? There's a circle.

I know the circumference is the perimeter of the circle.

The diameter is a line going across the circle through its centre.

The radius is a straight line from the centre of the circle to any point on its circumference.

You two do know a lot about circles.

This is called a pie chart.

Does it tell us about pies? I like pie, especially my granny's apple pie.

It could, but this one actually tells us about favourite colours.

You can see the titles appeared there now,.

Pie chart showing favourite colours of children in year six.

Oh, the biggest part is purple.

Is that important? The parts are called sectors, and the size of each one is important.

I've noticed that the smallest sector is green.

Izzy tells Jacob and Sofia about sectors.

The size of each sector is important.

They show the proportion of the whole.

I can see that one half of the pie chart is purple.

Well spotted.

This means half the children asked said purple was their favourite colour.

It looks to me like the blue sector makes up on quarter of the pie chart.

You're right, one quarter of the children said blue was their favourite colour.

I noticed that the purple sector, which is half, includes the diameter.

The blue sector, which is one quarter, includes a radius.

So the radius is half the length of the diameter.

Izzy asks some questions about the pie chart.

I asked 12 children for their favourite colour.

How many said purple? One half of 12 is equal to six, so six children said purple was their favourite.

How many children said blue was their favourite colour? One quarter of 12 is equal to three.

So three children said blue was their favourite." Now it's time for you to have a go answering some questions about the pie chart to check your understanding so far.

Izzy asks, "How many said red was their favourite colour and how many said green was their favourite colour?" And crucially, we're told to remember by Jacob that there are 12 children all together.

Have a go at those, and pause the video now to do so.

Good luck.

Welcome back.

Three children said red or green with twice as many saying red.

Two children said red was their favourite colour, and one child said green.

Izzy talks about how to make a pie chart.

The sectors in a pie chart are each made up of a number of parts.

The sectors are not usually equal in size, but the parts they are made from must be equal.

For example, if we asked eight children, the pie charts would have eight equal divisions.

If we asked 10 children, the pie chart would have 10 equal divisions.

I see a pattern here.

If we asked 16 children, the pie chart would have 16 equal divisions.

Izzy, Jacob, and Sofia create a pie chart.

15 children were asked to name their favourite big cat.

Five children said tiger.

This is equal to 5/15ths or one third of all the children.

Three children said cheetah.

This is equal to 3/15ths, or one fifth of all the children.

Six children said snow leopard.

This is equal to 6/15ths, or 2/5ths of all the children.

One child said lion.

This is equal to 1/15th of all of the children.

The completed pie chart would look like this.

Pie chart showing 15 children's favourite big cats.

Look at this pie chart.

Pie chart showing 16 children's favourite fruit.

Banana, apple, orange, strawberry.

16 children were asked to name their favourite fruit.

The same number gave apple or orange as their answer.

How many children chose each type of fruit? See if you can work that out.

Pause the video now.

Welcome back.

Izzy says, "Half the children said banana was their favourite, and half of 16 is equal to eight.

So did you get eight for banana? One quarter of the children said strawberry, so four children said that this was their favourite." Did you get four children for strawberry? "The apple and orange sectors are equal in size.

Together they add to one quarter of the children.

That means two children said orange was their favourite, and two said apple was their favourite.

Did you get two for each orange and apple? Hmm, well, I hope so.

It's time to move on then.

Let's look at the first task then.

24 children were asked how they travelled to school.

Here's a pie chart showing how 24 children travelled to school.

Two more children walked than came by scooter.

The same number of children came by bike, bus, and car.

How many children are shown by each sector of the pie chart?" Once you've calculated each sector, use that information to complete the statements below, and you can see there's missing numbers in each of those statements.

Pause the video here and give that a good go.

Enjoy.

Welcome back.

So, let's look at each of these statements.

We know that seven children walked and five children came by scooter.

"Half of the children either walked or came to school by scooter.

We know that two more children walked than came by scooter.

Seven is two more than five.

Seven add five is equal to 12, which is half of 24.

Some really good reasoning to justify the answers that we've just given.

For C, D, and E, we have four for each of those answers.

Half of the children either came to school by bike, bus, or car.

An equal number of children came by bike, bus, and car.

Half of 24 is equal to 12, 12 divided by three is equal to four.

Pause the video here if you need a little bit more time to digest that marking, and to make sure you understand all of the different answers.

Let's move on to the second part of the lesson then, using angles, fractions, and percentages.

A pie chart is divided into 10 equal sectors.

Each sector is equal to 1/10th of the pie chart.

1/10th is equal to 10%.

There are 360 degrees in a circle altogether.

360 degrees divided by 10 is equal to 36 degrees.

Each 1/10th is equal to a 36 degree part of the pie chart.

We can check this using a protractor.

A pie chart is divided into five equal sectors.

Hmm, slightly different now.

Each sector is equal to one fifth of the pie chart, one fifth is equal to 20%.

There are 360 degrees in a circle altogether, 360 degrees divided by five is equal to 72 degrees.

Each one fifth is equal to a 72 degree part of the pie chart.

We can check this using a protractor.

A pie chart is divided into three equal sectors this time.

Each sector is equal to one third of the pie chart.

One third is equal to 33.

3333333%.

There are 360 degrees in a circle altogether.

360 divided by three is equal to 120 degrees.

Each one third is equal to a 120 degrees part of the pie chart.

We can check this using a protractor.

360 can be divided by lots of different numbers." Very true, Jacob.

Okay, let's check your understanding so far.

"One sixth of the children in a school wear glasses.

I'm going to measure the sector that wear glasses using a protractor.

How many degrees would the protractor show there are in one sixth? Pause the video and work that out.

Welcome back.

360 degrees divided by six is equal to 60 degrees Each one sixth is equal to a 60 degrees part of the pie chart.

There we go, we can use a protractor to show that as well.

Izzy creates a pie chart.

Pie chart showing children's lunch choices on Monday.

Packed lunch, pizza, pasta.

The whole pie chart is equal to 100%.

360 degrees is equal to 100%.

42% of children chose pizza.

What percentage of children chose pasta? I can see a right angle in the packed lunch sector.

This means the angle is 90 degrees.

There are 360 degrees in a circle altogether, and 90 degrees is one quarter of 360 degrees.

One quarter is equal to 25%, so 25% of the children had packed lunch.

42% added to 25% is equal to 67%.

A hundred percent subtract 67% is equal to 33%.

33% of children chose pasta." Some great reasoning there.

Izzy creates another pie chart.

Pie chart sharing children's lunch choices on Tuesday.

Packed lunch, lasagna, burger.

What percentage of children chose lasagna? More than half of children chose lasagna, so I'm going to estimate 60% as the answer.

One quarter, or 25%, chose burger.

I'm going to measure the packed lunch sector using a protractor.

The sector measures 72 degrees.

This is one fifth, or 20% of the whole pie chart.

25% plus 20% is equal to 45%.

A hundred percent subtract 45% is equal to 55%.

55% of the children chose lasagna.

My estimate was pretty good.

There are 300 children in the school on Tuesday.

How many children chose each of the three options? Hmm.

Well, 25% of the children chose burger.

100% divided by four is equal to 25%.

300 divided by four is equal to 75.

75 children chose a burger.

20% had packed lunch.

A hundred divided by five is equal to 20%, so 300 divided by five is equal to 60.

60 children had packed lunch.

Let's add together 75 and 60, then subtract this from 300 to work out how many children chose lasagna.

75 plus 60 is equal to 135.

300 minus 135 is equal to 165.

165 children chose lasagna.

Let's check whether 55% of 300 is equal to 165." Good thinking, Izzy.

Always worth checking.

"50% of 300 equals 150, 5% of 300 equals 15, 150 plus 15 is equal to 165.

So 55% of 300 is equal to 165." Brilliant.

The answer is correct.

Okay, let's check your understanding then.

"Izzy creates another pie chart.

It's a pie chart showing children's lunch choices on Wednesday.

We've got pie, curry, packed lunch, and fish fingers.

What percentage of children chose each option though? I measured the pie sector using a protractor and got a measurement of 36 degrees." Okay, use that measurement to help you to fill in the rest of those statements that you can see underneath the pie chart.

Pause the video and give it a go.

Welcome back.

"One half or 50% chose curry." You can see that because it's half of the pie chart and it's a straight line.

The diameter is being shown.

"One quarter, or 25%, chose fish fingers." There's a right angle in there so you know that that's one quarter of the pie chart.

"36 degrees is one tenth or 10% of the whole pie chart.

10% of children chose pie.

50% plus 25% plus 10% is equal to 85%.

That means that 15% must have chosen packed lunch.

15% of children had packed lunch.

Ha-ha, the pie chart has pie on it." Okay, it's time for your second practise task then.

Tick the statements that are true.

Five children prefer Marmite, 50% of children prefer cheese, more children prefer Marmite to sausage, 10 children chose either egg or cheese.

This is a pie chart showing preferred sandwich fillings of 20 children with cheese, egg, marmite, and sausage.

Remember, the right angle shows that one quarter of children prefer Marmite.

A little clue there to help us out.

Here's number two then.

Using the same pie chart, can you use it to complete this table which has missing values for the percentage of children a number of children for each sandwich filling? Remember, Jacob says here's a clue.

"Twice as many children chose sausage as egg." For number three, we've got a different pie chart this time.

Pie chart showing preferred type of pie of 120 children.

We've got shepherd's pie, cheese and onion pie, minced pie, and apple pie.

You've got to fill in the missing values in the table again, which are percentage of children and number of children.

"5% more children chose apple pie than chose cheese and onion pie." That's a nice little clue from Sofia there.

Okay, pause the video here to have a go at those three questions.

Enjoy.

I'll be back in a little while with some feedback.

Welcome back.

Here's the answers for number one.

You should have ticked five children prefer Marmite, and more children prefer Marmite to sausage.

50% of children prefer cheese wasn't true, and you can see because the sector is less than half.

10 children chose either egg or cheese.

Well, that can't be true either because egg and cheese combined make up more than half of the pie chart, and half of 20 is 10 so those two combined must be more than 10.

Izzy says, "Less than 50% of children prefer cheese, but more than half chose cheese or egg." She summarised much better than I did.

Here's number two then.

Percentage of children reading down was 45% cheese, 10% egg, 25% Marmite, 20% sausage, and that meant nine children like cheese, two for egg, five for Marmite, and four for sausage.

"100% divided by 20 is equal to 5%.

Each child represents 5% of the chart.

Five multiplied by 5% is equal to 25%.

Twice as many children chose sausage as chose egg.

Four children said sausage and two children said egg." Okay, here's the answers for number three then.

Reading the percentage going down, we had 35% liked apple, 25% liked shepherd's pie, 30% liked cheese and onion, and 10% liked mince.

In terms of the number of children, it was 42 for apple, 30 for shepherd's pie, 36 for cheese and onion, and 12 for mince.

36 degrees is equal to 10% of the whole.

10% of 120 is equal to 12.

Apple and cheese and onion make up 65% of the answers.

30% plus 35% is equal to 65%.

Those were the answers then.

Take some time now if you need it to catch up with marking, or to make sure that you have got any misunderstandings sorted.

We've arrived at the end of the lesson then.

I really enjoyed that lesson.

I hope you did as well.

It's making me feel very hungry.

Here's a summary though of the things that we've learned.

A pie chart is a way of presenting data representing parts of a whole.

Pie charts can be interpreted using knowledge of angles.

Pie charts can be interpreted using knowledge of fractions and percentages.

My name is Mr. Taziman.

Maybe I'll see you again soon on another Maths lesson.

Bye for now.