Lesson video

Hi, everyone.

Thank you for joining me.

My name is Ms. Jeremy, and today's math lesson is focused on solving problems involving Roman numerals.

So get yourself sorted with a nice quiet space.

And once you're ready, press play to begin your lesson.

So let's begin by looking at your lesson agenda.

We're going to start with a warm up where we'll recap the Roman numerals to 1,000.

We'll then look at how we memorise Roman numerals before looking at missing values and equations, and then we'll finish with some Roman numeral problems before your independent task and quiz at the end of the lesson.

For today's lesson, you will need a pencil, and some paper, and a nice quiet space.

So pause the video now to get your resources ready.

And once you're ready, press play to begin the lesson.

So let's start with our warm up for today.

The question says, can you match the Roman numerals and Arabic numerals on your screen? So you can see in the light blue we've got some Roman numerals and in the dark blue we've got the numeral system that we use nowadays.

We call those Arabic numerals.

And what I'd like you to do is to see whether you could match the Roman numerals to the Arabic numerals.

I'm going to give you about 10 seconds.

If you feel like you need a little bit longer, pause the video now, and then restart when you're ready.

10 seconds starting now.

Okay, let's have a look at some of these examples together, and see whether we can work out what they represent using our Arabic numeral system.

The first number we've got is DCXXIII.

And using our knowledge of Roman numerals, I can tell you that a D represents 500.

The C comes straight after the D, and the C represents 100.

And when we place a smaller Roman numeral after larger Roman numeral like that, that demonstrates that we're adding them on.

So that means that DC represents 600.

Then we've got two X's.

One X would be 10, two X's is 20, and three ones.

So that represents 623, which I know matches all the way down to this one just here.

So, next one, let's have a look.

We're starting with CM.

So CM is our first number.

Now I know that M means 1,000.

The C coming before the M means I'm subtracting 100 because C is equal to 100.

I'm subtracting 100 from 1,000, so that is 900.

I've got two X's, which is 20.

And then VIII, which is eight.

So that is 928, which matches to this one here.

The next one has three C's to begin with.

Three C's in a row, that's 300.

Three X's in a row, that's 30.

Three ones in a row, that's three.

333.

It matches to this one just here.

And the final one, I've got a C before D and the D represents my 500.

But the C has come before it, so that would be 400.

Then I've got an L and an X.

L represents 50, but I've got the X right after, so that's 60.

And then VI is six.

So here we have our number, which is 466, our final one that we haven't matched up yet.

So it matches to that one just there.

So hopefully you've managed to recap how to identify the representations of Roman numerals and how to match them to Arabic numerals.

Let's move on with looking at a few Roman numeral problems. So the first thing I want us to talk about is the way that we memorise Roman numerals.

It's all well and good to have a key that shows us that I equals one, X equals 10, and M equals 1,000 for example.

But how do we memorise that? How do we remember that M is equivalent to 1,000, C is 100 for example? There's lots of different ways that people do this.

One of the ways that I do, one of the ways that I remember some of their letters, I think about I C as kind of representing cent, the word cent.

And the word cent when spelt like that refers to 100.

if you think about words like centimetre, centipede, they all are talking about 100.

So, cent of course starts with a C, and that reminds me that that means 100.

When I think about M, I think about words like millennium or millilitres, and that represents 1,000.

So I remind myself that the M for millennium or millilitre refers to 1,000 in Roman numerals.

But how do we remember the other ones? How do we remember the order? Well, you might come up with lots of different ways that you will remember the Roman numerals in the order they come in, but this is a little handy tip in case you would like one from me.

So, if you remember the word Medical Xavier.

Medical Xavier, have a practise of saying that.

Medical Xavier.

it's a bit of an odd combination of words, but the reason that this is helpful is that it contains all of the letters for the Roman numerals in order.

So you can see that the M there is the starting point, for medical, and that's 1,000.

That's the largest number.

Then we've got the D, which is the next one, 500.

The C is referring to the 100.

L is 50.

X is 10.

V is five.

I is one.

So you can see that the handy way that Medical Xavier helps us is that it places those Roman numeral letters in order of size.

So it will stop you from going, "I wonder whether D is 1,000 or M is 1,000," because you can remember the greatest number that we've learnt up to is 1,000.

That is represented by M.

It comes at the beginning of our mnemonic.

This is what we call a mnemonic.

It's a way of remembering something mathematical or something in general using words.

You can come up with your own mnemonic to help you memorise Roman numerals, but you can of course use Medical Xavier to help you if you need.

So let's have a look at some problems involving some Roman numerals.

Let's have a look at the equations on the screen here.

It says, what are the missing values in the following equations? So the first one has a combination of Arabic numerals and Roman numerals in the same equation.

And what we've got to do is work out what the final answer is in both Arabic numerals and Roman numerals.

So what I'd like you to do first of all is see whether you can decode this number here.

Can you identify what that number is based on your knowledge of Roman numerals? I'm going to give you five seconds.

Okay, let's have a look at it together.

So I started with CD, and I'm reminding myself that actually if you have a smaller Roman numeral before a larger Roman numeral like this, then you are subtracting it from that larger Roman numeral.

So, D would be equal to 500, but because I've got the C in front of it, I'm taking away 100.

So CD is 400.

Then I'm going to look at LX.

Now LX is going to represent 50 and then a 10 after it.

So 50 plus 10, which is equal to 60.

And then I've got my II, which is representative of two.

So overall, this number is 462.

So my question is asking me to complete 328 plus 462.

I'd like you to pause the video really quickly now to solve that any way that you would like.

You can use the column method if you like.

Resume it once you're ready.

Okay, so let's have a look together.

So we've got our ones first.

Eight ones plus two ones is 10.

One, so we're going to regroup for one 10.

We've got one 10 plus two 10s plus six 10s, which is equal to nine 10s.

And then 300 plus 400, which is equal to 700.

So I want to represent 790 using Roman numerals.

Five seconds to see if you can work out which letters I would need to represent 790.

Okay, so hopefully you've seen that we're going to need our 500 first.

So I'm going to put D for 500.

Then we're going to need to add on 200 to make it 700.

So I'm going to add on 200 using my 100 C's like that.

And then to make 90, I want to demonstrate that this is 10 before my 100.

And in order to do that, I'm going to choose my X and my C.

So here, this part here represents my 700, and this part here represents my 90.

Let's have a look at the next one.

So for the next one, we're going to have to identify, First of all, what the first number in our operation is, using our knowledge of Roman numerals, and then the answer as well.

And then we'll have to use that to work out what the missing part of our equation is.

So I'd like you to spend 10 seconds identifying what those two numbers are.

If you feel like you need a little bit more time, pause the video now, and resume it once you're ready.

Okay, let's have a look together.

So, I can see first of all that I'm looking at the first number there, which is written using Roman numerals.

And it's got two C's next to each other.

One C would be equivalent to 100, but two C's would be 200.

So that there is 200.

I've got three X's.

One x would be 10.

so three X's is 30, and one I, which is equivalent to one.

So that is 231.

Now looking at this number here.

I can see straight away that I've got a D and then CC.

So I've got my 500 plus 200 there, so that's 700.

And I've got three X's, which is 30, and three I's, which is three.

So overall, that is 733.

So in order to find out this missing value in the middle here, what I'm going to need to do is use my inverse method.

I'm going to need to take my answer.

Subtract my original starting point of my equation, and use that to work out the middle number.

So let's do that together.

We're doing 733, subtract 231.

You can say the numbers as I go along.

So three ones minus one one is equal to two ones.

Then I've got three 10s minus three 10s, which is equal to zero 10s, and 700 minus 200, which is equal to 500.

So what I need to do is represent 500 in that missing space in my equation.

So, 502, I beg your pardon.

502.

So I know how to represent 500, I used the D.

And then to represent two, I use my two ones like that, my two I's together to represent two.

That's 502.

So now it's your turn to have a go.

There are three questions on the board here that I'd like you to try and answer They use the same strategies that we have just practised.

So first of all, work out what those Roman numerals are, then see if you can use that to identify what the missing part of the equation is.

For the last one, you will need to use the inverse method.

Pause the video now to complete your task, and resume it once you're finished.

Okay, so hopefully you've managed to have a go at those three questions.

Let's see what the answers were and see how you got on.

So as you can see on the screen here, I've written the answers using Arabic numerals and then Roman numerals as well.

Spend a bit of time now correcting or ticking the answers that you've got, and seeing whether you agree with the answers that I've provided here.

If not, do go back and have a quick peek.

Have a look at what you might have done differently.

So, moving on to our next bit of learning.

One of the best ways to demonstrate you really understand Roman numerals is to be able to explain why and how errors have been made.

So what we're going to do is we're going to have a look at three examples of someone who has written Roman numerals incorrectly.

But what we need to do is not just explain what the correct version of that Roman numeral is, but also explain the rule that has been broken or the strategy that is incorrect, to demonstrate that we really understand the rules of using Roman numerals.

So let's have a look at a few together, and then I'd like you to practise this yourself.

On the screen here you can see there are three numbers that have been written incorrectly using Roman numerals.

Let's look at the first one.

So the first one says that number four is written using IIII.

What is wrong with that? What's the error that's been made here? Spend five seconds seeing if you can work this one out.

So as you might remember, one of the main rules of Roman numerals is that you're only allowed to use a symbol in the same number a maximum of three times in a row.

So, in this case, the I has been used four times in a row, and that's incorrect.

In order to write the number four, we would need to use the number five, which is a V, and place the I just before it to show that we're subtracting one from five to make four.

This would be incorrect.

Let's look at the next one.

890 has been represented using the Roman numeral symbols XCM.

What is the error here and how would you write it correctly instead? Spend five seconds seeing if you can write this one out.

Okay, so in this case, the error that we've made here is we started with a smaller Roman numeral, then we've put the CM after it.

And what this person has done is they thought, "Well, here we've got 1,000.

And if we subtract 100 from 1,000, and then we subtract another 10, we would get 890." But we need to remember that you can only place one symbol in front of another in order to complete the subtraction.

So in this case, if we wanted to represent 900, it would be absolutely fine to write CM, but we can't then add another digit to subtract in front of that.

That is wrong, and this is incorrect.

In order to actually write the number 890, we would need to use our Roman numeral for 500, so D, and then C, that would be 600, 700, 800.

And then to write 90, we'd have to put our X and C.

That represents 90, 10 before 100.

So you can see here that actually the rule that's been broken here is they placed too many digits in front of another Roman numeral to try and subtract.

You're only have to do that for one symbol.

Have a look at the last one.

The last one has represented 165 as CXLV.

What is incorrect about the way this has been represented? Five seconds.

So in this case, a lot of the number is actually correct.

The part that they represented correctly is the C.

that does mean 100, and the V does mean five, but the representation for the 60 is currently incorrect.

At the moment, what that says is 40, so that would be 145.

What we wanted to say is 165, and the issue is the X has been placed in the wrong place.

In order for us to add it on to the 50, we would need to place it after the 50 in our Roman numeral.

So here you can see that would be the correct version of 165.

Now it's your turn to have a go Have a look at these three areas on the screen.

Can you identify what errors have been made in these three examples? Pause the video to complete your task, and resume it once you're finished.

Okay, let's have a look together, and see if we can work out what the errors are, and why these people have made these errors, what what the mistakes are.

So the first one says 800, and the error here you might have spotted is that, once again, the person who's made this error has decided that they're going to try and subtract 200 from 1,000.

Now, absolutely correctly, 1,000 minus 200 is 800, but remember, you're only allowed to put one Roman numeral in front of another in order to subtract it.

So in this case, you can't represent 800 in this way.

In order to represent 800, you would need to start with your 500, and then add on 600, 700, 800, add on your hundreds like that instead.

The next one says 124.

And in fact, the first part of this is completely correct.

C doesn't mean 100, and XX doesn't mean 20, but this part here means six.

So instead, I should have been placed before the V to represent four.

And for the last one, 55 has been demonstrated using the digits five five.

So technically, the person has decided that actually that might represent 55 because two fives are placed together.

That is not corrected though.

That's incorrect.

In order to represent 55, we would need to use an L and a V.

next to each other like that.

So that reminds us that it's not the digits that we're individually representing using Roman numerals.

It's the value of each of those Roman numerals it makes that is really, really important.

So, some really nice lessons for us, looking at those areas in general there.

So, moving on to your independent task.

There are two questions I want you to complete.

Question one has three parts to it.

Question one says complete the following equations using Roman numerals and Arabic numerals.

So I'd like you to work out and decode what each of those room Roman numerals is, and then answer the question, writing your answer in both Roman numerals and Arabic numerals.

And then for question two, you need to identify what the error is that's been made, and correct the error as well.

Pause the video now to complete your task and resume it once you're finished.

Okay, let's go through your answers.

So as you can see on the screen now, the answers question one have been provided.

Feel free to pause the video now to mark those if you'd like.

And I'm going to explain the answers for question number two.

So as you can see, the first part of question two, the number 14 is being represented with four X's.

And remembering back to our rule about Roman numerals, you can only use the same symbol three times in a row as a maximum.

So four times in a row is incorrect.

In order to represent 40, we would have needed to use the knowledge that L is 50, and place the X before the L to create 40.

For the second one, as you can see here, the person's tried to represent 406.

Now six has been represented correctly, but 400 at the moment is not correct.

A D and then a C is equivalent to 500 plus 100, so this one in this case would be 606.

We would need to swap those that D and C around in order to represent 406 just like that.

And the final one is incorrect because the person has not partitioned their number correctly.

So they want to represent 990.

So they first of all need to represent 900, and then we need to represent 90.

So in order to represent 900, we would need to consider how to write the 100 before 1,000, so CM in this case.

A 90 would need to be represented with an XC to demonstrate the 10 before the 100.

So in that case, they have not partition the number properly, and they have forgotten kind of how to put those numbers together, partition numbers together using Roman numerals.

We come to the end of our lesson.

If you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you for joining me for another maths lesson.

It's been fantastic having you.

Do join me again soon.

Bye bye.