Lesson video

Hello, it's Mr. Etherton here again, and welcome back to another exciting day of year three maths.

Today our learning outcome is to be able to compare and order unit fractions.

What exactly are we going to be learning today? In this lesson, we will explore the size of different unit fractions.

We will then compare and order these fractions, focusing on their denominators before we apply this knowledge to compare unit fractions of the same quantity.

So we're going to have to put all of our learning about fractions together so far to try and remember what unit fraction is, and then we're going to have to apply our knowledge of bar modelling, and how to find fractions of an amount.

Today, you will need a pencil, a piece of paper or exercise book, to do your work out, and, if you can, you need to be able to thus a fraction wall.

This can either be printed, or you can get an online version.

So pause the video now to get your equipment ready.

Let's have a look at our first task.

You'll need to complete the introductory knowledge quiz if you haven't already.

So pause the video now to complete this.

If you have already done this then continue reading.

Alright, a quick warm up today.

How many different fractions can you find of this amount? So look at the stars on the screen.

What is the value of the whole? Can you divide that whole into different fractions? And can you find the value of those fractions? So pause the video for two minutes to complete this activity.

Go.

Let's have a quick look through our answers.

So, if we count the stars we would've seen the whole is eighteen.

When we're trying to find fractions of an amount you might work systematically, and try and split them into equal groups one after the other.

So we might try and split into two equal groups for a half.

We the then might try three equal groups for thirds, then four equal groups for quarters, five equal groups for fifths, but sometimes that will not work, and we're going to explore why.

So if my whole was eighteen, I might have tried to split it into two equal groups find a half.

So that just works so a half of eighteen is 9, and two halves of eighteen, a whole, is eighteen.

We could then try and split it into three equal groups.

And eighteen does split into thirds, because three is a factor of eighteen.

So one-third of eighteen is six, two-thirds of eighteen is twelve, and three-thirds, a whole of eighteen, is eighteen.

If you work it systematically, we might've now tried quarters.

But when I'm looking at my eighteen, I can't seem to split it into four equal groups.

And that's because four is not a factor of eighteen.

Eighteen is not in the four times table.

So we cannot find quarters of eighteen.

We cannot find fifths of eighteen, because they aren't equal groups.

But we can find six, because six is a factor of eighteen.

So one-sixth of eighteen is three, so split them into six equal groups.

And two-sixths of eighteen is six.

Three-sixths of eighteen is nine.

You might've started to notice a pattern here.

Three.

Six.

Nine.

The next one would be twelve.

Four-sixths of eighteen is twelve.

So we're counting up in our three times table here, and that's because the value of one-sixth, one part, is three.

So every part every sixths is equal to three.

So if you want to work out the answers for four-sixths, five-sixths, six-sixths, then we need to count in multiples of three.

The next one, is ninths, because nine is a factor of eighteen.

So one-ninth of eighteen is two.

Two-ninths of eighteen is four.

Three-ninths of eighteen is six.

Again, pattern.

Two.

Four.

Six.

We're counting in two's.

Eight.

Ten.

Twelve.

And that's because one-ninth, one part of eighteen is equal to two, so every part is equal to two.

So we're counting up in multiples of two.

And finally, one-eighth of eighteen so we've got this time we're splitting eighteen into eighteen groups, and one-eighteenth is one.

Two-eighteenths is two.

Three eighteenths is three.

And we continue this all the way up counting in multiples of one.

What I would like you to do is pause the video now if you need to continue, or mark your answers.

We're going to move on now, and start to have a look at our learning.

Okay.

So today are star words.

My turn your turn repeat them to me.

Unit fraction.

Compare.

Order.

Greater than.

Less than.

Is equal to.

Right, let's explore these words and what they mean.

So unit fractions.

Today, we are going to be working with unit fractions.

This is when a numerator is one, and one only.

Compare.

We're going to be looking at different fractions, and comparing the size of them.

So which is bigger, which is smaller? Order.

That's when we're looking on comparing more than two fractions, so we're going to start to try and put them in a size order.

We've got greater, more than, larger than, and less than, fewer than, smaller than.

So different words meaning the same things, so listen out for my vocabulary today.

And is equal to.

Meaning, has the same value.

Right, on your screen I have displayed a fraction wall.

Some of you might be thinking, "I've never seen this before." Some of you might be familiar, but what I would like you to do now is pause the video, and spend sometime thinking about what it shows us.

So pause the video now.

Okay.

Let's have a look at this together.

So this, slight wall we're building, our fraction wall is made of lots of bricks, and you might've already noticed that the bricks are all different sizes.

The brick at the very top is my biggest brick.

Okay? And that is equal to one whole, so just like we were using bar modelling the other day, this bar is equal to one whole.

Then, the next brick started off as one whole, but then it was cut into two equal groups.

So now, those two bricks have a value of one-half.

Then, the next row down, again it started as one whole, but it then got split into three equal groups.

So each brick has a value of one-third, and so on.

So quarters, fifths, one-sixth, sevenths, eighths, ninths, and tenths.

They're all different sizes, because the whole has been split into different equal parts.

As we go down the fraction wall, the whole is being cut up into more equal parts.

We can see a half is only being cut up into two equal parts, whereas, down on our tenths, they've been cut into ten equal parts.

The whole was the same size to start with.

So this means that my bricks at the bottom are much smaller fractions of the whole, than my bricks closer to the top.

So I'm already starting to compare the size of these fractions.

When we are comparing fractions, well fractions, unit fractions even, there is a rule.

That we're going explore that now.

Rule in comparing unit fractions is, the bigger the denominator, the smaller the fraction size.

This is because the whole has been split into more equal parts.

This might be a little bit confusing, because the bigger denominators, eight, nine, ten, are actually smaller fractions.

So remember that rule today.

Repeat after me, the bigger the denominator, the smaller the fraction.

Fantastic.

So let's explore this a little bit further.

So we're going to have a look at one-half and one-sixth.

We're going to use the fraction wall to help us, but which of these fractions is greater? Which of these fractions is smaller? And how do you know? I would like you to pause the video, think about this, and share this with an adult.

If there isn't an adult just keep that thought to yourself.

Pause the video now.

Okay.

So if we have a look at our fraction wall, we can find half, I know that the whole is being cut up into two equal parts, whereas, my sixth, the whole is being cut up into six equal parts.

I can see here, that if I go across the length of the half, and I go down, it is much bigger than my one-sixth here.

And, remembering, that's because the whole is being cut up into more equal parts so it's smaller.

So which is greater? One-half is greater.

Which is smaller? One-sixth.

But remember that rule.

We could have just looked at our denominators of these unit fractions to help us.

The bigger the denominator, the smaller the fraction.

Let's continue.

Now, it's going to be your turn.

I'd like you to select two of your own unit fractions to compare.

Which is greater? Which is smaller? And how do you know? Pause the video now.

Okay year three, let's have a look at some of the answers you might have chosen.

You might have chosen one-third, and you might have compared this to one-eighth.

So I know that one-third is greater than one-eighth.

I can see the length of this fraction, the size of this fraction is much bigger than the eighth here.

But to help me compare, I can look at the denominator of these unit fractions, and remember that rule the bigger the denominator of the unit fraction, the smaller the fraction size.

And that because the whole has been cut up into more equal parts.

So our greater fractions were the ones closer to the top of the fraction wall, and our smaller fractions were the ones closer to the bottom of our fraction wall.

Okay.

So comparing those two fractions.

Now, order fractions.

So, how do we order the fractions from smallest to largest? We can use our fraction wall to help us, but we're also going to use that rule.

So I have the fractions one-ninth, one-third, one-seventh, and a half.

I would like you to think carefully about what order would you put these in from smallest to largest? If you would like to pause the video, and have a go at this independently, you can do, but there is one for you to try afterwords, so let's work through this one together.

So I'm looking for my smallest fraction, and I remembered that rule, the bigger the denominators, the smaller the fraction.

So I'm going to look here, and I can see the the biggest denominator is nine.

So one-ninth.

I'm thinking, that's my smallest fraction, but if I check on my fraction wall oh, yes, I can see that it is much smaller in size compared to the other three fractions, because the whole has been cut up in to more parts.

So my smallest fraction one-ninth.

Then, I continue looking up denominators, and the next biggest denominator is one-seventh, and if I'm going my fraction wall from my ninth, yes, the seventh is the next smallest, because it has been cut up into more equal parts than the other two fractions remaining.

So one-seventh is next.

So between one-third and a half now.

Look at my denominators these unit fractions, and oh, three is much bigger than two so I can see that that is going to be the next smallest fraction, and I can check.

Oh, yes, because that has been cut up into three equal parts verse two equal parts, so on my ordering yes, third then my largest fraction is one-half.

If I look down here, you can see the denominators are in order.

Nine, seven, three, and two.

But remember that rule, the bigger the denominators, the smaller the fraction.

Okay.

It's your turn now, year three.

So can you order these five fractions from smallest to largest? You need your pencil.

You need your paper, because you need to draw the line with the different intervals on.

Can you work this out looking at the fraction wall, or can you use that rule to help you put them in size order? Pause the video now to complete this activity.

Welcome back, year three.

Let's have a look through our answers.

So my smallest fraction going to be that fraction with the biggest denominator.

That would make tenth is my smallest fraction since it's been cut up into the most equal parts, the most equal parts even.

Then would be one-eighth, the next biggest denominator, but it had been cut up into the next amount of equal parts.

So, one-eighth.

One-fifth.

One quarter, and then the largest value was one whole.

It hadn't been split into any equal parts at all.

Looking at the pattern.

Ten, eight, five, four.

Those denominators are in order, but the smallest fraction is always the one with the biggest denominator, because it's been cut up into more equal parts.

I keep saying that, because that is the rule that we are focusing on.

Right, we're going to explore a bit further now.

Thinking about Tuesday and Wednesday's lesson of finding fraction of the amounts.

So here is our question.

These sweets are sold in bags of 16.

Two girls buy one bag of sweets and share them equally.

Four boys buy one bag of sweets and share them equally.

Who will get the most sweets each? Hmm? I'm having a think about this question, and I'm trying to work out what fractions I need to split my whole into.

I want you to try and explore this question now.

So if you have your piece of paper, and your pen, or pencil, you can use the bar modelling strategy, or you might remember the rules.

But how would you start to work this question out? Pause the video to think about and explore this activity.

Okay.

Well done for through that to see let's have a look through our answers.

So the girls were going to split it into between two of them.

Boys were going to split between four of them.

Each had the same whole amount of sweets.

The whole had a value of sixteen.

If the girls were sharing their between two of them, then we know that this fraction is a half, because it's been split into two equal groups.

If the boys were splitting their bag between four of them, we know this is splitting into quarters, because there are four equal groups.

If we share the girls bag of sweets out between the two of them each girl would receive eight sweets.

And if we shared the sweets out between the boys, they would've received four sweets each.

So we can see here that the girls get more sweets than the boys.

The girls Have to do Couldn't we have just looked at the fractions? If we knew the girls were dividing the bag into half, and the boys were dividing their bag into quarters we know that a quarter is smaller than one-half, because the denominator is bigger.

And it's being cut, that whole is being cut into more equal parts.

Let's have a look at the fraction wall to help check that answer, and see one-half is bigger than a quarter.

It's being cut up into less equal parts.

So, whoever was receiving half of the whole was always going to have more.

So our answer.

Girls receive more sweets, because they have a larger fraction of the whole.

Well done if you got the answer correct by finding the different fractions of amounts.

Now, it's time for you to have a go at completing your.

So think about that rule, the bigger the denominator, the smaller the fraction size, and this is because the whole is being split into more equal parts.

Use the fraction wall to help you with your working out, and come back to this video to look through the answers, so pause the video now.

Okay, welcome back, year three.

Let's explore these answers to see how you got on.

Part one.

Compare these fractions.

Number one, we had a third and an eighth.

Which symbol or sign would've gone in the middle? So if I'm looking at my fraction wall a third, one-eighth, oh, I can see that one-third is more than one-eighth.

It's bigger, so I put the more than sign in there to compare those fractions, but I could've looked at my denominators.

I can see that eight is the bigger denominator, so that's the smaller fraction.

Number two.

One-seventh and one-quarter, so let's find seventh and one-quarter, oh yes, I can see that one-seventh is less than one-quarter.

So I've put the less than sign in there to compare.

I could've looked at my denominators, again seven is the the bigger denominator, so it's the smaller fraction as it's been cut up into more equal parts.

Number three and number four were for you to choose your own unit fractions.

I put the less than sign in to compare, and the more than sign.

We are looking at unit fractions early so a numerator must've had the value of one, but as long as you have had a fraction that has the bigger denominator been at the less than side because its smaller, then you have got those answers correct.

Part two.

Order the fractions.

So this time we are order out fractions from largest to smallest.

Okay.

So our largest was the whole.

We can see that that's the biggest part of our fraction wall, because it's not been split up into any equal parts.

Then, it was a half, because it's been split up into two parts.

Then, a quarter.

It's been split up into four equal parts, so it's getting smaller.

Then, a sixth.

It's been split up into six equal parts, so each part is even smaller.

And finally, the smallest fraction was one-seventh.

It's been split up into seven equal parts, so each part is smaller.

The bigger the denominator gets, the smaller the fraction becomes.

And part B, this time you need to choose three of your own unit fractions to compare following my sequence, one-ninth is less than something, is more than something.

So we start with one-ninth, and we're saying that that is less than another fraction.

So we're going to look at any fractions that are more than that.

So, one-eighth, one-seventh, one-sixth, fifth, fourth, third, or a half.

Then, we're looking at less than again, so again we need to pick another bigger fraction.

So working our way towards the top of the fraction wall.

And finally, we have the more than the more than sign.

So, the fraction that we have in our second gap has to be bigger than the final fraction.

So to complete that final part we need to work down the fraction wall to find a smaller fraction.

And finally, part three.

Comparing unit fractions of the same quantity.

You might have wanted to use a bar model, or use the rules from Wednesday's lesson to find these fractions of amounts, but A so, one-quarter of twelve.

Each part is three, so one-quarter of twelve is three, and a half of twelve is equal to six.

So here one-quarter of twelve is less than one- half of twelve.

And finally, one-third of twelve is I have do my twelves split them into three equal groups, so one-third of twelve is four, and one-sixth of twelve, so split my twelve dots into six equal groups is two.

I can compare those values, so one-third of twelve is more than one-sixth of twelve.

Well done if you managed to get those correct Right.

Time for our final activity.

I would like you to now complete a final knowledge quiz to prove what you have learned in today's lesson.

So pause the video now to complete this.

Well done, and finally, I just wanted to say a huge well done for today's learning, and you should now be able to compare and order unit fractions a lot more confidently.

Thinking of that rule, the bigger the denominator, the smaller the fraction size, and that's because the whole has been cut up into more equal parts.

So, goodbye from me, and hopefully we'll see you back here next week for more exciting maths learning.

Goodbye.