Lesson video

(door thudding) <v ->Hello, my name's Mrs. Hopper</v> and I'm really looking forward to working with you in our maths lesson today.

We are going to be thinking all about place value, numbers up to 100 and how we can apply that and other strategies to adding and subtracting.

So, I hope you're ready to work hard and have some fun in our maths lesson today.

So, the outcome for our lesson in this unit on securing place value to 100 and applying to addition subtraction is to represent 3-digit multiples of 10 in different ways.

So, by the end of the lesson, you should be able to represent 3-digit multiples of 10 in different ways.

Just one key word today in our lesson, and that word is equal.

So, let's have a go at saying that.

I'll take my turn then it will be your turn.

So, my turn equal, your turn.

Well done.

So, what does equal mean? Equal means exactly the same amount or value.

And the symbol we use is they're those two lines together.

So, that symbol for equals.

So, we can say that 10 tens are equal to 100.

10 tens equals 100.

So, look out for that word as we go through our lesson today.

So, there are two parts to our lesson today.

In the first part of our lesson, we are going to be looking at 3-digit multiples of 10 expressed as a number of tens.

So expressed means, talked about or written down in that way.

So the first part is expressing those 3-digit multiples of 10 as a number of tens.

In the second part of the lesson, we'll express those 3-digit multiples of 10 as hundreds and tens.

So, let's get into the first part of our lesson.

and Izzy and Jacob are gonna be helping us with our learning today.

So, let's count forwards and backwards with Jacob.

We're going to count in tens and Jacob's asking a couple of questions there.

"What do you notice as we count," and, "Can you see a pattern?" So are you ready to count in tens? Let's count forwards from zero all the way to 190.

Are you ready? Let's go.

0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190.

Well done, great counting in tens.

So, Jacob said, "Could we count backwards as well?" So see, again, think about what you notice.

Do you see any patterns? Let's count backwards from 190.

Are you ready? Okay, let's go.

190, 180, 170, 160, 150, 140, 130, 120, 110, 100, 90, 80, 70, 60, 50, 40, 30, 20, 10, and 0.

Great counting.

Well done.

So, what did you notice? Could you see a pattern? Izzy says, "I noticed that the pattern of 10, 20, 30, 40, 50, 60, 70, 80, 90 repeated in the bottom row." So, once we got over 100, Izzy noticed that, that 10, 20, 30 happened again.

That 110, 120.

I wonder if you noticed that as well.

So, we're going to use our counting now and we're gonna count some straws.

Now, straws come in bundles of 10.

So, if you look carefully, you can see ten straws in that bundle.

And we're gonna help Izzy to count the straws in different ways.

And we're going to use some stem sentences.

Here's our first one.

There are hmm groups of ten straws.

So, we're going to be counting groups of ten straws.

So Izzy says, "Let's count the tens and we can express the number as groups of ten." So, you ready to count the groups of 10? 1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens, 10 tens, 11 tens, 12 tens, 13 tens.

So, there are 13 groups of ten straws.

We're expressing that number of straws as groups of ten, 13 groups of ten straws.

Now, we've added an extra bit to our stem sentence.

So, we know there were 13 groups of ten straws, but now we're adding the bit that says there are hmm straws.

How many straws are there altogether, if we express that, those 13 groups of 10, as a multiple of ten straws? So, Izzy says, "Let's count in tens, and we can express the number as a 3-digit number." So, are you ready to count in tens? Let's go.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130.

So we can still see that there are 13 groups of ten straws, but this time we've counted them in tens and we can see that there are 130 straws.

So, let's just say those stem sentences.

There are 13 groups of ten straws.

There are 130 straws.

Can you say that? Your turn.

Excellent, well done.

So, remember those sentences, we're going to be using those a lot in our lesson today.

So, there's our stem sentence.

There are hmm groups of ten straws.

And Izzy says again, "Let's count the tens.

We can express the number as groups of ten." Are you ready to count the groups of ten straws? Okay, let's go.

1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens, 10 tens, 11 tens, 12 tens, 13 tens, 14 tens.

So, there are 14 groups of ten straws.

Okay, so we've expressed the number as groups of 10.

And here's the second part of our sentence.

There are 14 groups of ten straws.

There are hmm straws.

So Izzy says, "Let's count in tens this time and We can express the number as a 3-digit number." So, are you ready to count those 14 groups of straws in tens? Okay, let's go.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140.

So, there are 140 straws.

And you can see there's still the 14 groups of ten straws, but now we know there are 140 straws.

So, can we say those sentences together? I'll say them first and then you say them.

So my turn, there are 14 groups of ten straws.

There are 140 straws.

Your turn Well done.

Can you see a link there between the 14 and the 140? I wonder what you can see there.

Okay, time to check your understanding now.

We've got some groups of ten straws here and our stem sentence.

There are hmm groups of ten straws.

And Jacob says, "Can you count the groups of straws? 1 ten, 2 tens, 3 tens," like we've done on the other slides, and express the number of straws as a number of groups of ten.

So pause the video now and have a go.

How did you get on? Did you see that there were 12 groups of ten straws? So 12 tens, there are 12 groups of ten straws.

Okay, but we can express this another way, can't we? So Jacob says, "You can express the amount as 12 tens." Jacob says, "Can you now express the amount by counting in tens?" How many straws are there all together? So pause the video, count in tens and complete the other part of our stem sentence.

How did you get on counting in tens? Did you count up to 120? That's right.

So, the second part of our stem sentence says, there are 120 straws.

Well done.

Okay, so now we've got some packs of ten pencils.

So, we can't see the pencils this time, but we know from the packet that there's 10 pencils in each packet.

So, that same stem sentence, there are hmm groups of ten pencils.

Let's count the groups of ten pencils together.

Are you ready? We're gonna count 1 ten, 2 tens, 3 tens.

Let's go.

1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens, 10 tens, 11 tens, 12 tens, 13 tens, 14 tens, 15 tens.

So, there are 15 groups of ten pencils, and the number of pencils can be expressed as 15 tens.

Now, let's count the pencils in tens and let's find out how many pencils there are all together by counting in tens.

Are you ready? Let's go.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150.

That's right, there are 150 pencils.

The number of pencils can be expressed as 150.

So, even when we can't see the 10, we know there are 10 in there.

We can still use our counting in tens to find out how many pencils there are.

Time to check your understanding.

We've got some pencils here.

And do you agree with Jacob? Jacob says, "There are 120 groups of ten pencils." Do you agree with Jacob? Pause the video and see what you think.

What did you think then? Are there 120 groups of ten pencils? And how many pencils would that be all together? Izzy says, "No, 120 groups of ten pencils would be too many." How many groups of ten pencils can you see there? Izzy says, "There are 12 groups of ten pencils." And if we count that in tens, that would mean there were a 120 pencils.

So, Jacob's got muddled up, hasn't he? He's counted in tens, but thought he was counting the groups of ten pencils.

So, we need to be careful when we're counting.

Are we counting the groups of ten or are we counting in tens? Something to be careful for with when we are counting.

So, this time we've got some counters here and each counter represents 10, it represents 10 ones or 1 ten.

So, what can we see? We've also arranged them in a sort of tens frame for you as well.

So we can see really clearly what we've got.

Let's have a look.

So, we're going to say the number as you would normally read a 3-digit number.

So, that was sort of sort of counting in tens, wasn't it? So, if we counted those, we would count and we'd know that there are 10 tens in the frame on the left.

So, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, and two more, 110, 120.

So Izzy says, "That number would be 120." But we can also express the number as a number of tens.

So, we can see there that we've got 10 and two more.

We've got 12 tens altogether.

So, Jacob says, "We've got 12 tens." 120 is equal to 12 tens.

Can you say that? I'll have my turn then your turn.

My turn, 120 is equal to 12 tens.

Your turn.

Well done, and there's our keyword equal meaning exactly the same as.

120 is exactly the same value.

It's the same number as 12 tens.

So, time for you to have a think about this to check your understanding again.

So, we've got some more 10 counters there arranged in our tens frames.

So, you're going to say the number as you would normally read a 3-digit number.

And you are also going to express the number there as a number of tens.

So, pause the video and have a go.

So, how did you get on? Did you say the number as you would normally read it and counting in tens? And then did you find out how many groups of 10 there were? So, if you counted in tens, as Izzy says, you'd have seen there was 140 represented there with our tens counters.

And Jacob counted the number of tens, 14 tens.

So, we can say that 140 is equal to 14 tens.

If we count the number of tens, we see there are 14.

If we count in tens, we count to 140.

So, 140 is equal to 14 tens.

And there's that key word again, meaning exactly the same.

Time for you to do some practise.

So, there's a task for you here.

So, you're going to need some tens counters.

So, you might hopefully, you've got some tens counters in front of you and you're just going to take a handful of tens counters.

And you're going to count the number of tens and you're going to count in tens.

So, you can write and say the total in two different ways.

So the first way you're going to say it is with the number of tens you have.

So, how many tens counts have you got? And the second way is the way that, that 3-digit number is normally read.

So, Jacob's had a go here and he says, "There are 12 tens." So, he picked up 12 counters, there are 12 tens and he then counted in tens and he says the number is 120.

So, you're gonna repeat that activity several times.

Lots of practise at counting the number of tens and counting in tens to find out how many what that number is worth as a 3-digit number.

So, pause the video and have a go.

How did you get on? I wonder what you picked out in your handful of counters.

Jacob had another go and Jacob picked out 13 tens counters.

So, Izzy said it was 13 tens or 130 and she knows that 130 is equal to 13 tens.

I wonder what numbers you picked.

Okay, so time for the second part of our lesson.

So, this time we're going to express those multiples of 10 as hundreds and tens.

So, let's have a look.

So, we've got our pencils back again.

So, let's count the pencils in groups of 10 again.

Are you ready? Let's go.

1 ten, 2 tens, 3 tens, 4 tens, 5 tens, 6 tens, 7 tens, 8 tens, 9 tens, 10 tens.

Okay, so there are 10 tens and we know that 10 tens are equal to one group of 100.

So, we know that in there we've got one group of one hundred, there are 100 pencils.

If we tip them all out, there'd be 100 pencils.

10 groups of 10, it's equal a 100.

100 is composed from 10 tens.

You might have come across that idea before.

So, how many pencils are there? There are 100 pencils.

Now, then we've got our one group of 100.

So, we've got a new stem sentence here.

There is one group of one hundred and hmm more tens.

There are hmm pencils.

So, we're going to think about our pencils still in groups of 10, but we're going to know that our 10 tens is equal to 100.

And we're going to think about how many more tens we've got and how many pencils we've got altogether.

So, let's see how many more tens we've got.

So, we've got one group of one hundred, and one, two, three, four more tens.

So, we've got one group of one hundred and 4 more tens.

So, how many pencils is that altogether? Well, we could say we've got 14 groups of ten pencils and we could count on from 100.

So, we could say we've got one hundred and we've got four more tens, 140 more.

So, there are 140 pencils.

One group of one hundred and 4 more tens.

So, one group of one hundred can be expressed as 100 and 4 more tens is equal to 40.

There's our key word again, equal to 40.

So, we've got 100 and 40, which is equal to 140.

And we can show how that 140 is composed on a bar model.

So, we've got our whole is 140 and our two parts are 100 and 40.

Okay, so we're going to have another go.

So, there's one group of one hundred, we've got those already and we're going to have some more tens, and we're gonna work out how many pencils there are altogether.

So, are you ready? I wonder how many more groups of 10 we've got this time? Let's have a look.

1, 2, 3, 4, 5, 6.

So, we've got one group of one hundred and 6 more tens.

And what's 6 tens equal to? We know that 6 tens is equal to 60.

So, we've got one group of one hundred and 60 more.

So, there are 160 pencils in total.

And Jacob is reminding us, "One group of one hundred can be expressed as 100 and 6 more tens are equal to 60." And again, we can show that composition of 160 in a bar model.

So, our whole is 160 and our parts are 100 and 60.

Time to check your understanding.

So we've got another image here with some packs of ten pencils.

And you can see that there is one group of one hundred with the ring drawn around it, and there are hmm more tens.

So, Jacob asks, "How many pencils are there?" And Izzy's given you the stem sentence, "There are hmm pencils." So we're going to express that number as a 3-digit number and then I wonder what the bar model might look like.

I wonder if you can think about that.

Pause the video and then we'll have a look together.

Okay, so did you spot that there were two more tens? So, there is one group of one hundred and 2 more tens.

So, how many pencils is that? That's 120 pencils, isn't it? And then we've got the bar model there with 120 as our whole, our one group of one hundred as one part, and our two more tens, which we know is equal to 20 as the other part.

So, there are 120 pencils.

Okay, so Jacob's introducing us to a new chart here.

And Jacob says, "This is a Gattegno chart and we're going to use it to count in tens past 100." So, you'll see some rings appear as we count.

So, how does this help us to look at our numbers? And Izzy says, "Can you see the 100 and the number of tens when we count over 100?" So, thinking about that 100 and hmm more tens, can you see that as we count using this chart? Are you ready? Let's count from 10.

10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190.

What did you notice as we counted? Jacob says, "What did you notice as we counted past 100?" And Izzy says, "I can see 100 and one more 10." So, once we got over 100, we had our one hundred and 1 more 10.

And then did you notice that that ring moved along from 10 to 20 to 30 to 40 all the way along till we got to 190? So, we could see those extra tens being added onto our 100 as we counted.

And Izzy says, "What we can see here is that there is one group of 100 and there is one more 10." So you can imagine that would be the pencils in the green ring.

One group of one hundred and 1 more pack of pencils.

And here we can see it as 100 and 1 more ten on the Gattegno chart.

And Jacob's just pointing out there, "One hundred and 1 more ten is equal to 110." Okay, so we've got a lot of base 10 blocks on our screen here.

I wonder if you want to just have a moment to have a look at them.

Let's see what we can see.

So, I think underneath Jacob I can see one hundred and 3 more tens.

And underneath Izzy I can see an awful lot of tens, but they're not arranged in any way are they? So ooh, think about it.

We've been thinking about our numbers as one hundred and hmm more tens and we've been thinking about our numbers as there are hmm tens.

So, let's see what we're going to have a look at here.

So Jacob says, "What do you notice about the representations?" Jacob says, "What's the same?" Let's see what Izzy's noticed.

Izzy says, "They both represent 130." Jacob says, "Yes, but what's different?" So Izzy says, "On the right-hand side, I can see that there are 13 tens." So Izzy's counted them.

All those tens and there are 13 tens.

And then she says, "On the other side of the screen there is 100 and 3 more tens." So, they actually represent the same number, but they're organised in different ways.

I wonder if you can think about those organisations, which is the easiest to see? Maybe sometimes it's useful to think of them in one way and useful to think of them in another way on another occasion.

But they both represent the same number, 13 tens and one hundred and 3 more tens.

They both represent 130.

So, let's have a look at our tens counters here and we've got them arranged into our tens frames.

So again, Jacob says, "What do you notice about the representations? What's the same?" And Izzy says, "They both represent 160." So, can you have a look at that? How do they both represent 160? Jacob says, "Well, what's different then?" Now Izzy says, "In the tens frames we can see we've got 16 tens." And then there they are within our circle.

And then underneath we've got 100.

So, we've got one counter representing one hundred and 6 more tens, which we know is 160.

They both represent 160.

But on the left, we've got the tens frames representing it as 16 tens.

And then underneath where Izzy is, we've got it represented as one hundred and 6 more tens.

Okay, so Jacob says again, "What do you notice about the representations here?" I wonder what you can see? What's the same? And Izzy says, "They all represent 100." Jacob says, "Well, what's different?" Well, Izzy says, "We can see that there are 10 tens in 100," and we can see that with the counters in the tens frame, can't we? There are 10 tens in 100.

There are 100 ones in 100.

So, our base 10 block there shows us 100 ones organised into one 100.

And then we've got this box of 100 sweets on the end and she says, "I can see a box representing 100 sweets." And there it is.

So, what do we notice about the representations? And Izzy says, "When the representation is grouped together, we can count it as a whole group without counting each part individually." So, we've got our box of 100 sweets.

Oh, now we've got another packet of sweets.

And if I count carefully, I know that, that packet has got 10 sweets in it.

So, I wonder how many extra packets of 10 we've got.

Remember our stem sentence there are, there's one group of a hundred and hmm more tens.

I wonder how many more tens we've got.

So, we've got 1 ten there, 2, 3, 4.

So, we've got 4 more packs of ten sweets.

And Izzy says, "There is one group of one hundred and 4 more tens." And one group of one hundred and 4 more tens is equal to 140.

So, we've got 140 sweets altogether.

One hundred and 4 groups of ten sweets.

Okay, so time to check your understanding.

Izzy says, "How many groups of one hundred and how many more tens?" And you've got your stem sentences there.

There is one group of 100 and hmm more tens.

There are hmm sweets.

So, pause the video, and fill in those gaps in the stem sentences.

So, did you count that there were five more tens? And we know that five more tens is equal to 50.

So, there are 150 sweets.

Time for you to have some practise.

We've got lots of statements here and you'll have a sheet of them hopefully to cut out.

So, you're going to cut out those statements and you're going to put them together and make sort of equations that compare.

So, we could find some that are equal to each other, but then we could find some that are worth less than or some that are worth more than the other.

So, have a play around with those.

And you'll notice that some of them have got blanks in the stem sentences.

So you could write your own numbers in there to make up some other equations.

So, you're going to match a number or a number of tens with the statement there that says one group of one hundred and hmm more tens.

And see if you can find some that are equal to each other or find some that are not equal to each other and work out which one is greater than and which one is less than.

Then your second task is another similar one.

Thinking about that, those equal to or greater than or less than.

This time, they're all blanks for you to cut them up and make your own equations.

So, pause the video, and then we'll have a talk about them.

I wonder how you got on.

This is how I arranged mine.

So, I said that 160 was greater than one group of one hundred and 1 more ten, 'cause I know that 160 is one group of one hundred and 6 more tens.

What did I find that was equal? Oh, I made one up for myself that was equal.

So we can see there, I made up one that had 15 tens in it, but it was equal to one group of one hundred and 5 more tens.

And then let's have another one.

Oh, there's an interesting one.

There's one up from the bottom.

140 is greater than one hundred and no more tens.

So, one hundred and no more tens, That's just 100 isn't it? So, 140 is greater than one hundred.

I wonder how you got on and what statements you came up with? So, in the second task you could create your own.

So, for my first one I said there are 17 groups of ten and that was greater than one group of 100 and more tens.

So, then I had 130 and that was less than my statement that there were 14 groups of ten.

And then I wanted one that was equal.

So, I said there is one group of one hundred and 4 more tens and that is equal to the statement, there are 140.

Oh, did you spot there? I kept my 140 and I expressed it as 14 groups of ten and also as one group of one hundred and 4 more tens, and then I compared it to some other numbers.

I hope you enjoyed making those statements up.

We've got to the end of our lesson.

Thank you so much for all your hard work today.

I hope you have enjoyed exploring 3-digit multiples of 10 in different ways.

So, we now know that we can represent a 3-digit multiple of 10 as a number of tens, so 12 tens, 13 tens, 14 tens.

We can represent a 3-digit multiple of 10 as a number of hundreds and tens.

So, 130, one hundred and 3 more tens.

130 is the same as 13 tens.

The number of tens and the number of hundreds and tens when we got it right, were equivalent.

So, here are a couple of examples.

140 is equal to 14 tens, and one hundred and 4 more tens is equal to 140, and it would also be equal to 14 tens.

So, I hope you've enjoyed that.

Thank you very much for your hard work and I hope to see you another time, thank you.