Lesson video

Hello everybody.

Thank you once again for joining me here at Oak National Academy as we continue our unit on line graphs and timetables.

My name's Mr. Ward.

And if it's the first time for you on Oak National Academy, welcome, we are glad to have you here.

Now, today in our unit on line graphs and timetables, I have dusted off the visualizer as I will be modelling how to construct a line graph.

And hopefully, you can follow the simple steps to create your own by the end of the lesson.

So please get yourself in a quiet space, free of distraction and ready to begin the lesson.

If you are familiar with the lessons that I've taught here on Oak National Academy, you will know that we like to start our lesson with a math joke.

If you are new to a Mr. Ward lesson or new to Oak National Academy, rest assured that we like to share a joke at the start of a lesson to get a smile on your face and get you thinking mathematically.

So today's cracking massive pun is this.

Why do people never talk to circles? Because there really is no point.

Now, if you think you can do better than that, and I really think you could, if you'd like to share a math joke along with some of your fantastic work, there'll be details on how to share them with us here at Oak National Academy at the end of this lesson.

So please continue to watch the video slides until the end.

If you'd just like to have a little look at the outline of the letter very quickly, you will see that we're going to start by looking at the new learning, which is, why should we choose a line graph? Why would we want to use a line graph to show our data? Then we're going to do a talk task in which I'm going to visualise step by step how to construct a line graph.

Then we're going to develop our learning by taking a line graph and comparing different sets of data within it.

And then finally, it's going to be over to you as always.

You're going to have a go at an independent task in which you construct a line graph putting in the data from a table.

And then, as is custom here at Oak National Academy, at the end of the lesson, we ask you to have a go at the final quiz to see which bits of the lesson have been embedded.

And if there's anything you're missing, you can always come back and rewatch the video for the parts in which you may not be quite so familiar or sure at the moment.

Before we make a start on the lesson itself, we always make sure we've got our equipment.

So just do a quick equipment check.

Have you got a pencil? Have you got a ruler? You are going to definitely need those today.

And have you got some paper or a notebook that your school may have provided to you.

Ideally, we would like grid paper, squared paper, but if you've only got plain paper, that's absolutely fine, not to worry whatsoever.

We can make do.

The rubber is always optional in my lessons.

Just to remind you that I like to see pupils cross out their work neatly, because it shows that actually they've identified the mistake, and they've learned from their misconceptions, which is the best part of our maths learning.

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

And then come back, join us, resume the video, and we can make a start on the main lesson.

Off we go.

So on your first page, you will see a table of data.

And the title is Olympic gold medals won by the USA.

What is this table showing us? Take a few moments to look at the information presented.

You should have assessed that the information is showing the amount of gold medals won by the USA Olympics teams across the 6 previous Olympic Games.

There are 6 columns with the year of the Olympics and the city in which the Olympics took place.

And then underneath that, the next row has the number of gold medals won in those Olympics of that year.

So for instance, in 1996 in Atlanta, USA, the USA won 44 gold medals and so on and so on until you end up 2016 in Rio, where they won 26 gold medals.

And with that information presented in the table, we can still answer a number of questions and work out a number of things from that information.

There are 3 example questions below.

Pause the video for a moment to read the questions, and then answer them verbally.

Which year was the most successful for team USA? How many more did they win in Atlanta than Rio? What was the range for gold medals won by the USA? And we have some answers to that question.

So the first question was 2008.

You can see they won 48 gold medals.

How many more did they win in Atlanta than Rio? Well, in Atlanta they got 44, and in Rio they achieved 26.

So take that away from 44, and you're left with 18.

That's the difference.

And finally, what was the range for gold medals won by the USA? To find the range, a reminder, you need to find the top value, which was 48, and you need to take away the smallest value, which in this instance was 26.

And that leaves you with a range of 22.

And now we're going to look at the different ways in which we could possibly present the data from that table.

Now, you recognise, I hope, a pie chart on your screen.

And you see that the gold medals are represented in sectors, in portions.

So we can say, actually, the pie chart shows us that 48 gold medals was the biggest sector, and therefore it would be the biggest amount of gold medals won.

And 26 is the smallest part there.

However, I've got a question that says, "Why isn't this the best choice to present the data?" Hmm.

Have a think.

I've got a couple of reasons.

I wonder if you have the same.

For one, there's a lot of information going on there.

I have to keep looking down at the key just to remember which colour represents which year and which city.

Secondly, it's really hard to compare the data or to see any patterns or contrast.

I don't quite know what's happening from Olympic to Olympic, and I can't see a pattern over time.

Therefore, I don't think this represents the information in the best visual way.

You might recognise this as a pictogram, which is often used in Key Stage 1, but it's also a fantastic resource to use all the way to Key Stage 2 and beyond, because it does provide more of a visual representation of the data.

What can it show us? Well, you can see by using the key below that for each medal represents 4 gold medals, I can count up the number of medals, times it by 4, and it will tell me the amount of gold medals.

So it does work in that respect.

At Atlanta, there were 11 medals.

Therefore, I count up 11 times 4: 44.

In Sydney, there are 7 medals represented on the pictogram, and each one represents 4.

So 7 times 4 is 28.

However, again, although it's more of a visual representation of the amount of medals.

It's really hard to see any patterns.

It's really hard to see the contrast.

It's really hard to see how things have increased or decreased from the Olympic game to Olympic game.

And we can't really see the trend over time very easily.

Therefore, I would think the best solution would be to use the line graph, but can you suggest a reason why? I think that using a line graph is the best choice for representing the data from the table.

And if we're going to construct a line graph, can you remember some of the features we need to include when creating a line graph? Well, hopefully, having had a moment to pause, you would've identified that a line graph will allow change over time to be easily seen.

It will allow us to spot patterns to see how there has been change over a period of years.

And it is a lot easier to see without having to keep looking up, down, left, right at every key.

We can follow the data, and we can spot the trends as it increases, decreases, or perhaps stays the same.

And when we construct the line graph, at the moment, we've got a piece of grid paper that is bare with nothing on it, we're going to have to include some of the following features.

A title.

An x-axis, which we're going to label the Olympic years, and a y-axis.

If you remember, the y-axis goes up, but we haven't yet decided on a scale.

So I'm going to check the table again to make sure that I know what the highest and lowest value of the table is.

And that will allow me to identify where I can start my scale appropriately.

Now, the talk, actually, it's a little bit different today because talk task is going to be me modelling how to construct a line graph step-by-step.

Now you could follow the video and watch my steps, or you could pause it every minute or so and follow my steps to create your own line graphs.

There will be a task later in the lesson in which you construct a line graph yourself.

So if you choose to follow and watch the video at this time, that will be absolutely fine.

Okay, I'm about to start modelling how to create a line graph.

The first thing I need to do is to check the table once more to find what the highest and lowest value are.

I can see that the lowest number of medals was 26, and the highest number of medals was 48.

So when I create my y-axis, I want to make sure that I'm not going over 48 so I've got wasted space, but I also, I'm going to have unnecessary space.

I'm not going to really need to go from 0, because there is a large part of that line graph that wouldn't have any data in.

So as long as my y-axis includes a scale that goes from at least 24.

As you can see on the right hand side, we're going to try and create a line graph that looks very similar to the picture in your screen.

So the first thing we need to do is to construct our line graph, including all the features, which is the title and the labels, and making sure it's nice and accurate.

Now, I'm going to use a ruler.

And now I've only got a small ruler here, but this is going to do a perfectly good job because it's nice and straight.

Make sure you put your ruler on your paper.

I'm going to start at the bottom here, the end of my axes.

And I'm going to go up.

Now, I have thought about my axes, and I know that the best way to show the Olympic years here is to do a long way x-axis, and put a little x there.

I am going to put every 4 squares, 1, 2, 3, 4.

That will be 2000.

1, 2, 3, 4.

1, 2.

So that's going to be 1996.

That's going to be 2000.

1, 2, 3, 4, 2004.

1, 2, 3, 4.

Now take your time when you're constructing a line graph, because accuracy's very important.

You need to be able to read the data.

1, 2, 3, 4, 2016 is going to be my last data point for today.

And then I'm going to go up my y-axis.

Now, I know, looking at the table, that the lowest number of medals was 24, but I'm going to start on 20 just so I can show you a little bit.

We'll start on 4, and I'm going to go in 4s, okay? Now, fortunately on these pages, these squares are quite small, so actually each square can represent 1, but my value is going to be 4.

So my intervals are going to be 4, but each box actually represents 1.

So 1, 2, 3, 4.

28, 2, 3, 32.

3, 4, 36.

Again, I'm taking my time, be as accurate as I can.

44, and we're going to end today on 48 because the top value in my tables is 48.

I don't think I need anymore.

So now I've got to label it, so I've got my x-axis.

So down here, I'm going to call them.

I'm going to say that's the Olympic Games years.

And on my y-axis, I'm going to put a y at the top just so you know what they are and the x at the side there.

On my y-axis at the top, I'm just going to turn it round.

I'm just going to write, I think, number of gold medals.

It's a nice title there.

So let's go back to where we were so you can see, okay.

Now, I'm almost complete, ready to input the data, but I am missing something important that we should include each time.

And that is, of course, the title.

So I'm going to put at the top here number of gold medals won.

And I've deliberately put it out of the reach of 48.

That's my top value.

I don't want to be mixing in case there's any lines woven up.

So I've just put my title at the top of my line graph out of reach of the data.

I'm going to put a little line underneath so it's nice and neat.

So let's just double check how's my line graph.

Have I got my intervals correct? Fours, fours, fours, they represent the Olympic Games, nicely spread out.

Lovely on my x-axis.

And then on my y-axis, my intervals didn't need to start at 0, and I'll show you that when we plot the points why we don't start at 0 if we don't need to.

Let's start at 20 because the lowest point on my table is 24.

And I'm going to go up in intervals of 4, knowing full well that's halfway between 24 and 20, 22.

So I know that actually I can mentally know it's going up in 2s as well.

So it's intervals of 4.

I've got a title.

I've got labels for my x-axis and y-axis.

And my line graph, it's looking nice and neat and accurate and is ready for data to be put in.

So now that we have constructed the outline of our line graph, we've got our axis, and we've got our title, and we've agreed a scale, we can now start plotting the points by taking the data from the table and putting it onto our line graph so that we can present that data.

Just a reminder that we're not going to go from 0, because there would be no point.

And we started our scale from 20 in intervals of 4 because the first data point is 26.

So I think that's a good way of representing that information.

And the scale goes all the way up to 48.

We don't need to go any further, because the information in the table does not go any further than 48.

Okay, so next go onto the next stage, which is plotting the points on our line graph.

So our second step now is to take the information from the table and put that data by plotting the points on our line graph, and then connecting those points together accurately so that we can start interpreting the information.

Now, before I do this, I'd just like to point out I'm using a pen.

Normally, you would use a pencil, but I'm using a pen just so it stands out and you can see it on the screen.

Okay, so ideally, a sharpened pencil would work.

Now, because I haven't got the table right in front of me, I've made a little jotting.

You don't have to do this normally on your line graph, but you might do; it might help you.

I just jot it down underneath my line graph the total number of medals for each of the years.

So I know what I'm plotting.

And now I'm going to look at each of the years, and I'm going to put in a little cross on the correct place.

Going to use my ruler still.

It's important to have that.

So we'll start in 1996, which was 44 gold medals were won.

So let's go up all the way, and I can see, if I follow all the way up.

Okay, I've found 44 here.

So I come across, I come across, come across, and here I am.

So I'm going to put a little cross right there.

My first one.

Second one, it drops to 28 in 2000.

So again, 24's here, and I find 28.

So I've come across a little pinpoint there.

I'm going to do little dashes.

I can annotate my line graph.

It's my line graph after all.

I can create some perpendicular lines if I want to add dashes.

I'm going to put my little cross there, 28.

Then I've got 2004, 32.

So again, I find 32 on my y-axis.

I come across it with dashes, little dashes here.

And then I'm mix it with my ruler all the way up little dashes up, and I can find that that is the point, 2004.

2008, 48, right at the top this one.

Nice and easy one here because it's right at the top.

It's a top value that we've got.

So I need to just go all the way up, all the way up, all the way, dash, there it is.

And I just match that in, little dashes.

Yes, I can see that's the right one there.

So I put a little cross in, lovely.

And I can see that 2012 was 38.

So again, I'm going to find 38 on the side.

Now, I've got 36 and 40, as we remember, we know that half way is obviously, 2.

So it'll be 38.

So I know that 38 here.

So therefore I can go across.

Dash, dash, dash it along, dash it along.

Where I need to go.

That's a rough estimate down there, and then I'm going to dash up if I need to.

Dash, dash, dash, dash, dash, dash.

And I meet here, my perpendicular dashes meet there.

And therefore I'm just going to put a little cross in.

And then lastly, in Rio, 2016, there's 26.

So a drop again.

I can find 28 here, 24, again, I know halfway between 28 and 24 is 26.

So I'm going to come across.

I'm going to dash dash all the way to about here.

Yeah.

And then just check.

Yeah, that's the right one.

And put my little cross in.

So now I've got 6 points: 1, 2, 3, 4, 5, 6.

And now I need to, using my ruler, connect those data points together.

Now I'm going to use a green pen for this, again, to help show and visualise the differences and to help stand out.

So I'm going to very accurately find that centre of that cross.

I'm going to make my ruler alongside the points and go all the way, that's one, Okay, so now we're going from 2000 to 2004.

So I need to make a small jump.

There is an increase.

You can see it's gone up.

It's gone up from 28 to 32, so I go up by 4 medals.

And then massive leap, big increase from 2004 in Athens to 2008 in Beijing, it went from 32 to 48, so there's a big jump of 16.

Big jump there.

Again, I'm just going to connect those up.

And then two more.

So from 2008, there was a drop, quite a significant drop from 48 to 38, so a drop of 10.

And again, middle of the cross.

And there we go.

And then one last one.

Another fall as well.

Significant one at that.

38 to 26, so a drop of 12.

So an even steeper decline here.

And there we have our plotted line graph.

We're ready now to start interpreting the information and answering some questions and creating some factual statements about the information that has been presented here in a very neat and accurate line graph.

Now that we've created our line graph, we can now start to interpret the data that has been presented visually.

So I'm going to ask you to pause video for a few moments to think about the next two questions for you to create.

The first is, what questions can we ask about the data that's been presented? And secondly, what factual statements can we make about the information? I'll give you a few moments now to think of some possible examples.

I'm hopeful that you've come up with some great questions and some very accurate statements based on the information that's provided to you, the evidence to support your statements.

Here are a few examples I came up with.

Questions could be, which was the most successful year? The answer, of course, would be 2008.

How many fewer medals did they win in 2016 compared to 1996? Well, we can see in 2016, they won 26.

And in 1996, they won 44.

So the difference, there were 18 fewer medals.

And how many gold medals did the USA win before 2004? Well, in 1996, they won 44 ,and in 2001, they won 28.

So we got those two numbers together, 44 and 28.

If you can do it mentally, that's fantastic.

And we get 72.

So before 2004, the USA won 72 gold medals over the course of the previous two Olympic Games.

And my two statements of fact based on what the data tells me is that in 2000 and 2016, they were the least two successful years for the USA team.

You can see that in 2000 they got 28, and 2016, they had only 26, because they are the two lowest data points.

And I found out that the range of gold medals, remember the range being from the largest value to the lowest value, was 22, between 48 and 26.

So as you can see on your page, we're going to introduce another set of data.

You've now got two tables on the page with information in them.

Now, the first you'll recognise as being the data we've been plotting.

And as you can see on the line graph we created, we accurately plotted the data for the team USA.

However, now we've introduced a second set of data, which is Olympic gold medals won by China.

And we're going to try and compare the two sets of data.

The only thing I'm going to ask you to do is just look at those two tables and try to compare the information that is presented within the data tables.

Now, it is possible to look two set point, Atlanta, for instance, and see that it's 24 for China and 44 for the USA.

But visually, it's quite difficult to do.

So in order to get the best out of our comparison and to really be able to see some patterns or connections, similarities, or differences, what do you think we need to do? Of course, we need to plot the second set of data so that it can be compared directly on the line graph with the first set of data are the USA.

And now that, and we can continue our lesson.

Now, if you look at the two data now, now that I've plotted the points accurately for both the team USA and for China, it's a lot easier for us to compare each individual year or collectively over time.

I also want to point out that in the top right hand corner you should notice that I've added a key.

Now, because I've got two sets of data on the same line graph, it's important that I put a key in, and if possible use a different set of colours.

Because that allows me to easily identify the individual set of data.

Otherwise we wouldn't want to be getting confused between China and USA if we try and compare their achievements at the Olympic Games.

So now that I've got those two data lines, it's a lot easier for me to come up with some suggestions and comparisons.

So I'd like you pause the video in a few moments and think of some comparison sentences that you can make when looking at the two different sets of data for the USA and China.

Now, before you do that, I just want to draw your attention to some key words.

This is vocabulary that we can use in our comparison sentences.

So when you're creating those sentences, try and include some of this language within those sentences.

So the words are greater, fewer, which means less of, more than, is equal to, less than, and total.

So again, please spend a few moments thinking verbally or writing down comparison sentences that you are confident about making when you are comparing the data that you visually presented in front of you.

Excellent stuff.

I wonder what you've come up with.

I'm sure, knowing you lot and how hard you work, you've come up with some fantastic comparison sentences.

I've just done a few examples to try and model what we could have done.

And I hope that you've got something very similar.

You may have spotted these patterns.

You may have spotted something very different.

The USA achieved a greater number of medals in 1996, 2008, and 2016.

And how do I know that? Well, because in those years of 2008 into 1996 and 2016, the data point for the USA is higher in value than the data point for China in those years.

The number of gold medals achieved by China in 2004 and 2012 is equal to the number achieved by the USA.

And that's quite straightforward when we look at the line graph, we see there are two points on the line graph where the lines, the data lines, intersect each other at the exact the same point.

Happens to be in 2012, when they both achieve 38, and 2004 when they both achieve 32.

Number 3, the total number of gold medals won by both countries in 2004 was 64.

Go to 2004, and you can see that, that one of those intersecting points, they both achieve 32.

So I multiply by 2 or double it, and I get 64.

And finally, my final factual statement where I compared the data, was that in 1996, China achieved 20 fewer medals than the USA, fewer being less of.

So I know that USA got 44, looking at my data, and I can identify that China got 24, and I know 44 take away 24 is a difference of 20.

There's therefore 20 fewer medals achieved in that year.

Okay, I feel like I've done a lot of talking and modelling today.

I've really enjoyed it, but it is now your turn to have a go at an independent task.

Now, if you're still not feeling confident about accurately constructing a line graph, feel free to go back earlier in the video and have a look at the steps that I presented again and try and follow them step by step.

However, hopefully, if you've got a ruler and a pencil, and you're feeling like you're willing to give it a go, I think this is a task straight for you.

So what I'd like you to do is I'd like you to look at the data that's presented in the two tables.

You'll see that it's no longer the USA or China.

It's now Australia and Team GB, but we are still looking at the gold Olympic medals won by both of those countries across the 6 different Olympic Games.

Your task is first to take that information and construct a line graph.

One line graph which can have both sets of data presented within it.

Once your line graph has been created and constructed with the current labels and title, I want you to present the data on that line graph from both of the tables.

Remember, you might want to use different coloured pens or a light or dark shading to show the different countries sets of data.

And finally, once you have got your line graph, and you've presented that data accurately, I want you then to come up with sort of factual sentences which show that you can and have compared the set of data for both Australia and Team GB.

I've enlarged the tables so you can look at the values.

A little hint for you.

Look at the top and bottom value, the highest and lowest value for each table, because that might help you identify what scale is appropriate to use in your line graph today.

Now please pause the video, take as long as you want.

There's no time limits.

Until you're happy and comfortable with the work you produce.

You're pretty pleased with it and proud and you want to come and share it with us.

Come back, resume the video, and we'll see how we've got on.

Okay.

Best of luck.

And I'll see you very, very soon.

Welcome back, everybody.

And hopefully you've got your work in front of you from the task that you have just completed.

And just briefly, I just want to show what your line graph hopefully looks like.

Now I've done the same task as you, and I've plotted two sets of data for both Australia and Team GB.

And I've presented it on to my single line graph.

I use a scale of going up in 2s, but actually because of the paper I had on the grid, I was able to know that each square represented 1.

So my scale went up in 2, went all the way up to 30, because the highest value on the tables was 29.

So there's no point going higher than 29, really.

So I capped it at 30.

But I did start at 0 this time because the lowest value was 1.

So actually I did have to start at 0.

Remember, earlier in the video, we talked about how you don't always have to start your scale at 0 if there's no data up until a certain point.

So we started earlier on at 20, but in this instance, you can see that we have to start at 0 because our very first data point is just one solitary gold medal.

And hopefully, looking at your line graph, looking at mine, and hopefully, it should be very similar.

Now, I've used a key at the top again.

Got blue for Australia and purple for Team GB because they were the only colours I had available.

That's okay.

If you haven't got any colours, and you've got a pencil, you could find another way maybe by doing a dark line and a light line, or maybe doing a little bit of a thicker line, and then just doing little crosses on there or little stripes.

Whatever way helps you identify the different data.

And so we can just finish off with some factual statements.

We can see that, actually, both teams have made improvements over the years, but Australia have had quite a decline in comparison to Great Britain.

So for instance, I might say that in 1996, Australia started with 9 and Great Britain started with only 1 medal.

So Australia were more successful in 1996, but if we come all the way to 2016, by this stage, Great Britain are now far more successful, having achieved 27 gold medals, and Australia had only achieved 8, a difference of 19.

We might also say that the year between 2004, 2008, if you look at this here, the intersecting lines, where they cross over.

Between 2004 and 2008 seems to the change where Team GB improved, and Australia seemed to decline a little bit in performance.

Before that, Australia were clearly better equipped.

The first three Olympics here, Australia were more successful, but after 2004, so for the next three Olympics, Great Britain have been far more successful on each occasion than Australia.

Okay, I hope you enjoyed that task, and, again, you did a really good job.

It was a lot of information there.

It may have took a little bit of time.

As long as you use your ruler and you remembered the steps that we talked about, then you would have constructed, I am sure, an absolutely fantastic line graph.

If having completed and constructed your line graph and plotted that information hasn't quite been enough work for you, you can always have a go at our challenge slide.

Please take a few moments to pause the video, read the instructions.

See if you can work out the answers to my challenge questions today.

And that just leaves me to say thank you for your efforts again.

And to remind you that the lesson is not quite over until you've completed the quiz.

Now, we've worked very hard today, and we covered a lot of material, and I'm hoping that that's allowed it to embed within you so that you feel confident and familiar when constructing line graphs.

So take the time now to have a go at the quiz.

And if there's anything you're not sure about or you missed, free again to go back on the video slides, to earlier in the lesson, and look out for the bits of information that you didn't quite pick up the first time.

Best of luck.

See you in a few minutes.

Now, it's after the lesson when I share with you another one my tremendous jokes.

I did say that you are welcome to send in your mathematical jokes or puns if you feel it will make our day here at Oak National Academy.

So along with some of your fantastic work that you're proud of, feel free to send jokes and work into us here at Oak National.

Please ask your parent or carer to share your work on Twitter, tagging @OakNational, and #LearnwithOak.

And that has brought us to the end of the lesson for today.

Once again, time has flown by as we've been captivated by the maths that we've been learning today.

You've done another fantastic lesson.

You've really worked hard, and I've really enjoyed that.

I hope you appreciated me using the visualizer.

It's a really good tool.

I think I might use it again in other lessons.

Have a great rest of the day.

And I look forward to seeing you again soon here on Oak National Academy.

So from me, Mr. Ward, goodbye.