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Hi Year 6, this is our fifth lesson in the percentage and statistics unit.

Today we'll be learning to interpret line graphs.

All you'll need as always is a pencil and a piece of paper, so get your things together if you haven't done so already.

Here's our agenda for today's learning.

So we're looking at interpreting line graphs.

You'll start with a quiz to test your knowledge from our previous lesson.

Then we'll look at discrete data, then cumulative data, before you do some independent learning and a final quiz.

So lets start with our initial knowledge.

Pause the video now and complete the quiz and click restart once you're finished.

So your first job is to have a look at this graph and think about what it might show and what you can tell from the data.

So pause the video now and write down some ideas.

So these are some of the ideas that you may have had.

The graph is showing us the amount of something from 1960, all the way up to 2016.

And its showing you one pice of data per year and I can tell that because the data points are evenly spread, there's an equal distance between them.

And for over a decade there are 10 data points.

It's also telling me that it begins in 1960 and ends in 2016, whatever the data is.

The highest value of the data is approximately 38, so this is the highest point in the graph.

And if I used a ruler to go along to the y-axis, I would see that it's approximately at 38.

And the lowest value is at 0, and we've got that at 1960 and we've also got it in 1967.

And I know its '67 because then it's '68, '69 and then 1970.

And the data has been collected annually as I mentioned before, annually meaning every year.

Because there are 10 data points in a decade, a decade being 10 years, so I've got one, two, three, four, five, six, seven, eight, nine, 10.

And then I start the new decade with another 10.

Now we can tell all of these things from the graph, but we can't actually tell what it is talking about.

We need a little bit more information.

So lets add some more information.

So here our title shows that this graph shows the number of astronauts sent to space each year.

And then along the bottom we have the x-axis labelled 'Year' and the y-axis labelled the 'Number'.

So, thinking back to when we did coordinates, we've got the same vocabulary and it just means the same thing.

They've got the axes, which is the plural of axis.

The x-axis is going across, along the bottom there, and the y-axis is going up the side.

And then we have data in our graph which has been plotted, or drawn at different points, and these are our data points.

And as with coordinates, we would read our graph along the x-axis and then up, if we were looking for years.

But unlike coordinates, if we wanted to look for specific numbers, then we would read up the x-axis first and then across.

And this will make more sense as we start to explore the graph further.

So lets answer some questions about the graph.

First of all, before we go straight to the questions, we'll just talk through what we notice about the graph in general.

So, what we can is that in this year, 1985, we've got the greatest number of astronauts sent to space.

And we know this because it's the point of the line graph which has the highest value.

And then, if we go across to the y-axis, that's where we see that its that it's approximately 38.

And as we mentioned earlier, in 1960 and in 1967, no astronauts were sent to space.

Because on the y-axis we can see that that is at zero, okay? So lets start to look at the questions now.

So the first question we have to answer is, approximately how many astronauts went to space in 1970? So in this case, we're going along the x-axis first to 1970, and then we go up the y-axis to see where that approximately reaches.

Now if you are looking at a graph that you have in front of you, the best way to look at it is using a ruler.

So to draw a line up to 1970 and then a line across to your y-axis.

And we can see that it's approximately three people that went to space in that time.

Now I want you to have a go at the next question.

Approximately how many astronauts went to space in 1990? So pause the video, and if you have it on the screen in front of you, go along to 1990 and then have a look on the y-axis approximately the number of astronauts that went to space then.

Pause the video now.

So we can see, if we go along to 1990, and we go up the y-axis here, we can see that this is the data point that we're looking at.

So if we took a ruler along to the y-axis, we can see that that's approximately 17 people.

Let's look at another question.

On average, how many astronauts went to space each year, between 2000 and 2009? Now, we're thinking about averages, we think back to our previous lesson where we were calculating the mean.

What we need to do is have a look at what the data point value is for each of those points, add them together, and then we're going to divide them by 10 because there are 10 data points.

So I've written them out here, so I'll just go through these very quickly.

In 2000, this is our data point, and if we go across to the y-axis, that's about seven people.

So that's why I've got seven there.

2001, if we went across to our y-axis, that's about 12, and so on, all the way up to 2009.

And you can see that 2008 and 2009 are the same, both 22.

And in fact, you can see that 2003, 2004 and 2005, they had the same number which was five people.

So all of those data points added together and divided by 10 will give us the average number of astronauts that went to space between those years.

So that's 119, and we divide that by 10, to give us 11.

9.

Obviously you can't have 11.

9 of a pers- well you can't have 0.

9 of a person, so we need to round it to the nearest whole number, which is 12.

So, if you are answering a question concerned with things like people or animals or something like that that can't be divided into decimals, you need to round to the nearest whole number.

Now you're going to have a look at this graph independently and answer a question about it, but before we do we'll just have a quick look through it together.

So on our x-axis we have the months, it doesn't go up in jumps of one month, so be careful there.

And up the side, up the y-axis I should say, we have the time in minutes, okay? And this data line, although you can't see the actual data points, you can see the line that shows us the number of minutes.

And you're going to use this graph to sort these statements into two piles.

Questions that can be answered using the graph and questions that cannot be answered using the graph.

If you can answer it then do, and if you can't, think about why you can't.

Pause the video now and sort the statements.

So this is how your statements should've been sorted.

So we'll start of with the 'Can be answered'.

There are approximately ___ minutes of daylight in February.

That can be answered because we can find February on the graph, it's halfway between January and March.

And we can find that actual piece of data.

___ has the greatest number of minutes of daylight.

We can look at where's the highest point on the graph, in terms of minutes, so we can answer that with an actual number.

And true or false, all months have more than eight hours of daylight.

Again, we can look at the graph and find the data to answer the question, and we will do so in a minute.

Let's look at the ones that can't be answered.

___ is the hottest month of the year.

Well this graph has absolutely nothing to do with temperature.

So we can kind of guess maybe, one of the summer months, but it wouldn't be a factual answer, this is just concerned about time.

And there are ___ days in March.

You know how many days there are in March, but the graph doesn't tell us, and that we're asking, "Can you tell this from the graph?' So that one cannot be answered by the graph.

Now let's go through and answer these questions.

So how many minutes of daylight approximately, are there in February? So you will have gone along to February and up the graph and then back along to the y-axis, and that tells us that there are approximately 600 minutes of daylight in February.

Which day has the greatest number of minutes of daylight? We're looking for the peak of the graph, and we can see that that is in July.

And then all months have more than eight hours of daylight.

Well we need to use our conversion, so eight hours is 480 minutes, that's 8 x 60 minutes.

And then if we go to 480 minutes on here, we can see that halfway here is 500, so it's slightly below.

And it's not really clear, we would need a more detailed scale.

It's probably true, but January might have a bit less than 480, but we can't really tell because the scale is not detailed enough.

So, I think that that's a bit of a tricky question to answer with this type of graph.

So now, we're going to look at a different type of graph, and this is called a cumulative graph with cumulative data.

So this is the same information as shown on the last astronaut graph, okay.

And I want you to think about what is the same and what is different about both of these graphs.

So pause the video now and make some notes.

So both of the graphs, they show data between 1960 and 2016.

So we have the same timescale of data.

And they both have the same data.

And we'll talk more about this in a minute.

What's different though, is that on the y-axis the scale only is going up much higher than it did in the previous graph.

Because what is happening in this graph, is it's giving us a running total of the cumulative number of astronauts in space, ever.

Now I'm going to put both graphs next to each other to help us to understand this.

So we can see that between, we'll focus in, on this first decade between 1960 and 1970.

We can see that this, this is the approximate number of people that went to space in each year, using the first graph.

So in total, that's approximately 49 astronauts.

Now if we look at the second graph, then we can see on graph B, that those numbers have been added together to show the number of astronauts in total, that were sent to space by 1970.

So if we go to 1970 and we draw a line up, then we go across to our y-axis, we can see that that is around 49, it's about halfway between zero and 100.

So it's approximately showing us 49 astronauts.

So what this graph is doing, is this is adding the numbers building on each other giving us cumulative data, whereas the first graph is giving us discrete data, which is stand-alone data points for each year.

Now let's have a look at another cumulative graph.

This is Fatma's journey for a 24 hour charity walk.

So we'll look at what this graph shows.

Along the x-axis, we can see the time that has passed in hours.

And up the y-axis, we can see the kilometres that have been walked.

So you can see as we go across the x-axis, as time passes, the distance increases.

So as she- the more time that passes by, the further she walks.

Now if we just zoom in on some different parts, if we look at 12 hours then we draw a line up to the data line, we can see that at 12 hours, she has walked around eight kilometres.

Let's have a look at how far she walked in total.

How far up does it go in terms of kilometres.

We can see that she walked 22 kilometres altogether.

And if we go down the line, we know that that took 24 hours and that's because it's a 24 hour walk.

So she walked 22 kilometres in 24 hours, and in her first half she walked eight kilometres, so that means in her second half she walked 14 kilometres.

So she walked further in the second part of her walk.

Now we're going to zoom in on a specific part of the graph.

So we're looking at the part between the two red lines.

And I'd like you to have a think about this.

What is happening at the part of the graph between the two red lines? So we can see that time is passing, so it's gone from six hours to 10 hours, so that's four hours of time has passed.

But the distance has stayed the same.

It hasn't increased, it's static.

That means that Fatma is not moving.

So it's at five kilometres, and she stays having only walked five kilometres for those four hours on the graph.

So she's stationary.

And have a look on the graph.

Can you see any other points at which she is stationary? So yeah, up here between hour 16 and hour 18, again she's static at 14 kilometres.

And that's why the line on the graph is flat there.

What might be happening here, why might she be static? What could be going on in her journey? Maybe she's stopping for a rest, or she's stopping to have lunch.

So let's have a look at another part of the journey.

Now we're going to think about, between which of these two sets of lines did she walk the furthest? So we're going to do the first red section together.

And then you will answer the purple section.

So if we look at the red section, okay, this is at two hours.

And we can see that at two hours, by the time it was two hours into her walk she'd walked two kilometres.

Then we're looking up to six hours, and if we go up the y-axis here, we can see that she had walked five kilometres by the time six hours came around.

So we're looking at the distance, difference sorry, between five kilometres and two kilometres, which is equal to three kilometres.

And we know this because her distance increased from two kilometres to five kilometres.

Now I'd like you to do the same for the purple section and you've got a sentence structure below to help you.

So, we're looking at the purple section and we can see that this is the 10th hour, so between hour 10 and the 14th hour, so between hour 10 and hour 14, and we need to think about how far she's walked.

So, at hour 10 she was on five kilometres.

By hour 14, she was on approximately 11 kilometres, which tells us that she had walked six kilometres because the difference between five and 11 is six.

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

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

So for question one, you were given three graphs and asked to match them to two different stories, and each of the graphs shows time on the x-axis and distance from home on the y-axis.

So the first story says, "I was on my way to school when I felt unwell, so I turned around and went home." so if I'm on my way to school, I'm getting further away from home, but then if I turn around to come home, then I'm going to get closer to home.

So looking at graph A, let's have a look.

The time passes by and I get further from school, then I'm stationary for a little bit, so maybe I go into the shop.

And then time carries on passing by and I continue to become further away from home.

So it's not going to be this one.

Let's have a look at the next one.

Time is passing by and I am steadily getting further and further away from home.

So I'm walking at a constant speed, it's not this one.

The last one, time passes by, I get further from home.

But then, as time continues to pass by, I then get closer to home, without a pause, so that must've been a quick turnaround to come back home.

So Story A much match to this graph.

Story B, I travelled to school at the same speed and I didn't stop until I got there.

Now, we can see from this one that the flat part of the line shows that they are stationary, and this one is a constant speed, so it must be that one.

For question two, you have got a graph showing the volume of water in a bath.

Time going along the bottom, the x-axis.

And the volume of water in litres up the y-axis.

And it's always worth, before even looking at the questions, just to get your head around what the graph is showing.

So, the bath starts to be filled at six o'clock, 6:00pm.

And then we can see that it's being filled at a pretty steady speed.

Then it seems to be slowing down, and then it's a flat level, so it's the same constant level for a section.

Then it's filled up a bit more, and then another constant level.

And then as it's going down, the volume is becoming smaller.

That must be the bath emptying.

And finally, completely empty by 7:50pm, which is an hour and fifty minutes later, which is a very long bath, if you ask me.

And I think, we can also think about our knowledge of baths.

So, it could be being filled up, then a person got into the bath.

They sat in the bath for a little bit, maybe it was getting a bit cold so they added a bit more water.

And then they turned the tap off for a while and then they got bored and got out of the bath.

So now we've got a general idea of what the graph is showing.

Now it's time to approach the questions.

So at what time did the bath reach its highest level of water? We look up to see, up the y-axis, to see when it gets to its highest point.

The first time it's at its highest point is here.

And that is at about 19:10 or ten past seven.

And if I had the graph in front of me I would be drawing a line up using a ruler, and across the y-axis.

Estimate the volume of water in the bath at 6:45pm.

So 6:45pm is 18:45 so it's going to be halfway between 18:40 and 18:50.

So I'll draw a line up there using my ruler and then across to the y-axis, so I can see that's approximately 73 litres.

You can have anything, probably, from 72 to 74 and you still get the mark for that.

For C, how much did the volume of water increase between 6:10pm and 6:20pm, so 18:10 and 18:20.

At 18:10 the volume of water is 20 litres.

At, so I've written that there, at 6:10pm or 18:10 it's approximately 20 litres.

And then at 18:20 or 6:20pm I've drawn my lines up using my ruler, it's approximately 43 litres.

So the increase is approximately 23 litres.

So that's 43 subtract 20.

And finally, how long did it take for the bath to empty? So, we talked about here, being the point at which it starts to decrease the volume.

So I've drawn some lines to show starting to empty, and then fully empty, and we can see that's between 19:20 or 7:20pm, and 19:50, and that is 30 minutes.

Then we're back to our astronaut graph.

And we've already gone through this and we've got a good general idea of what's going on in the graph.

So we'll go straight to the questions.

Approximately how many astronauts were sent to space in 2010? So I'm drawing my line up to 2010 and across to the y-axis and I see that's approximately nine astronauts.

How many were sent between 1990 and 1999? So I've added up all of the values between 1990 and 1999.

And they're all approximate, so you might be slightly above or slightly below than me because it's difficult with this scale, you don't have enough lines on to be really accurate in this case.

Now, in which year were approximately 17 astronauts sent to space? This is one of those where you need to go up the y-axis first and then along.

So I'm going to approximately 17, I've drawn a line across.

And I'm looking at where different data points hit that line.

So I can see that there's one here, and I can draw my line down and then again, draw my lines down as I go, and I can see that there approximate- there are four years in which 17 astronauts were sent to space.

And they are 1983, 1990, 1995 and 2002.

And then finally, what can you say about the general trend of the graph? So this is just a general comment on what is generally happening as the years pass by.

So we can see that we've got a peak in 1985.

And then after 1985 we actually have a steady decrease in the number of astronauts being sent to space.

Your next graph is Metila's 10k run.

So we've got the time in minutes along the x-axis and the distance in kilometres up the y-axis.

And this one we have got some more lines on to help us be more accurate with the data.

So for the first one, you were asked to fill in the table to complete the missing times.

So by four kilometres how far had she run? So I have a line drawn along from four and down to the x-axis, and I know that this is going up in jumps of two minutes.

So this is halfway between 20 and 22, so that's 21 minutes.

And then the eight kilometres, so I have a line drawn across from eight and down.

Going up in two's, that must be 42.

My last question is, how long did Metila take to run from the four kilometre mark to the end of the race? So we know at four km, she was at, it was 21 minutes by the time she had run four km.

And then her final time to run the whole race is, you can see in the table, 55 minutes, we'll check.

We go along and down and it's halfway between 54 and 56.

So it's the difference between 55 minutes and 21 minutes which is equal to 34 minutes in total.

Now it's time for your final quiz.

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

Excellent work today Year 6.

In our next lesson, we'll be constructing line graphs, so it would be really helpful if you had a ruler and a piece of graph paper or square paper like your maths book to help you with that lesson.

I'll see you then.