Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you in this lesson.

The lesson comes from our unit on multiples of 1,000, so we're gonna be looking at those bigger numbers.

How are they put together? How are they composed? Where do we find them in real life? And how can we learn about them so that we can work with them when we're solving problems? So if you're ready to make a start, let's get going.

So in this lesson, we're going to be reading and writing numbers up to one million in a range of contexts.

So let's make a start.

We've got three key words.

We've got comma, represent, and numeral.

So I'll say them and then you can repeat them back.

My turn, comma.

Your turn.

My turn, represent.

Your turn.

My turn, numeral.

Your turn.

Excellent.

I'm sure you're familiar with some of those words.

And again, one from your English lessons perhaps.

So let's have a look at what they mean.

They're gonna be useful today.

A comma is a punctuation mark used to indicate a break in a sentence, and it looks like this, but a comma can also be used to mark a break in a number between those place value headings.

So remember to use your commas when you're writing longer numbers to separate your millions from your thousands, from your hundreds, tens, and ones.

To represent something is to show it in a different way.

And a numeral is a symbol or name that stands for a number.

So it could be words, it could be a picture, it could be all sorts of things, but it stands for the number it's representing.

We've got two parts to our lesson today.

In the first part, we're going to be representing multiples of 1,000.

And in the second part, we're going to be looking at Roman numerals.

You may have come across them before.

So let's make a start on part one of our lesson.

And we've got Andeep and Jun to help us today.

And here you can see a Gattegno chart or part of it.

We've got the 100,000s, the 10,000s, and the 1,000s.

And Jun says, "I'm going to make a number on the Gattegno chart, and then you have to make it with the counters.

Are you ready?" I think Andeep's gonna help us, but if you've got some counters, you might want to join in.

"First one." "4,000 is four lots of 1,000," says Andeep.

So he's got his four counters representing 1,000 each.

"Nice," says Jun.

"Second one." Andeep says, "That's five lots of 10,000 and 4,000 is four lots of 1,000." So he's got his four 1,000s and his five 10,000 counters.

"Try this now," says Jun.

What's he put a circle around this time? Andeep says, "I just need another three lots of 100,000 to complete the number." So he's got his 4,000, his five 10,000s, and now his three 100,000s.

Can you think what that number would be? "Okay, one more," says Jun.

"Oh, I see," says Andeep.

We don't have the 10,000s anymore.

So he's just got 300 1,000s and four 1,000s.

I wonder if you can think how that would look written down as one number.

Jun says, "I nearly got you there," missing out the 10,000s.

Andeep says, "Okay, my turn to make up a challenge now.

I'm going to write a number down and you have to make it with the counters and say it." So what's he written down? That's 6,000.

Six 1,000 counters.

Hmm.

Now what does Andeep's number say? Jun says, "We now have 63 in the 1,000s columns and no additional ones, So that's 63,000.

Six lots of 10,000, and three 1,000s." "What about this now?" says Andeep.

Oh, can you see what he's done? Jun says, "Now we have 632 in the thousands columns.

Six 100,000s, three 10,000s, and two 1,000.

So that's 632,000.

"Okay, here you go," says Andeep.

Oh, what's he done now? "Easy," says Jun.

There are now 602 in the thousands columns.

So that's 602,000, six 100,000s and two 1,000.

What did Andeep got rid of? That's right.

There are no 10,000s this time, but we need that zero there to show that the six is still in the 600s column and the two is in the 2,000s, and there are no 10,000s.

"One more," says Andeep.

"What do you notice about this one?" Jun says, "Good try.

It needs a comma, though." Ah, Andeep's put his comma in.

But Jun says, "Or you could leave a space between the thousands and the ones," and you might well see numbers written down with a space rather than the comma.

So it could look like this or it could look like this.

Jun says, "That's 612,000." 600 1,000s, one 10,000, and two 1,000s.

Jun says, "This is just one way of representing 612,000.

Oh, "Go on then, Jun, show us some more ways." "I could do it like this, too." Yeah, we've still got 600 1,000, one 10,000 and two 1,000s.

We just haven't written them down in order.

"Or this way", he says.

There we go, with the 2,000s written in the middle.

Andeep says, "We could also mix them up.

It still represents the same value.

We've still got six 100 thousands, one 10,000, and two 1,000s.

Time to check your understanding.

Can you tick all the correct ways of writing 700,000? Pause the video, have a go, and come back for some feedback.

How did you get on? There were two correct ways.

We can use a comma or a space to show where our thousands stop and where our hundreds, tens, and ones start.

Another check.

What number is represented with the counters? Pause the video and have a think It was 704,000.

We've got seven 100,000 counters and four 1,000 counters.

We've got no 10,000 counters, so we need a zero there to show that we've got no 10,000s.

Time for you to do some practise.

Can you represent each number written on the Gattegno chart in numerals and using counters? If you've got counts, you can use them.

If not, you might like to draw them.

So there's a number written above each of those Gattegno charts.

Can you show the number on the chart with the counters and written in numerals as well? And you've got three on here and three more here to do.

So pause the video, have a go, and we'll get back together to look at the answers.

How did you get on? So the first one was 3,000.

So we're just looking for the 3,000.

Three 1,000 counters and written there with a comma to separate the thousands from the hundreds, tens, and ones.

What about 23,000? We've still got our 3,000, but this time we've got an additional 20,000, so we need two 10,000 counters and three 1,000 counters.

And our number written down is 23,000.

What about 423,000? Can you spot what's happening here? So we've still got our 23,000, but we've got an additional 400,000.

So we need four 100,000 counters, two 10,000 counters, and three 1,000 counters.

And our number written down 423,000 with the comma to separate the thousands from our hundreds, tens, and ones.

53,000 was next.

So five 10,000 counters, three 1,000 counters, 53,000.

503,000.

Hmm, gotta think about the zero here carefully, haven't we? We've got five 100,000s and three 1,000s, but we've got no 10,000s.

So we've got 503,000.

Really important that the zero is there to show us that our five is 500,000 and our three is 3,000, and we have no extra 10,000s.

And what about the last one? 530,000.

So again, we've got to think about the zero here.

We've got 500,000 again, but this time we've got three 10,000s and no 1,000s.

So 530,000.

Did you spot something there? We had a five and a three each time, but they represented different values and we had to think carefully about whether it was a six-digit or a five-digit number and where the zero needed to go to make sure that those digits had the correct place value in our numbers.

Okay, and on into the second part of our lesson, and we're going to look at Roman numerals.

Jun says, "Historically numbers have been represented in different ways." It's really interesting to research how numbers have changed over the years, where the numbers that we use come from now and how people over history have represented numbers in different ways.

Jun says, "So for example, the Romans represented numbers using different numerals to our digits." So different ways of writing things down to represent the numbers.

And we can still see some examples of Roman numerals today.

You might have seen them on clocks, book chapters perhaps.

And at the end of television programmes, often the very last bit of a television programme, the credits at the end where they tell you who was involved in the making of the programme.

And at the very end it will have a series of letters and that represents a number.

We'll look at that in a moment.

So let's have a look at how the Romans built their numbers.

The Romans used an I to represent one, so we can fill that in.

They used V to represent five, and they used X to represent 10.

So we can see one, five and 10.

Jun says, "I wonder if that's why you get an X when you knock all your 10 pins at bowling." (chuckles) Have you attempted bowling? Do you get an X when you get a strike and get all 10? I wonder.

Also, an X is like two Vs, one upright and one upside down.

One V and another V.

Oh, that's interesting.

What did V represent? It represented five, didn't it? And that reminds me that V is equal to five because two fives are equivalent to 10.

When a numeral is placed after a numeral of equal or greater value, the values add together.

So for example, I plus I is equal to II, which is two.

II plus I is equal to III, which is three.

V plus I is equal to VI, which is six.

And V plus II is equal to VII, which is seven.

And V plus III is equal to VIII, which is eight.

We've got some gaps, though.

"However," says Andeep, "They decided that you can't place more than three of the same numeral in a row." So once we've got three I we can't have any more I's.

So four couldn't be written as IIII or nine couldn't be written as VIIII.

So they decided that if they place a numeral with a smaller value before a numeral with a larger value, the smaller value is subtracted.

So that means that IV is equal to V subtract I.

V is equal to five, I is one.

Five subtract one is equal to four, so IV is equal to four.

Can you see how we're gonna fill in the nine now? That's right.

IX is equal to X subtract I.

10 subtract one is nine, so IX is equal to nine.

We can read four as one before five and nine as one before 10.

Some larger numbers use different numerals.

So we've got our I for one, V for five, and X for 10, but then 50, 100, 500 and 1,000 have different letters.

Andeep says, "It's easy to remember 100 and 1,000 as they relate to the prefixes cent- and mille-.

Cent is Latin for 100 and mille is Latin for 1,000.

"There are 100 centimetres in a metre," says Jun, "or 1,000 millimetres in a metre." So if we remember centimetres and millimetres and the fact that there are 1,000 millimetres in a metre, we'll know that 1,000 is represented by the letter M.

And if we remember that 100 centimetres are equal to a metre, we can remember that 100 is represented with the letter C.

I wonder about the other ones, though.

50 was originally an I with a V placed over it, like that.

Over time, the V dropped to the bottom and then flattened into a T, and then that became an L.

So a slightly long-winded route, but 50 is represented with an L.

And D is used for 500 because the original numeral for 1,000 was a circle.

So the original numeral for 500 was a semicircle, which looks a bit like a D.

That makes sense, doesn't it? Okay, so we can apply the rules from before to make larger numbers.

So let's make the multiples of 10.

So 10 we know is X, 50 is L, and 100 is C.

So what do you think the other multiples of 10 are going to be? You might want to have a think about this before we fill it in.

Okay, let's put the numbers in.

20 is XX.

30 is XXX.

60 is LX.

Remember, when we put a smaller value after a larger value, we added them together.

70, LXX.

80, LXXX.

But remember, there was a rule about three in a row, wasn't there? So what do you think we're going to do for 40? Do you remember that when we put a smaller value in front of a larger value, it was subtracted? So 40 is XL, 10 less than 50, the 10 before 50.

And so 90 will be XC, 10 before 100.

So those are on multiples of 10.

"What do you notice?" says Jun.

"Well, they follow the same rules, don't they?" Time to check your understanding.

You are going to complete the table for multiples of 100.

Can you apply what we know from numbers up to 10 and from the multiples of 10, how we could make the multiples of 100? Pause the video, have a go, and then we'll look at the answers together.

How did you get on? Well, we can follow that same pattern.

If 100 is C, then 200 is CC, 300 is CCC.

600 must be DC, 700, DCC, and 800 DCCC.

And then you remember that we put the smaller value in front of a larger value to show that we'd subtracted it.

So 400 must be CD and 900 must be CM.

So well done if you've got those right, I expect you could do that for multiples of 1,000 now, couldn't you? Now you remember we talked about seeing Roman numerals at the end of a television programme? After you've seen all the people who've been involved in making the programme, there's often that series of letters, they're Roman numerals, and they represent the date that the programme was made.

So Roman numerals are quite often seen representing the date somewhere.

So Jun says, "Now we can make lots of different numbers.

Let's make the year we are in." So the year we're in at the moment is 2024.

Wonder what year it is with you.

You might need to adapt this slide.

So let's make 2024.

Well, we know that 1,000 is M, so 2,000 must be MM.

We know that 10 is X, so 20 must be XX.

And now finally we need the four, which is IV.

So 2024 in Roman numerals is MMXXIV.

"What do you notice?" says Jun.

Anything you've spotted? We can see the 2,000.

We can see the 20 and we can see the four.

The Romans didn't have a numeral for zero to represent a placeholder.

So we know that the MM represents 2,000, but we've got nothing to represent the no hundreds.

We just know that because there's nothing representing it, there aren't any.

So there's no sort of place value in Roman numerals.

The numbers are all different lengths.

And we don't have the idea of a zero, there's no placeholder because there's no place value.

Andeep says, "Let's make the year my dad was born, 1988." "Well, we know 1,000 is M," so just one M this time, "900 is 10 less than 1,000, so that is CM.

80 is LXXX.

And eight is VIII." So there's our 1,000, our 900, our 80, and our eight.

That's a pretty long number.

It's much quicker writing numbers the way we do, isn't it? Time to check your understanding.

Can you tick the Roman numeral that represents 2009? Pause the video, have a go, and we'll come back for some feedback.

There we go.

It was B.

MM is 2,000 and IX is nine.

So that was all we needed, 2009.

And remember, Roman numerals do not have placeholder numerals.

There's no real idea of place value in here.

Another check.

Can you write 2,146 in Roman numerals? Pause the video, have a go, and we'll look at the answer together.

How did you get on? 2,000 is MM, 100 is C, 40 is XL, 10 less than 50, and six is VI.

So MMXCLVI is 2,146 in Roman numerals.

There you can see the different elements of the number.

Time for you to do some practise.

So in question one, you are going to add these numbers onto the Roman numerals and then give the answer in a Roman numeral.

So we're starting with MM each time, and then we're adding on those numbers.

Can you write the answer in Roman numerals? And the same for two? Question three, can you write the following numbers in Roman numerals? And question four, what's the longest number written in Roman numerals that is less than 1,000? Think about how the numbers are constructed.

Can you work that one out? Pause the video, have a go, and we'll come back together for some feedback.

How did you get on? So we were starting with MM, 2,000 each time, weren't we? So MM plus one, so 2,001, MMI.

What about 2,000 plus 10? That's right, X was 10, so MMX.

What was the Roman numeral for 100? For C? It was C, wasn't it? MMC.

And what about D? What was the Roman numeral for 1,000? That's right, it was MMM, because we already had 2,000 to start with.

And M we can remember because of the millilitre.

M meaning 1,000.

And what about e? We started off with MM, and we were adding 1,111, so adding sort of one of each in there.

So we were adding another 1,000, so we must have MMM.

Adding 100, which is C, adding a 10, which is X, and a one, which is I.

So we get MMMCXI, 3,000, 100, one 10, and one one.

3,111.

Well done if you got those right.

So how did you get on with question two? This time we were doing some subtraction.

So in a, we had 2,000, subtract one.

So we are looking for 1,999.

So all those one befores.

So 1,999 is represented by 1,000, and then CM is our one less than 1,000 for 900.

XC, 10 less than 100 for 90, and IX, one less than 10 for nine.

What about B? This time we were subtracting 10.

So 2,000, subtract 10 is 1,990.

So it's going to look very much like the number above, but without the IX.

There we go.

So for C, MM subtract 100 is going to be 1,900, isn't it? So we can get rid of the 99.

So MCM 1,000 and then 100 less than 1,000.

In D we've got MM, which is 2,000.

Subtract 1,000.

Well, that's easy, isn't it? It's just M, isn't it? What is 2,000 subtract 1,111.

So let's just think about the number we're going to be representing.

So MM represents 2,000.

So 2,000 subtract 1,000 is 1,000.

1,000 subtract 100 is 900.

900 subtract 10 is 890, and subtract another one is 889.

So we need to represent 889.

So 800 was 503 more hundreds, DXXX.

80 is 50 and three tens, LXXX and the nine, IX.

Wow, there was a lot of thinking to do with that last one, wasn't there, but well done if you've got those correct.

Did you manage to write the following numbers in Roman numerals? So 45, four tens.

So it's one 10 less than 50 plus five.

So XLV, one 10 less than 50, which is L, and then a V for five.

405.

So what were our hundreds? Our hundreds were Cs, our 500 was D, so it must be CDV.

Yes, CDV.

Well done.

1,405.

Well, we've got our 405, so we just need 1,000, M in front of it.

MCDV.

1,045.

So we've got no hundreds this time, so we've got our M and then our 40, which is one less than 50, which is XL again.

Oh, so we've got that XLV, so MXLV.

We can use A to help us there, can't we? I wonder if we can use some of the answers from a, b, c, and d to help us with e, f, g, and h.

I think we can.

We've just done 1,045, so 2,045, we'll just have another M.

2,145 will have a C in there as well.

2,155.

So we've replaced our 40.

Oh, so we just get rid of the X, don't we? There we go.

And 2,956.

That's a bit different, isn't it? 2000 will be MM.

Our 900 is 100 less than 1,000, so it's CM.

And then 50 is our L, and six is VI.

So MM for 2,000, CM for 900, L for 50, and VI for six.

Wow.

There was lots of thinking to do there.

I hope you enjoyed it and I hope you were successful.

So for question four, we asked you what is the longest number written in Roman numerals that is less than 1,000? So we're sort of looking for that longest way we can write anything down.

And we've got 880 and eight here.

And Jun says, Eight, 80, and 800 all have four numerals that represent them." Remember, we could only have three the same together, but if we think about eight, that's three added to something else, isn't it? So that's got to be the longest number that we can make.

So 888 is the largest number written in Roman numerals, which is less than 1,000.

And there it is.

And Andeep says, "It has 12 numerals in it." Much quicker to write it with three eights like we can in our number system, isn't it? And we've come to the end of our lesson.

We've been reading and writing numbers up to one million in a range of contexts.

What have we learned about today? We've learned that multiples of 1,000 can be read more easily by grouping the thousands digits, and we use commas or spaces to separate these.

We've also learned about another number system and that other number systems use different numerals to represent numbers.

Roman numerals can be used on clock faces or to represent dates.

And I hope you've had fun exploring Roman numerals and creating other numbers with them today.

I've certainly enjoyed it and I hope I get to work with you again soon.

Bye-Bye.