Lesson video

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

I'm sure you're going to have lots of fun.

And here is our lesson outcome.

So the lesson outcome is, "I can order a set of three digit numbers." And let's look at those keywords.

Two keywords today.

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

Can you say that? Compare, excellent.

And the next key word is order.

Can you say that? Order, brilliant.

And let's look at what those words mean.

So you can 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.

15 is less than 51, and 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 let's look at our lesson outline.

In the first part of the lesson, you are going to be using hundreds, tens, and ones digits to order numbers.

And in the second part of the lesson, you're going to be solving problems by ordering numbers.

Let's get started.

In this lesson today, you will meet Sophia and Andeep who are going to be solving lots and lots of problems and showing you how to answer questions.

Andeep and Sophia compare numbers.

"You can use these symbols to compare numbers," says Andeep.

So this symbol here means less than.

So the number on the left is smaller than the number on the right.

For example, 496 is less than 499.

This symbol here means greater than.

So this time the number on the left is greater than the number on the right.

For example, 933 is greater than 930.

And finally this symbol means equals.

So the two numbers are equal to each other.

They have the same value.

243 is equal to 243.

Sophia orders numbers using the symbols.

"I'm going to order these three numbers, starting with the smallest," says Sophia.

So there are Sophia's three numbers, 250, 50, 180.

says Sophia orders them using the less than symbol.

So 50 is less than 180, and 180 is less than 250.

So 50 is the smallest number.

It is less than 180.

180 is greater than 50, 180 is less than 250.

250 is the largest number.

It is greater than 180.

Sophia uses base 10 blocks to represent the problem.

You can look at the digits to compare and order numbers.

Start with the hundreds digit, then look at the tens, then the ones.

Very good advice Sophia.

When you are comparing three digit numbers, always look at the hundreds digit first, then the tens digits, then the ones digits.

So here's 50.

The 50 is just made out of five-tens.

180 is made out of 100 and eight-tens.

250 is made out of 200 and five-tens.

So you can see there are more hundreds.

If the hundreds digit is larger, the number must be bigger.

250 is greater than 180.

Andeep and Sophia order four numbers, starting with the smallest.

Start with the hundreds numbers.

The number that has the lowest value, hundreds digit is the smallest.

So let's look at those hundreds numbers.

298 is the smallest number because the hundreds digit has the lowest value.

So because the hundreds digit is two, that's the smallest number.

355 is the next smallest.

It is greater than 298, but it's less than the other numbers.

So 355 would go next.

494 is the next smallest.

It is greater than 355.

And then lastly, 648 is the largest number.

It is greater than 494.

So you can see there that the hundreds digit starts off as a two.

Then we have a three, then we have a four, then we have a six.

When you are comparing three digit numbers always start with the hundreds digit first.

Andeep orders the height of the gaffes.

So here we have four giraffes.

We've got Jack, Jenny, Jill, and Jim.

"Which giraffe is the shortest?" Asks Andeep.

"Start with the hundreds numbers," says Sophia.

So Jenny is shortest.

She is 430 centimetres tall.

She's the only giraffe who has a height of 400 and something centimetres.

She must be shortest.

Which giraffe is next in height order? If the hundreds numbers are the same, compare the tens numbers.

So if you look carefully, there are two giraffes who have a height of 500 and something centimetres.

So Jack is 543 centimetres tall, and Jill is 514 centimetres tall.

So who's next shortest? 543 is greater than 514.

Jack is taller than Jill.

So if the hundreds digits are the same, compare the tens digits.

Jack's height has a four as the tens digit.

Jill's height has a one as the tens digit.

So Jack is taller than Jill.

So Jill will come next and then it would be Jack.

And finally we've got Jim.

605 centimetres is greater than 545 centimetres.

Jim is the tallest.

So Jim would go last.

Andeep orders the weights of the giraffes.

So he works out how heavy they are, what their mass is next.

So here are our four giraffes.

So we've still got Jack and Jenny and Jill and Jim.

And we've got their masses as well, how heavy they are underneath them.

So which giraffe is the lightest? So Andeep has to start off with the lightest giraffe.

We look carefully at our giraffes.

We can see there that the smallest hundreds digit we've got is six.

So we've got Jenny and Jill.

They've both got a mass of 600 and something kilogrammes.

Jenny is 645 kilogrammes, and Jill is 643 kilogrammes.

So they're hundreds digits the same.

And so are the tens digits.

So which one is the lightest? "If the hundreds and tens numbers are the same, compare the ones numbers," says Sophia.

Very good advice Sophia.

So who is the lightest? So Jill is lightest.

643 kilogrammes is less than 645 kilogrammes.

So Jill would come first and then it would be Jenny.

Jack is next.

805 kilogrammes is more than 645 kilogrammes and is also less than 850 kilogrammes.

So Jack would come next because 805 kilogrammes is less than 850 kilogrammes.

And finally, Jim is the heaviest.

850 kilogrammes is more than 805 kilogrammes.

Next, Andeep chooses three numbers cards.

So he's got the numbers two, three, and five.

"I'm going to rearrange the cars to make some three digit numbers," says Andeep.

So he uses the number of cards to make the numbers.

532, 325, 523, and 352.

Andeep orders the three digit numbers starting with the smallest, which three digit number is the smallest? What do you think? Start off by comparing the hundreds digits first.

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

So 325 is the smallest.

It is less than 352.

So 325 would be first, and then it would be 352.

We've still got two numbers to compare.

So which one is next? 523 is next.

523 is greater than 352 and 523 is less than 532.

The hundreds digits the same.

So compare the tens digits and three is greater than two.

So 523 would be next.

And finally, it would be 532.

Here's a problem for you to look at on your own and see if you can answer.

So Andeep chooses three number cards.

So this time he chooses the numbers five, four, and nine.

"I'm going to rearrange the cards to make some three digit numbers," says Andeep.

So there are the three digit numbers that Andeep has made.

Can you order the numbers starting with the smallest? So can you work out the order of those numbers? Pause the video and see if you can work out the answer.

And welcome back.

Let's see whether you got the right answer.

So first of all, which is the smallest number? 459 is the smallest.

It is less than 594.

So 459 will come first, and then we'd have 594 and we're left with our two 900s numbers.

So which one is smaller and which one is larger? 945 is greater than 594.

And 945 is also less than 954.

So 945 will come next and then 954.

Very well done if you ordered those four numbers correctly.

And let's have a look at task A.

So the first part of task A, you've got to order the heights of the giraffes.

So you've got four giraffes there.

Can you order there heights? The second part of task A is order the mass of the giraffes.

So this time you're going to order how heavy they are and again, can you put them into order of heaviness.

And then finally, part three of task A.

Use these number cards.

So you've got seven, one, and two.

Rearrange them to make some three digit numbers.

Can you then order the numbers starting with the smallest? And if you've managed to do that, choose three number cards of your own, make some three digit numbers with them and then order them.

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

And welcome back.

And let's look at those answers.

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

So there are the heights of the giraffes in order.

So 436 was the shortest height and 610 centimetres was the tallest height.

So well done if you order those correctly.

Here's part two of task A.

So you had to order the mass of the giraffes.

So 556 kilogrammes was the lightest mass, and 739 kilogrammes was the heaviest mass.

So again, very well done if you order those correctly.

And then finally, part three.

So your answers may have looked like these, and then your own numbers completely depends upon which numbers you chose yourself, but hopefully you put them into size order starting with the smallest correctly.

So very well done.

Have you got on two task three, excellent work.

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

So the second part of the lesson is solving problems by ordering numbers.

So Andeep uses these number cards, five, nine and two.

"I'm going to make a number that could be used to complete the problem below." So he needs to come up with a number that is greater than 280, but is also less than 300.

What number could Andeep make? This number must have two as the hundreds digit because it's greater than 280, but it's less than 300.

So the hundreds digit must be a two and the tens digit must be a nine.

We couldn't use five as the tens digit because that would be a number that was 250 something and that is not larger than 280.

So the number must be 295.

Let's look at a different problem.

Andeep uses these numbers cards.

So he uses the numbers five, nine and two.

"I'm going to make a number that could be used to complete the problem below," says Andeep.

So this time he's looking for a number that is larger than 910 but is smaller than is less than 930.

"What number could Andeep make this time?" So this number must be greater than 910, but less than 930.

This number must have a nine as the hundreds digit.

So it must be 900 and something and the tens digit must be a two.

The tens digit can't be a five because that would make the number 950 something and 950 is not less than 930.

So the number must be 925.

Now is time for you to try a problem on your own.

So Andeep uses these number cards, five, nine and two.

"I'm going to make a number that could be used to complete the problem below." "What number could Andeep make?" Pause the video and see if you can work out the answer.

Welcome back, did you come up with an answer? Let's see whether you got it right.

So the number that Andeep is looking for is greater than 500, but less than 530.

So this number must have a five as the hundreds digit.

The tens digit must be a two.

So that makes the number 529.

Very well done if you solve that problem.

Andeep uses these number cards.

So he is got the numbers this time, two, three, and four.

"I'm going to make numbers that could be used to complete the problem below," says Andeep.

So this time there are two missing numbers.

So the first missing number is greater than 240, but less than 300.

And the second number is greater than 300, but less than 330.

What numbers could Andeep use? Let's have a look.

So that first one, this number must be greater than 240, but less than 300.

So the number must have a two as the a hundreds digit and the tens digit must be a four.

The tens digit couldn't be a three because it wouldn't be larger than 240.

The number must be 243.

What about the next one? What would that be? This number must be greater than 300, but less than 330.

This number must have a three as the hundreds digits, so it must be 300 and something, and the tens digit must be a two.

The number must be 324.

It couldn't be 342 because that wouldn't be less than 330.

Andeep uses these number cards.

He's using the same three number cards, two, three, and four.

"I'm going to make numbers that could be used to complete the problem below," says Andeep.

What numbers could Andeep use? So that first problem, we're looking for a number that is greater than 420 but is less than 430.

What number could Andeep come up with? So this number must have a four as the hundreds digit and the tens digit must be a two.

So Andeep has to use the number 423.

And then let's look at the other number.

So this number must have a four as the hundreds digit and the tens digit must be a three.

So this number must be 432.

It's larger than 430, but it's less than 440.

And here's a problem for you to try on your own.

Andeep uses these number cards.

So this time he's using the number cards, four, five, and six.

"I'm going to make numbers that could be used to complete the problem below," says Andeep.

Here's Andeep's problem.

What numbers could Andeep use? Can you work out what the two mystery numbers are? Pause the video and see if you can work out what they are.

Welcome back and let's see how you got on.

Let's look at that first missing number.

So this number must have a five as the hundreds digit.

It must be 500 and something, and the tens digit must be a four.

So the number must be 546.

Let's look at the other number.

This number must have five as the hundreds digit.

The tens digit must be a six.

So this number must be 564.

It's greater than 550, but less than 570.

Very well done if you've got both of those correct.

Sophia uses these number cards.

So Sophia's got the number cards, zero, one and two.

"I'm going to use the number cards to make this problem correct," says Sophia.

Three numbers have a missing digit.

Sophia can use each card once to solve the problem.

Let's see if we can work out where Sophia needs to use those number cards to solve the problem.

Where would she start off? So we've got 166 is less than something 79, and that is less than 200 and something, and that is less than something and 11.

Which number can she work at first? Well, in fact, you could start off with this one.

The hundreds digit must be a two.

This number is between 200 and something and 220.

So it must be a two.

Couldn't be a 111 and it certainly can just be 11.

The missing digit here must be a two.

The tens digit must be a zero because it's less than 211.

So Sophia couldn't use the one there because that would make the number 214 and 214 is not less than 211.

So Sophia needs to use the zero here, and that means that the one has to be used here.

The one hundreds digit must be one because it is less than 204, but more than 166, the one must be used there to finish off the problem.

Use these number cards.

This time, use the number cards, one, two, and three.

Use the number cards to make this problem correct.

Three numbers have a missing digit, use each card once to solve the problem.

So pause the video and see if you can work out where you have to use those number cards.

And welcome back.

Let's see how you got on.

So a bit of a tricky problem this one.

Let's find out whether you did it correctly.

So which number card would you use first when in fact we could use the one first.

The hundreds digit must be a one, it must be 140.

The number before has one as the a hundreds digits, so it's 100 and something.

And the number afterwards is 140 something.

So the number in the middle must be 140.

So which one could you do next? So we've got two and three left.

Let's do this one next.

So the tens digit must be three because the number is less than 140, but more than 129.

So the three has to be used here, and that means the two must be used here.

So the ones digit must be a two.

So very, very well done if you manage to solve that problem.

And a slightly trickier problem next.

So Sophia uses these number cards.

So this time she's got five number cards, zero, one, two, three, and four.

"I'm going to use the number cards to make this problem correct," says Sophia.

Each number has a missing digit and Sophia can use each card once to solve the problem.

So how would she solve that problem? Where would she start off? It's quite a difficult problem this one.

Quite a tricky one.

I wonder if you can see where she'd start off.

Look at the numbers where is only one possible answer first? So for some of the numbers, there's lots of different number cards you could use, but for some of them there's only one and they're the ones you have to start off with.

Is there one number where you can only use one card and not the others? Well, in fact, this one in the middle here, the tens digit must be a zero because the number it's less than has a zero as the tens digit.

So the zero should be used here.

So we've used the zero already, so that number in the middle there is 201.

The hundreds digit here must be one because it is less than 201, but more than 100 and something three.

So the one must go there.

That number there must be 130.

And next we can work out what the missing digit is here.

So the tens digit must be a two.

This number has to be less than 130.

And because Sophia has used the zero and one already, she has to put the two there to make this 123.

So that leaves us with the number cards three and four, and 203 is less than 204.

So that number here must be 203, and that number must be 204.

Here's one to try on your own.

Use these number cards.

So you've got the number cards, one, two, three, four and five.

Find a way to fill in the missing digits so the numbers are in order, starting with the smallest.

That's quite a tricky problem this one.

Can you work out where you would use the number cards to make this correct? Pause the video and see if you can come up with a solution.

And welcome back, let's look to see whether you were right or not.

So here is the solution.

Here's the answer to the problem.

The first number is 318, which is less than 326, which is less than 427 and 427 is less than 438.

And finally 438 is less than 452.

That was a very, very tricky problem.

So very, very well done if you solve that problem correctly.

And let's look at task B.

So for the first part of task B, you've got to use these number cards.

So you've got six, two, and four.

Can you rearrange those number cards to solve each problem? And remember, you can only use each number card once for each problem.

So the first one, you've got to find a number which is greater than 400 and less than 430.

So what number could you use? What number could fit in between those two numbers? Here's the second part of task B.

So use these number cards.

So this time you've got the number cards, five, eight, and one.

Can you rearrange the number cards to solve the problems below? So for each answer, you can only use the number cards once.

So that first one, 175, this number is greater than 175, but less than 500.

And the next number is greater than 500, but less than 520.

So see if you can solve those problems. And here's part three of task B.

So use these number cards, four, five, six, seven, and eight.

Find ways to fill in the missing digits so that the numbers are in order, starting with the smallest, you can only use a card once for each answer and there's more than one possible solution.

So see if you can come up with more than one way of solving that problem.

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

Welcome back.

Let's see how you got on.

Here are the answers for part one of task B.

So use these number cards, rearrange them to solve each problem.

So that first missing number was 426.

426 is greater than 400 and less than 430.

So well done if you completed part one of task B.

Here are the answers for part two.

So rearrange the number cars to solve the problems below.

So the first missing number was 185.

185 is greater than 175 and less than 500.

The next missing number was 518.

518 is greater than 500, but less than 520.

So very well done if you got onto to part two and managed to solve those problems. And finally, part three, here are some possible solutions.

There's different answers for this one.

So you could have had the numbers 573, 589, 641, 656 and 701, and that will put those numbers in size order.

So very well done if you managed to solve that problem.

And if you came up with more than one solution, that is excellent work.

Very, very well done.

So very, very well done today and hopefully you are feeling much more confident at ordering numbers and using that to help you solve problems. Excellent work today.

Very, very well done indeed.

And finally, let's look at our lesson summary.

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

When ordering three digit numbers, look at the hundreds digit first.

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

If the tens numbers are the same, compare the ones numbers.