Lesson video

Hello, my name is Mr. Tilstone and it's my great pleasure to be working with you today on something that's an important part of day-to-day life and that is money.

So if you're ready to explore today's lesson, let's begin.

The outcome of today's lesson is I can explain how to compare amounts of money without converting.

So if you've been successful, you'll be able to say that at the end of today's lesson.

We've got some important vocabulary to discuss, some keywords before we proceed.

They are compare, inequality symbols, you might recognise those, greater than and less than, and ascending and descending.

Some of those might already be familiar, but let's have a reminder of what they mean.

We can compare different numbers by, for example, saying which one has a higher value.

There are other ways we can compare too.

An inequality symbol is used to compare two values.

Two examples are that symbol, which it means less than, and that symbol which reads as greater than.

Greater than means a number is bigger than another number, and less than means it is smaller.

Ascending means going up, and descending means going down.

And I like to remember that by D for down, descending, down.

Our first lesson cycle is going to be comparing money using understanding of decimals.

In this lesson, you're going to meet Alex and Jun.

They're gonna be there to help us out.

Jun and Alex compare the amount of money that they have.

So this is what Jun's got.

You might notice the coins are jumbled up.

I wonder what you could do about that? And that's what Alex has got.

So just take a moment just to see if you can figure out how much they've got each.

But Alex says that he's got a higher amount because he has more coins.

Let's have a think about that, is that true? Does Alex have a higher amount because he's got more coins? Well, he definitely has got more coins, I can see that.

He's got six coins, Jun's got five coins.

But has Alex got more money? Let's investigate.

They organise their money to compare.

That's a good idea.

It's not jumbled anymore.

They've started with the highest value, which is pounds, and then moved on to the 10p.

So they made groups of their coins.

That's sensible, isn't it? So that's how much Jun's got, I can see it very clearly now it's easy to recognise.

And that's how much Alex has got.

Now I can see straightaway, Jun has got more one pound coins, so Jun must have more money.

We don't even need to look at the 10 pences.

They start by doing what I've just described, which is comparing their greatest value coin first.

So when you are comparing money amounts, start with the one that's got the greatest value.

In this case it's pounds.

So Jun's got more pounds than Alex, therefore, he's got more money.

Jun says, "I can see my set has more pound coins.

I don't even need to look at the 10p coins to know that my set is worth more." We've got a generalisation here, when comparing money start by considering the largest coin value.

Will you say that with me please? When comparing money, start by considering the largest coin value.

Now, just you say it, please.

We could also use a place value grid to compare the money amounts that we have.

So they've written down the money amounts.

Let's start with Jun, so he's got three one pounds.

So he is put that into the one pound column and he's got two 10p, so he is put two into the 10p column.

He hasn't got any 1p.

Alex has done the same thing.

So he's written his two in the one pound column 'cause he's got two one pounds and he is written four in the 10p column because it's got four 10 pences.

We can compare them that way.

Again, just like before, we're going to start with the highest value, which is a pound coins.

We can see that the top row has got three one pounds and the bottom row has got two.

So therefore Jun has got more money.

There is a higher value in my pounds column.

He's right.

Alex, meanwhile, has looked at that from the other point of view, that he's got less money.

There is a lower value in his pounds column.

So whenever you say that there's more of something, you can also say there's less of something.

So Alex says, "Comparing money is just like comparing decimals." He's right, it is.

You can also say that 3.

20 pounds, is greater than 2.

40 pounds, as it's got a higher value.

So we're starting to use that language now, the language of inequality.

You can use an inequality symbol to show the relationship.

Which one do you think we're going between those? Let's have a look, shall we? There we go.

So that now reads as 3.

20 pounds is greater than 2.

40 pounds, 3.

20 pounds is greater than 2.

40 pounds.

And we can also say that 2.

40 pounds is less than 3.

20 pounds.

We can flip it around like that as it's got a lower value.

You can use an inequality symbol to show the relationship.

Which one would it be this time I wonder? Let's find out.

And now the number sentence reads 2.

40 pounds is less than 3.

20 pounds.

And this is the less than inequality symbol.

So 2.

40 pounds is less than 3.

20 pounds.

Jun and Alex compare how much money they have now.

They've got the same amount of one pound coins, I can see that.

I can see that Jun's got three and that Alex has got three.

I don't need to count that.

I can subitize that.

So that's not helpful looking at the number of pound coins.

To compare this time, they need to look at the next greatest value, and that's 10 pences.

So we're going to compare how many 10 pences they've got this time.

The value of the 10 pence column is different.

Alex has a greater value in this column.

Jun's got two 10 pences, Alex has got four.

So we can say 3.

24 pounds is less than 3.

44 pounds.

Likewise, we can also say 3.

44 pounds is greater than 3.

24 pounds.

What do you notice this time? What's the same and what's different about the totals that Jun and Alex have got? Hmm, have a look.

I think they've got two things in common, and one thing different.

Can you spot it? Jun's got three one pound coins and so has Alex.

So they've got that in common, so it's not helpful to compare using the pound coins.

That is the highest value, but they're the same.

So we're going to move on to the next highest value and that is the 10p coins.

They're also the same, they've both got two.

So we can't compare them using the 10p coin.

So we move on to the next highest value and that is the pennies.

Now you can see there is a difference between the number of pennies.

Jun's got four, and Alex has got seven.

So Alex has got more.

So he's got a higher total, not by much, but he has got more money.

So this time the value of the one pence column is different.

Alex has a greater value in this column, so he's got more money.

We can use our inequality symbols once more, and we can say 3.

24 pounds is less than 3.

27 pounds.

What about the other way round? How would we say that? Can you remember? Can you think? We can say 3.

27 pounds is greater than 3.

24 pounds.

We can also compare amounts when we want to buy something.

So Jun wants to buy Alex a large birthday cake.

Which cake costs more? Okay, the cake on the left costs 13.

76 pounds, and the cake on the right costs 12.

38 pounds.

So they're quite similar.

They've both got one in the 10 pounds column.

So we need to move on to the next highest value, which is a one pound column.

Which one has more? Well, let's start with the column of the greatest value.

They've both got the same value in the 10 pounds column, but they've got a different value in the one pounds column.

So that's our point of comparison.

We can see that 13.

76 pounds is greater than 12.

38 pounds.

So that cake costs more, it's worth more.

Likewise, we can say 12.

38 pounds is less than 13.

76 pounds.

So that cake costs less.

You can also compare money without using a place value chart to save time.

Which is greater in value 25.

44 pounds or 25.

82 pounds? So this time we're not going to use coins, we're not going to use a place value chart.

We're just going to look at the two different money amounts and see if we can compare that way.

Remember to start with the highest placed value.

Writing both amounts and aligning the digits can help you.

So if I write one underneath the other, that's going to help with comparison.

So 25.

44 pounds is less than 25.

82 pounds, 'cause it's got a lower value in the 10p column.

The 10 pounds column was the same, the one pounds column was the same, the 10p column was where it differed.

So 25.

44 pounds is less than 25.

82 pounds, or 25.

82 pounds is greater than 25.

44 pounds.

I think we are ready for a check for understanding.

Is this true or false? 3.

08 pounds.

Hmm.

3.

40 pounds.

I'm not going to read that symbol because I'm hoping that you'd know it what it is by now.

But is that statement true, or is that false? And you'd like to justify your answer as well.

We've got a couple of options there.

Option a, they both have the same amount of pounds.

The next largest coin value is the 10 pences and four is greater than zero.

And option b, three plus zero plus eight equals 11, but three plus four plus zero equals seven.

So 3.

08 pounds must be greater.

So pause the video, have a look, look at the options, and see if you can decide whether that's true or false, and which one justifies the answer.

Okay, should we check? Let's have a look.

It's false.

That's not true.

And the justification is, yes, they both have the same amount of pounds, they've both got three pounds, haven't they? The next largest coin value is 10 pences, and four is greater than zero.

So in fact we can say 3.

08 pounds is less than 3.

40 pounds, or if we want to start with the 3.

40 pounds, we can say 3.

40 pounds is greater than 3.

08 pounds.

Well done if you've got that.

I think you are ready for a practise.

You're doing really well.

So you're going to use the inequality symbols, remember that's less than and greater than, to compare these money amounts.

Let's have a look at these examples.

So a, all of the coins are in order, they're all lined up and grouped together.

So that should make it easy.

So see what you notice about them.

Remember to start with your highest place value when comparing.

B is similar, they're all lined up, but I can see that something's different about those.

It's a different coin that differs.

And likewise with C, they're all lined up, but something's different about it.

So can you compare them using the inequality symbols please? For task A 2, can you use those inequality symbols, less than and greater than, to compare these money amounts? So compare 6.

63 pounds and 6.

48 pounds, compare 7.

63 pounds and 7.

84 pounds, and finally compare 7.

63 pounds and 7.

68 pounds.

For task 3, "A new board game costs 27.

56 pounds.

Jun finds the same game for less than this price," less than that price.

"It still has the same value of pounds." So it's still 27 pounds something.

"What could it cost? Can you say the biggest and the smallest price?" Let's have a look at some answers, shall we? How did you get on? For the first question, the money total on the left has got more pound coins, so I didn't even need to look at the 10p or the 1p.

So that is greater than.

The second example, it's less than, and I can see that because although they've got the same amount of one pound coins, the one on the left's got fewer 10p coins.

So that's less.

It's worth less.

And for the third example, it is greater than.

They've got the same amount of pound coins, they've got the same amount of 10p coins, but the one on the left's got more pennies.

It's got six and the other's got three, so that's greater than.

And let's have a look at some answers for task A 2.

So using those inequality symbols, we can say that 7.

63 pounds is greater than 6.

48 pounds.

And if we look at the most significant digit there, that's the pounds, and you can see they differ.

So there's quite easy to compare.

For b, 7.

63 pounds is less than 7.

84 pounds.

Those two values were quite close.

We had to look at the 10p column, and it's got fewer.

And for c, 7.

63 pounds is less than 7.

68 pounds.

The pounds were the same, the 10p were the same, it was the penny column where it differed.

And for number 3, a new board came cost 27.

56 pounds.

So if you find that game cheaper, but it's still got the same number of pounds, the smallest amount would be 27 pounds and no pennies.

The greatest amount would be 27.

55 pounds.

And you can have any value in between.

So well done if you've got any of those, and especially well done if you've got all of them.

I think we are ready to move on to cycle two of the lesson.

And that is ordering.

So we're going to use a slightly different skill here, ordering amounts of money.

Class 5 have been raising money for charity.

Aren't they good? Here's Lucas.

He's raised 10.

84 pounds.

Fantastic.

This is Laura.

Laura's raised 9.

50 pounds.

Bravo Laura.

Here's Andeep, and he's raised 10.

76 pounds.

Well done, Andeep.

And finally Izzy has raised 10.

89 pounds.

Fabulous.

Now we're going to order those money totals, and we're going to do it from the lowest up to the highest, and we call that ascending order.

Just like before, we could use a place value grid and we could write each amount on the chart, like so.

So this is Lucas.

He's raised 10.

84 pounds, so that's one 10 pound, no one pounds, eight 10p, and four 1p.

Andeep's raised 10.

76 pounds.

And that's how that looks.

Laura's raised 9.

50 pounds, so she's not quite raised as much there.

So she's not raised as much as 10 pounds.

So she's got no 10 pounds, but she has got nine one pounds.

And then Izzy has raised 10.

89 pounds.

And that's how we represent that on the place value grid.

Now to put those into ascending order, we need to find the lowest value first, so the person that's raised the lowest amount of money.

Let's start by looking at the column with the greatest value, which is the 10 pounds.

Laura's total is the only one less than 10 pounds, so it must be the lowest.

So we can start with her.

Let's cross that out, so that we know not to use that again.

Let's make it easy.

We can focus on the other three now.

The others have all got one in the 10 pounds column, so that's not helpful in terms of comparing them.

So we need to move on to the next column with the next highest value.

So we're going to look at the pounds column, but as you can see, we've got a bit of an issue here.

This is zero in all of them, so we can't compare them using that column.

Andeep has got the lowest number of 10 pences at seven, so his value is next when putting the totals into ascending order.

So we're gonna add into the list and we're gonna cross out his value on the table.

Now if we look at the 10p, the other two are eight and eight, so we can't compare them in that way, so we need to move on to the 1p now.

Now we've got four and nine, four's lower than nine, so Lucas's total goes next.

Let's add him, and let's cross him off.

That just leaves one total, which is Liz's.

Liz's total is the greatest, so we can put hers on the end of the list.

So that list is now in ascending order, it goes up from lowest to highest.

They begin with the lowest value and increase to the greatest value.

So 9.

50 pounds, then 10.

76 pounds, 10.

84 pounds, 10.

89 pounds.

They're in order.

They're in ascending order to be specific.

We can put them into descending order by going from highest to lowest.

So go the other way around.

So start with the highest value.

That was 10.

89 pounds and then it was 10.

84 pounds, and then it was 10.

76 pounds, and finally 9.

50 pounds.

So they're still in an order, but the opposite order, they're descending, D for down remember.

I think it's time for a check for understanding.

Look at the table.

We started to put the money values in order, into ascending order, specifically, from lowest to highest.

We started with 8.

57 pounds, and crossed that out, that was the lowest.

And then the next highest after that was 9.

39 pounds, which we've crossed out.

But what comes next? You've got two options there.

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

How did you get on? You had a choice of two.

Let's see if you chose the right one.

10.

09 pounds would be next.

They're very similar, aren't they? They're both 10 pounds something, but 10.

09 pounds has got nothing in the 10p, so that's got to be next, whereas 10.

27 pounds has got two in the 10p.

Let's do another check.

True or false? The following money totals are in ascending order.

I'm not going to say what ascending means this time, because I hope you can remember.

So 4.

57 pounds, 14.

83 pounds, 14.

73 pounds, and 22.

80 pounds.

Are they in ascending order? And you're going to justify your answer.

Is it true or false? Your justification choices are a, "The third total has fewer 10 pences than the second, so they need to be swapped." And b is, "Four is greater than one, so the first total should be at the end." Time to pause the video, time to have a think.

It was false.

They're not quite in ascending order, though it starts off that way.

The third total has fewer 10 pences than the second, so they need to be swapped.

So the third total looks 14.

73 pounds.

Now that's got seven 10 pences, but 14.

83 pounds has got eight 10 pences, so they need to be swapped over.

The order should go 4.

57 pounds, 14.

73 pounds, 14.

83 pounds, 22.

80 pounds.

And now they're in ascending order.

I think you're ready for some independent practise because you are doing fantastically well.

So question one is, "Class 5 have been fundraising again.

Use the table to order the values in ascending order." See if you can remember what ascending means.

Question two, "Put the following money amounts into ascending order." What does ascending mean? Now I can see that's going to be slightly trickier because of the mixed notation.

Some have got pound symbols, some have got pence.

There's a bit of a mixture.

Likewise for three, there's a mixture there.

This time you're going to put those into descending order.

So pause the video.

Off you go.

Are you ready for some feedback for task B? Let's have a look, shall we? Let's see how you got on.

So number one, "Class 5 have been fundraising again." If we put their totals into ascending order.

So from lowest to highest, it goes 10.

86 pounds, 11.

19 pounds, 11.

43 pounds, and finally the greatest is 12.

05 pounds.

And for number two, "Put the following money amounts in ascending order." Again though, it's the highest that goes, 0.

83 pounds, 83 pence, 91 pence, 2.

73 pounds, 2.

83 pounds, and 5 pounds.

And that was quite tricky because of the mixed representations.

And for number three, "Put the following money amounts in descending order." So going down from the highest to the lowest, we've got 9.

10 pounds, 9.

01 pounds, 6.

40 pounds, 6.

04 pounds, and 64 pence.

You have been fantastic.

We've come to the end of the lesson now, so let's summarise our learning, shall we? The lesson has been about explaining how to compare different amounts of money without actually converting.

We can compare different amounts of money by starting with the most significant digits.

So start on the left, start with the one that's got the highest value, then move right if you need to.

Inequality signs can be used to compare different amounts of money.

So we've got an example here, 25.

82 pounds is greater than 25.

44 pounds.

Now the 10 pound column was the same, two in both of those.

The one pound column was also the same, five in both of those.

It was the 10p column that differed.

One had eight, one had four, so eight's got more.

Eight is greater than four.

Hope you've enjoyed the lesson and hopefully I'll see you very soon.

Goodbye.