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Hello there, my name is Mr. Goldie and welcome to today's maths lesson.

So the lesson now come today is I can represent three digit numbers in different ways and here are the key words.

So three keywords today.

So I'm going to say the word, can you repeat the word back to me? So the first word is represent.

Can you say that, represent? The next key words are three digit number.

Can you say three digit number? Fantastic stuff.

And the last one is place value.

So can you say place value? Wonderful.

Let's look at what those words mean.

So represent means showing something or standing for something.

The number 10 can be represented as 10 in digits or as a full 10s frame or as a base 10 block.

A three digit number represents a number of hundreds, 10s, and ones.

127 is an example of a three digit number.

There is 100, two 10s and seven ones.

Place value means how much a digit is worth in a number.

In 127, the digit two has a value of two 10s or 20.

In the first part of the lesson, we're going to be representing three digit numbers using base 10 blocks.

And in the second part of the lesson we're going to be understanding place value in three digit numbers.

Let's get started.

And in this lesson you'll meet Sophia and Andeep.

So you can represent three digit numbers using base 10 blocks.

100 looks like this, 10 looks like this and one looks like this.

You can represent any three digit number using base 10 blocks, says Andeep.

You can represent different hundreds numbers using base 10 blocks.

There are three hundreds, there are 300 altogether, three hundreds equals 300.

In this example there are five hundreds.

So Sophia is saying there are 500 altogether.

The hundredth digit would be a five Andeep represents another hundreds number.

There are 800 altogether.

So in that example the hundreds digit is eight.

A three digit number is made out of hundreds, 10s, and ones.

342 is a three digit number.

"342 has three digits" says Andeep.

It has hundreds, 10s and ones.

There's 342, there are three hundreds.

So the three in 342 represents three hundreds.

There are four 10s.

So the four digit represents four 10s or 40.

There are two ones.

So the two in 342 represents two ones, which is also worth two.

How would you represent 212 using base 10 blocks? There are two one hundreds, so we'd need two one hundreds.

Two hundreds would be worth 200.

There is one 10.

There it is.

There is our 10.

There are two ones.

That'd be represented by two ones which is worth two.

So 200 add 10, add two equals 212.

Which representation shows 231? What do you think? Is it A, is it B or is it C? Which representation shows 231? Pause the video and see if you can work out the answer.

And welcome back.

Did you manage to work out the answer? Well, hopefully you picked C.

C has two hundreds, it has three 10s and it has one one.

Those base 10 blocks represent the number 231.

Very well done if you've got the right answer.

Sophia represents a three digit number using base 10 blocks.

She uses two one hundreds.

There are the two one hundreds.

She uses six 10s.

There are her six 10s, she uses eight ones.

"What number have I made?" asks Sophia.

What number has Sophia represented do you think? Sophia has used two 100s.

She's used six 10s and she's used eight ones.

And that makes the number 268.

200 and 60 and eight equals 268.

Sophia represents a different three digit number using base 10 blocks.

This time she uses three hundreds.

There are other three hundreds.

She uses nine 10s, there are her nine 10s, and she uses three ones.

There are the three ones.

"What number have I made?" asks Sophia.

What do you think? What number has she made this time? Sophia has represented the number 393.

300 add 90, add three equals 393.

Sophia represents another three digit number using base 10 blocks.

This time she uses four one hundreds.

There are the four one hundreds she's used, she uses one 10.

There's the one 10 she's used.

And she uses seven ones.

There are the seven ones.

"What number have I made?" asks Sophia.

So four one hundreds, one 10 and seven ones.

Sophia has made the number 417, 400 add 10 add seven equals 417.

Which representation shows 256.

There's one representation.

Does it show 256? There's another representation.

Does that show 256? What do you think? "They both represent 256," says Andeep.

So in both of them there are two 100 blocks.

There are five 10 blocks and there are six ones.

They both represent 256.

They both have two one hundreds, five 10s, and six ones, says Sophia.

So it doesn't matter if they're jumbled up and all over the place or if they're very, very neatly laid out.

You still have to count the number of blocks that you've got to find out what number is represented.

And here's one to try on your own.

So Andeep represents a three digit number.

He uses five hundreds, he uses four 10s, he uses two ones.

"What number have I made?" asks Andeep.

Pause the video and see if you can work out the answer.

And welcome back.

Let's see if you managed to get it right.

So what number has Andeep made? Andeep has made the number 542.

500 add 40 add two equals 542.

Very well done if you've got the right answer.

Sophia represents a three digit number.

She uses four one hundreds.

There are the four one hundreds, she uses seven 10s.

There are the seven 10s she uses zero ones.

"What number have I made?" asks Sophia.

Now the tricky bit here is that zero ones.

So 470 equals 470 for 470 is made up of four one hundreds, seven 10s and zero ones.

Zero is used to show that there are no ones.

Sophia represents another three digit number.

This time she uses six one hundreds.

There's the six one hundreds, she uses zero 10s.

So this time she doesn't use any 10s in the number, she uses nine ones.

There are the nine ones.

"What number have I made?" asks Sophia.

So this time we've got to use a zero to represent the number of 10s.

So the number that Sophia has made is 609.

Zero is used to show that there are no 10s.

Andeep represents a three digit number.

He uses five hundreds, he uses eight 10s and he uses zero ones.

"I've represented the number 508" says Andeep.

Is Andeep correct? Is Andeep right? Has he represented the number 508? Pause the video and see if you can work out whether Andeep is correct or not.

And again, welcome back.

Let's see whether you got it right.

So is Andeep correct? Has he represented the number 508? No, Andeep is not correct.

He's actually represented the number 580.

The zero shows that there are zero ones.

In 508, the zeros representing zero 10s.

So well done if you managed to get that right and managed to work out that Andeep was actually not correct.

Excellent work.

And we are going to go on to our task.

So task A, the first part of task A is represent these numbers using base 10 blocks.

So you've got six numbers there.

You've got to represent those numbers using base 10 blocks.

So for A, the number is 135, you should be using 100, three 10s and five ones.

Part two, which number is represented by the base 10 blocks? You've got pictures, representations of different numbers.

You've got to work out what number is represented.

So pause the video and have a go at task A.

And welcome back.

Let's see how you got on.

The first part of task A, this is how you should have represented the different numbers.

So 135 is made up of 100, three 10s and five ones.

And the representation for 135 should look just like that.

216 should be represented with two 100s, one 10 and six ones.

And again, if you lay it out really clearly, it's much easier to see rather than having a jumble of different base 10 blocks.

And here are the answers four part two of task A.

So which number is represented by the base 10 blocks.

So A was 235.

There are two hundreds, three 10s, and five ones.

So the number represented was 235.

B was 314.

There were three hundreds, one 10 and four ones.

So the number represented is 314.

And again, very, very well done if you've got those correct.

And let's move on to the second part of the lesson.

So the second part of the lesson is understanding place value in three digit numbers.

So the position of a digit tells us it's place value.

There's number 342.

The three has a value of three one hundreds.

So three is worth three one hundreds.

The three in 432 has a value of three 10s.

So that represents 30.

And the last number is 423.

So the three this time has a value of three ones.

So three, this time represents three.

The place value of a digit is really, really important.

Where the number is in a number tells us exactly what it is worth.

Three digit numbers can be represented using place value grids.

And there's an example of a place value grid.

This place value grid has hundreds, 10s and ones.

So this is the number of hundreds, got there just 100.

This is the number of 10s.

So we've got there represented two 10s.

The number of 10s will be two.

This is the number of ones at the end, four ones.

The number there is four.

So the whole number there represented is 124.

Andeep represents a three digit number, so he uses 200 and he adds to that five 10s or 50.

And then he adds six ones or six.

Andeep uses the place value grid to represent the number.

So we've got two hundreds, five 10s, and six ones.

200 add 50, add six equals 256.

So place value grids can be quite useful in working out what the number is, particularly if the numbers are in a different order, which we'll look at later.

Andeep represents another three digit number.

This time it uses 400, say 400 and he adds to that seven Tens or 70.

And then he adds eight ones or eight.

Andeep uses a place value grid to represent the number.

So how many hundreds are there? There are four hundreds.

How many 10s are there? There are seven.

How many ones are there? There are eight.

So this time he's represented the number four hundred and seventy eight, four hundred add 70, add eight equals 478.

Andeep represents yet another three digit number.

This time he uses three hundreds and he adds to that nine ones.

Andeep uses a place value grid to represent the number.

There are three hundreds.

How many 10s are represented at that number? There are 309.

How many 10s are there? There are zero 10s.

There are zero 10s represented.

Now of course the hundreds are made outta 10s, but we're counting those 10s on their own because those hundreds go together to make it a hundred.

There are no 10s represented.

So zero is used here and there are nine ones in this number.

300 add nine equals 309.

And now we have one for you to try on your own.

So Andeep represents a three digit number.

What number have I represented? How should he complete the place value grid.

There's the place value grid.

How would he use it to represent that number? So pause the video, have a think about how we use the place value grid and see whether you can work out what number Andeep has represented.

And welcome back.

Let's see how you got on.

Let's see whether you were right.

So using the place value grid Andeep would have four one hundreds, 400.

There are four hundreds altogether.

How many 10s are there? There are six 10s.

Then how many ones are represented? How many ones on their own are represented? There are zero ones, there are no ones represented.

So zero is used here, zero is used to show that there are no ones that's really important.

So Andeep has represented the number 460, 400 add 60 equals 460.

Very well done if you've got the right number and if you've filled in that place value grid correctly as well.

Excellent work.

Sophia represents a three digit number.

So she's used three ones, four hundreds and two 10s.

This is where it gets a little bit tricky because Sophia hasn't represented the number in size order.

She has not put the hundreds first, but Sophia uses the place value grid to represent the number.

So the place value grid can be really, really helpful here 'cause the numbers aren't in the right order.

So how many hundreds has Sophia used? There are four one hundreds and it doesn't matter the three ones appears first because that's three ones not three hundreds.

So there are four one hundreds, there are two 10s, 20 is two 10s, and then there are three ones.

So Sophia has represented the number 423.

Three add 400, add 20 equals 423.

Although the numbers are represented in a different order, they are still equal to 400, add 20, add three.

Sophia represent a different three digit number.

So this time she's used six 10s, 60 and a one and five hundreds, 500.

Sophia uses a place value grid to represent the number.

So here's our place value grid.

What's she going to complete first? The biggest value there are the hundreds and there are five of those.

So Sophia would first of all put there are five hundreds, then she's gotta look at the number of 10s.

How many 10s are there? There are six 10s.

The value is 60 of course, but there are just six 10s.

Six 10s equals 60.

And there is one one.

So the number represented is 561.

60 add one, add 500 equals 561.

500 add 60, add one also equals 561.

Sophia represents another three digit number.

This time she uses three and 600.

Sophia uses a place value grid to represent the number.

So Sophia is going to start off with a number of hundreds first.

So how many hundreds are represented? Well there are six, six hundreds.

How many 10s are represented in that number? There are zero, there are no 10s represented.

So zero is used here.

That's really important.

Gotta remember that.

And then lastly, there are how many ones? Three ones.

So the number that Sophia has represented is 603.

Three add 600 equals 603.

600 add three also equals 603.

Sophia represents a three digit number.

So two add 40, add 300.

Which place value grid represents the same number.

So three place value grids, which one represents the same number as the base 10 blocks? Pause the video and see if you can work out the answer.

And welcome back.

Let's see how you got on.

And let's see whether you were right.

So you should have said it was C.

C represents the same number as the base 10 blocks.

There are three hundreds, there are four 10s and there are two ones.

Number represented is 342.

Very well done if you've got the right answer.

Andeep uses a place value grid to help him work out the three digit number.

So 20, add 400, add nine.

First time there are no base 10 blocks to help Andeep.

He's just going to be using the numbers.

And again, Andeep is going to start with the hundreds.

So how many hundreds are represented? There are four hundreds.

So 400 represents 400.

Let's put a four as our hundreds digit.

There are two 10s.

So 20 represents two 10s.

So let's put two in as our 10s digit.

And lastly there are nine ones.

Nine ones.

We're going to use a nine as our ones digit.

So the number represented there is 429.

Four hundreds, two 10s and nine ones.

Andeep uses place value grids to work out the three digit numbers.

I'm going to use place value grids to represent the numbers.

So the first number is seven, add 600, add 90.

So Andy's going to complete the place value grid to work out what the number is.

So there are six hundreds, there are nine 10s and there are seven ones.

So the number they're represented is 697 and the next one is 50 add 800.

So again, Andeep's going to use the pace value grid to help him work out the number.

So there are eight hundreds, 800, there are five 10s, 50 is worth five 10s.

And there are zero ones, there are no ones represented.

There are zero ones.

50 add 800 equals 850.

Andeep's gonna have a go at some more.

"I'm going to use place value grids to represent the numbers" says Andeep.

So the first one is something equals 60, add five, add 300.

How many hundreds are there? There are three hundreds.

There are how many 10s? Six 10s.

60 equals six 10s.

And there are five ones.

So the number there is 365.

Next number is this one here.

So something equals nine, add 800.

So Andeep again, use the place value grid to help him.

So he's gonna start off with the hundreds as usual.

So there are eight hundreds, 800 equals eight hundreds.

There are how many 10s? How many 10s are represented? There are zero, there are zero 10s.

And lastly, how many ones are there? There are are nine ones.

So the number there represented is 809.

And here's one to try your own.

Complete the place value grid to find the three digit number.

There's a place value grid there.

So the three digit number is made up of three, add 700, add 60.

Pause the video and see if you can work it out.

And welcome back.

Let's see whether you were right.

So let's start off with our hundreds.

Hopefully you start off with your hundreds.

Always easy to start with those.

So there are 700.

How many 10s are there? There are six 10s.

60 of course is six 10s.

And then lastly, how many ones? Three.

Three represents three ones.

So the number represented there is 763.

Very well done if you got that correct.

Sophia and Andeep work out the three digit numbers.

So Andeep got this one here.

So 500 add 60, add three.

"I can work out the three digit number without using a place value grid" says Andeep.

That one's fairly straightforward because the numbers are actually written in the right order.

Got there 500, add 60, add three.

So that one's fairly straightforward and easy to work out.

That is 563.

This one's slightly harder.

So Sophia's got the slightly more tricky one.

"This one is trickier.

So I'm going to use a place value grid" says Sophia.

Now you might be able to work it out without one, but sometimes it's easier to use one just to check to make sure you are right.

So Sophia's got her place value grid ready and she's gonna start off with the hundreds.

So how many hundreds are represented? There are four hundreds.

How many 10s are there? There are eight 10s.

80 is eight 10s.

How many ones? Six.

The correct answer is 486.

Very well done Sophia.

And very sensible for using a place value grid to work the answer out there.

Can you work out the three digit numbers? So you've got two numbers there.

Can you work out what both of them are? Now you might want to use a place value grid for both of them or for one of them, but pause the video and have a go trying to work out those two answers.

And welcome back.

Let's see how you got on.

So again, that first one is quite straightforward, 600 add 90 add one is quite straightforward and quite easy 'cause again, the numbers are written in the right order.

So you might have been able to do that one without to place value grid.

So the answer would be 691.

Second one's a bit trickier because the number's a bit jumbled up.

We've got the ones first, then the hundreds, then the 10s.

So you might have one to use a place value grid to work out the answer there.

So there are seven hundreds, there are two 10s and there are nine ones.

The answer would be 729.

Very well done if you've got those correct.

Andeep has six counters.

"I'm going to put them in different places in the place value grid," says Andeep.

So he puts three in the hundreds.

There are three hundreds.

He puts one in the 10s.

So there is one 10 and he puts two in the ones, there are two ones.

What number has Andeep represented? What do you think? Let's have a look see if we could work out the answer.

So would be 300, there are three hundreds, add 10, there's one 10, add two, there are two ones 300 add 10, add two, add 300, add 10, add two would equal 312.

Andeep moves one of the counters.

So he's moved the 10 and he's put it in the hundreds.

"What number is represented now?" says Andeep.

Pause the video and see whether you can work out the answer.

What number is represented by the counters in that place value grid? And welcome back.

Let's see how you got on.

Let's see again whether you got the right answer.

So you should have said 400, add two.

There are no 10s, there are four hundreds and there are two ones, 400 add two equals 402.

And again, excellent work if you've got the right answer.

And we're going to look now at task B.

So task B, the first part of task B is use the place value grids to work out the three digit numbers.

So you've got a calculation and you've got to add together the numbers and work out what the three digit number is.

And underneath each one there is a place value grid to help you.

So our first one is 460 add four.

So fill in that place value grid to help you work out what the number is.

And of course some of them are jumbled up and some of them you might need to use a zero four as well.

Here's part two of task B.

So work out the missing numbers.

So you've got to add the numbers together and work out what number is missing.

And again, you can use place value grids to help you if it is helpful and it might be for some of those.

And lastly, part three, put seven counters on the place value grid.

So there's a place value grid and you've gotta use seven counters and put 'em in different places.

What different three digit numbers can you make? And write your answers like this.

So you could put five in the hundreds, which will make 500.

You put one in the 10s, which would equal 10 and one in the ones which would equal one.

So you could end up with a number 511, 500 add 10 add one equals 511.

So pause the video and have a go at your different tasks.

And welcome back and let's have a look at those answers.

So part one here are the answers.

So for a 400 add 60, add four equals 464.

D was a bit of a tricky one 'cause D was 60, add 200, which equals 260.

There are no ones represented, so you could remember to put a zero in as that ones digit.

Here are the answers for part two.

So A was 713, 700, add 10, add three equals 713.

And a more tricky one was D, 901 equals one, add 900.

There are no 10s.

You've got to remember to use a zero as the 10s digit.

And here's the answers for part three.

There are lots and lots of different answers for part three.

So you might have done 300, add 10, add three equals 313.

You could have had 100 add 30, add three equals 133 or you could have put no counts at all in the 10s as a 10s digit.

You could have put no counts at all in the 10s and had to use a zero for the 10 digit.

So you could have had 400 add three equals 403.

Hopefully you got onto that third part and you managed to come up with lots and lots of different answers.

Very well done and excellent work today.

Absolutely brilliant.

Very, very well done indeed.

And hopefully you're feeling much more confident in using base 10 blocks and representing three digit numbers using place value grids and thinking very, very carefully about when you have to use zero in a three digit number to represent maybe that there are no 10s or there are no ones.

Excellent work today.

Very, very well done indeed.

And let's look at our lesson summary.

So our lesson summary is a three digit number is made out of hundreds, 10s, and ones.

Three digit numbers can be represented using base 10 blocks or place value grids.

And the position of the digit tells you its place value.