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Hi there, welcome to our sixth lesson in the percentage and statistics topic.

Today we'll be learning to construct line graphs.

You'll need a pencil, ruler and a piece of paper.

And if you can get hold of grid paper, or line paper, that will be really helpful for today's lesson.

So pause the video now and get your things together.

Here's our agenda for today's learning.

So you'll be constructing line graphs beginning with a quiz to test your knowledge from our previous lesson.

Then you'll look at drawing line graphs using discrete data, then cumulative data, and then you'll do some independent learning.

So begin with your knowledge quiz.

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

So we'll jump straight in to drawing line graphs using discrete data.

So here we have a table of data and it shows the length of a shadow which has been recorded at different times of the day.

And we're going to show this information using a line graph.

So if we just first of all, get our head around the data, we've got this first column telling us the time of the day.

And then the second column telling us the length of the shadow in centimetres.

So at 6:00 am the length of the shadow is 170 centimetres.

At 9:00 am, it's 45 centimetres.

At 12 noon, it's 20 centimetres.

At 3:00 pm, 45 centimetres, and 6:00 pm, it's at 170 centimetres.

So you can see that the bits of data have been recorded in intervals of three hours.

So that will be reflected in our graph.

So the first thing that we need to do is to draw a set of axes.

So here we've got along the bottom, we've got the x axis and up the side the vertical one is our y axis and they're perpendicular to one another, so they meet at a right angle in the bottom corner there.

Then it's really important to label your axes so that you know what each of them represents.

So here I've put time on the x axis, and the length of the shadow on the y axis.

And it's always really important to put your units as well.

So I've put the length of the shadow, and put the units in brackets, which is centimetres.

So then we need to look at an appropriate scale.

So if we look at the scale that I've put on here at the side, where I've put the scale is going up and jumps or intervals of 50 centimetres, we need to think about whether this is an appropriate scale to represent this data.

So let's look at the greatest value on the data, which is 170 centimetres.

So the scale needs to reflect this.

So it needs to allow for up to 170 centimetres to be recorded, which it does.

But the only problem with this scale is that the intervals are extremely close together.

So then the points that we would plot would be extremely close together.

We have to look at, we've got 20 and 45.

We're going to have to plot these underneath the 50 line.

And it will be really difficult to get an accurate reading from the graph, which means it would be really difficult to interpret.

So this is not an appropriate scale.

So let's keep working to find a better one.

Now on this one, my scale is going up in intervals between the thicker lines of 10, which means that each of these five intervals up to it represents two centimetres, two, four, six, eight, 10 centimetres.

So we know that we'll get a graph that will be easier to interpret because the scale is larger, but let's check whether this will be appropriate for our data.

So we know that we are looking at a maximum length of 170 centimetres.

So that only goes up to 40.

So we're not going to be able to record this on this graph.

And if we did go up in this scale, we would have to go up extremely high, and it will be a very tall graph, and it wouldn't be very practical.

So this scale is not going to work.

Let's look at one that will work.

So here I've got the scale, which is going up in fifties, and I know that it will encompass this 170 centimetres because it goes up to 200 centimetres.

And then each of these lines are slightly thicker lines in between represents 10 centimetres.

So I can be much more accurate.

And the reason this is on different papers, just to show you that graph paper looks different.

Sometimes it's one centimetre square, and sometimes each small square represents one millimetre.

So just so that you can see different types of graph paper.

So here we have the appropriate scale for our graph, and we have our axes drawn accurately.

I've got the time of the day at equal intervals.

It's really important that they're equally spread, so that distance is equal.

And then I've also put a title on my graph to show exactly what it is showing us, what the data actually means.

So we're now at the point where we're ready to plot some data.

So the first bit of data is at 6:00 am and the shadow length is 170 centimetres.

So what I want to do in order to be accurate is use a ruler to draw a line up from 6:00 am.

So now you can see that my line has appeared up from 6:00 am, and then I'm going to turn my ruler around and draw a line across from 170 centimetres.

And my point will be plotted at the point at which these two lines intersect.

So you can see that that's where my point is going to be at 6:00 am and 170 centimetres.

And I've used my ruler so that I can be more accurate, and then I'll take those away.

So that as we continue to plot the graph, it doesn't get really messy.

So the next one is 9:00 am and 45 centimetres.

So a line up from 9:00 am doesn't need to go all the way up to the top.

It needs to go roughly around where it is that I'm going to be plotting my next line, which is across from 45.

And then my point is plotted where the lines intersect.

And now I've carefully plotted the rest of my points.

And you can see that I've got one at 12 noon, which is at 20 centimetres.

One at 3:00 pm, which is at 45 centimetres.

So that's inline with the other 45 centimetre line, and then one at 6:00 pm, and that is at 170 centimetres.

So it's in line with the one at 6:00 am.

And then I'm going to join my points with a line so that I can clearly see how the graph, and how the data has changed across the day.

And now I'm going to use this data to answer some questions.

So here's the first question.

What does the line graph tell us about the length of the shadow across the day? Well, I can see that the length of the shadow starts longer then it becomes shorter as we get towards lunchtime.

And then it goes after 12 noon, it gradually becomes longer again, to then be the same length as it was at the point at which the data started to be collected.

So it starts off long, shortens at 12:00 pm, and then lengthens after 12:00 pm.

At what time was the shadow shortest? So we're looking on the y axis and we're seeing what point is it lowest on the y axis.

And that is this point here where it was 20 centimetres, and that is at 12 noon.

And that's when the sun is at the highest point.

So that's why the shadow is the shortest.

Now here's an example of a question that you couldn't answer using the data and the table.

You needed it to be in the graph.

So here we're being asked, what was the approximate length of the shadow at 10:00 am.

So here I need to draw a line up from 10 o'clock.

Remember these are in intervals of three hours, and I've left three intervals between, so each of these ones in between represents one hour.

So I've gone up at 10 o'clock and then across the y axis, and I can see that that's approximately 35 centimetres, and I would not have been able to draw that conclusion, looking at the data in the table, not as accurately as using the line graph.

So now we're going to use cumulative data to construct a line graph.

So here we've got a description of a car journey.

And what I would like you to do is to take the information from the description and put it into the table.

So I'm going to read it through, and you can think about trying to fill in this table as I read.

So this is Tom's car journey.

So he had a great start.

He left at 9:00 am and in the first hour he managed to travel 60 kilometres.

So what we'll do is we'll do this one together.

So in the first hour, by 10:00 am, he had travelled 60 kilometres.

Unfortunately the traffic from 10:00 am for two hours meant that he only travelled further 25 kilometres.

So have a think about by 12 o'clock, by 12:00 pm, he travelled a further 25 kilometres.

How far would he have travelled altogether so far? And then at mid day, at 12:00 pm, he stopped for lunch for an hour before carrying on.

So how much distance would be travelled during this lunch hour? He then travelled 35 kilometres an hour for the next three hours, stopped for an hour and a half for another break.

And then in the final hour of his journey travelled 45 kilometres.

So pause the video now and try and complete the rest of the table.

So, as we said between 10:00 am and 12:00 pm, he only travelled two hours.

I'm sorry, not two hours.

He only travelled 25 kilometres, and that's 25 kilometres further than the initial 60 kilometres.

So when we come to do this in our graph, this will actually be up to 85 kilometres that he's travelled.

Then at mid day he stopped for lunch or an hour, which means that he didn't travel any distance at all.

Then between one and four.

So for those three hours, he travelled 35 kilometres an hour.

So three lots of 35.

So he travelled 105 kilometres in that space of time.

Then he had another break.

So he didn't travel any distance at all.

And then the final hour was another 45 kilometres.

So when we look at this in our line graph, we're going to be recording this cumulatively.

So we're going to be adding the data as we go along.

So before moving on to construct the line graph, it's important to really have your head around what the data is telling you.

So what I would like you to do now is to pause the video, and have a go at answering these three questions using the data in the table.

So for question one, how long did Tom stop for in total? You're looking at these two periods of time where he stopped for lunch for an hour, and then he stopped for a break between 4:00 and 5:30 for an hour and a half.

So he stopped in total for two hours and 30 minutes.

How far did he travel altogether? That was the case of adding up all of these different distances.

So 60 kilometres, 25, 105 and 45, which means that altogether he travelled 235 kilometres.

So this tells us, this helps us with the scale of the graph, because we know that it needs to go up to 235 kilometres.

And how long was Tom's journey in total? So how long did it take for him to, from the minute he set off up until when he arrived? So it's 9:00 am to 6:30 pm.

So it was nine hours and 30 minutes.

So now I would like you to use the information given, to try and construct a set of axes to represent this data.

So you need to think about what intervals you should use, and remember that the x axis needs intervals from 9:00 am until 6:30 pm.

And then the y axis, which is the distance will need to go up to 235 kilometres.

So pause the video now, and have a go at constructing the axes.

So here is a scale that you could have used.

What I've done here is I've gone up in intervals of 75 kilometres.

And then if I look at the smaller intervals, there's five intervals up to the initial 75 kilometres.

And that means that they are going up in jumps of 15 kilometres because 75 divided by five is equal to 15.

And then I've plotted the hours along the bottom.

And I've actually put on every hour that even though we don't actually need them all, I think it's important to show a clear representation of the data with equal intervals.

So what we'll do is we'll plot the first two points together, and then you'll do the rest independently.

So we'll go to the first one.

The first point we're going to plot will be at 10:00 am because at 9:00 am he hadn't travelled any distance, but at 10:00 am he had travelled 60 kilometres.

So that's where our first point will be plotted.

So 10:00 am and 60 kilometres.

Remember this is going up in fifteens, 15, 30, 45, 60.

So that's our first point.

The second one will be at 12:00 pm where he's travelled a further 25 kilometres.

Remember it's 60 plus 25 here, which means that he will have travelled 85 kilometres in total.

So up from 12:00 pm to 85 kilometres, there's my next point plotted.

Now if you're feeling confident to continue plotting your points, then pause the video and do so now, if not, just keep watching as I do the rest of the points.

So we've got our next one where he stopped for lunch.

So at 1:00 pm we're still at 85 kilometres.

So that is on the same line as the one at 12:00 pm because he hasn't travelled any further, which means that he's stationary.

Then the next point is going to be at four o'clock, and that's 105 kilometres further than the initial 85.

So we plot this point here, 85 plus 105 is 190 kilometres.

So that's where we're up to there.

Then he stopped for a break.

So we'll put 5:30 is our next point, which is the end of his break, which means that he didn't travel any further at all.

And then the last part is a further 45 kilometres on from this 190, which takes us to 235 kilometres.

And then we can join our power points with a ruler so that we can see our clear line, and we can interpret further information from the graph.

So we can just see some things to quickly look at our two horizontal parts of the line means that he was stationary.

So they represent his breaks.

And then we'll answer some questions about the graph.

So the first question.

At what points did Tom not to move, and how does the graph show this? Well, we've just talked about this.

He doesn't move between 12:00 and 1:00 pm, and it shows that because it's a horizontal line on the graph.

So it doesn't go any further up the y axis.

And again, between 4:00 pm and 5:30 pm.

And then the second question, what can you say about how far Tom travelled between 10:00 am and 12 noon compared to two o'clock and four o'clock pm? And how does the graph show this? So if we have a look first of all at 10:00 am and 12 o'clock, we're looking at the distance here between these two points, and then we're looking at between two o'clock here.

I know here, sorry, two o'clock and four o'clock on the graph.

So we need to talk about the comparison of how far he's travelled.

And what we can say is that these are both intervals of two hours, but we can see that this line here between two and four is much steeper than the line between 10 and 12, which tells us that he travelled further in the time between two and four.

And he travelled less distance between 10 and 12.

And it is the steepness of the line that helps you to see that on the graph.

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

So you're going to construct some line graphs independently using some given data.

So pause the video now and construct your line graphs, and then click restart once you're finished.

So for your first line graph you had another shadow length set of data, and your longest length of shadow was 4.

22 metres.

So you knew that your graph had to go up to at least 4.

22 metres, and then your x axis showing the time of day.

So your, the way you scaled your graph, the way you've put your numbers at the side may look different to mine.

You might have gone up in smaller intervals so that you could see a different looking line on your graph.

So you could be more accurate with your data, but this is, however you've done your scale, your line should start higher up, dip down towards 12:00 pm, and then back up again towards the afternoon to 10:00 pm.

For question two you were to use the graph to construct your journey from your friend's house.

So again, your scale may look slightly different.

Mine I did going up in intervals of one kilometre, and then I have my time from 10:30 am to 12:30 pm.

So we'll just go through the story of the journey.

So today I walked my dog to my friend's house.

I set off for my house at 10:30.

So at 10:30 am I hadn't travelled any distance.

So my first point is at zero, and then I walked 1.

5 kilometres to the park, arriving at 11:00 am.

So by 11:00 I'd walked 1.

5 kilometres.

That's why I've plotted my second point here.

Then we spent 30 minutes in the park.

So that's up to 11:30, which means that no further distance was travelled, and then continued to walk 3.

2 kilometres to the ice cream shop, and arrived there at 12:30.

So between 11:30 and 12:30, 3.

2 kilometres were walked and we were on 1.

5.

So that means that 1.

5 plus 3.

2 is 4.

7 kilometres.

That's where I've plotted my next point.

Then I spent half an hour choosing an ice cream, and eating it.

So that took us up to one o'clock from 12:30 to one o'clock at the ice cream shop.

So that's a flat line, which shows that I was stationary.

And then after 90 minutes we arrived at my friend's house.

So that's an hour and a half further.

And we walked another 4.

2 kilometres.

So we were at 4.

7, we walked another 4.

2, which takes us up to 8.

9 kilometres by 2:30 pm.

And again, your scale may be different, but the look of the line should look similar to this one.

Well done for your hard work today, I'm looking forward to seeing you in our next lesson.