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 we'll do really well.

So let's get started.

So, our less than today is called represent a number from 20 to 99.

And it comes from the unit counting and representing the numbers from 20 to 99.

So in our lesson today, we're going to learn to represent those numbers from 20 to 99 in different ways, and think about what different parts of the number represent.

Okay, so let's get started.

So our keywords for today are; 10s digit, my turn, 10s digit, your turn.

And one's digit, my turn, one's digit, your turn.

And two digit number, my turn, two digit number, your turn.

Well done.

Okay, so the first part of our lesson today is all about representing two digit numbers.

And in our lesson, we're going to meet Andeep and Laura, and they'll help us with our learning today.

So Andeep needs to collect straws for his art project.

They are stored in 10s with some extra ones.

Every time he needs some more, he writes down the number he needs and Laura collects the correct number.

That's very helpful of her, isn't it? Let's see if we can help her.

So what's that number there, can you read it? Say it out loud, think carefully about what each digit represents.

So that's right, Laura's telling us, "I know that 45 is made up of four 10s and five more ones." So it was the number 45, wasn't it? Did you get that? So 10, 20, 30, 40.

So Laura's got the 40.

"45 is made up of 40 and five ones." So there's 40, and then how many more does she need? 41, 42, 43, 44, 45.

That's right, she needed five more, didn't she? "45 is also made up of 45 ones." If we separated those bundles of 10 and counted them in ones, we would have 45 ones, wouldn't we? Laura is building a model, and this time Andeep is helping her.

Laura writes down how many bricks she needs and Andeep collects them.

Hmm, so can we read that number there? What does that number say? That's right, Andeep knows, doesn't he? He says 34.

"I know that 34 is made up of three 10s and four more ones." So he's given those bricks there.

Hmm, something a bit tricky about those.

Did you spot anything? Yes, Laura spotted it too.

You gave me the ones first.

So instead of giving three 10s and then four more ones, he gave four ones and then three more 10s, didn't he? "I wonder if I should still count them in the same way," says Laura.

Hmm, what do you think? It doesn't matter how the bricks are arranged, we must count the 10s first, then count on in ones.

Okay, so let's do that now.

10, 20, 30.

So we've got 30 so far, haven't we? We've counted the 10s, and now we need to count on in ones.

"34 is made up of 30 and four more." So there's 31, 32, 33, 34.

If we separated the bricks, how many would there be if we counted them in ones do you think? That's right, if we count them in ones there will be 34 ones because there's still 34 bricks there, aren't there? So well done.

The children play a game called Show Me with Base 10 blocks.

Hmm, this sounds like a good game, doesn't it? "I will write down the amount needed, and you have to show me that amount," says Laura.

Hmm, what does that say? Can you think about what that number represents.

That's right, it says six 10s and two ones.

"Six 10s is the same as 60, so that is 60 and two ones," isn't it? It's the same, represents the same amount.

So there's 60, six 10s, and there's two more ones.

"I wonder how many ones are in the number 62," says Andeep.

Ooh, I wonder as well.

If we counted those in ones, how many would there be? "If we separated them and counted, there would be 62 ones," says Laura.

That's right, so we know that one 10 is equal to 10 ones.

So we know that that will be 62 ones, won't it? Well done if you notice that.

Okay, so now it's time to check your understanding.

It's your turn to play Show Me.

Okay, and we've got two different amounts there, haven't we? So can you read them and use Base 10 blocks to show those numbers? Think about what you notice about the numbers.

So after you've made them, think about if you notice anything about them.

Think about what's the same and what's different.

Pause the video now while you have a try with that.

And now let's see how you got on.

We've got three 10s and six ones.

Okay, there they are.

So we know that that will be 36, that represents the number 36.

And then we've got 63, which is six 10s and three ones, isn't it? So what do we notice about those numbers once we've made them? Did you notice that each number can be made with the digits three and six? But in the first example the three represents three 10s and the six represents six ones, so the number made is 36.

And then in the second example, the six represents six 10s and the three represents ones, so the number made is 63.

So the digits were the same, but they represented different amounts in each number, didn't they? So well done if you notice that.

Here's the second part of your check.

Match each description to the representation that shows the same value.

So we've got 85 ones there, and 50 and eight more ones, and then we've got some Base 10 blocks there to represent each number.

So you need to draw a line to match each number to the correct representation.

Okay, so pause the video now while you have a think about that.

Let's see how you got on.

Okay, so 85 ones, that's right, is the same as eight 10s and five more ones, isn't it? So it needed the representation with eight 10 blocks and five ones.

And then 50 and eight more ones is 50, we know is five 10s.

And then eight more ones is there to make the number 58.

So well done if you notice that.

Okay, so the children are playing the Show Me game again, but this time they decide to colour the squares on a 100 square.

Hmm, I wonder if you could do this.

"Show me 70 and nine more," says Andeep.

"I know 70 is made up of seven 10s, so I will colour seven 10s and nine ones." And there we are, seven rows of 10 and nine more ones.

"It is the same as 79 ones." If we counted all of those in ones, we would have 79, wouldn't we? So now it's time to check your understanding of that.

Okay, so colour the squares on a 100 square to show 80 and seven more.

Remember to think about the rows on the 100 square to help you.

So pause the video now while you do that.

And let's see how you got on.

So how many rows would we need to colour to show 80? That's right, we'd need eight rows of 10, and then seven more ones coloured as well, wouldn't we? And there they are.

80 is eight 10s, so you must colour eight rows of 10 and seven more ones.

You may have used the darker lines to help you find seven more ones without counting, because we know that seven is two more than five.

So well done if you noticed that.

The children represent some two digit numbers, but they hide a part.

Their partner has to guess what their number could be.

Oh, this is another game you could try perhaps.

Let's help them.

So we can have a practise now.

There's Andeep and he says, "What could my number be?" And there he's given some Base 10 blocks, hasn't he? And he's given some Base 10 blocks that are in ones, hasn't he? And he's hidden some of those ones, so part of his number is hidden.

Hmm, I wonder what it could be.

Laura's saying, "There are at eight 10s, the number is 80 something." Hmm, did you spot that? There are more than four ones, so it must be more than 84, but it is in the 80s.

Hmm, your number could be 85, 86, 87, 88, or 89, couldn't it? Well done if you notice that.

And there we can see his number was actually 86 because there were six more ones to go with the 80.

"I had six ones, 80 and six more ones is 86." Okay, so now it's time to check your understanding again.

Andeep has made this number, but he's hidden a part.

Oh, slightly different from the last one.

This time he's hidden some 10s instead of some ones, hasn't he? He has less than eight 10s, what is his number? So have a look carefully at what's there and have a think about that.

So pause a video now while you have a try.

And let's see, what did you think? So his number had to have less than eight 10s, okay? And we can see that he already had six 10s.

We can see six 10s.

His number had less than eight 10s, so it must have had, that's right, seven 10s.

So his number must have been, that's right, 78.

Seven 10s and eight more ones.

Seven 10s and eight ones is equal to 78, so his number must be 78.

So well done if you got that? Okay, so we can also use digits to represent two digit numbers.

We've been represented it with Base 10 blocks so far, haven't we? For example, to represent this number in digits, we would write, that's right, 36 because it's got three 10s and six more ones.

This represents the number 36.

The 10s digit is three, it represents the three 10s, doesn't it? The ones digit is six, it represents the six ones.

The children play I'm thinking of a number.

"I'm thinking of a two digit number," says Andeep.

"The 10s digit is two more than the ones digit.

What could my number be?" Hmm, I wonder, how could we work that out? Ooh, Laura's got a good idea.

She's saying, "I will work systematically to find that out." So she's going to have a system.

Work in a certain order to make sure that she finds all the possibilities.

"I will write down all the possible ones digits and leave a gap for the 10s digits." Mm, that's a really good idea, isn't it? "Then I will think of two more than each ones digit." So let's have a think about this.

So two more than zero is two.

Two more than one is three.

And then four, five, six, seven, eight, nine.

Oh, now what do we do? That's right, so we know that two more than eight will be 10.

And then if we had a 10, that would be a three digit number, wouldn't it? So we know that we've found all the possible numbers there.

And I wonder what Andeep's number was.

That's right, "My number was 53," he says.

So we knew it had to be one of those numbers, didn't it? Okay, now it's Laura's turn.

"I'm thinking of a two digit number.

The one's digit is too less than the 10s digit.

What could my number be?" Hmm, I wonder how we could work that out.

Could we use any ideas from how Laura worked to find Andeep's number? Hmm, we may be able to work systematically like she did.

Andeep's decided to do just that.

"I will write down all the possible 10s digits and leave a gap for the ones digit." Hmm, what a good idea there.

So he's written the 10s digits down.

And then he says, "I can't find two less than one, so this is not a possibility." Hmm, so now he has to find two less than each of the 10s digits there, doesn't he? So two less than two is zero, two less than three is one, two less than four is two, and so on.

And he's found all the possible numbers now, because he worked systematically.

"Now I've found all the possible numbers," he says.

So I wonder what Laura's number was then.

Oh, "My number was also 53," she says.

Oh, so she picked the same number as Andeep, didn't she? But just gave some different clues.

So let's have a look at Laura and Andeep's numbers here.

Explain what you notice about them.

Do we notice anything? That's right.

The numbers we found are exactly the same, aren't they? If the 10s digit is two more than the ones digit, then the ones digit must be two less than the 10s digit.

So the clues they gave led to the same numbers, didn't they? So we can see one and two more is equal to three.

Three and two less is equal to one.

So well done if you spotted that.

Okay, so now here's the task for the first part of our lesson.

Now, it's your turn.

Use the clue to find all the possible numbers Andeep could be thinking of.

Okay, so here's his clue.

"I'm thinking of a two digit number.

The 10s digit is three more than the ones digit.

What could my number be?" Hmm, I wonder.

Remember to work systematically like Laura and Andeep did to find all the possibilities.

So use what they did to help you work in a systematic way.

Okay, and then when you've done that, can you predict what the possible numbers would be if the ones digit was three less than the 10s digit? Hmm, so have a think about that as well, okay? So pause the video now while you try that.

And let's see how you got on.

Did you do this? So here's Andeep and he says, "I wrote out all the possible ones digits and left a gap for the 10s digit." Did you do that? There, like that.

"I found three more than each ones digit until I reach nine." So three more than zero is three.

Three more than one is four.

Three more than two is five and so on.

And he did that all the way up to nine.

And then there are no more ones digits to make two digit numbers, are there? If he had three more than seven, it would be 10, and that would make a three digit number.

So we know that he's found all the possible two digit numbers there, hasn't he? "When I reached nine, I knew there were no more possible two digit numbers," says Andeep.

What did you predict the numbers would be if the ones digit was three less than the 10s digit? Hmm, that's right, the numbers would be exactly the same, wouldn't they? Because if the 10s digit is three more than the ones digit, the ones digit will also be three less than the 10s digit.

So well done if you notice that.

Excellent, you've worked really hard in our lesson so far, haven't you? Okay, so the second part of our lesson is looking at number patterns.

So we're going to explore number patterns in two digit numbers.

And when we spot and notice those patterns, it can make the maths, the number work, much, much easier.

And it helps us to work more efficiently, so it's really important that we learn to look at those number patterns and to use them to help us.

Okay, so Laura writes a list of numbers for Andeep to represent.

And there they are, can you read them? That's right; 35, 36, 37, 38.

"I will tap each number on a Gattegno chart to help me," says Andeep.

So there's his Gattegno chart, and he's going to tap the first number there.

"I will represent 35 like this," he says.

And we know 35 is three 10s five or a 30 and a five, isn't it? And he represents it with Base 10 blocks like that.

Then the next number.

Ooh, that will be, what will he tap on the Gattegno chart? That's right, a 30 and a six for 36.

"I will represent 36 like this." And then his Base 10 blocks? 10, 20, 30, 31, 32, 33, 34, 35, 36.

Let's think about what's the same and what's different in each number.

Hmm, have a good look.

That's right, the 10s digit stays the same, doesn't it? It's got three 10s or 30 in each number, but the ones digit is changing.

And Andeeps noticed something.

Each number is one more than the last because the ones digit is increasing by one each time, isn't it? "I can just add one to the amount already there." So the next number, 37, is a 30 and a seven.

It's exactly the same as the last number, except the ones digit is one more.

So does he need to take all of that Base 10 away, the Base 10 blocks, and start again to make 37 do you think? No, that's right.

You can just add one more block, can't he? And let's have a look at 38 then, so we know it'll be a 30 and a eight.

That's right, because eight is one more than seven.

And what will he do with the Base 10 blocks.

That's right, he just puts one more on, doesn't he? Perhaps you could continue the pattern using your Base 10 blocks.

Think about what might happen once you get to the end of the 30s, the end of that decade.

Hmm, that would be interesting to explore, wouldn't it? Okay, so now it's time to check your understanding again.

Use Base 10 blocks to represent this list of numbers.

So you can read them there, can't you? Tap out each number on a Gattegno chart first to help you? 'Cause that can help you spot any patterns, can't it? Remember to think about what's the same and what's different in each number.

Pause the video now while you have a try at that.

Let's see how you got on.

48 was the first number, wasn't it? And you can represent that with four 10s and eight ones because 48 is the same as four 10s eight, isn't it? And then what did we notice about this next number? That's right, the 40 stayed the same, didn't it? It still had four 10s, but the ones digit changed.

It went from 48 to 47.

What do you notice about those ones digits.

That's right, the seven is one less than the eight.

So you could just take one off the eight ones, couldn't you, to make 47.

And then the next number is 46.

So again, you could just remove one's block, couldn't you? And then 45, and you remove one's block again there.

So did you notice the 10s digit remained the same, but each one's digit was one less than in the previous number.

So you could just remove a one each time to make the next number, couldn't you? So well done if you spotted that pattern and used it to help you.

Now, Andeep gives Laura some numbers to represent.

And there they are, look.

What's the same and what is different this time? Hmm, look carefully.

Could we tap them on the Gattegno chart to help us? 57, and then we've got 67, and then we've got 27.

Is this helping you? And 97, did that help you spot what was the same and what's different? Andeep has found it useful.

He says, "I've noticed that the ones digit remains the same." So that ones digit is seven in each case.

So, "I can put out seven ones, and I will only need to change the 10s digit in each number." So he's working more efficiently.

Instead of taking all of his Base 10 blocks away and starting from the beginning again with each number, he knows that he can keep the ones blocks the same.

So there's his seven ones.

And then to make 57, that's right, he needs five 10s, doesn't he? And then to make 67, that's right, he'll need six 10s and the seven ones.

To make 27, two 10s and seven ones.

And 97, nine 10s and seven ones.

So did you see how spotting that the ones stayed the same all the time helped him when he was making those numbers and representing them with Base 10 blocks, didn't it? So we can see how important those patterns in numbers are to help us work more efficiently.

Laura says, "That has given me an idea for a new set of numbers." Oh, and here's her numbers.

Let's have a think about these ones then, what's the same and what's different this time? Explain what you notice.

So we've got 32, and then we've got 42, and then we've got 52, and then we've got 62.

Did we notice any pattern there? Andeep did.

He says, "I notice that the ones digit remains the same so I don't need to change these." That was like in the last example that he did.

And so there's the two ones, he's put those out.

And then the 10s digit had a pattern as well, but they increased by one each time.

So we had 32, which was three 10s and two ones.

And then 42.

So you didn't have to take the three 10s away and put four on, you could just add one more 10, couldn't you, to the 32.

So 42, and then what will we do to 42 to make it into 52? That's right, we just need to add another 10.

So that's five 10s and two ones.

And then what can we do to make 52 into 62? That's right, we add another 10.

So well done if you've spotted that pattern and used it to help you.

Now, the children are playing a game.

They fill a bag with Base 10 blocks, 10s and ones, and then take it in turns to pick out six blocks.

Let's see what numbers they make.

Andeep says, "I picked out two 10s and four ones." And there's the two 10s and four ones.

"I made the number 24." Can you see he's picked up six blocks altogether.

Some of them were 10 blocks and some of them were one blocks, but there were six blocks altogether, weren't there? Laura says, "I think I will be able to make the number 25." Is Laura right, can she make 25 with six Base 10 blocks? "My brain must be growing, I spotted my own mistake," she says.

"You would need two 10s and five ones to make 25, so you would need a total of seven Base 10 blocks." So she can't make that number with six blocks, can she? "I can only use six Base 10 blocks altogether." So she's found a different number that she could make using six blocks.

"I could use three 10s and three ones altogether." She's used six blocks and she's made the number 33.

That's right, that would make the number 33.

So well done if you notice that.

Perhaps you could play this game with a partner, and try and predict some of the numbers you could make.

That would be an interesting thing to do.

Perhaps you could look for any patterns that you may spot to help you.

Okay, so here's a task for the second part of our lesson.

Use Base 10 blocks to make a list of two digit numbers which all have the same ones digit.

So that's your first part.

And then use Base 10 blocks to make a list of two digit numbers which all have the same 10s digit.

Hmm.

And then use Base 10 blocks to make a list of two digit numbers which can be made using only seven base 10 blocks.

Remember to write down the numbers as you make them, and to look for those patterns that can help you.

Can you predict any of the numbers before you make them? And remember how we've been practising working systematically to help us to work more efficiently and to make our number work easier.

Pause the video while you have a think about that.

Let's see how we got on.

You may have done this.

So this was for the numbers that all have the same ones digit.

Andeep saying, "I know the ones digit must remain the same in each number.

I will choose numbers with a ones digit of five." So he decided to use five ones in his numbers.

And then he went through systematically, he had one 10 and five ones, which is 15.

Two 10s and five ones, which is 25.

Three 10s and five ones, 35.

Four 10s and five ones, 45.

I wonder what's coming next.

That's right, five 10s and five ones, 55.

Six 10s and five ones, 65.

Seven 10s and five ones, 75.

Ooh, what's coming next? Eight 10s and five ones, 85.

And nine 10s and five ones, 95.

So did you notice how working systematically helped him to work more efficiently and made the number work easier? It also allowed him to see that he'd found all the possible answers that would have a ones digit of five.

So well done if you work systematically and did that as well, excellent.

So now we're going to look at the example where they all have the same 10s digit.

So Andeep says, "I know the 10s digit must remain the same in each number.

I will choose a 10s digit of three." I wonder what digit you chose.

So there's three 10s and one one, 31.

And what do you think his next number that he tried is going to be if he's working systematically? That's right, three 10s and two ones, 32.

Three 10s and three ones, 33.

Three 10s and four ones, 34.

What will be next I wonder.

That's right, three 10s and five ones, 35.

And then three 10s and six ones, 36.

And then 37, and 38, and 39.

So well done if you work systematically and use the patterns to help you as well.

Let's look at the numbers that can be made using only seven Base 10 blocks.

So the first one that Andeep tried was seven ones.

And then what are the numbers if you had any 10s there? So if you had one 10 and six ones, then that's still seven blocks, isn't it? And it makes the number 16.

And then he took one of his one blocks away and replaced it with a 10s block to make two 10s and five ones, 25.

And then he takes another ones block away and replaces it with a 10.

So what will that number be? That's right, three 10s and four ones, 34.

I wonder what the next number could be then.

That's right, four 10s and three ones, 43.

And then five 10s and two ones, 52.

Six 10s and one one, 61.

And what will the last number be, do you think? That's right, seven 10s, 70.

And did you notice again how Andeep worked systematically? He used the patterns to help him there, didn't he? And that's how he knows he's found all the possible answers.

So well done if you did that.

You've worked really hard in our lesson today.

And hopefully you are feeling much more confident about spotting those number patterns and seeing how useful they can be in helping us to make our number work easier, and helping us to work more efficiently.

So well done.

So let's think about what we learned in our lesson today then.

So the order in which 10s and ones are arranged does not affect the value of the number, does it? So you can put your ones down first and then your 10s, or your 10s down first and then your ones, and the number represented will still be the same, won't it? And then we can use the patterns in numbers to help us represent new numbers.

And we've seen how we can work more efficiently and make our number work easier by looking for and using those patterns.

So well done.

You've worked really hard in our lesson today, and I've really enjoyed working with you.

And perhaps you can use some of those pattern spotting strategies that we've practised to help you in your work in the future as well.