Lesson video

Hi, I'm Mrs. Wheelhouse.

Thank you for choosing to watch this video and to join me as we learn some more maths today.

Let's get started.

Welcome to today's lesson.

In this lesson,, we're going to be checking your understanding of ordering and comparing numbers.

By the end of today's lesson, you'll be able to order and compare numbers using three special symbols that may well be familiar to you.

You can see them now on the screen.

Let's start by considering some important words that we're going to be using in our lesson today.

On the screen you can see our key words.

These should be familiar to you, but if you need to, please feel free to pause the video and have a read through the definitions.

Our lesson today has two parts to it.

In the first part, we'll be reviewing how we use the particular notation we saw in our objective today.

And in the second part of today's lesson, we're going to be extending this understanding to two symbols that may well be new to you.

Let's get started with part one.

The symbol that you see on the screen here means less than.

We would read our statement below as follows: the value on the left is less than the value on the right.

Let's review that.

We would read this as 4.

07 is less than 4.

7.

4.

07 is less than 4.

7.

So this is the symbol that means less than.

Now, this symbol that you can see now on the screen means greater than.

The value on the left is greater than the value on the right, but let's try reading this now.

0.

13 is greater than 0.

098.

So that's the symbol for greater than.

Now this symbol I suspect you're very familiar with, and this symbol means equal to.

So we would read this statement as follows: The value on the left is equal to the value on the right, and that should be something you are familiar with from your prior learning, but it's still worth recapping these things.

So we would read this as 2000 is equal to 20 hundreds.

It's now time for a check.

What I'd like you to do is look at the sentence you can see at the top of the screen and fill in the words that should go in that gap.

When you've done that, write down or state what symbol you think should go in the dotted square that you can see in the centre of the screen.

Pause the video now while you do this.

Welcome back.

Let's see how you got on.

You should have written that the value on the left is less than the value on the right, or in other words, 4 is less than 12.

What about this one? Again, pause the video while you complete it.

Welcome back.

You should have written the value on the left is equal to the value on the right, four 10s is equal to 40.

Pause the video again while you have a go at this one.

Welcome back.

You should have written that the value on the left is greater than the value on the right.

0.

6 is greater than 0.

06.

Now in this one we're gonna compare these two numbers and write a statement showing which is greater.

Now up to this point, we've given you numbers that are fairly easy to compare, but here I've got 0.

4 million and 40,000.

It isn't quite as obvious which one of these is greater.

However, I know from my earlier learning about place value that there's something I can use to help me here.

Can you remember what it was? That's right.

A place value chart.

I'm going to use this to help me write these numbers out to make it easy to compare.

The 0.

4 million tells me there are zero millions, so a zero in the million column, and then the four must go in the hundred thousands column.

I can therefore use zeroes as placeholders, going to the right to see that 0.

4 million can be read as 400,000.

When I now fill in the 40,000 into the place value chart, it's now a lot clearer to see which of these two values is greater.

I can see that the 400,000 or 0.

4 million is greater than 40,000.

What about this one? Here, I've got two numbers written in decimal form, and we're going to write a statement showing which is greater.

Now, you might be able to do this straight away, and it's fantastic if you can, but remember, if you're not too certain, we can always use a modified version of our place value chart.

Well, what do I mean by that? I mean I know that my columns each have a place value heading above them, but rather than write them out this time, I'm just going to use the boxes to help me align the digits that have the same place value.

Let's see what that looks like.

So I'm gonna start by putting in the two decimal points, and this is to help me align the digits correctly.

I've now written both of my values into my chart, and we can see that one of them looks a lot longer than the other.

Now we might think that because it's longer, this means that it has to be greater.

It's not necessarily the case.

What I'm going to do is start with the ones column and compare the two digits, one from each number, to see which is greater.

Now, they both have an eight.

Because it's the same, I'm going to move to the next column and compare those two digits.

Still the same, still the same, still the same, and yet more of the same.

It isn't until I get to here, which is the fifth column after the decimal point, that I actually have a difference.

I can see that the one has a greater value than the zero.

Can we see that? So now I'm ready to write a statement that compares these two numbers and shows which one is greater.

In this case, the number with the longer, so in other words, more digits after the decimal point, is in fact the greater number.

So 8.

04781009 is greater than 8.

047809.

Now, did I have to write those numbers that way round? What do you think? You are right.

I don't.

I could have written my statement as follows: 8.

047809 is less than 8.

04781009.

Notice what's happened there.

The two numbers have swapped sides, and what's happened is my inequality sign has also swapped the way round that it's facing, because it's really important that it correctly shows me which number is smaller and which number is greater.

So I can see here these are still saying the same thing even though they're written the other way round.

Now it's your turn to have a quick check.

Which of the following mathematical sentences are correct? What we'd like you to do, of course, is to change the symbol to correct the ones that are not right.

So either it's correct and you can leave it as it is, or it's incorrect, and the symbol is what needs to change.

So either the less than, the greater than, or the equal to sign.

Pause the video now while you have a go.

Welcome back.

Let's see how you got on.

Well, A and C are correctly written.

50.

425 is less than 50.

453.

When we compare the second column after the decimal point, in other words not the tenths column, because that had two 4s in it, but when we went to the hundredths column, we could see one was a 2 and 1 was a 5.

Remember the tens, the ones and the tenths column both had the same digits for each number.

So we had to get to the hundredths column before we could be truly certain which one was greater.

And then in C, 43 hundreds is the same as 4,300.

And you could have used a place value chart to be sure about that.

But what's about B and D? Well, to rewrite B, I would've said 4.

32 is greater than 4.

032.

That zero really had an effect there.

And then in D, 47 thousandths is equal to 4.

7 hundredths.

So we should have changed that sign to an equal to sign.

It's now time for you to practise this.

For each of the cards you see, I'd like you to write a statement using the less than, greater than, or equal to symbol in order to compare these values.

When you've done that, try to write your own comparison statements using the digits 0 1, 4, and 9.

See if you can write a statement that no one else has thought of.

Pause the video now while you have a go.

Welcome back.

Let's see how you got on.

In the first one, we should have the equal to symbol, because 9 is equal to 9.

00.

In the second one, we should have that 1,900, or 1,900, is less than 14,000.

And then the third one, as we move across the top, 9,350,647 is less than 9.

5 million.

Looking at the second row now, 1.

09 is less than 1.

4, 109,000 is less than 140,000, and 0.

4 is greater than 0.

09.

Let's check the bottom row now.

0.

04 is greater than 0.

019, 190,000 is less than 1.

4 million, and 19.

04 is less than 19.

104.

Well done if you got all those right.

Now at the bottom we asked you to write a comparison statement.

I've just got some examples here for you.

You might have written something different, but it's still correct.

So do check if you're not sure.

I tried to come up with statements that were a bit unusual because I was trying to come up with something that no one else had thought of.

It's now time for part two of our lesson, and in this part we're going to be looking at two different symbols.

Now, you may have seen this before, but equally you may not.

And that's absolutely fine because we're going to go through what they mean.

Let's look at them.

Look at the sign on the screen.

What do you think that sign means? Now, you may have seen it before.

Can you think where you've seen it? Well, Andeep here thinks that this sign means that the speed limit is 30 miles per hour.

Do you agree with Andeep? Jacob thinks something slightly different.

Jacob says the maximum speed is 30.

Now, what he's saying is different to what Andeep said in that it's not the same words, but do we think they mean the same thing? Is one of them right and one of them wrong? What do you think? Now Sam here has said the speed of the vehicles must be less than or equal to 30.

Hmm, is that the same as what the others have said? Is it slightly different? Let's explore this.

This sign means that the speed that you can travel at has to be less than or equal to 30 miles per hour.

And you may have seen this on the road if you've been in a car that's been driven along.

Our speed must be less than or equal to 30 miles per hour.

So let's think about that.

If that's our speed and that's our constraint limitation, we are allowed to go up to, but not over, 30 miles per hour.

So our speed can be less than or equal to 30 miles per hour.

And that's how we read that sign.

So which speeds can go in the box? Pause the video while you have a go at this.

Welcome back.

Let's see how you got on.

What do you think can go in the box? Well, the 30.

001 miles per hour cannot go in the box.

Although it's only a very small amount over 30, it is greater than 30, so it can't go in there.

But the 21.

09 miles per hour can definitely go in the box, that's less than 30.

What about the 29.

999? Well, it's really close to 30, but it is smaller.

Into the box it goes.

What about the 0.

67 miles per hour? It's a lot smaller than 30, so it can go in the box.

Although I have to say if you are travelling at that speed, I suspect you're going to be annoying a lot of other drivers.

What about the 32? Nope, greater than 30.

Can't go in there.

What about if I travel at exactly 30 miles per hour? Ah, that can go in the box, because remember that symbol is read as less than or equal to, so you are allowed to be equal to it.

So that's allowed.

Now, 37 and 97 absolutely cannot go in the box.

And 1.

02 definitely can.

Well done if you got those all right.

Now it's time for a quick check.

Which of the following numbers from A, B and C could go in the box? Remember, we read that symbol as less than or equal to.

Pause the video now while you have a go.

Welcome back.

Let's find out how you got on.

Did you also pick A and B? That's right, you're allowed a number that is smaller than 30, you're allowed to be equal to 30, but what you are not allowed to do is go over 30.

Now this is interesting, Jun said, "Why not just use speed is less than 31? Then we wouldn't need to introduce these new symbols." Hmm, that's a good point.

Can you find an example to help change Jun's mind? What argument could you use to persuade him? Pause the video while you have a quick think.

Welcome back.

What examples did you come up with? In fact, if you came up with any number that was between 30 and 31, that would work as a counter example.

For example, if we'd said 30.

05.

Now that's only a little bit bigger than 30, but it is over 30, and under what Jun said, that would be allowed.

But our speed limit says it's not.

So we can't use that other symbol.

We have to have this new one.

Here's some examples that you could have used as well.

So 30.

5, 30.

403, 30.

927.

They're all above the speed limit of 30 but are all less than 31.

Now, Jun would've been right if the numbers had to be integers, but that isn't the case here.

So these new symbols really help us.

Let's have a quick check.

For each statement below, write the number sentence using less than, greater than, less than or equal to, greater than or equal to, or the equal to symbol.

And then tell us which of the numbers fit the statement.

You've got three statements here.

It takes me at least 12 minutes to talk to school, a hummingbird's wings beat more than 4,000 times minute, and the maximum capacity at Wembley Stadium is 90,000.

Pause the video now while you have a go at this.

Welcome back.

Let's see how you got on.

So you should have written, if it takes me at least 12 minutes, it means that I can take 12 minutes or I can take longer.

So we need the greater than or equal to symbol, and I need to pick any values that are greater than or equal to 12.

So that'll be 21 and 12.

In the second statement, it says a hummingbirds wings beat more than 4,000 times a minute.

Well, it can't be equal to 4,000 times therefore.

So I need the greater than symbol, and therefore the only value that works is 4,010.

In my final statement, I've got the maximum capacity at Wembley Stadium is 90,000, which means the number of people that can fit into the stadium is anything up to 90,000.

So I want less than or equal to, which means I can have nine, seems like a very small number for Wembley Stadium, or I can have the 90,000, but 90,001, that is one person too many.

It's now time for our final task, and in this, Laura is trying to organise a birthday party.

Now, there are different stages to this, so we're gonna get started with the first part now.

Laura is taking her friends to her theme park for a birthday party.

And at this theme park, you get half price entry if you are under 1.

5 metres tall.

Complete the statement to describe the situation, so what symbol will go in that box, and then tell us out of the children coming to Laura's party, don't forget Laura as well, who's going to get half price entry? Pause the video now while you do this.

Welcome back.

Time for part two.

At the theme park, Laura wants to ride a big rollercoaster.

I love rollercoasters.

I can completely see why Laura wants to do this.

Oh, it says you have to be at least 1.

45 metres tall in order to ride it.

There's probably a safety reason.

What I'd like you to do first is to write a mathematical statement to describe this.

So very similar to part one, only this time I'm not giving you the words in the other two boxes.

You've got to do the whole thing yourself now.

And then in question four, tell me which of the children can ride on the rollercoaster.

Pause the video now while you do this.

Welcome back, final part now.

After visiting the theme park, Laura is going to go to the cinema to watch a film that has a rating of a 12.

Write a mathematical statement to describe this.

So in other words, talking about the film rating.

And in question six, is Laura's choice of film a good one if she wants her friends to come along? Can you justify your answer? Now we're assuming that the cinema is going to check everybody's ages before they're allowed into the film.

So bear that in mind when you answer question six.

Pause the video now and have a go.

Welcome back, let's go through the answers regarding Laura's party.

So the first thing we had to do is talk about the half price entry.

Remember, you've got half price entry if you are under 1.

5 metres tall.

So the symbol I needed to use is the less than symbol.

So who's gonna get half price entry? Well, that'd be Sofia, her height's 1.

44; Andeep, his height's 1.

49; and Izzy, her height is 1.

45.

They're going to be the ones with half price entry.

Lucky them.

Now, in question three, you had to write a statement to describe whether or not we could go on the rollercoaster.

You had to be at least 1.

45 metres.

Well, that means that your height had to be greater than or equal to 1.

45.

Now, you might not have written height, you might have described that, but it's okay as long as you've said something along the lines of a person's height or the height of the person, that's absolutely fine.

So who can ride on the rollercoaster? Well, who's got a height that is greater than or equal to 1.

45? Oh, not Sofia, but Laura can and Lucas and Andeep, Alex and Izzy.

Oh, poor Sofia.

Let's hope she doesn't like rollercoasters.

Now the final bit of Laura's birthday party was going to finish with everyone going to the cinema to watch a film with a rating of a 12.

Now, the statement to describe this means that your age has to be greater than or equal to 12.

Now, you might have written more than that, and that's fine too, as long as you're conveying the same meaning.

So has Laura chosen a good film for her to watch with her friends? Well, let's look at everyone's ages.

Oh, Laura is the only person old enough to watch this film.

It sounds like perhaps you should choose a different film if she wants to watch with her friends.

Let's summarise our learning today.

This symbol means less than.

The symbol underneath, so in line two, means greater than.

The symbol in line three means less than or equal to, in line four greater than or equal to.

Remember, place value as we saw today is so important if we're going to be able to compare numbers to see which value is greater.

Well done.

You've worked really, really well today.

I hope to see you again for one of our future lessons.