Lesson video

Hello, my name's Mrs. Cornwell and I'm going to be helping you with your learning today.

Now, today we're going to be finding out all about two-digit numbers.

We're going to be looking very carefully, thinking about what we notice, looking for any patterns that can help us so we can use things that we already know to help us with new learning.

So I'm really looking forward to working with you today.

I know you're going to work really hard and will do really well, so let's get started.

So our lesson today is called Use a Number Line to Position and Estimate the Numbers 20 to 99 and it comes from the unit Counting and Representing the Numbers from 20 to 99.

So in our lesson, we're going to learn to position the numbers from 20 to 99 on a number line, including in the context of measures as well.

So we'll think about what we can use on a number line to help us to position those numbers without having to count from zero all the way up each time.

So let's get started with that.

So our keywords today are midpoint, my turn, midpoint, your turn, and previous, my turn, previous, your turn, well done.

So the first part of our lesson then is where we're going to identify the previous and next multiple of 10.

In this lesson you will meet Andeep and Laura and they will help us with our learning today.

Laura and Andeep are counting up to 100 using their number line to help them.

There it is there and you can see it's got the multiples of 10 marked upon it, hasn't it? Let's count with them, one, two, three.

"Let's keep counting until we reach 100," says Laura, are you ready? One, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20.

So now we're in the 20s decade, aren't we? Are you ready? 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60.

That's right, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.

Well done, excellent.

"I wonder if we can use dual counting on a number line," says Laura.

So dual counting is when you say the number of 10s in the number, isn't it? So let's use dual counting to count from 20 to 50.

So it would start off with 20, then it would go two 10s one, two 10s two, two 10s three, wouldn't it? "Let's keep counting until we reach 50," says Andeep.

So let's start from 20 again and we'll say two 10s, two 10s one, two 10s two, two 10s three, two 10s four, two 10s five, two 10s six, two 10s seven, two 10s eight, two 10s nine, three 10s, three 10s one, three 10s two, three 10s three, three 10s four, three 10s five, three 10s six, three 10s seven, three 10s eight, three 10s nine, four 10s, four 10s one, four 10s two, four 10s three, four 10s four, four 10s five, four 10s six, four 10s seven, four 10s eight, four 10s nine, five 10s.

We know five 10s is 50, so we can stop counting.

So well done if you joined in with that.

Perhaps you could use dual counting to count from zero to 100.

That would be a really good thing to do.

Perhaps you could dry that.

Now the children want to count back from 100 to zero.

"Crossing the 10s boundary is tricky when we count backwards," says Laura.

"Let's mark on some numbers to help us." Oh, which numbers is Andeep marked on? That's right, he's marked on the number before each multiple of 10, hasn't he? So the number that has a nine in the ones digit from the previous decade, that makes it easier.

Let's count backwards with them.

100, 99, 98, 97, 96, 95, 94, 93, 92, 91, 90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 68, 67, 66, 65, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, nine, eight, seven, six, five, four, three, two, one, zero.

So well done If you did that.

Those numbers that Andeep marked on from the previous decade were really helpful, weren't they? Let's use dual counting now to count from 100 to 80.

Are you ready? 10 10s, nine 10s nine, nine 10s eight, nine 10s seven, nine 10s six, nine 10s five, nine 10s four, nine 10s three, nine 10s two, nine 10s one, nine 10s, eight 10s nine, eight 10s eight, eight 10s seven, eight 10s six, eight 10s five, eight 10s four, eight 10s three, eight 10s two, eight 10s one, eight 10s.

So well done, excellent.

Perhaps you could use dual counting to count from 100 to zero.

That will be a really good thing to do.

We can use the decades to help us place numbers on number lines and number tracks.

Where are the 70s? Hmm, which decade is that on the number line? The 70s have seven 10s.

We know that the numbers after 70 have seven 10s and some more ones.

These must be within the 70s decade.

And there they are, all of the numbers that have seven 10s.

Where are the 30s? The 30s have three 10s.

We know the numbers after 30 have three 10s and some more ones.

These must be the 30s decade, and there we are, all of the ones with three 10s there.

We know crossing the 10s boundary can be tricky, but we can think of the previous and next decade to help us.

What is the number that is one more than 59? So we know 59 is the end of the 50s decade.

The 60s come after the 50s.

The number after 59 is 60, and there we have it, look.

What is the number that is one less than 70? So we know the 60s come before the 70s, don't they? So the number before 70 must be 69.

I don't think we need the numbers now to help us, do we? So those extra numbers Andeep marked on, we don't need them anymore because when we think of the previous decade, that can help us to find the numbers when we cross the 10s boundary, can't it? Andeep writes some two-digit numbers from the number line on some cards and hides some from Laura.

Let's help her find the missing numbers.

I know in the 60s only the ones digit changes.

The number after 67 is 68.

So she's using that pattern to help her, isn't she? I know that the 70s follow the 60s.

So the number after 69 must be 70.

In the 70s only the ones digit changes.

So the number after 72 must be 73.

So those patterns really helped to find those missing numbers.

Laura marks two numbers on the number line and hides them from Andeep, and there they are.

Look, so we've got number A and number B, but she hasn't told him what those numbers are.

Let's use the multiples of 10 to help him find what decade they are in.

So A is between 40 and 50.

40 is the previous multiple of 10, the one before, and 50 is the next multiple of 10.

A must be in the 40s, it is 40 something.

So now let's find B.

B is between, oh, so let's have a look, which multiples of 10 is it in between? That's right, 70 and 80.

So hmm is the previous multiple of 10, which one is the previous one? That's right, 70 is the previous multiple of 10.

And which is the next multiple of 10? That's right, 80 is the next multiple of 10.

B must be in the 70s, it is 70 something.

Well done if you noticed that.

So now it's time to check your understanding.

Use the number line to find the previous and next multiple of 10.

So we can see we've got a missing number there or an unknown number rather, A, and we need to say A is between hmm and hmm, which multiples of 10? And then you've got to say hmm is the previous multiple of 10, hmm is the next multiple of 10.

So pause the video now while you have a try at that.

And let's see how we got on.

So A is between 60 and 70, isn't it? And which is a previous multiple of 10? That's right, 60 is the previous multiple of 10.

70 is the next multiple of 10.

So well done if you did that.

This time, Andeep marks two different numbers on the number line, but he doesn't hide them.

Okay, we can see that there's 52 and there's 86.

So let's find out which decade these numbers are in and we can use the multiples of 10 to help us, can't we? So the first number 52 is between, that's right, 50 and 60.

50 is the previous multiple of 10, 60 is the next multiple of 10.

So 52 is in the 50s, isn't it? Well done if you did that.

Okay, and then let's have a look at the next one, 86.

So 86 is between, that's right, 80 and 90, and what's the previous multiple of 10? 80 is the previous multiple of 10, 90 is the next multiple of 10.

So what decade is 86 in then? That's right, 86 is in the 80s.

Now it's time to check your understanding of that.

Use the number line to find the previous and next multiple of 10, then say which decade 67 belongs to.

You need to say 67 is between hmm and hmm, which multiples of 10 is it in between, and then say, hmm is the previous multiple of 10, hmm is a next multiple of 10.

And then you'll be able to say which decade 67 is from.

So pause the video now while you try that.

Okay, and let's see how you got on then.

So 67 is between 60 and 70, that's right.

60 is the previous multiple of 10, 70 is the next multiple of 10.

So we can see that 67 is in the 60s decade, isn't it? So well done if you did that.

Laura says she can imagine the number line to help find the previous and next multiple of 10.

So you can see she's got a number there, 34, and she hasn't got the number line, but she's imagining it.

Perhaps you could do that.

"34 is 30 and four more, so I know that the previous multiple of 10 must be 30," she says.

And then, "The decade after the 30s is the 40s.

So then the next multiple of 10 must be 40." Perhaps you could try that with some different numbers.

Andeep is trying to find the previous multiple of 10 in this example.

"I know 50 is the multiple of 10 before 60.

The previous multiple of 10 must be 50." Is Andeep right, what do we think? So imagine that number line, hmm, what do you think the previous multiple of 10 would be? And then perhaps you can find a number line and check to see.

63 is the same as 60 and three more.

So the previous multiple of 10 must be 60.

There's some number line there.

Look 63, we can see that multiple of 10 before it is 60.

And Andeep spots his mistake there, doesn't he? He says, "I must remember to go back to the multiple of 10 at the start of the decade." So well done if you spotted his mistake as well there.

So now here's the task for the first part of our lesson.

So we have got some numbers here and you have to identify the previous or the next multiple of 10.

So they've given you one of the multiples of 10 and that might help you as well.

So you can have a try at that and then when you've done it you can use a number line to check that you are right.

And we can see there are some more examples here as well with some different numbers.

And for these ones you have to find the previous and the next multiple of 10, don't you? Pause the video now while you try that.

So let's have a look, did you do this? So we have a look at A, you can see that 28, well, we know 28 is in the 20s, okay? And the decade after the 20s is the 30s.

So the next multiple of 10 must be 30.

You may have also looked and thought if the previous multiple of 10 was 20, the next multiple of 10 must be 30.

So you may have used that strategy as well.

Let's look at B, so 38.

So we know the decade after the 30s is the 40s, 38 is in the 30s, isn't it? So it must be 40.

And again you may have looked at the previous multiple of 10 and seen that was 30 and thought the next one must be 40.

Then if we look at C, this time we're finding the previous multiple of 10.

So we've got 48 and we know 48 is 40 and eight more.

So 40 must be at the start of the 40s decade and 48's in the 40 decade.

So the previous multiple of 10 must have been 40.

And if you looked to see the next multiple of 10 was 50, you may have used that to help you and thought the multiple of 10 before 50 is 40.

And then if we look at D, we've got 58, 58 is 50 and eight more.

So it's in the 50s and 50 is at the start of the 50s decade, isn't it? And then you may have also used the next multiple of 10, that was 60.

So 50 must be the multiple of 10 before it.

Okay, so let's have a look at these next examples.

And in these we don't have any of the multiples of 10 already marked on to help us, do we? So we've got to find the previous and the next multiple of 10.

So 36 is in the 30s, it's 30 and six more.

So we know the previous multiple of 10 must have been at the start of that decade, which is 30.

And then after the 30s comes the 40s.

So the next multiple of 10 must be 40.

Then if we look at F here, 63 is 60 and three more.

It is in the 60s decade.

So the start of the 60s decade is 60, and then we know that after the 60s come the 70s, so the next multiple of 10 must be 70.

Then we've got G here, 73 is 70 and three more, so the previous multiple of 10 must be 70, and after the 70s come the 80s.

So the next multiple of 10 must be 80.

And then we've got 78, we know 78 is 70 and eight more.

So we know that 70 must have been at the start of the 70s decade there, and then the next multiple of 10 after the 70s come the 80s, so it must have been 80.

So well done if you did that, excellent work.

So the second part of our lesson then is to use a number line to find and estimate numbers.

We can use the lines on the number line to help us find other numbers more easily and we can see that we've got the multiples of 10 marked on there and that can help us, can't it? We know the multiples of 10 can help us find which decade a number is in.

We've already done that, haven't we? Halfway between each multiple of 10 there is also a line to mark the midpoint.

Can you see it there? This can help us find other numbers as well.

Half of 10 is five.

So each midpoint has a ones digit of five.

Can you see them there? Laura draws some arrows to four numbers on the number line.

So we've got A, B, C, and D there, haven't we? So if we look at A first, I wonder how we can use the lines on the number line to help us find out which number A represents.

Laura's got an idea here.

"I can see that A is between 20 and 30.

"It is 20 and some more ones." So it's 20 something.

"I will count on from 20." So it's very near the multiple of 10 there, isn't it? It's very near 20.

"So I will count on from 20, 21, 22, 23," says Andeep.

So well done if you did that.

And there it is, 23.

Then, "B is between 40 and 50." So we know it's in the 40s.

"It is 40 and some more ones." "It is exactly at the midpoint between 40 and 50, so it must be 45." So there we are, well done if you did that.

"C is between 60 and 70, it is 60 and some more ones." Oh, so will we count 60 and all of those ones do you think? Or is there a more efficient way to work that out? Oh, Andeep's noticed, "It is one less than 70, so it must be 69." There we go.

And then, "D is between 80 and 90.

It is 80 and some more ones." So we know it must be 80 something.

"The midpoint between 80 and 90 is 85." That's the halfway line there, isn't it? "This number is two more, so it must be 87," 'cause five and two more is seven, so two more than 85 must be 87.

So excellent if you noticed any of those and used them to help you.

So now it's time to check your understanding of that.

Use the lines on the number line to help you find the missing numbers.

Okay, so we're trying to find A and B.

Remember to use those multiples of 10 and the midpoint to help you and explain how you know you are right.

So pause the video now while you try that.

Let's see how we got on with that.

A is the midpoint between 30 and 40.

It is 35, so well done if you used that midpoint to help you.

B is in the 70s because we know it's between 70 and 80, and the midpoint between 70 and 80 is 75.

One less than five is four, so one less than 75 must be 74.

So B must be 74.

So well done if you used those lines on the number line to help you.

So Laura is playing with these number cards and that she's got a two, a three and an eight.

Let's see how many different numbers she can make.

"I will try the two with the three," she says, to start off with.

So she makes the number 23.

"Now I will try the two with the eight," she says and she makes the number 28.

"I have used the two with the other numbers, but I haven't used the three and eight together yet." So she tries the three with the eight now and she makes the number 38.

"Now I will reverse the digits in the numbers I made.

I could make six different numbers." Did you notice that Laura worked systematically to make sure she found all the possible numbers? Hmm, so perhaps you could try this with some number cards and you could practise working systematically to find all the possible numbers you could make.

Andeep wonders if they could mark some of the numbers they made on a number line.

So he's picked 23 and 38.

Let's use the multiples of 10 and the mid points between the multiples of 10 to help us.

"23 is in the 20s, it is 20 and three more." So there, 20 and then we count three more and we can see as 23.

"38 is in the 30s, it has eight ones, so I can use the five and a bit," we can use the midpoint.

"35 is the midpoint between 30 and 40.

Three more than five is eight.

So three more than 35 is 38." Well done if you notice that as well.

Laura says she's thought of a different way.

"I knew 38 is two less than 40." So you could have used the multiple of 10, the 40 to help you.

So now it's time to check your understanding.

Use the lines on the number line to position the numbers on the number line and you've got 21 and 56 to position, and then explain how you know you are right.

So pause the video now while you do that.

And let's see how you got on.

So 21 is one more than 20, isn't it? So there's one more than 20.

Okay, so we used the multiple of 10 to help us there.

What about 56 then, what would we use to help us with that? 56 is in the 50s, it's between 50 and 60, and the midpoint between 50 and 60 is 55.

So one more than five is six, so one more than 55 is 56.

So well done if you used that midpoint as well.

The children play a game, they each give some clues and their partner has to mark the correct number on the number line.

Let's use the clues to find out what Andeep's number could be.

"I'm thinking of a number.

The 10s digit is the same as the ones digit.

What could my number be?" We can write all the possible 10s digits, then find the ones that are the same.

So there he's done that there.

So that's a really systematic way to work, isn't it? And make sure that you find all the possible combinations.

So we've got 11 is 10 and one more, 22, which is two more than 20.

What will the next number be, do you think? That's right, 33 which is three more than 30, and then it'll be 44.

Now we know 45 is the midpoint between 40 and 50.

So 44 must be one before the midpoint.

So the next number would be? That's right, 55.

So 55 is the midpoint between 50 and 60, isn't it? That goes exactly on the halfway mark.

Then the next number would be, that's right, 66, 65 is the midpoint between 60 and 70.

So 66 must be one more than the midpoint.

Then now our next number would be 77, 75 is the midpoint between 70 and 80, so 77 must be two after the midpoint.

What would our next number be? That's right, 88.

So 85 is the midpoint between 80 and 90.

So 88 must be three more than the midpoint.

You may also have thought that 88 is two less than 90, so you could have used that of 10 to help you there as well.

And then the last number will be? That's right, 99, and we know that 99 is one before 100, isn't it? So I wonder if you used those multiples of 10 and the mid points between them to help you think about where you would mark on those numbers as well.

Now it's Laura's turn, here's her clue.

"What is my number? It is between 20 and 30.

The ones digit is odd.

The 10s and ones digit add up to three." Hmm, I wonder what her number will be.

Let's use the clues to find out what Laura's number could be.

So let's look at one at a time.

"It is between 20 and 30," so we know it's in the 20s.

The ones digit is odd.

So there are all the 20s numbers that have an odd ones digit, one, three, five, seven, nine are the odd ones digits there.

The 10s and the ones digit add up to three, hmm.

So which number there has a 10s and ones digit that add up to three? That's right, 21, two plus one is equal to three.

So that must be the number.

So now it's time to check your understanding again.

Use the clues to find the missing number, then position it on your number line.

Let's have a look at these clues.

So the first clue, the previous multiple of 10 is 60 and the next multiple of 10 is 70.

So pause the video now while you have a think about what decade this number is going to be in.

Let's have a look at the next clue.

So the ones digit is even.

So have a think about which numbers it could be, then write them down, pause the video while you do that.

And then the last clue, the digits sum to eight.

So have a look at the numbers you've written down and see which one has the 10s digit and the ones digit that sum to eight.

Pause the video while you look at that.

And then what did you do? Let's have a look at the clues together.

So the previous multiple of 10 is 60 and the next multiple of 10 is 70.

So there they are, look, so the number must be in the 60.

And then the ones digit is even.

So that means it could be 62, 64, 66 or 68.

And then the digits need to sum to eight.

So which of those numbers have a 10s digit and a ones digit that's sum to eight? That's right, six plus two is equal to eight.

So it's 62, isn't it? So where would we place 62 on the number line then I wonder.

That's right, we know the previous multiple of 10 is 60 because 62 is 60 and some more isn't it? 62 is 60 and two more.

So we can use our multiple of 10 and count two more ones to place it on the number line.

So well done if you did that.

Here we have a metre stick.

A metre stick is 100 centimetres long.

It looks just like the number line we've been using, doesn't it? The children use a metre stick to draw a line that is 100 centimetres long outside.

We can use it to measure the length of objects.

So you use metre sticks to measure length, don't you? Now, Andeep says, "We know the line that they've drawn is 100 centimetres long.

I think we could use the line to estimate the length of other lines," says Andeep.

Oh, that's a good idea, isn't it? So there we've taken the metre stick away, but we know that the line on the top was 100 centimetres long, wasn't it? "I know that 50 is halfway between zero and 100," says Laura.

"So I think this line is a bit more than 50.

I think it's about 53 centimetres long." So they used the top line that they knew was 100 centimetres to estimate the length of the other line, didn't they? And then here's another line.

Andeep says, "This line is quite near to 100 centimetres.

I think it is an 80s or 90s number.

I think it is about 85 centimetres long." So they knew the top line was 100 centimetres.

They used that to make some sensible estimates of what the other line could be.

So perhaps you could try that.

So here's a task for the second part of our lesson.

There are three or unknown numbers on the number line.

Can you see them, A, B, and C? Let's use the clues the children give to help us identify them.

So this number has a 10s digit larger than the ones digit, okay? So you have to think about which of those numbers A, B, or C would fit that clue.

And then we've got this number has a ones digit larger than the 10s digit.

And we've got this number has two digits which sum to 10.

So you can have a think about which number fits which clue, and then when you've done that, write down all the other two-digit numbers which have digits that sum to 10 and mark them on the number line.

What pattern do you notice? Have a think about that as you are doing it.

Pause the video now while you do that.

So here's the second part of our task.

The top line in each question represents 100.

Use this line to estimate the length of the other lines.

So use the 100 line and think, oh, I think the other line is hmm because, and give a reason why you think that.

So remember, you can think about the midpoint, the halfway point, can't you? And where numbers would be about on that line.

So pause the video now while you try that.

So this number has a 10s digit larger than the ones digit.

So it would be? That's right, C, because C is 81, the 10s digit is larger than the ones digit there.

This number has a ones digit larger than the 10s digit.

That's right, it was 26, wasn't it? And then this number has two digits which sum to 10.

And did you notice 55 is exactly on the midpoint between 50 and 60? And five plus five is equal to 10.

And the other two-digit numbers, which sum to 10 are? So 19, one plus nine is equal to 10.

So 19 is the first two-digit number there, and we can find 19 on the number line.

19 is one less than 20.

And then the next number two plus eight is equal to 10.

28 is our next number, and we know 28 is two less than 30.

So again, we can use our multiple of 10 to help us to place that.

You may have also known that 25 is the midpoint between 20 and 30.

Eight is three more than five, so 28 is three more than 25.

And our next number, that's right, it's 37, three plus seven is equal to 10.

So 35 is the midpoint between 30 and 40.

Seven is two more than five, so 37 is two more than 35.

Our next number is 46.

45 is the midpoint between 40 and 50, six is one more than five, so 46 is one more than 45.

What will our next number be, I wonder.

So one plus nine, two plus eight, three plus seven, four plus six, that's right, the next number will be five plus five or 55.

But we already had that one in the first part of our task, didn't we? So the one after that will be? That's right, 64.

So we know 65 is the midpoint between 60 and 70, four is one less than five, so 64 is one less than 65.

And the next number will be? That's right, 73, seven plus three is equal to 10, 73 is 70 and three more, so we can use the multiple of 10 to place that.

You may also have known that 75 is a midpoint between 70 and 80, three is two less than five, so 73 is two less than 75.

Our next number will be? That's right, 82.

82 is 80 and two more.

So we used the multiple of 10 to place that, didn't we? Then our next number is 91, nine plus one is equal to 10, 91 is 90 and one more.

We used our multiple of 10 again to place that, didn't we? So did you notice a pattern in those numbers? That's right, the pattern was that as the 10s digit increased by one, the ones digit decreased by one, didn't it? So well done if you used that pattern to find all the possible numbers that would sum to 10, excellent.

Now let's look at part two of your task.

Did you do this? So we knew the first line was 100.

So let's have a look at what we think on A, that second line would be.

So we can think 50 is the midpoint because it is half of 100.

So and this line is over halfway, isn't it? So I think it's about 60.

So you may have had an estimate of about 60.

So for B, this is nearer to zero than the midpoint of 50.

So I think it's maybe about 20.

So you might not have got exactly 20, but somewhere around that.

And then if we have a look at C, this is quite near to 100, I think it's about 90.

So you may have something around about the 90 mark there.

And then D, this is not near to zero, but not as far as the midpoint.

So I think it's about 35.

Okay, so that would be a sensible sort of estimate there, wouldn't it? So well done if you had estimates that were roundabout those numbers and well done with all your hard work today.

You've worked really hard.

We've used some patterns to help us with our work, haven't we? And we have found out a lot more about how we can use the number line to place numbers and also how to help use that to estimate numbers as well.

So well done, you've worked really hard.

So let's look at what we found out then.

In our lesson today, we found out that we can use the lines marked on a number line to help us find and position other numbers.

The multiples of 10 can help us find which decade a number is in.

The midpoint we refer to is halfway between each multiple of 10.

The midpoint we refer to has a ones digit of five and the midpoint can help us position numbers that are not close to a multiple of 10.

Well done, you've worked really hard and we found out lots about how we can use the lines on a number line to help us find and position numbers.

So well done, excellent work today.