# Lesson video

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Welcome to our seventh and final lesson in the percentage and statistics unit.

Today we'll be learning to interpret pie charts.

All you'll need is a pencil and piece of paper.

So pause the video now and get your equipment together.

So here's our agenda for today's learning.

Then we'll look at what pay charts tell us, we'll assign values to pie charts before you do some independent learning and then a final quiz.

So here's our first pie chart to interpret.

The pie chart shows the nationality of the astronauts on board the International Space Station in January, 2017.

So I want you to think first of all, what can you say about this pie chart? Pause the video now and make some notes.

So here are some things that you may have gathered from the pie chart so far.

The majority of the astronauts are from Russia so the orange section, if you use the key at the bottom, the orange section represents Russian astronauts so we can see that this is the largest section therefore this represents the majority.

And the French astronauts are in the minority so the purple section represents astronauts from France, and this is the smallest section.

And then half of the astronauts are Russian.

And we can see that because the pie chart is split exactly in half and one whole half of it are representing Russian astronauts and the other half are either American in the blue section or French.

But let's look at this statement, 50% of astronauts on the ISS are Russian.

How do we know that 50% are Russian? Well, if we look at the pie chart, the segment, the Russian segment is half of the whole chart, and we know that half is equivalent to 50%.

So again, we're always linking back our fractions and percentages together.

Now here's our next statement.

There are more astronauts from the USA than there are from France.

And how do we know that this is true? Well, we can see that the segment of the pie chart representing astronauts from the USA, the blue section is greater than the segment representing the French astronauts, the purple section.

And actually, if we look a little bit closer, we can see that this USA section is approximately double the size of the French segment of the pie chart.

Now here's another pie chart for us to look at.

This one shows us the gender of the astronauts aboard the International Space Station in January, 2017.

So the blue section represents the male astronauts and the red section represents the female astronauts.

So I want you to think now about these two questions.

What does the pie chart tell us and what does it not tell us? Pause the video now to make some notes.

So what the pie chart does tell us is the gender of the astronauts, but it doesn't tell us much more than that.

So it doesn't tell us how many astronauts are on board the ISS, therefore we don't know how many are men and how many are women.

And it doesn't show us the gender in relation to the nationality, it's like we saw on the last pie chart.

So it only tells us one aspect of this group of astronauts on the ISS.

Let's go back to our previous pie chart.

So this one is showing us the nationalities of the astronauts on the ISS.

We're going to now assign some numbers to the pie chart, to estimate how many astronauts of each nationality there were.

So first of all, I'm going to annotate the pie chart to help us think about the American and French half.

So I'm going to put some lines across to help me to understand approximately how many American and French astronauts there were.

So what we can see is that approximately one sixth of the astronauts were French and two sixths or one third were American and three sixths or one half were Russian.

So we can assign these fractions, these are approximate fractions to the pie chart to help us deal with the numbers that are coming.

So, if the total number of astronauts is 60, how many of are there of each nationality? So we'll start off with Russian.

So half of those 60 astronauts were Russian.

So half of 60 is equal to 30.

Then we'll go to America.

A third of those 60 are American, a third of 60 is 20.

Remember that 60 divided into three equal parts.

And the six of those astronauts were French.

So a sixth of 30 is equal to 10.

So if there were fixed the astronauts on board, this would be the number of each different nationality.

And what you can also see is that if I add these back together, 30 plus 20 plus 10, it equals to 60, which is the whole.

So a quick way of just checking that you've worked out these fractions correctly is to add up your resulting numbers and make sure they still equal to the whole.

So now it's your turn, I would like you to think about what if there were 300 astronauts on board and what if there were 12 astronauts on board? What would be the number of each nationality? Pause the video now and do some calculations.

So if the total number of astronauts was 300, then if we look at the section of French astronauts, we know that that represents one sixth of the whole, one sixth of 300 is equal to 50.

Then if we look at the Russian section, that's one half of 300, which is equal to 150.

And the American section is a third of 300, which is equal to 100.

And again, we just go back and check 50 plus 150 plus 100 is equal to 300.

Onto the next one.

If there were 12 astronauts, the French section is a sixth of 12, which is 12 divided by six, which is equal to two.

The Russian section, a half of 12, which is equal to six.

And the American section, a third of 12, which is equal to four.

Two plus six is eight plus four is equal to 12.

Now we're going to think about what if we were given the number of only one nationality and how can we use that to work out the numbers of the other nationalities? So what we'll be able to do is to use it to work out the whole, and then we'll be able to work out the rest of them.

So in my first example, there are 75 Russian astronauts.

So then we know that if half of them are Russian, then the whole is double 75.

So the whole is 150.

So we can find a sixth of 150, and then a third of 150.

The other way we can look at it is to look at the relationship between the fractions.

So we're sixth is a third of a half.

So you can see here that a sixth, one sixth is equal to a third of a half of the whole.

So I can find a third of a half of the total and that's 75 because a half are Russian and we know that 75 are Russian astronauts.

So we can find a third of 75 to find the number of French astronauts, which is equal to 25.

And then I also know if I look at the American section, then I know that two thirds of a half is equal to one third.

So I'm looking to find two thirds of the half which is 75 to find the number of American astronauts, or I can double the number of French astronauts because I know that the number of Americans is double the number of French, and that will give me 50 astronauts.

And then we just check it, 50 and 25 is equal to 75.

So 75 on this half and 75 on this half, that's 150 astronauts all together.

So now I'd like you to think about these two scenarios.

If there are 27 French astronauts, how many American and Russian astronauts are there.

And then if there are 44 American astronauts, how many French and Russian astronauts? Pause the video now and do some calculations? So if we know that there are 27 French astronauts, we know that there are double that number of American astronauts.

So there are 54 American astronauts, and we know that the French and American added together gives us the number of Russian astronauts, which is 81.

Onto the next one.

There are 44 American astronauts.

So we know that the French astronauts represent half of that number.

So the French astronauts, there are 22 French astronauts.

And then we know that the Russian astronauts are the number of French plus American astronauts, 44 plus 22 is equal to 66.

So now we're going to look at one final pie chart before you move on to some independent learning.

This one represents the number of astronauts sent to space each decade.

And that key helps us to understand it.

So the dark blue is representing the 1960s, and then it goes around clockwise up to the 2010s.

If I add some annotations onto my pie chart, I can see some approximate fractions here.

So I can see that the 1980s represents approximately one quarter of the pie chart as does the year to the decade of the 2000s.

I can also see that the 2010s, the 1960s and the 1970s together represent approximately a quarter of the pie chart.

So each of them represents a third of a quarter, which is a 12th of the pie chart.

I can also see that the 1990s represents the biggest section of the pie chart.

So the most astronauts were sent to space in the 1990s.

So now we're just going to do some approximation.

So if we think if there were 547 astronauts in total, approximately how many people went to space in the 1980s.

So we see that this represents approximately a quarter of the whole of the pie chart.

So we could find a quarter of the total by dividing 547 by four.

And as I'm creating an approximate answer, I could just use my number sense to round this to 548, to the nearest multiple of four.

And then I can have it twice to divide it by four so that tells me approximately 138 astronauts went to space in the 1980s.

So let's also look at the 1970s, approximately how many people went to space then? Well, we said that this section represents approximately a third of a quarter of the pie chart.

And a third of a quarter is equal to one twelfth of the total pie chart.

So we could work out by finding a 12th of 547 by dividing it by 12.

So as you're looking to find approximate values for your pie chart, make sure you do some annotations to find the approximate fraction of each section.

Now it's time for you to complete some independent learning.

So pause the video and complete the tasks and then click restart once you're finished.

So your first pie chart represented pets owned by 150 people.

And you were asked to identify the statements that were true and then rewrite the ones that were false.

So the first one says approximately 40% of people own a dog.

So the dog is represented by the red section, but I can see that if I drew some lines to annotate this pie chart, this actually represents more like a quarter of the people and a quarter of the whole would be 25%.

The next one, approximately a third of people own a cat.

So the cat is this dark blue section.

And if I did some annotations on that, I can see that that does represent approximately a third of the pie chart, so I say that's true.

About 10% of people either own a hamster or a lizard.

So if I look at hamster and lizard together, I can see that that actually represents approximately a quarter of the pie chart, so I would say that was false, 25%.

Approximately 75 people own a cat, so the cat section, we said represented a third and a third of 150 is 50.

So I would say that that was false.

One person owns a lizard, this is false because this is approximately one 16th of the whole pie chart because it's approximately a quarter of a quarter and that would be nine people.

Twice as many people own a dog than fish.

So if I look at the dog, the red section, the fish is this light blue section, I would say that this is approximately double this area so I'd say that it's true.

On to question two, an ice cream still sells vanilla, strawberry and chocolate ice creams. The pie chart illustrates the sales of ice cream today.

The number of vanilla and the number of chocolate ice cream sold were the same.

The stall sold 60 strawberry ice creams. So how many chocolate ice creams were sold? So we can see that strawberry represents 25% of the whole and therefore vanilla and chocolate represents 75% of the whole.

If 25% is 60, because 60 strawberry ice creams were sold, then 75% is three times 25%, which is equal to 180, but chocolate represents only half of that amount because these two chocolate and vanilla represents equal amounts.

So we would divide 180 by two to give us 90 chocolate ice cream sold.

In your third question, this represents a survey of people that were asked whether they believed that life could be found beyond earth and in which locations so we've got The Moon, Mars, Venus, Neptune, and then the section of people that believe there's no life beyond earth.

And I added some guidelines to help me and this actually, the way I have split it up has split it into tenths, okay? So 10 people believe that life could be found on The Moon.

So we're going to use this information to approximate the number of people in the survey.

So The Moon that's this dark blue section, represents 10 people.

So this section is two tenths or one fifth of the number of people.

So one fifth of the number think that life could be found on The Moon.

And we know that that is representing 10 people.

So if we multiply that by five, that gives us five fifths or the whole, which means that 50 people were asked in total.

In question four you had a pie chart to show how the children in class 6 like their potatoes cooked.

So we know that 32 children took part in the survey.

Then you were asked to put a tick if the statement was correct and a cross if it's incorrect.

So actually I've further annotated the pie chart with some fractions so I can see that jacket potatoes represents three eights of the choices, chips represents two eights or one quarter's, mashed potatoes, also two eights or one quarter and roast potatoes, an eighth of people like the best.

That's my favourite, I can't believe only an eight like roast potatoes.

So let's go to our statements.

The first one, 10 children liked chips the best.

Well, we know that 32 children took part in the survey and we know that a quarter like chips.

So if we think of a quarter of 32, that is equal to eight, so this must be false because this is 10 children but it's actually only eight children.

So the first one is false.

The second one, 25% of the children like mashed potatoes the best.

That's true because we know that it's a quarter of the whole and a quarter is equal to 25%.

The third one, a fifth of the children like roast potatoes best.

We'd already prepared this answer, it's actually equal to an eighth of the children so that's false.

And the final one, 12 children like jacket potatoes the best.

Well, if we think about what is three eights of 32, one eighth of 32 is four, so three eight is equal to 12 so this one is true as well.

Well done for your hard work today.

I'm looking forward to seeing you in our next lesson.

Before you go, make sure you complete your final quiz.