Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you today in this lesson from our unit on comparing, ordering and partitioning two-digit numbers.

Have you done lots of work with two-digit numbers before? I wonder, well, I hope you're ready to work hard and think hard today.

So let's make a start.

So in this lesson, we're going to be comparing two two-digit numbers and at the end of the lesson, you're going to be really confident talking about and comparing two-digit numbers, so let's make a start.

We've got quite a few keywords in our lesson today.

We've compare, greater, greater than and less than.

So I'll take my turn to say them and then you have your turn.

So my turn, compare.

Your turn.

My turn, greater.

Your turn.

My turn, greater than.

Your turn.

My turn, less than.

Your turn.

Well done.

So listen out carefully for those words as we go through our lesson today and I expect you'll be using them too to talk about your work.

So there are two parts to our lesson today.

In the first part, we're going to be comparing using practical equipment.

So you might have some base 10 blocks out to help you.

And in the second part, we're going to be comparing using digits in the numbers.

So we're going to look at the numbers themselves to help us decide which number is greater than or less than another one.

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

And we've got Izzy and Lucas helping us with our learning today.

Izzy and Lucas are representing numbers with base 10 blocks.

So you can they've got two numbers here.

Which is number is greater? You might be able to see.

Izzy says, "I wonder how we can find out." And Lucas says, "Well, tens are greater than ones, so let's compare the tens." And you can there, we've put a box around our tens.

Izzy says, "43 has more tens than 29." Is she right? I think she is, isn't she? And Lucas says, "43 is greater than 29, because it has more tens.

That means that 29 is less than 43, because it has fewer tens." Izzy uses a different strategy to find out.

"I can think of a number line to help me," she says.

I know that 43 is greater than 29, because it comes later in the counting sequence.

Ah, she's imagining counting.

She says, "When I count to 43, I count past 29." There's 29 on the number line and there's 43 and if she was counting forwards from zero, she would count past 29 to get to 43.

So 43 must be greater.

We can use greater than and less than signs to compare the numbers.

43 is greater than 29, because it comes further along the number line and 29 is less than 43, because it is not as far along the number line.

And you could also explain the greater than, less than thinking about the number of tens as we did when we saw the base 10 blocks.

Lucas wonders if they can use his strategy to see who has more money.

Can you see we've got some 10 ps and some one ps.

When comparing two-digit numbers, we can find which is greater by comparing the number of tens.

So what can you see there? Lucas says, "The number with more tens will be the greater number." He says, "I know that 71 p is greater than 45 p, because it has more tens." So Izzy says, "I have more money." And you can see, she's drawn around her seven tens.

Seven tens is greater than four tens, so 71 p is greater than 45 p.

Izzy says, "The number with fewer tens will be the smaller number." So Lucas says, "I have less money." Ah, that's a shame, Lucas.

I know that 45 p is less than 71 p, because it has fewer tens.

Let's use Izzy's strategy to check we are right.

Do you remember, she thought about counting on on a number line and which number she would say first if she was counting up from zero.

She says, "When I count to 71, I go past 45." So there's 45 on our number line, 45 p, and there's 71 for our 71 p.

I know that 71 p is greater than 45 p, because it is further along the number line.

And we can use our greater than sign.

71 p is greater than 45 p.

And let's think the other way around.

I know that 45 p is less than 71 p, because, that's right, it is not as far along the number line.

So 45 p is less than 71 p.

Time to check your understanding now.

Use Lucas's strategy in base 10 blocks to find out which of the following numbers is greater than 63.

So we've got three numbers there.

So can you think about the base 10 blocks, you might even have some to use, to find out which of the numbers, A, B or C, is greater than 63 and you can use the stem sentence.

I know that is greater than 63 because.

Pause the video and have a go.

How did you get on? Which one did you decide is greater than 63? Let's complete the stem sentences.

So I know that, ah, seven.

I know that, yes, 73 is greater than 63, because, why is it greater than 63? Ah, it has more tens, doesn't it? In 63 we have six tens, in 73 we have seven tens.

There's our 73 with seven tens, so it's greater than 63 which only has six tens and remember, Lucas said the two-digit number with the most tens will be the greatest.

Time to check your understanding again.

This time, use Izzy's strategy to check if you are right and complete the stem sentence to explain.

So remember, Izzy used the number line.

So there's our number line.

I know 73 is greater than 63 because.

Pause the video and use Izzy's strategy to complete the sentence.

How did you get on? So there's 63 on our number line and 73 on our number line.

So what would Izzy's strategy tell us? I know 73 is greater than 63, because it is further along the number line.

Well done if you spotted that.

73 is greater than 63 and 63 is less than 73.

Ah, so the children are given some more base 10 blocks, but they cannot see the ones yet.

Ooh, do you think that's going to matter? Lucas says, "I can't see what each number is so we can't compare them." Do you think he's right? Izzy says, "I think we can." I think Lucas needs to remember what he said earlier in the lesson, doesn't he? Izzy says, "Tens are greater than ones, so the number with more tens will be the greater number." So Lucas says, "Six tens is greater than four tens, so 60 something will always be greater than 40 something." That's good thinking, Lucas.

So it doesn't matter how many ones are in each number.

The number with more tens will be the greater number.

So we actually had 49 and 67, but because there were more in the 60s number, then that number was always going to be greater.

Four tens is less than six tens, so 49 is less than 67.

Izzy says, "Let's check this on a number line." It doesn't matter how many ones are in each number, the number with more tens will be the greater number.

I wonder how we can think about this one a number line.

So there's 49 and there's 67.

A number in the 60s is greater than a number in the 40s, because it is further along the number line.

So 67 is greater than 49.

And a number in the 40s is less than a number in the 60s, because it is not as far along the number line.

So 49 is less than 67.

Time to check your understanding.

Tick the number which is greater.

Is it A or B? And then complete those stem sentences, I know because.

And can you think of a second why to explain how you know? So pause the video, have a go and then we'll discuss our answers.

How did you get on? Did you complete the stem sentence in two ways to explain how you know? Well, A was the greater number, wasn't it? And I know because it has more tens.

And if we think about the number line, we know that any number in the 20s, which is our number for B, only had two tens, so there are the numbers in the 20s and there are our numbers in the 40s, and they're going to be further along the number line, aren't they? So I can also complete the sentence, I know because it is further along the number line.

Any number in the 40s is going to be greater than the number in the 20s.

Izzy hides the number of tens in her number.

Let's see if we can compare the numbers now.

Do you think we can? Izzy says, "It doesn't matter which number has more ones.

The number with more tens will always be the greater number.

So we can't compare the numbers if we can only see the ones." And Lucas says, "We need to see the tens in each number to find out which is greater." Ah, we can see how many tens Izzy has now.

Now we can compare the numbers.

What do you notice? We've got 27 and 33.

So let's complete the stem sentences.

So which one is greater? Do you want to have a go? That's right, 33 is greater than 27, because it has more tens, that's right.

And can we turn it around the other way? 27 is less than 33, because it has fewer tens.

So in this case, 27 has got more ones, but because it's got fewer tens, it's always going to be the smaller number when we're comparing it with 33.

So the children compare their base 10 blocks again.

I wonder what you notice this time.

Mm.

Izzy says, "Each of our numbers has the same number of tens, so how can we find which is greater?" So far all the numbers we've been comparing have had different numbers of tens, but these two numbers are the same number of tens.

So can we compare them? Lucas says, "This is more tricky.

The tens are the same, so we will need to see the ones." Ah, so we need to see the ones now to find out which number is greater.

And there are the ones.

So which number is greater? Lucas says, "We know that eight is greater than three, so 38 must be greater than 33." And there he's used the greater than sign to compare them.

38 is greater than 33.

We know that three is less than eight, so 33 is less than 38.

So we know that to compare two-digit numbers, we need to compare then tens digits and if the tens digits are the same, we need to compare the ones digits.

Let's use the number line to check that we're right.

So we had 33 and 38.

So both numbers are in the 30s this time, but 38 is greater than 33, because it is further along the number line.

So if Izzy was counting, say from 30 up to 40, she would count past 33 to get to 38.

She'd say 38 later in her count.

So 38 is greater than 33 and 33 is less than 38, because it is not as far along the number line.

Time for you to do some practise.

Use the greater than, less than or equals signs to compare the numbers, and in each case, explain how you know that you are right.

So you've got four pairs of numbers to compare there.

You've got them are base 10 blocks and written out as the numbers themselves.

So you're going to put in the symbols.

And for the second part, you're going to draw the base 10 blocks and write the number to make each of the following correct.

So in A, we can see we've got 36 represented in base 10 blocks, but that number is less than the number that you're going to draw.

So can you draw some base 10 blocks to make those correct? Pause the video, have a go at your tasks and we'll get together and look at the answers.

How did you get on? So in question one, you have the numbers given to you and you were asked to put in the correct symbol in the circle.

So for A, we have 36 and 53 and if you remember, we knew that if a number had more tens, it was going to be the greater number.

So we can say that 36 is less than 53, because it has fewer tens.

And 36 is less than 53, because it is not as far along the number line.

Okay, what about B? We've got four tens and five ones and five ones and four tens.

We've got 45 and 45.

45 is equal to 45 because it had the same number of tens and ones.

What about C, we've got 59 and 22? 59 is greater than 22, because it has more tens and because it is further along the number line.

So what about D? 68 and 62, ah, we've got the same number of tens this time, haven't we? So we've got to compare the ones and eight ones is greater than two ones.

So 68 is greater than 62, because it has more ones.

When then tens are the same, we compare the ones and it will be further along the number line when we count up from zero.

So part two, you had to draw some blocks to make those comparisons correct.

So in A, we had 36 blocks, but that was less than.

Well, you could've drawn anything that either more tens or had three tens and more ones.

In this case, we've drawn four tens and three ones, which is 43.

So 36 would be less than any number with more than three tens or a number with three tens and more than six ones.

So lots of different answers you could've drawn there.

What about B? 45 is greater than a number.

So how could we think about that number? Well, we've drawn 25.

But 45 would be greater than any number with less than four tens or a number with four tens and less than five ones.

So again, lots of different possibilities there.

What about C? 52 is equal to.

Ah, well 52 has got to be equal to 52.

We've drawn it the other way around, five tens and two ones, we've drawn two ones and five tens.

So 52 is equal to 52, because it has five tens and two ones.

And for D, we had to draw a number that was less than 68.

So how can we think about that? Well, we've drawn 67, just taken away one of the ones.

So any number that has less than six tens or has six tens and less than eight ones would be less than 68.

I hope you had fun thinking about those and drawing different representations to make those correct.

So let's move into the second part of our lesson.

This time, we are comparing using the digits in the numbers.

So the teacher gives the children some number cards.

So what have we got? We've got 83 and 75.

We have no base 10 blocks, can we still compare the numbers? Lucas says, "We can look at the tens digit." So can you see the tens digits there? The tens are greater than the ones, so the number with more tens will be the greater number.

We saw that with the base 10 blocks, didn't we? So 83 and 75.

We've written them in a place value chart so that we can see the tens and the ones more clearly.

Eight tens is more than seven tens, so 83 is the greater number.

83 is greater than 75.

"And we can also say that 75 is less than 83, because is has fewer tens," says Izzy.

Let's use a number line to check they were right.

And Izzy says, "When I count to 83, I count past 75 if we're counting up." So there's 75 and there's 83.

And if we're counting on, we will go past 75 to get to 83.

So 83 is greater than 75, because it is further along the number line.

And we can also say that 75 is less than 83, because it is not as far along the number line.

75 is less than 83.

Izzy compares these two numbers and then hides the tens in one of them.

We've got lots of eights there, haven't we? She gives Lucas some clues to help him find the missing number.

Let's help him find it.

"So the missing number," she says, "It is less than 100, but greater than 88." Ah.

Lucas says, "Well nine tens is greater than eight tens but it's less than 100.

So the missing number must have nine tens.

It must be 98," says Lucas.

Let's have a look.

He was right.

98 is greater than 88, because it has more tens and 88 is less than 98, because it has fewer tens.

Let's use a number line to check they were right.

Can you think where those numbers would go? There's 88 and there's 98.

98 is greater than 88, because it is further along the number line and 88 is less than 98, because it is not as far along the number line." So they were correct again looking at the number line.

The children wonder if they can compare their numbers now.

What numbers have we got there? Lucas says, "They have the same digits.

I wonder if that means they are equal?" They've both got a five and a six, haven't they? Are they equal though? Izzy says, "We must think about what each digit represents." So let's think about it using a place value chart.

So we've got 56 and we've got a five in the tens and a six in the ones, haven't we? And Lucas says, "In 56, the five represents five tens." What about in 65? In 65, the six represents six tens.

Six tens is greater than five tens, so 65 is greater than 56 and five tens is less than six tens, so 56 is less than 65.

And Izzy says, "If I counted, 65 would be further along the number line." Time to check your understanding.

Which number, A, B or C, is less than 48? Remember, you could check you answer with the base 10 blocks or with a number line.

So pause the video, have a go and see if you can work out which number is less than 48.

How did you get on? Did you spot that it was 38? We know 38 is less than 48, because it has fewer tens and we also know that 38 is less than 48, because it is not as far along the number line.

Well done if you got that right.

Let's compare some more numbers.

What do you notice about these numbers? Izzy says, "We can think about what's the same and what's different." So can you think about that? What's the same and what's different about these numbers? Ah, Lucas has remembered when the tens digits are the same, we must compare the ones.

So in these numbers, they've got five tens, haven't they? So they're both in the 50s.

So we've got 56 and we've got 53.

So something that's the same is they've got the same number of tens, but what about the ones? Ah, they haven't got the same number of ones.

Six is greater than three.

So 56 is greater than 53.

Three is less than six, so 53 is less than 56.

Let's look at the number line to check they were right.

So there's 53 and there's 56.

They're quite close together, aren't they, on the number line? But if we were counting up, we would say 53 first.

56 is greater than 53, because it is further along the number line and 53 is less than 56, because it is not as far along the number line.

Time to check your understanding.

Which of these numbers is less than 57? And Lucas again says, "Remember, you could check your answer with base 10 blocks or a number line." So pause the video and find out which of these numbers is less than 57.

How did you get on? Did you spot that it was 53? A number with the same number of tens, but fewer ones.

When the tens digits are the same, we compare the ones.

We know that 53 is less than 57, because it has fewer ones.

We also know 53 is less than 57, because when we count, it is not as far along the number line.

Time for you to do some practise.

Oh gosh, you got lots of numbers to compare here.

Can you use the greater than, less than and equals signs to compare these pairs of numbers? Remember to think about what is the same and what is different in each set of numbers.

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

How did you get on? Let's have a look.

So had 33 and 35.

Oh, and we had lots of 30s in A, did we? So lots of numbers where the tens were the same.

So we have to compare the ones.

So 33 is less than 35 because it has fewer ones.

35 is less than 36 because it has fewer ones.

But 36 and 36 are equal.

They have the same number of tens and the same number of ones.

37 and 36, well, 37 is greater than 36 because it has more ones.

And then 40 and 36.

Ah, 40 has four tens, doesn't it? So it has a greater number of tens, so 40 is greater than 36.

So in A, in each pair of numbers, except the last, the tens digits were the same, so we had to compare the ones.

What about B then? All those numbers compared to 60.

Well, 60 is greater than 59, 'cause 60 has six tens, 59 only has five tens.

Now we've got all numbers with six tens, so we've got to compare the ones.

Well, 60 is equal to 60.

Neither of them have any ones.

60 is less than 61, 61 has one one.

60 is less than 62.

And 60 is less than 63.

Each number was compared to 60, so when the tens digits were the same, we compared the ones and if the tens digit was different, we compared the tens.

Let's have a look at C.

What do you notice about these? Mm.

I can see some digits are the same here.

I think the ones digits are the same here, aren't they? So let's have a look.

87 is less than 97.

24 is less than 54.

73 is greater than 63.

48 is equal to 48.

And 48 is greater than 38.

In each pair of numbers, the ones digits were the same, so we had to compare the tens.

And what about D? Ooh, all sorts of different numbers here to look at.

So let's have a think.

86 and 68, well, we've got the same digits there, but they represent different things.

So our eight in 86 represents eight tens and eight tens is greater than six tens, so 86 must be greater than 68.

We've got 30 and three, we've got a three, haven't we? But in 30 obviously it represents three tens, so 30 is greater than three.

28 and 57, all the digits are different, so we can think about the tens and five tens is greater than two tens.

So a number in the 50s will always be greater than a number in the 20s.

So 28 is less than 57.

46 is less than 93 and 45 is less than 53.

So in each pair of numbers, both the tens and the ones were different.

Tens are greater than ones, so we had to compare the tens.

I hope you were successful and got all those symbols in the right places.

And we've come to the end of our lesson.

So we've been comparing two-digit numbers and you've worked really hard and done lots of thinking.

So have we learnt about? We've learnt that when comparing two-digit numbers, we can find which number is greater by comparing the number of tens, but sometimes the tens are the same.

And when the tens numbers are the same, we can find the greater number by comparing the number of ones.

And we can also find the greater number using a number line.

The greater number comes further in the counting sequence, so it will be further along the number line.

Thank you for all your hard work today.

I've really enjoyed working with you and I hope I get to work with you again soon.

Bye-bye.