Lesson video

In progress...

Hello, my name's Mrs. Hopper and I'm excited to be working with you in this lesson from the unit on comparing fractions using equivalents and decimals.

I love fractions and I hope you do too.

And I hope during this lesson you'll be able to see and understand a little bit more about them and how they link to decimals.

So if you're ready, let's make a start.

So in this lesson, we're going to be thinking about dividing one into different numbers of equal parts.

So we're gonna be thinking about a whole in different ways and thinking about how we can represent the size of those equal parts.

We've got some keywords, so I'll say them and then it'll be your turn.

So my turn.

Equal parts.

Your turn.

My turn.

Divide.

Your turn.

My turn.

Equivalent.

Your turn.

I'm fairly sure you'll be pretty familiar with those words, but they are gonna be useful.

So let's just remind ourselves what they mean, and how we're going to be defining them in our lesson today.

So when we divide, we split an object, number or quantity into equal parts.

Each equal part will have the same value as the others in the whole.

We know that numbers are equivalent if they have exactly the same value.

So there are two parts to our lesson today.

In the first part, we will be dividing one into equal parts, and in the second part, we will be describing those parts of one in different ways.

So let's make a start on part one.

And we've got Lucas and Sam helping us with our learning today.

So Lucas and Sam are thinking about fractions and decimals.

Lucas says fractions can describe a part of a whole, and Sam says decimals describe part of one.

So part of a whole as well.

Lucas says, let's see if fractions and decimals can describe the same parts of a whole.

Sam says, let's imagine this 100 square represents one and think about the parts.

So this is our one whole.

Can we divide the square into two equal parts? Oh, there's one way to do it.

I wonder if you could think of another way.

So one out of two equal parts is shaded.

How can you describe this part of the whole? Sam says, let's think of this 100 square as one hole, One out of two equal parts is the same as 1/2.

You can also think of this as 5 out of 10 equal parts, which is 5/10 or 0.

Let's think of this one hole divided into 10 equal parts.

Each part is one row.

And we had five of those rows shaded, which gave us our fraction of a half and our decimal of 5 out of 10 equal parts or 5/10, 0.

What about dividing the square into four equal parts? You might want to have a think about this.

What could it look like? Aha.

So this is how we've divided our square into four equal parts.

Can you see the four equal parts and one out of four shaded? How can you describe this part? Well, one out of four equal parts is the same as 1/4.

Sam says, think of the whole divided into 100 equal parts.

Each part is one small square.

So if each part is one small square, then this time we've shaded 25 out of 100 equal parts, which is 2,500 or 0.

25.

Our 2/10 would be 20/100 and our five hundredths extra, so 25/100.

And Sam says you can describe the part using a fraction or a decimal.

One quarter is equal to 25/100 which is equal to 0.

25.

So turning the fraction that we recognise into a fraction out of a hundred can help us when we are thinking about converting into a decimal.

What about dividing the square into five equal parts? You might want to have a think about how that might look.

That's how we've divided it into five equal parts and we've shaded one of them.

So one out of five equal parts is shaded.

How can you describe this part? Well as a fraction, one out of five equal parts is the same as 1/5.

Now Lucas says, let's think about the whole divided into 10 equal parts.

So each part is one column.

We had one row before.

This time we've got one column.

How many of those have we shaded? We've shaded two of them.

So we can think of this as two out of 10 equal parts which we can represent as a fraction as 2/10 and therefore as a decimal as 0.

Is there anything else you notice? Yes, we can think about our equivalent fractions, can't we? So you can describe the part using a fraction or a decimal.

We know that we shaded in one out of five equal parts, which is 1/5, but we can see from our square, our whole, that this is equal to 2/10.

And we know that from our equivalent fractions, if we scale up the numerator and denominator by the same factor, two in this case, we can see that 1/5 is equivalent to 2/10.

They represent the same part of the whole and we know that we can represent tenths as a decimal.

So our fraction of 1/5 or 2/10 is equivalent to 0.

2 as a decimal.

Time to check your understanding now.

You're going to divide the square into 10 equal parts.

Now you don't have to, but we've divided it up this way with one column and you're going to think that one out of 10 equal parts is shaded.

How can you describe this part using a fraction and a decimal? So pause the video, have a go, and then we'll get back together for some feedback.

How did you get on? We've thought about tenths as we've gone through when we thought about fifths, we identified that 1/10 column as well, didn't we? So we could say that one out of 10 equal parts is the same as 1/10 as a fraction.

That each of those equal parts is one column and 1/10 as a decimal is equal to 0.

1, a one in the tenths column.

So you can describe the part using a fraction or a decimal.

1/10 is equivalent to 0.

What about three equal parts? You might want to pause here and have a think about that.

Can we divide the square into three equal parts? Well, one out of three equal parts is tricky.

You can't do it exactly.

Why is that? Hmm.

Well I've got three parts there that are equal, but we've got one square left that is not shaded.

So can you have a look there and see how many is in each of those equal parts? We've got a dark grey, we've got a yellowy colour and a paler grey and we've got three complete rows plus three.

So we've got three lots of 10, 30 and three more.

So we've got three lots of 33, which is 99, and we've got that one square unshaded.

one out of three equal parts is the same as 1/3, but as Sam says, there's one square left over, the parts are equal, but they don't represent the whole when we put them together, there is one extra square.

How many is it out of a hundred equal parts? And Sam says there are three equal parts of 33 with one square left over.

So we've got 99 out of a hundred represented.

Ah, you could divide the leftover square into equal parts.

Let's have a think.

Let's blow that extra square up and divide it into a hundred equal parts and we'll be able to see that we've got the same problem, haven't we? We've got three lots of 33 and one square leftover.

Let's divide that leftover square over into equal parts.

Let's divide the leftover square into equal parts again.

There we go.

You can see they're not to scale.

We wouldn't be able to see them very clearly if we had, but there's another one blown up.

Same problem.

Sam says, we could keep dividing the leftover square into equal parts forever.

We've also put it there as a short division.

So we are dividing one by three.

So how many groups of three ones are there in one, one? There aren't any.

So we're going to exchange that one hole for 10/10.

How many groups of 3/10 are there in 10 tenths? Well there are three with one leftover.

So we've now exchanged that leftover 10th for 10/100.

And you can see that this is going on and on and on and on.

So we could keep doing this forever and ever that one little square would keep being divided into three lots of 33 with one leftover.

And we can see that carrying on with our division.

And when you look at these fractions in more detail later on, you'll learn that they're called recurring fractions because the same remainder recurs time and time again.

And so that 0.

3333333 will stretch on forever.

So you can't divide it exactly because a hundred is not a multiple of three.

One third is approximately equal to 33/100 and as a decimal it's 0.

3333333 with the threes going on forever as we saw in that previous slide.

The decimal goes on forever just like the squares did.

So we've been thinking about dividing one into equal parts using a hundred square, but we could use a calculator to help divide one into equal parts.

Let's have a think.

One divided into two equal parts.

Well we can represent that as one divided by two.

And if we punch that into a calculator, our answer will be 0.

5 and we know that that is equivalent to a half.

What about one divided into five equal parts? Well one divided by five would be equal to 0.

2 on the calculator.

And we know that one divided into five equal parts is 1/5.

So 1/5 is equal to 0.

So for one divided into 10 equal parts, we do one divided by 10, which is equal to 0.

And we know that one divided into 10 equal parts is the same as 1/10.

And we also know that that one in the tenths column represents 1/10.

And we could find one divided into four equal parts, one divided by four and the calculator will be equal to 0.

25, 25/100, 2/10 and five hundredths, 25 hundredths equal to one quarter.

And we could carry on, we could work out any fraction as a decimal by dividing the numerator by the denominator.

So one divided into eight equal parts, one divided by eight is equal to 0.

125, which is the same as 1/8.

And Lucas says 1/8 is half of one quarter.

If you imagine something divided into four equal parts, and if we divide each of those parts in two, we'll have eight equal parts.

So 1/8 is a half of a quarter and 0.

125 is half of 0.

25.

So Lucas asks, can you estimate the decimals for the remaining fractions? So we've put in the ones that we've worked on there, but there are some other ones there.

Can you see a possible problem with them? You are thinking about those factors of a hundred.

Hmm, I wonder.

You might want to pause and have a think and then we'll go through them together.

So 1/6 is a half of a 1/3 and you might be able to imagine that if you imagine a shape divided into three equal parts.

And then if we divide each of those parts in half, we'd have six equal parts.

So the fraction will be a half of 0.

333 and its equivalent decimal will be just over 0.

16.

In fact it's 0.

1666666 all the way through again.

There we go.

What about 1/7? Well a seventh is smaller than a six but bigger than an eighth.

So the equivalent decimal will be between 0.

125 and 0.

16.

And we've done it on the calculator here to a certain number of decimal places and we've got a fraction of around 0.

14286 and then it carries on.

So if you had something around 0.

14, then that was about right.

A good estimate, well done.

What about a ninth then? Well, a ninth is smaller than an eighth, but bigger than a 10th.

So the equivalent decimal will be between 0.

125 and 0.

So 0.

11, that sort of thing, maybe? Absolutely right.

1111.

And because again, nine is not a factor of 100 and nine is related to threes and sixes, isn't it? We've got that fraction that keeps ongoing forever and ever.

1111111 all the way through.

And you could explore those divisions using a short division if you wanted to and see how those numbers keep repeating.

So what do you notice about the fractions and the equivalent decimals? Well if you look at the difference between them, the difference between the decimals get smaller as the fractions get smaller.

The difference in size between a half and a third or a half, a third and a quarter is is bigger than the difference between a seventh and eighth, an eighth and a ninth or a ninth and a 10th.

And so the difference between the decimals will also get smaller.

And some decimals never stop.

So using a fraction is more accurate as you don't have to round them.

And that's an interesting thought, isn't it? That a fraction can be more accurate than a decimal.

Time for you to do some practise now.

We've got six little equations here for you and your task is to put the correct symbol in to make each one correct.

So the less than the greater than or the equal sign between those fractions and decimals to make those equations correct.

And then in part two, you're going to create your own equations using one fraction and one decimal each time.

How many different ways can you complete the equations? So pause the video, have a go, and then we'll get back together for some feedback.

How did you get on? So these were the correct symbols, so hopefully you were able to think about what we've been doing about dividing one whole, a hundred square in our case into equal parts.

So we can see that 0.

1 is equal to 1/10, 0.

01 is equal to 1/100 but 0.

1 is greater than 1/100.

That's a one in the 10th column and we've got 100th in the fraction.

For D, 0.

01 1/100 is less than 1/10.

In E, one-tenth is greater than 100th.

And in F, one 100th as a decimal is less than 1/10 as a decimal, well as a decimal or a fraction.

Okay, bit of revision there and a bit of practise around really thinking about what our decimals and our fractions represent.

So I hope you were successful there.

Then you could be a bit more creative here, couldn't you? So we were thinking about fraction and decimal equivalences and then thinking about those slightly trickier fractions where there wasn't a very neat and tidy decimal equivalence.

So we've got in here, we've chosen 1/7 is greater than 0.

125.

125 we know is 1/8 as a decimal and 1/7 is greater than 1/8.

1/5 is equal to 0.

2 and we went for 0.

1, which is 1/10 as a decimal is smaller than or less than one ninth represented here as a fraction.

Lots and lots of different ways for you to complete those and I hope you had fun coming up with some interesting ones.

Okay, so into part two of our lesson where we're going to be describing parts of one in different ways.

So we're gonna think about number lines.

So what are the missing fractions and decimals on the number lines? You might want to have a think before we fill these in.

Well, we can see that this top number line is zero to one and it's divided into two equal parts.

So as a fraction that middle unlabeled point would be one half and we could say that our whole is two halves as well.

What about the decimal then? That's right, 0.

5 we know is equivalent to a half.

So from zero to one on our number line, we will stop at 0.

5 halfway along.

What about the bottom number line? Can you see something that's the same and something that's different.

This time, we've got four equal parts.

So we've got one quarter, two quarters, three quarters and four quarters.

And then for decimals, 0.

25, 0.

5, 0.

75 for three quarters.

So you can see our half is directly above each other, one half is equivalent to two quarters.

But this time we also needed to know that we had one quarter, two quarters and three quarters.

And if we know that one quarter is 0.

25 as a decimal, we can use our knowledge of the sort of 25 times table.

So one quarter is 0.

25, two quarters is 0.

5 and three quarters is 0.

75.

What about the steps along these number lines? Can we label them with fractions on the top and decimals on the bottom? What do you think? Again, you might want to pause and have a think yourself before we fill them in together.

So for our top line we've got one, two, three, four, five equal parts.

So we must be thinking about fifths.

So 1/5, 2/5, 3/5, 4/5, and 5/5 for our whole.

Now what did we know about fifths and decimals? So 1/5 there was equivalent to 2/10.

So 1/5 is a decimal is 0.

So 0.

2, 0.

4, 0.

6, 0.

8 and one.

And what about the bottom part? Can you see, sort of similarities and differences? I think we're in 10 equal parts on this bottom line, aren't we? So we are counting in tenths, you might want to count all the way along.

We are going to fill them all in.

So zero, one tenths and then counting along in tenths all the way up to 10 tenths, one whole.

And we know that tenths is a decimal as that 0.

It's that first column after the decimal point.

So 0.

1 and then we can fill in the rest, 0.

2 all the way through to 0.

9 and then one whole, 10 tenths, is the same as one whole.

And we can see that on the number line as well.

Time to check your understanding.

Okay, we've moved on from just counting in our number system, we've got a metres here represented.

So can you think about what the missing fraction and decimal values are on these one metre lines? So pause the video, have a think and we'll get back together and talk about the answers.

How did you get on? So we're just again, dividing into five equal parts, aren't we? So we'd have a fifth of a metre and we can see that one metre is our one unit, so we can think about what that would look like as a decimal as well.

So let's have a look.

So we are just counting in fifths again.

So a fifth, 2/5, 3/5, 4/5, and 5/5 of a metre this time.

So what about our decimals? So yeah, 0.

2 of a metre, 0.

4 of a metre, 0.

6 of a metre, 0.

8 of a metre and one metre.

So for our bottom number line, again, we're counting in tenths, so we will be counting in one tenths of a metre and you might have had discussion about what that would be in centimetres.

I wonder.

Oh, so let's have a look at a measuring jug, a scale.

So this time we've got a one litre jug here.

So what are the missing values on the scale, on our measuring jug? Can we think about this infractions and in decimals? Well we've got two equal parts, haven't we? Lucas says the whole is one litre and it's divided into two equal parts.

So we know what these fractions are going to be, don't we? Each part is one half, so we've got one half and two halves of a litre to make a whole litre.

And half a litre is equal to 0.

5 of a litre.

So 0.

5 of a litre on our measuring scale.

And you might know what 0.

5 of a litre is in millilitres, which might be another way that your scale is labelled.

What about this one? So again, we're just looking at those common divisions, but looking at them in different contexts.

So how many equal parts? Lucas says, yep, the whole litre is divided into four equal parts.

So each part is one quarter.

So our fractions will be one quarter, two quarters, three quarters, and four quarters.

And on our decimal side we know that one quarter of a litre will be equal to 0.

25 litres.

So 0.

25, 0.

5, 0.

75 of a litre, and then one whole litre.

So we've put some juice into our jugs this time we've got blank scales, but how much juice is in the jugs? Can you describe it using a fraction and a decimal, I wonder? You might want to pause and have a go, but we'll have a look at these together.

So let's look at that left hand side jug.

We've got one, two, three, four, five equal parts in our scale.

So we are thinking about fifths here.

So we could label our scale in fifths and we can see that our juice comes up to the 3/5 line.

What would that look like as decimals though? That's right, 0.

2, 0.

4, 0.

6 and 0.

8 of a litre.

So in our first jug we've got 3/5 of a litre or 0.

6 of a litre.

What about the next one? That's divided into 10 equal parts, isn't it? So we're thinking about tenths and maybe that idea of the one tenths column for our decimals? Oh, lots of fractions there.

So we're counting up our scale in tenths.

Easier to see it like that I think, isn't it? 0.

1, 0.

2, 0.

3, 3/10.

So this time we have 3/10 of a litre or 0.

3 of a litre.

Now that's interesting, there is half as much juice on the right.

Can you see the link between those fractions? We had 3/5 of a litre, now we've got 3/10 of a litre.

We had 0.

6 of a litre and now we've got 0.

3 of a litre.

So we've halved the amount of juice.

I wonder who drank it.

Was it Sam or Lucas, do you think? Time to check your understanding now.

We've got two jugs again, we've got juice in one jug, but we haven't got any juice in the other jug.

So where would 0.

3 litres of juice come to in the jug on the left? Pause the video, have a think and then we'll come back and discuss the answer.

How did you get on? What did you spot? Did you notice that both jugs have a scale that goes up to one litre? So presumably it's gonna come to the same point, isn't it? But we haven't got a 0.

3 marked on the scale on the left because we're counting in fifths and 0.

3 doesn't come into being 1/5 of a litre.

So where's it going to come to? That's right, 0.

3 is halfway between 0.

2 and 0.

And of course the juice is going to come to the same level, but 0.

3 sits between 0.

2 and 0.

So we also then know that 3/10 sits between 1/5 and 2/5, which makes sense, doesn't it? 1/5 is 2/10.

2/5 is 4/10.

So 3-10 is going to be in the middle.

Hope you got that right.

Another check.

This time we're thinking about coins.

So we're asked what fraction of one pound are the 10 p coins worth and what is their value as a decimal? And this is useful when we are recording money.

So have a look at the coins, decide what fraction of a pound each set of coins represents, and then how would you record it as a decimal? Pause the video, have a go and we'll get back together for some feedback.

How did you get on? So in the first one we've got four 10 p coins.

So we've got 4/10 of a pound.

We know there are 10 10 p coins in a pound and 4/10 is equivalent to 2/5 and we'd record that as 0.

4 pounds and we've used pounds and pence notation there.

What about the next one? How many coins have we got there? Well, we've got seven coins, haven't we? So we've got 7/10 of a pound or 0.

7 of a pound.

One 10 p coin, that's 1/10 of the pound.

So 1/10 or 0.

And finally we've got five 10 p coins.

So we've got 5/10 or one half, and we can see that that 0.

5 represents both 5/10 and 1/2.

And as you saw there, we could use equivalent fractions to record the same amount in different ways and sometimes one way can help us to translate into a decimal better than the other one can.

Time for you to do some practise.

So can you write the alternative representations of each value into these tables? So we've got decimals and we've got fractions.

So can you write the alternative versions into these gaps? Pause the video, have a go, and then we'll get back together for some feedback.

How did you get on? Here are all the answers.

I wonder how you thought about them though.

You might have thought about how the decimals relate to each other and relate to the fractions and used your knowledge of those to help you.

You might have used some known facts from the fractions to the decimals.

But the other thing it's useful to do is to think about what the fraction would be as a fraction out of 10 or a hundred to help you to convert it into a decimal.

And you can also think about the relationship between the fractions.

If we know 1/10 is 0.

1, then 3-10 must be 0.

If we know that 1/4 as a fraction is 0.

25, then 1/8, which is half the value must be 0.

125.

And did you spot also those fractions that just keep going? So we had 1/3 and 2/3 in there, 0.

33333 forever and 0.

66666, possibly rounding to a seven at some point for 2/3.

Well done and I hope you were successful in those and I hope you had some interesting discussions as you filled in those gaps.

And we've come to the end of our lesson.

So we've been explaining and representing how to divide one into different numbers of equal parts.

So what have we learned about today? Well, we've learned that you can divide one into different numbers of equal parts and you can represent the part with a fraction or a decimal.

Tenths and hundredths can be easily represented as fractions and decimals because we can link those straight to the tenths and hundredths columns in our decimal representation.

And equivalent fractions and decimals mark the same point on a number line or a scale.

You may have seen that with equivalent fractions in your work recently, but now we can see that those decimals and fractions sit at the same point on the number line when they are equivalent.

Thank you for all your hard work today.

I've really enjoyed working with you and I look forward to working with you again at some point soon, I hope.

Bye-Bye.

I've finished the video