Lesson video

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

I'm sure you're going to have lots and lots of fun, and here is the outcome for today's lesson.

I can compare and order numbers with up to three digits.

And here are our keywords.

So the first keyword is compare.

Can you say that, compare.

Brilliant.

And the second keyword is order.

Can you say that? Order.

Excellent.

And let's look at what those keywords mean.

So you compare to find out what is the same and what is different.

You can compare numbers to find out if one is more than, or less than another.

So 15 is less than 51.

51 is more than 15.

You can order numbers from the smallest to the largest or from the largest to the smallest.

The order stays the same when you count.

These numbers are in size, order smallest to largest.

145, 154, 451, 541.

And here is our lesson outline.

In the first part of the lesson, we are going to be comparing numbers with up to three digits.

And in the second part of the lesson we're going to be ordering numbers with up to three digits.

Let's get started.

In this lesson you'll meet Sophia and Andeep and they're going to be asking you questions and going to be showing you how to play a game later as well.

Sophia and Andeep are comparing numbers.

Sophia says, "Two digit whole numbers are always larger than one digit whole numbers." Andeep says, "Three digit whole numbers are always larger than two digit whole numbers." Are they both correct? What do you think? Sophia says that two digit whole numbers are always larger than one digit whole numbers.

"The largest one digit number is nine," says Sophia.

"The smallest two digit number is 10." And there's a representation of nine and 10 and you can see that 10 is larger than nine, and 10 is the smallest two digit number, and nine is the largest one digit whole number.

This can be shown on a number line.

All two digit whole numbers are larger than any of the one digit numbers.

There's our number line from zero to a hundred, and all the one digit numbers are less than 10 and all the two digit numbers are 10 or more.

So Sophia is right, any two digit whole number is larger than any one digit whole number.

So which is larger? For each pair of numbers, which is larger? Pause the video and see if you can work out the answers.

And welcome back, let's see how you got on.

So for the first pair, we've got 19 or nine, which one's larger? 19 is larger.

It's a two digit whole number, so it must be bigger than the one digit whole number.

51 is larger than five and 11 is larger than eight.

Well done if you've got those correct.

"Two digit whole numbers are always larger than one digit whole numbers." Thank you Sophia for reminding us about that.

Andeep says that, "Three digit whole numbers are always larger than two digit whole numbers.

The largest two digit number is 99," says Andeep, "the smallest three digit number is 100." And there's 99 and 100.

And you can see that 99 is less than 100.

This means that any three digit whole number is larger than any two digit whole number.

This can also be represented on a number line.

Any of the two digit whole numbers, we go here with the largest of them being 99.

That's the largest two digit whole number you can have.

And then the three digit numbers we go here.

So all the way from 100 to 999, which is the largest three digit whole number.

"Which number is larger?" Asks Andeep, "340 or 96?" What do you think? "Three digit whole numbers are always larger than two digit whole numbers." Thank you Sophia for reminding us about that.

So 340 is larger because it is a three digit whole number and 96 is a two digit number.

So 96 would be there on the number line amongst the two digit numbers.

And 340 would be there quite a lot larger.

Which is larger? So for each pair of numbers, which one do you think is bigger? Pause the video and see if you can out them out.

And again, welcome back.

Let's see how you got on.

So for that first pair of numbers, the numbers are 105 and 98.

105 is larger than 98.

105 is a three digit whole number, 98 is a two digit whole number, so 105 must be bigger.

The next pair of numbers 150 is bigger.

And for the last pair of numbers, 106 is larger.

"Three digit whole numbers are always larger than than two digit whole numbers." Thank you Andeep for reminding us about that.

So very well done, if you've got all three correct.

So we've learned how to compare three digit whole numbers and two digit whole numbers.

How would you compare a three digit whole number with another three digit whole number? How can you compare three digit numbers? "Start with the hundreds number," says Andeep.

The number that has the higher value hundreds digit is larger.

"Compare 451 and 501 which is larger?" asks Sophia.

Let's represent those numbers using base 10 blocks.

So here we have 451 and here we have 501.

Can you see which one is larger? Now you should be able to see that 501 is made out of five hundreds.

451 only has four hundreds.

Sophia compares 501 and 451 using place value grids.

So let's look at those hundreds digits.

501 has a five as the hundreds digit, and 451 has a four as the hundreds digit.

501 has a higher value, hundreds digit than 451 so it must be larger.

You can also use a number line to compare the numbers.

So 451 would be here just slightly larger than 450 and 501 would be here slightly larger than 500.

Which is larger? So for each of the pairs of numbers, which one do you think is larger? Pause the video and see if you can work it out.

And welcome back let's look at the answers.

So for that first pair of numbers, which one is larger? Well it must be 719.

719 has a seven as the hundreds digit 197 has a one as the hundreds digit.

If the hundreds digits are different, look to see which one is larger and that will give you the larger three digit whole number.

The next pair of numbers 761 is larger and the last pair of numbers 543 is larger.

And here's Andeep just to remind us what we've learned.

The number that has a higher value, hundreds digit is larger.

How can you compare three digit numbers with the same one hundreds digit.

"So which is larger?" asks Andeep.

"267 or 276?" And they both have a two as the hundreds digit.

So which one is larger? Sophia says, "If the hundreds number is the same, then look to see which tens number is larger." Let's again use base 10 blocks to represent the numbers.

So here we've got the number 267, and here we've got the number 276.

Which one is larger? Well you can see they've got the same number of hundreds.

Which one has more tens? 276 has seven tens.

267 has six tens.

So 276 is larger.

Andeep compares 267 and 276 using place value grids.

So let's look at those tens numbers.

267 has a six as the tens number 276 has a seven as the tens number.

276 has a higher value tens digit than 267, so it must be larger.

You can also use a number line to compare the numbers.

There is a number line.

This time from 200 to 300 and we can find 267.

So that is less than 270 and 276 would be here that is more than 270.

Which is larger? Look at each of the pairs of three digit numbers, which one is larger? Pause the video and see if you can open them out.

And again, welcome back let's see how you got on.

So for that first pair of numbers, which one is larger? 263.

The hundreds digit for both the numbers is the same for the tens digit is different.

263 has a six as the tens digit, 236 has a three and six is larger than three.

So 263 must be larger.

For the next pair of numbers, 254 is larger.

And for the last pair of numbers, 782 is larger.

So if the hundreds digits are the same, the number that has a higher value tens digit is larger.

Thank you Andeep.

Very well done, if you've got all three of those correct.

How can you compare three digit numbers with the same hundreds and tens digits? Which is larger, 388 or 381? You can see 381 and 388 both have the same hundreds digit and the same tens digit.

So how would you compare the numbers? If the hundreds and tens digits are the same, then look to see which ones digit is larger.

And again, let's represent those numbers using base 10 blocks.

So here we've got the number 388 made outta three hundreds and eight tens and eight ones.

And here we've got the number 381 made outta 300 and eight tens and one one.

You can see there the 388 is larger, it has more ones, the ones digit is larger.

Andeep compares 388 and 381 using place value grids.

So you can see both numbers have the same value hundreds and tens digits.

So it's the ones digit we've got to look at.

So 388 as an eight as the ones digit 381 has a one as the ones digit.

388 has a higher value, one's digit than 381 so it must be larger.

You can also use a number line to compare the numbers.

So this time we're going to be using a number line from 300 to 400.

Let's have a look where the numbers are.

So 381 is here, so it's quite close to 380, 388 is much nearer to 390.

Here are some questions for you to look at on your own.

So which is larger? So for each pair of numbers, which one is larger? Pause the video and see if you can work out the answers.

And welcome back let's see how you got on.

So if that first pair of numbers, which one is larger? The answer is 506.

The hundreds and tens digits are the same.

So we've got to compare the ones digit and six is larger than three.

So 506 is larger than 503.

What about the next pair of numbers? The larger number is 933.

And for the last pair of numbers, 499 is larger.

So here's Andeep just to remind us "If the hundreds and tens digits are the same, the number that has a higher value ones digit is larger." So very well done if you've got all three of those correct.

Is there an easier way to show that one number is larger or smaller than another? "You can use symbols to compare numbers," says Andeep.

So this symbol here means less than.

And this diagram helps you to remember that the number to the left is smaller than, is less than the number to the right.

For example, 496 is less than 499.

This symbol here means greater than.

So this time the number to the left is larger than the number to the right.

Again, for example, 933 is larger than 930.

And this symbol means equals.

The number to the left and the number to the right are equal to each other.

So 243 equals 243.

Andeep uses the symbols less than and greater than to compare the numbers he has already looked at.

So remember this means less than, and this symbol here means greater than 501 is greater than 451.

The hundreds digits are different.

501 is greater than 451.

267 is less than 276.

The hundreds digits are the same, but the tens digits are different.

267 is less than 276.

And 388 is greater than 381.

The hundreds and tens digits are the same, but the ones digits are different.

388 is greater than 381.

Use the symbols less than and greater than to compare the numbers.

So there are three sets of numbers there.

What symbol would you put in the circles? Pause the video and see if you can work out the answers.

And again, welcome back.

Let's see how you got on.

So the first pair of numbers 689 is less than 701.

The next pair of numbers 787 is greater than 778.

And for the last pair of numbers, 626 is greater than 624.

Well done if you've got all three correct.

Sophia has these number cards.

So she's got the numbers.

two, three, three, four, four and five.

She arranges them to make this correct.

So she's got there, a three digit number is less than another three digit number.

Sophia uses three of the cards to make the number 432.

I've used three of the cards to make the number 432.

What three digit number can I make using the other three cards? So remember 432 has to be less than this other three digit number.

What number could Sophia make? Well she could make the number 543.

432 is less than 543.

Sophia could also have used the numbers 435, or 453, or 534.

So Sophia has these number cards.

So it's the same six number cards she's using.

She arranges them to make this correct.

So this time a three digit number is greater than a three digit number.

Sophia starts off by making the number 345.

So 345 is greater than what other number? I've used three of the cards to make the number 345.

What three digit number can I make using the other three cards? What do you think? Can you think of a number? Well she could make the number 342.

345 is greater than 342.

Sophia could also have used the numbers, 324, 243, or 234.

How else could Sophia arrange the number cards? So she's still got the same six number cards.

two, three, three, four, four and five.

Rearrange the cards to make these correct.

So you've got there a three digit number is less than another three digit number and the other one says, a three digit number is greater than another three digit number.

Can you think about how you've made those correct? Pause the video and see if you can work out an answer for each using those six number cards.

And welcome back, let's see what you managed to get.

Did you manage to rearrange the cards to make both of them correct? Very well done if you did.

Let's have a look at some of the possible solutions.

So are lots, lots of different answers you may have come up with, but here's one possible solution for each of them.

So you could have done the number 324 is less than 354.

You could have done 424 is greater than 353.

So lots, lots of possible answers there.

Very well done if you managed to make both of them correct.

And let's have a look at task A.

So for the first part of task A, use the symbols less than and greater than to compare the numbers.

Which symbol would you use to compare each pair of numbers? So the first one is 245 and 145 is 245 less than or greater than 145.

And don't forget, start off by comparing the hundreds digit first.

And if the hundred digits are the same, compare the tens digits.

And if the tens digits and the hundreds digits are the same, then compare the ones digits.

And the second part of task A, use these number cards.

So you've got the numbers three, three, four, four and five and six, can you arrange them to make these correct? And how many different solutions can you find? So pause the video and have a go at task A.

And welcome back and let's look at some of those answers.

So here are the answers for part one of task A.

So 245 was greater than 145.

395 is less than 405 and 716 is greater than 671.

Very well done If you managed to finish off part one.

And here are some possible solutions for part two of task A.

So there were lots and lots of different answers you could have come up with and here were just some of them.

So you may have done 335 is less than 446, you may have come up with, 643 is greater than 543.

Very well done if you've got onto part two of task A and you managed to come up with lots and lots of different solutions to those problems. And let's move on to part two of the lesson, which is ordering numbers with up to three digits.

And in this part of the lesson you're gonna be taught how to play a game.

Andeep and Sophia play a game using number cards and they've got the number cards from zero all the way up to nine.

"We have to choose three cards and use them to make a three digit number," says Andeep.

So each of them is going to shuffle up the cards and choose three of the numbers at random so it could be any of the three numbers.

We have to order the numbers into our own ladder.

So we've got that Andeep ladder and Sophia's ladder and when they've made a number, they're going to put it somewhere on their ladder.

We can place the numbers in any space in the ladder.

So once they've made a number, they can put it anywhere on their ladder.

However, the numbers must go in order.

A larger number must go above a smaller number.

So as you go up the ladder, the numbers get larger.

The larger numbers are always towards the top.

The first player to fill in every step of their ladder wins the game.

"I'll let Andeep go first," says Sophia, maybe she wants to find out how to play the game.

Maybe she wants to get some clues about Andeep's tactics.

Andeep shuffles the number cards and picks three.

So he takes the numbers three, seven, and eight.

"I'm going to make the number 873 and put it on my ladder." So Andeep rearranges the numbers to make the number 873.

And he puts 873 on his ladder.

Now he's not put it in the very, very top step of the ladder, he's put it in the one underneath.

I think Andeep is thinking he might get some numbers which are larger than 873.

Sophia shuffles number cards and picks three.

"I'm going to make the number 971 and put it at the of the ladder," says Sophia.

So she makes the number 971 and she puts it right at the top of her ladder.

971 is one of the largest numbers that can be made using the cards.

Sophia has very sensibly put it at the top.

Andeep shuffles the number cards and picks three.

This time he chooses the number cards six, two and zero.

"I'm going to make the number 26 and put it on my ladder." How has he got the number 26? Oh he's used the zero as a hundreds digit.

So 26 goes right down the bottom of his ladder.

Andeep has used zero to represent the hundreds.

Making this a two digit number, he very sensibly puts it at the bottom of his ladder.

So there aren't many numbers that are going to be less than 26.

Sophia Shuffles number cards and picks three.

Sophia chooses numbers three, zero and five.

I'm going to make the number 503 and put it in the middle of the ladder.

There's her number 503.

So she's rearranged the cards to make 503.

Andeep shuffles the number cards and picks three.

This time he chooses the number cards five, six and one.

I'm going to make the number 651 and put it on my ladder.

So the numbers must be in order, remember.

651 is less than 873 and greater than 26.

So Andeep positions it underneath 873.

So he puts it there and there are lots and lots of numbers that are still in between 651 and 26.

So Andeep still has lots and lots of chances of winning.

It's Sophia's go next, so Sophia shuffles number cards and picks three.

She ends up with the numbers six, three and zero.

"I'm going to make the number 36 and put it at the bottom of the ladder," says Sophia.

So again she's used the zero as the hundred digit.

So the 36 goes right to the bottom of Sophia's ladder.

So Sophia has used zero to represent the hundreds, making this a two digit number and she very sensibly puts it at the bottom of her ladder.

Andeep shuffles number cards and picks three, five, one and three.

"I'm going to make the number 531 and put it on my ladder," says Andeep.

So he's arranged the digits slightly to make 531.

531 is less than 651 and is also greater than 26.

So it does fit on Andeep's ladder.

Andeep could also have made the number 513 or even the number 351 or even the number 135, any of those numbers would've fitted on Andeep's ladder in the same place, because they're all less than 651 and greater than 26.

Sophia shuffles number cards and picks three.

So she gets digits one, eight and three.

"I'm going to make the number 813 and put it on my ladder," says Sophia.

And 813 is less than 971 and is also greater than 503.

So it does fit onto Sophia's ladder.

So Sophia puts her number there.

Andeep shuffles the number cards and picks three.

So he chooses the number cards, six, eight, and five.

"Can I make a number to complete my ladder and win?" asks Andeep.

What do you think, can he rearrange those number cards to make a number that he can fit onto his ladder? Pause the video and see if you can work out the answer.

And welcome back, how did you get on? Do you think Andeep can make a number that will allow him to win the game? Well the biggest number that Andeep can make is 865.

Will that fit onto Andeep's ladder? No, Andeep cannot win.

The largest number he can make is 865, which is less than 873.

So Andeep misses a go.

So that gives Sophia a chance to win.

So Sophia shuffles number cards and picks three.

She chooses the number cards six, nine and four.

"Can I make a number to complete my ladder and win? asks Sophia.

What do you think, can she win? Pause the video and see if you can find a number that Sophia could make to allow her to win the game? And welcome back did you come up with a number? Can Sophia win the game? Yes, Sophia can win using either of those numbers.

She chooses to make 496, which is larger than 36 and smaller than 503, so she can fit it onto her ladder.

So Sophia puts her number on the ladder and wins the game.

Very well done Sophia, and very, very well tried Andeep, you were very close as well.

So in task B, you are going to play that game with a partner.

Take it in turns to choose three number cards.

So remember, shuffle the number cards up so you don't know what the number cards are going to be.

You're going to arrange them into a three digit number.

You may choose the cards two, five, and three and you may arrange them into the number 253.

You're going to decide where to put the number.

So whereabouts on the number ladder will it go? Will it go at the bottom, at the top, in the middle or somewhere else? And remember, the numbers must go in order.

A larger number must go above a smaller number.

So good luck, enjoy playing the game with a partner.

And remember, it's nice to win a game, but it's even nicer if your friend wins a game.

So good luck, pause the video and enjoy playing the game.

And welcome back and I hope you enjoy playing that game.

Your winning games may have looked like these, but hopefully you are feeling much more confident at ordering numbers with up to three digits.

Excellent work today, very, very well done.

Let's look at our lesson summary.

So two digit whole numbers are always larger than one digit hole numbers.

Three digit whole numbers are always larger than two digit whole numbers.

The symbols less than and greater than can be used to compare numbers.

And when ordering or comparing three digit numbers, look at the hundreds digit first.

If the hundreds digits are the same, compare the tens digits.

And if the tens digits are the same, compare the ones digits.