Lesson video

Hello everyone again, and welcome to Oak National Academy, with me Mr Ward.

As we continue our unit, online graphs and timetables.

Now, the sun is sadly not shining outside, it's a bit cool where I am.

I hope it's a little bit better to where you are, but I have had a haircut.

So I'm feeling great, I'm feeling refreshed, And I'm feeling ready for my mathematics.

Now today, we're going to be looking at a slightly different type of line graph, we just call it a conversion graph.

So, I need you to be in a nice quiet space, if possible.

Focused and ready to go cause a lot of information that I need to present to you today.

If you're ready to begin, let's get started.

If you are new to Oak National Academy or you're new to a lesson taught by myself, Mr ward.

You wont be familiar with my style, but what I like to do at the start of a lesson is just tell a mathematical joke, get a smile on your face, get some mathematical vocabulary flowing, but also give you an indication of what I'm like as a teacher.

So today's mathematical joke is simply this, which type of snake is excellent at maths? Is it called, Adders.

Now, I'm sure you could do much better than I do.

So please feel free to share some of your mathematical jokes with me and the rest of the teachers here at Oak Nation Academy.

Details of how to share and the approval you need from your parents and carers will be shared at the end of today's lesson.

As you can see on the breakdown of today's lesson, we're going to be introducing the idea of conversion graphs and what they are and how you use them.

Then you're going to have an opportunity to have a talk task where you can pause the video and reflect on the information and how you use one.

Then we're going to look at constructing a conversion graph, following a few steps that I'm going to model.

And then you're going to put that learning and that understanding into practise by having a go at an independent task and you should interpret the graph yourself.

And then at the end of the lesson as is a custom here at Oak National Academy, we ask you to complete the end of lesson quiz, to demonstrate how much of that information has been embedded and how confident you are leaving the lesson.

Before we make it start on our learning, it's important you got all the equipment.

Now as you're probably familiar with, if you are a regular on Oak National Academy, we pretty much ask for the same equipment every day.

You need to have somewhere to record your work on, a pencil is ideal in math because you can probably or you can put a line through it.

You will need a ruler today, we are constructing conversion graphs and you are going to need some paper or a notebook that your school might have provided.

Now, ideally we'd like some grid squared paper, but it does not matter, if you've got lined or plain paper because that's absolutely fine.

We can still do our mathematical learning and we can still construct our graphs on plain paper so long as you've got a ruler and a pencil.

So, if you haven't got any of that equipment and you need to go and get it, pause the video, go and get anything you need, then come back, resume the video and we can get started.

Right everyone, now I think it's time we make a start on our learning.

On the screen you'll see an image.

But my question for you to ponder, what do we use kilogrammes for? You often see the acronym kg to represent kilogrammes, but what do we use kilogrammes for? In the end, I'm hoping you'll identify what it is we use it to measure the mass of people or objects.

You may see kilogrammes when we're being weighed for instance, you may see kilogrammes on the side of weights, such as the example of the image in front of you.

What are the units of measure? Can you think of them? We're trying to measure mass.

You might think of grammes for instance, kilogrammes and grammes are part of the metric system of measurement in which we use in this country.

However, there is another form of measurement called imperial measures.

And one part of imperial measures is pounds.

Often, you'll see pounds on the side of an object or an item, when you're shopping for instance, or with the doctors, they may measure you in kilogrammes, they may measure you in pounds.

They can convert between measures today because we can find by using metric and imperial measures, we can go between the two.

So pounds, which is often represented as lb, is another unit that we use to measure mass.

Now on the screen, I've circled the symbol that sits between the kilogramme and the pounds.

Can you think for a moment, by all means pause the video and have a discussion if you want to, about what that symbol means, two wavy lines, it looks like an equal sign, but it's not straight line.

So what does that possibly mean? Well, the two wavy lines means that the answer is approximately equal to, so in this context, we're saying that one kilogramme is approximately equal to 2.

2 pounds, which is about the same as a jar of jam.

So a jar of cherry jam there.

And that weighs about 2.

2 pounds or probably equal to one kilogramme.

You can go between the two.

Now approximately equal of course is not the same as exactly equal.

It's almost rounded up to the nearest suitable unit, so it is very, very close.

It's approximately equal, but it's not exact.

We use an equal sign when we want to show that on both sides of an equation, things are exact.

And here's a little rhyme for you to remember, about kilogrammes are how they're equivalent to pounds.

A kilo of jam bubbling in a pot is two point two pounds and that's your lot.

We've be looking at line graph that you would have identified hopefully remember that, when we use line graph, often the x-axis has a label that's associated with time.

Because a line graph allows us to interpret information over a period of time.

Now conversion graph is different.

Instead of time, we're now looking at the relationship between units of measure between imperial and metric often.

So in this case, we're able to go between the equivalent of the same amount of kilogramme mass to pounds.

So we use a conversion graph that allows us to go between the two units of measure.

So in the top right-hand corner, you will see that's key information for our graph here, the conversion graph, at the top, kilogrammes to pounds.

And you can see, looks like a line graph because it has what it is a line graph, but it looks like the line graphs we've been using in older lessons within the unit, because it has a label X and Y, and it has a title and it has a line.

But this time the line is absolutely straight and it doesn't go from plot to plot to plot, not going from individual events, it's one straight line.

Using the conversion graph that one kilogramme proximately equals 2.

2 pounds, I can plot and identify the equivalent of other kilogrammes.

So for instance, if I know that one kilogramme is approximately equal to 2.

2 pounds, If I times both by 10, I will get the answer of 10 kilogrammes is appropriately equal to 22 pounds.

And if I just show you with one little clicker, where 10 kilogrammes is, if I go up you will see it's just past the 20.

And that is just to examine our line graph here.

You see on the x-axis at the bottom, it goes from zero to 10.

So we can identify that in between is five, and we have to estimate the individual units so we have to estimate six, seven, eight, nine, 10.

Five, 10, 15, 20.

On our y-axis, we can see on our grid lines is one, two, three, four.

There's three grid lines and then 20.

So it must be going up in a five.

Zero, five, 10, 15, 20.

Okay, so coming back to the next grid line here would be 25, but actually it's not 25 here.

It's below 25, it's around about 22, I think that's approximately equal to 22 there.

Just to identify on my conversion graph, I use my ruler.

I can draw a line, it's always great to annotate your work, to be accurate, put three lines across and you can see that that is 22 pounds on my conversion graph.

Now, because I know that 10 kilogrammes is the same as 22 pounds, if I double that I would have 20 kilogrammes, I would have 44 pounds.

by 10 and then by two, therefore I know that if 10 kilogrammes is approximately equal to 22 pounds, then 20 kilogrammes must be approximately equal to 44 pounds.

Okay, now you're going to have a go.

Pause the video, spend a few minutes, either talking in groups or with an adult that you have at home, or just have a moment on your own work independently, reflecting on the information.

Can you convert the four missing pound values? So if you look at the table, there are four missing values.

Using the information, of one kilogramme being approximately equal to 2.

2 pounds, can you finish the table off? Alright every one, let's see how you got on, bring your answers either written down on the sheet to the screen and I have revealed the answers to be, 30 kilogrammes is 66 pounds, 40 kilogrammes is approximately equal to 88 pounds, 50 kilogrammes is approximately equal to 110 pounds, and 60 kilogrammes is approximately equal to 132 pounds.

Now on each occasion, I've simply multiplied both sides by the same number.

Because you'll see that actually the kilogrammes in the table are multiples of 10.

So, for instance, 40 kilogrammes, I times 10 kilogrammes by four, I times 22 by four to get 88.

And we can use that with our answers, I annotated my fig here using a ruler and a line I hope you've done the same.

And you can see that 66 is just past 66, 88 is just between 88 and 90.

50 kilogrammes here is exactly on 110 and 60 here, which is 120, 121, 130, right around 132.

You can see that my conversion graph is as accurate as it can be.

For the next part of this lesson, I'm going to do some modelling of constructing a conversion graph, using steps that you can replicate to create your own conversion graph for the independent task.

To be prepared you're going to need a pencil and ruler and some paper preferably squared or grid paper, but any paper will do as long as you've got your ruler and you're able to accurately plot the information.

Okay, let's make a start.

Okay, for this conversion graph, we're going to change it now from kilogrammes to pounds and we're going to be looking at measurements of height and length, using centimetres to inches.

For this graph, the information I need to help is 10 centimetres is approximately equal to four inches.

Okay, for this modelling, I'm going to a use pen to help stand out.

If you've got a pencil, a sharp pencil is probably ideal, but I'm going to use some coloured pens just for the focus of this lesson, so that it stands out on video.

And I've also made a note from the screen, just so it reminds me that 10 centimetres is approximately equal to four inches.

And that's going to help me when I start plotting the line to help me convert.

First thing I'm going to do is use my ruler here.

I've got a small ruler, it's ideal for me.

If you've got a full sized one, that's fantastic.

Okay, first of all, I'm going to do my two axes.

I'm going to start with my x-axis, which is going to be my centimetres, okay? Conversion graph can go however big, but we're only going to do a minimal size one today.

We're just going to show you it and what it looks like.

So I'm going to kind of scale it down and I'm just going to go to 50 centimetres, but I'm not going to use it to scale, we're not doing 50 centimetres to scale.

So I want to do equivalent of 50 centimetres, okay? And we're going to go up and start on zero and we're going to go up in intervals of five, but everyone of my squares is going to be worth two, for me.

Okay, so that's every one of my squares Sorry that's my mistake, isn't it? Yeah, 10, it's going to be worth two.

So two, four, six, eight, 10.

So I'm going to go into intervals of 10.

So start with 10, so two, four, six, eight.

That will be two, four six, eight, 20, two, four six, eight, 10.

two, four six, eight, 10.

two, four six, eight, 10.

So, 20, two, four six, eight, 10.

I did it out loud cause it helps me think.

Two, four, six, eight, and just so I don't make any mistakes, two, four, six, eight, 50.

And of course, I don't have to put an x-axis so I'm just going to put it in here anyway just to remind me.

And then underneath, I'm just going to give you a label.

I'm going to say centimetres.

Okay I'm just going to put the cm in case I ever need to use that acronym, abbreviation.

And now, up the y we've got our x, we put our y.

This time I'm going to go to 25, I've decided.

Because obviously looking at my 10 centimetres is approximately equal to four inches, I'm going to need more of that.

So that's 50.

The maximum it can be if I times that by five, is 50 centimetres.

Four times five is 20, so the maximum is 20 inches.

I'm going to go up to 25 just to show you how I'm going to half it, okay? I'm going to go up this time.

Each little square is going to be worth one.

So I actually going to start on zero.

I'm going to go up in intervals of five.

One, two, three, four, five.

So that is going to be worth five.

So I'm going to go all the way.

So I need 10 25.

I'm talking to myself, which is a sign of madness.

Six, seven, eight, nine, 10.

But I think it's okay in math to talk to yourself.

Seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 25, there we go.

So I am going mad but I'm also doing my graph correctly.

I'm going to put a y at the top, you don't need to do that, but it's useful to have.

And then I'm just going to turn around with the word inches.

I'm going to try to do this sideways.

So that I don't loose focus, inches, okay? And what I'm going to do now is I'm going to put a title at the top, just so I don't get confused in case anyone comes across.

So let's move it downward a bit.

And my title is simply this, conversion graph centimetres to inches.

I might underline it.

And if you remember from early lessons in this unit, not to worry if you haven't seen any lessons, I'll just remind you that when we do a line graph or any sort of chart or graph, actually, if you give a title that is as literal as it can be.

So literally the title tell you the information, what you're going to see.

It's quite straightforward.

So this title clearly I'm converting from centimetres to inches that we get no mistaken.

So that's my line and my conversion graph, my x and y axes and my title.

And now it's left for me to plot the line so that I can do my conversions.

Now this is key, 10 centimetres to four inches.

I'm going to use your ruler again just so I'm clear.

10 centimetres here, I'm going to go up to four.

So I got to find where four is.

So I know where 10 is and I plot.

And then I know I'm going up in.

Although inches going in intervals of five, actually each square I've done is worth one.

One, two, three, four.

And of course the scale might change depending on what paper you've got, but it works for me.

So four and 10, excellent.

Then I double that cause if 10 centimetres is worth four, then 20 centimetres is approximately equal to eight.

So I've got my 20, six, seven, eight, there I've got my eight, no not.

Five, six, seven, eight there I got my eight.

See how it's easy to make those mistakes.

I always make one myself.

You can see I put a little spot in there.

Just double check there across.

Yeah, that's eight, nine, 10, okay? And now I'm going to do 30.

So again, 10 times four, 10 times three is 30.

Four times three is 12.

So I'm looking at the 12, one, two, 12 here.

I'm going to come across.

There we are, it must be there, excellent, okay? Now actually, you can plot it, it helps me to plot.

Yeah, it's helping me to plot.

You can see that actually they do measure up in line, okay? So actually what I should be able to do with this, I'm just going to do a check.

Now I've got 40.

So 10 times four is 40, four times four is 16.

So 15, 16 come across and we're there, yes we are.

And finally, five times 10 is 50, five times four is 20, as we said earlier on.

So I find 20, which is on the line, come across, there we are, okay? So now I get my ruler and I should be able to connect those little dots together.

They're not plot points as such, but it's absolutely fine to do so because it allows me to be accurate when I'm putting my line in.

So yep down from zero, of course we're starting at zero because that's a scale which we need, all the way down, reinforce it a few times, lovely.

So now, you can say that I've got everything I need for my conversion graph and I've got a line and I'm just double checking.

So 10 centimetre equal to four, 20 centimetres equals to approximately eight inches.

We're ready to use it to convert between centimetres and inches.

So now that we've produced an accurate conversion graph, we can then use it to convert between centimetres and inches.

So using the idea of 10 centimetres, approximately equal to four inches, we could work out both 10, 20, 30, 40.

But we can also start using it to work out the in between values.

So for instance, we can work out 25 centimetres, which is half 20, 30, is approximately equal to 10 inches.

You work out that 35 centimetres is approximately equal to 14 inches.

But it's not just a one way ticket, we can convert the other way as well.

So we can use our y-axis, our inches to convert to centimetres.

So here we have an example where, because I know that 10 centimetres equals four inches.

I can use that to find out that five inches is equal to 12.

5 centimetres.

I've done that because I've accurately measured.

And I'm very confident that my conversion graph here is accurate and therefore, when I use my ruler, I can find that going from five inches gives me it's over 12, gives me 12.

5.

It's over 12, but it's not at 14.

So if you remember, if we look here, it went up in two, so 10, 12, 14.

Now it's not even halfway and that would be about 13.

So I know it's half of half of in sense so it must be around 12 and a half centimetres.

Now, conversion graphs are used for a variety of things, height, weight to mass.

But they're also used for money.

So you may see this more regularly when you're trying to exchange money for holidays.

So euros to dollars, euros to Sterling, euros to any other currency from another part of the world.

And these line graphs are actually used by people that work within the travel industry to help accurately identify the correct conversion rates.

Right everyone, now that we spent a lot of time looking at conversion graphs, why we use them, how we use them, how we construct them.

So now over to you to put that into practise.

So here's your task today.

Follow the steps that have been provided today to construct a conversion graph for centimetres to inches.

You can plot the conversion line using the information below.

10 centimetres is approximately equal to four inches, which means 20 centimetres is approximately equal to eight inches.

Now using that information, plot and construct your own conversion graph, and then use that graph to fill in the blanks on the table.

And you could print off the grid paper in front of you if you need, as an example, or if you've got a ruler, pencil and paper, you can construct your own following the steps that I shared in the modelling process.

And then take that conversion graph and try and complete the table with the information that you have worked out.

Pause the video now, for as long as you need for this independent task.

And when you are happy that you've done the best you can, and you're ready to resume, bring it back, bring your work, and we can reference it on the next slide.

Welcome back everybody and let's just quickly spend a minute going through our answers.

Hopefully you were able to take your time and create a conversion graph that looks very similar to the example on your page.

If you were able to do that, and use the information of 10 centimetres is approximately equal to four inches, you will be able to create a accurate conversion graph, which will allows you to find the information.

Knowing that 10 centimetres equals four inches means I could have doubled that to 20 centimetres equals eight inches.

And I could double that again to make 40 centimetres, which is approximately equal to 16 inches.

I also knew by using my graph that 15 centimetres equal to six inches, and therefore I could double that to make 30 centimetres, I double six to make 12.

And I could also add 15 again, because you'll notice at 15 in the third of 45 and six is a third of 18.

And 50 centimetres equals 20 inches or 10 centimetres equals to four inches.

So I times both by five and I got to 50 centimetres equals 20 inches.

And the only thing left there was 12.

5 centimetres equals to five inches.

Okay, and I could do this by using my graph.

I go a long where it was five inches.

And I noticed that it was just past this line and just past it.

And we agreed earlier on that its going in intervals of two, so, two, four, six, eight.

If it was just past 12, but not at 14, it was in between, just about, that must be 12.

5.

So around it 12.

5 approximately equal to five inches.

And after all of that mathematical learning, if you're still not ready to end the lesson, then you may continue today by having a go at the challenge slide, the make 24 investigation.

Now you'll need to pause the video if you want to have a go at this challenge, read the instructions and take your time.

It's an open investigation and you can return to it as many times as you want.

There is no time limit, and I hope you enjoy investigating the numbers.

Best of luck with the challenge.

But that does bring us to the end of our lesson on conversion graphs today.

Barring one final thing and that is of course the quiz.

So it'll be your opportunity to embed and demonstrate lots of your learning from today's lesson.

Now, of course, if at any point to the quiz, you're a little confused, or you may have missed some of the information, feel free to come back to the video slides again, go back to the parts in which you want to rewatch and just allow yourself to embed that information so that you feel confident and familiar with all of the information that we learned today.

We mentioned at the start of the lesson that you can, of course, share your fantastic work and your brilliant mathematical jokes with us here at Oak National Academy.

Now, we would love to see some of the constructed conversion graphs that you have been creating today.

So if would you like to share your work, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #learnwithOak.

I look forward to seeing some of your amazing work from today's lesson and lessons from across the unit.

And that brings us to the end of our lessons today.

You have done a fantastic job and so have I.

I think I deserve a snack for all that modelling when I was constructing that conversion graph.

Really enjoyed today's lesson, you've done really, really well.

And hopefully you feel confident and familiar with the content which we taught today.

So, enjoy the rest of your day, I hope things go well.

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

Bye from me, Mr Ward for now, have a great.