Lesson video

Hello everyone and thank you for joining me once again on Oak National Academy, my name is Mr Ward.

We're going to continue our unit on line graphs and timetables.

And in particular today, we're going to look at the scale and how the changing scales of a line graph can change how that information is presented and you need to be focused and without distraction.

So when you feel able to continue and able to focus on our lesson, then we shall make us start.

That those of you who may have seen one of Mr Ward's lessons before you will know that it is in accustom of mine, to start our lesson with a math joke.

So here is today's.

Its my personal joke to hopefully put a smile on your face.

Which famous irritable king absolutely loved his fractions? The answer of course is Henry the eighth.

Now, if you're sitting at home with a smiley face and chuckling, you'll be delighted to know that this is merely a fraction of my comic material.

But if you happen to be shaking your head and groaning, you'll be relieved to know that this is merely a part of the whole lesson.

Have you got your own mathematical joke you'd like to share with us here at Oak National Academy, Please wait at the end of the lesson where I will share details of how you can share your work or my practical jokes with us here.

A quick run through the lesson today, we'll have a new learning, talk task in which you can pause the video, or you can continue the discussion with myself during the lesson, I'm going to try to extend our learning slightly with our develop our learnings.

We add an extra element to it and to our understanding.

So we take it a little bit further and then it will be down to you.

You'll have a go at an independent task, some questions before signing off at the end of our lesson with the quiz, which is a tradition here at Oak National Academy.

And you have to make sure that you are ready for the lesson.

You've got all the things that you need.

You're going to need a pencil, a ruler and paper or notebook that your school may have provided.

A rubber as always in this lessons is optional as I prefer to see people draw a line through their mistakes to show that they are learning and they've identified their misconceptions.

If you haven't got any of this equipment, please pause the video now, go and get exactly what you need.

Then come back, join us so we can make a start.

Okay.

The first thing you can see on your screen is a line graph titled temperature in Rio on Saturday 6th of August, 2016.

Now its got the title and its got the labels for our X and Y axis, so is a perfectly formed line graph.

I've got two questions for you to start off this lesson.

What benefits do you think the gridlines provides and that's looking at our line graph, the lines that go across and up or horizontal and vertical lines.

What benefits do they provide it when using them on a line graph? And what do you notice about the X and Y axis? Well hopefully you have identified that the grid lines actually allow us to be really accurate when identifying the data.

So let's go for instance to 6:00 PM, 1800 hours or 6:00 PM in analogue.

And I go up and I use a grid lines and I'll have to be really accurate, to find line to go to that data point.

And then I can go across the grid lines to find that the answer would be 24.

The temperature would be 24 at 6:00 PM.

And the grid lines have allowed me to be really, really accurate.

And then if I look at the X and Y axis, I asked you to look at the values you'd notice that the intervals down the X axis, they go in threes, okay.

It goes up in three hours each time.

Now I'm using digital time here, 24 hour clock.

But of course, hopefully you can convert into 12 hour analogue clock as well.

So that would be 3:00 AM 6:00 AM, 9:00 AM, 12 noon, midday, 12:00 PM, 3:00 PM, 6:00 PM, 9:00 PM and midnight or 12:00 AM.

And then the Y axis the values the intervals are going up in four, but I know that half between four and zero is two that I know that this little lines can be worth two to two, four, six, eight.

Now I'd like to look at both of these line graph.

What do you notice? Pause video.

If you need to spend a minute or two to discuss it, to reflect, what do you notice about the, this two line graphs.

Now, hopefully you've noticed that actually the data presented, presented is very different.

As a title gives away.

One line graph has information about temperature.

And one has about the number of athletes participating in the Olympics.

I'm not too concerned about what the data shows at the moment, but what you may have noticed is how the line graph itself is very, very different.

Now on our left hand side, the temperature, the values go up into the four, eight, twelve.

So actually it's quite small numbers, allows us to be quite specific.

Whereas on the right hand side, they're going up, the value is going to 2000, 2,004,.

That's a lot of information and lots of data.

We also might notice is that while on the left hand side, there's small crosses, which have been to indicate where each specific data should be plotted And then we can, can join those crosses together to make one big line, over here it doesn't appear to be any of those data points individually and just a line.

So that makes it a lot harder to be very accurate around them.

Finally and I think more importantly for our lessons, there are no grid lines on the right hand side.

So therefore in it be accurate to identify the information, it's alot more of a challenge.

Whereas on the left hand side, we can use our grid lines alone again.

So for instance, on my 3:00 AM, I can use my grid lines that go across up and across to find specifically where I need to be in the final correct value.

There are no grid lines on the right and that to me, presents a challenge to us.

So I made that a line graph bigger, the line graph without the grid lines.

What do you notice? Take a minute to pause the video again and think.

What do you notice about this line graph in particular? Well, I notice that the value starts at zero, but actually the line graph itself does not stop until 8,000.

So we've got a lot of information in there or rather We've got a lot off our scale that's not necessarily or not needed.

I also love to note kind of individual plot lines.

So it's very difficult to show that relationship between the individual points of data.

Because there are no grid line, We are going to have to be very specific when we are finding the answers to any question we might have or to identify correct value.

So as you can see, I have drawn with a ruler, a straight line, because straight lines are important.

And I've gone to try and find out the information about Atlanta 1996.

So the question that was proposed to me was what was the number of athletes or how many athletes participated in the 1996 Olympic games? Okay.

So I'll do a nice straight line and a nice line across.

So we can say that approximately about 11,000 athletes took part 1996.

Are you happy with that answer? Of course you're not.

Because what I've failed to do is accurately draw lines.

I've used straight lines, but they're not necessarily accurate.

So let's look at how I should have been doing it.

I should have got my ruler and yes, I drew a straight line, but I did not draw them vertically straight.

So the first thing I'm going to ask you to do is draw a nice straight line, identify 1996.

I know you would draw a nice straight line, but vertical, that means straight up, until I reached the data point.

So at this point I've drawn a vertical line, But next stage it did draw a horizontal line on that data point all the way across, again, it has to be nice and straight, and that's why you need to use a ruler.

I've got no grid lines to help me.

So I have to be very accurate and I can see that the answer is just over 10,000.

Now because I've used a horizontal line, What I've actually created now is a perpendicular line because they meet at right angle.

These now become perpendicular.

But I've also by drawing a horizontal line, created a parallel line with my bottom line here.

So they become parallel, but at the corner here, they become perpendicular, because they're a right angle.

And I can use that to try and find out that my answer, I could probably, if I want to approximate, my answer to be 10,000, but as it's just over 10,000, 11,000 would be about here.

I'm going to say that my answer rounded to the nearest 500 or rather my answers would rounded into the nearest hundred is going to be 10,100.

But again, I would say if we were to round to the nearest thousand, we would say 10,000 athletes participate in 1996.

That would be absolutely fine.

Just to show you once again, how many athletes participated in 1988 in Seoul? Well, first of all, we do our vertical line, nice and straight.

Then we do a horizontal line so that we create a perpendicular point, perpendicular lines here that is the perfect point And again, the answer to that would be approximately 8,000 if we were rounding to the nearest thousand and if you wanted to try and figure out a bit more of a challenge to the nearest hundred, for instance, you know that in the middle of about 9,000.

So I'm going to say that roughly around about 100.

So I'm going to say 8,100 to the nearest hundred, but actually I think it's perfectly acceptable to have an answer to the nearest thousands which would be 8,000.

We're going to continue the lesson now by spending a few minutes on a talk task.

Now, generally at school, when we do talk tasks, we can do them in pairs or groups or even a whole class situation.

And that might not be possible if you're working on your own home.

But that's okay, you can still take part.

Either pause the video, spend a few minutes, reflecting on the information as provided to you or continue the video and we are going to have a discussion on the information together.

As you can see our talk task today, involves comparing two different line graphs.

But are they different? One way to do it, is to think, what's the same about the two line graph you can see and what's different.

Now what factual statements can you make when you compare the data.

As explained previously, you may pause the video now and spend a few minutes at home having a go at this, or we can continue to talk about it together.

Now, hopefully you've noticed that what's the same, well, actually the title and the labels are exactly the same Olympic games and the number of athletes participating in the Olympics.

So actually the data presented is exactly the same on both of the line graphs and yet it looked very different.

So why does the same data look very different on two line graphs? It's to do with the labels and the value and scales of the Y axis.

So if look, on the left hand side, we will see this scale goes up in 500.

Eight thousand, eight thousand five hundred, nine thousand.

And on the right hand side, the scale and the intervals are going up in 2000 and that makes a big difference.

So while our line graph on the left hand side, the data seemed to start near the bottom of our line graph on the right hand side, actually there's a big half of a line graph that is not really being used because there's no data plotted within it.

It looks very strange.

It's innocence being squashed.

What facts can we do? And what statements can we make? Well on the line graph itself and the data, we can see that there are far more athlete competing in 2016 than was in 1988.

Okay? We can see there was a slight drop from 2000 to 2004.

It dropped slightly.

And we can see that between 2008 and 2012, it dropped quite dramatically.

However, we can see that generally there's been a big jump across the different Olympic games from just below 8,500 in 1988 to just below 11,500 in 2016.

So nearly a jump of 3000 competitors.

Okay? What other statements might we make? Well we could suggest that in 2000 there was about 10,500, approximately athletes taking part.

We could suggest that there were more athletes taking part in 2008 than there were in 1996.

And we can say that 2016 has the highest amount of athletes that have ever taken part in the Olympic games.

Okay.

Do you want a talk task? You compared to line graphs that were actually presenting the same information, but it looked very different.

And the reason for that was because we identified that scales with different.

Now one side had scales going up in 2000, but a lot of that line graph is actually unused.

It was empty space.

On the left hand side, we went up in 500 and that allowed it to be easy to read.

Now I've represented that line graph here.

So it's bigger.

And you can see that actually the first thing you should notice that I don't start off at zero.

Because actually, the data plotted had nothing between zero and 8,000.

So actually it was wasted space and why make a line graph more comprehensive than it needs to be? So I could have started off at 8,000.

I started off at 7,500 to try and make it easy to see, but you see that the scale is going up in 500 and they're smaller increment, smaller intervals, the scale is smaller, but it makes it a lot easier to see the journey of that data.

Instead of it being bunched up and condensed, we can actually see real change between the data points.

Now, to make it even easier for me to analyse the data, it would be really useful to work out what the mid points are between the two, between two values on the scale.

So although it's going up in 500, I need to know what is the difference between 500 and zero.

I know that is 250.

So therefore I know that the midpoint will be an additional 250.

You can also set it out on the number line to help you, pause the video now if anyone wants to add an extra quick extension task to work out the missing values.

If not, we'll just do what we just talked about.

We know that actually the midpoint between the 500 scale is 250, so in a sense I'm going to be adding 250 to each of the given values there to find those mid points.

So even though the scale is 500, I can find halfway along which is 250 plus 250 plus 250.

You might also want to work out on a slightly easier notion that the scale here between the years given the scale given here is eight years, but we know that Olympic games are every four years, I also know that four is half of eight and that's going to allow me to find the missing values in this number line as well.

There they are, our answers.

Okay.

So now that I've got that information and now that I know what the scale is and what all the intervals are, I can start accurately and confidently answering some of the questions.

My first question here is, approximately how many athletes participated in the 1996 Olympic games? Now the word approximately means I can get an estimated answer.

It does not have to be exactly right.

And that allows me to round perhaps to at appropriate scale.

So I'm probably going to round to the nearest thousand or the nearest hundreds, depending on how close I want to be.

Now, as we looked earlier in the lesson, it's very important that when we're trying to identify the current data, that we are very accurate and that we start using those straight lines again, to get your ruler out.

When you do an activity like this, because it's really useful to make annotated notes on your sheet and draw lines.

That's what I'm going to do.

I'll get my ruler out, I draw a line from 1996, all the way up, a nice straight vertical line.

I'm then going to use my ruler to make a nice straight, horizontal line that creates a perpendicular point.

A perpendicular line because they meet at 90 degrees.

Thank you for telling me once again.

Okay? So now I go across and I can see that my answer is not quite at 10,500, but it is way above 10,000.

So it's actually above that midpoint.

Now we worked out in our info didn't we, that the increment in the scale goes up every 250, actually, even though the scale is 500.

Going up in 500, the midpoint is 250.

So if I add 250 to 10,000, I get 10,250.

So I know my answer is actually between 10,250 and 10,500.

Okay? I'm going to estimate and approximate that actually I think that's an extra hundred people.

So my approximate answer will be 10,350.

Next on your screen, You're going to see a different line graph.

First of all, I'd like you to look at the labels and identify what themed those are and what this line graph is showing us.

Well, hopefully you've noticed that and the title gives it away, the temperature cooling water that the scales are going across the x axis in intervals of five minutes and the Y axis intervals of Ten.

But although the scale is going up in intervals of ten, actually, we can also identify the midpoint, which would be five because we know half of ten is five.

Now this line graph provides temperature of cooling water and it looks a lot more consistent.

So what story does the data give us? What is it showing us? Well, by looking at the information we can see that it starts off high and that by 30 minutes there's been a pretty constant cooling period for the water.

So that over the course of 30 minutes, temperature of cooling water has dropped at a quite a consistent pace.

So after half an hour, the water is around 20 degrees.

Whereas it started around about two at 76, 77 degrees.

Now, why do I show you this line graph? It's because I want to explain a little bit for a minute about the importance of consistent data.

Now when we look at one of our Olympic games' time graphs, Just come up now on the right hand side, you will notice that there's a lot more variation between the different data points.

Now a lot of that is because it's an event over a period of time, but also the difference it's over four years.

So we don't know what's happened in the intervening years.

We don't know why they're vastly more people in 2016 than it was 2012.

It's such a big gap between the years.

That is understandable the data might be vastly different.

Whereas when we do a line graph like the temperature cooling water, because it's taken place over a small period of time, we can see that there's a lot more consistency to it.

Again, it's a good example of how line graphs, when even if the line is created the same way, obviously, and have the same structure, the data could be wildly different.

It's easy to predict a more consistent approach to this.

So it'll be easy for us to predict that after 35 minutes, for instance, that the water will continue to drop because the line, the data story tells us that consistency.

Then if we were to try and predict how many athletes might participate in the next Olympics, and we could suggest it might be more than already stated.

However, there are periods of time when that information has gone down is not consistent and therefore it's harder to make a prediction.

Now you're going to have a go at the independent task and here's your task today.

I would like you to look very carefully at the graph provided to you, the line graph in front of you.

The title is altitude of a plane flight from London to Rio.

The X axis is time since take off in hours and the Y axis is altitude measured in metres.

I would like you to use the information from the graph to answer the questions very carefully.

I've enlarged the line graph.

I provided a line graph that has grid lines.

If you feel more comfortable using grid lines to help you answer those questions and I've provided you with the questions written a little larger.

So I'd like to pause the video so you can have a go the independent task and then come back so we can have a look at the answers together briefly.

Okay.

Best of luck.

See you in a few minutes.

Okay.

Lets briefly look at the answers that you have created.

I've put in a couple of lines there to help with my answers.

So question one, what was the approximate altitude of the plane at these times.

We were going to approximately give an answer.

So for A You could see when I try and identify the three hours.

So three hours must be between two and four, because its the halfway stage, it was approximately 11,500.

I round it to the nearest, hundred.

B half an hour before it landed.

You'll notice that it lands at 13 hours after take off.

It's a 13 hour flight, although they didn't get off the plane for 14 hours, half an hour, there would have been in between 12 and 13, and it was approximately 3000 metres and for C halfway again, it was in the air for 13 hours, but it was actually a 14 hour flight because they didn't get off the plane for 14 hours.

So halfway that is seven.

And therefore I want to go straight to my vertical line.

I saw that it was 11,000 metres.

Question 2 was, 12,000 metres.

I hope we can see here.

Question 3.

Was the pilot dipped four hours into the flight? Come across here where it says four, we can see that the four hours he dropped down and it dropped down to 3000 metres.

Question 4, was an open answer.

So you have to create the stories and you would have come up with information based on the data and how it's presented.

And finally, any questions that you may have come up with.

Here's an example of a question I came up with.

How much time did he take the plane to reach its highest altitude during the flight? The answer would be of course, four hours, because that's the time period where it reads the highest altitude during the flight, which was 12,000 feet.

Okay.

I know you have a challenge slide as accustomed to my lessons.

If you would like to have a go at the challenge, you may pause the video and take your time reading the slide.

So that brings us almost to the end of the lesson.

All that's left for you to do at the end of this video is to have a go at the quiz to answer a series of questions based on the information from today's lesson.

Hopefully you're going your way today a bit more confident, and familiar with the idea of how scale on line graphs can change how the line graph appears now, why it's important to identify correctly an appropriate scale in order to construct a line graph, but also to allow you to accurately identify the correct information for the questions.

Well done everybody on completion of that lesson, there's a lot of information there.

You did really, really well.

I've really enjoyed teaching that.

And we covered a lot of information on line graph today, but you didn't fault that.

So Pat on the back for a fantastic job well done.

If you're sitting at home and you've got either a mathematical joke that you cannot wait to share or some work that you're really happy with then please we would like to share with us here at Oak National Academy.

As always, we really recommend and encourage you to do so.

So please speak to your parent or carer and ask them to share your work on Twitter, tagging @OakNational and #LearnwithOak Okay everyone.

That does bring us to the end of our lesson today, the sun still out, it's nice and warm outside.

So I'm going out to play.

I think you probably deserve a little treat too.

If you feel like there's a few bit of information you're not sure about, or you may miss some, the lessons in a unit, feel free to go back and have a go at some of the early lessons that I've taught on the unit of line graphs and timetables.

Until next time, stay safe everybody and I hope to see you soon.

Goodbye for me, Mr. Ward.