Lesson video

Hi everyone, I am just turning my notifications off so that I know I will be distraction free for the next 20 minutes.

You need to do the same, please.

I need your full attention so that you're able to focus on your maths learning with me for the next 20 minutes.

For that to happen, you might need to press pause, find a quiet space to go and work in and play again when you're ready to start.

Press pause now, come back when you're ready.

In this lesson, we will be comparing and ordering fractions.

We're going to start off with an Always, Sometimes or Never activity, before we look at Ordering fractions, Comparing fractions, all of which will leave you ready to tackle the independent task.

Things that you're going to need, pen or pencil, some paper, a pad or a book from school and a ruler.

Press pause, go and get yourself sorted with all of those items, come back and we will start.

Starting off then with our Always, Sometimes or Never activity.

Here are two sentences, give them a read and decide, is it always true, sometimes true or never true.

Press pause, come back when you're ready.

How did you get on, looking at the first one, every fraction can be written in more than one way that we think always true, sometimes true or never true.

Give me a wave for always, thumbs up for sometimes and give me an arms crossed for never.

Okay most of us going forward always true, every fraction can be written in more than one way.

We've been looking at equivalent fractions in previous lessons, with that knowledge in mind, if we're given a fraction, we know we can find an equivalent or simplified form.

Second sentence, if two fractions have denominators that are multiples of the same number, then they are equivalent, what do you think? give me a wave for always, thumbs up for sometimes, arms crossed for never.

Most of us going for sometimes true.

What would make it always? Fantastic, if the numerators are multiples of the same number as well, not of the same number as the denominators, but as a pair, then it would be always true, however, if that's not the case, then those particular fractions would not be equivalent, we need to have that relationship between the numerators and denominators.

Let's have a look now at this rectangle above a number line, what is represented by it? Tell me? A whole divided into four equal parts yeah, something else.

One of those equal parts highlighted so if one-quarter is coming through, fantastic.

One-quarter of the rectangle is shaded yellow along the number line we're representing the number one-quarter, from here what else can you tell me? Any other fractions that we could represent on the line? Absolutely connecting the rectangles with the number line, if we know that one-quarter is represented as highlighted yellow, we can also talk about where two-quarters or girdle one-half would be along the number line and equally we could talk about where three-quarters would be represented along the number line.

Look at those numbers along the number line, equally spaced, an equal distance between each of them representing quarter's four equal parts.

Having a look now at this number line and the fractions that I've left for you, how would you order them along the number line? Use the rectangle to help you as well.

Press pause, come back when you're ready to share.

How did you get on? Hold up your paper, let me see what you've drawn.

Let me see what you've represented these fractions.

Looking good and I could see how hard you've worked to keep the distance equal between the fractions as well where relevant.

So I approached it like this started off thinking about where one-eighth would be, one-eighth of the way along the number line.

Thinking about that rectangle if one of the eighths was shaded in, where would my eight sit? And from there I continued next thinking about one-quarter.

Now here, I had to make a connection back to my knowledge of equivalent fractions.

One-quarter is equal to how many eights, eighths sorry, eighths.

It's tricky to say isn't it? Eighths, how many of them? Two, one-quarter, two-eighths, which makes sense when we look at that rectangle as well.

I can visualise the rectangle as eighth or as quarters.

One-quarter, two-eighths.

Next three-eighths.

I placed here, which one might I go for next? Fantastic one-half, how many eighths? Four-eighths, they are equivalent leaving us with our final free three fractions, five-eighths, six-eighths, seven-eighths.

How many eighths would the one whole be equal to? Eight-eighths of course.

Well done, fantastic work.

This time, how would you order these fractions? So it's looking a little bit more complex.

I've got two rectangles, each rectangle representing a different number of equal parts as well as the number line.

Have a go low, pause, where would you place each of the fractions? Come back when you're ready to share, ready? Hold up your paper let me have a look, looking good shall we compare? Okay so this time I've got some fifths.

I've got some 10ths.

I can think about the relationships between them.

One-half is already marked on, going to start by representing, did you see it disappear? Nine-10ths I'm working from left to right, where would nine-10ths be? Hold on the screen with your finger where it should be, very good nine-10ths of the way along the number line.

Nine-10ths of the rectangle shaded in, this is where it would be marked.

Six-10ths next, where would that be? Hold with your finger.

Good is more than a half, is right there, six-10ths of the way along the line.

How about two-fifths? Hold your finger where it would be, be careful, are you showing me two-10ths or two-fifths? How do you know? Good, two-fifths of the way along the line.

How many 10ths would that be? Four-10ths, there equivalent.

Five-10ths next, oh problem, already showing where it is aren't we? Which fraction is equivalent to five-10ths? One-half, five-10ths, we can change it or we could have it underneath.

One-fifth next, where would that be? Is that one-fifth or one-10th? How do you know? Super, one-fifth there, the distance between zero and one-fifth is the same as the distance between one-fifth and two-fifths.

Next three-10ths, where would that be? Hold it with your finger, well done, it's how would you describe its location between one-fifth and two-fifths? It's halfway between them isn't it? And then think about it, one-fifth is two-10ths, two-fifths, four-10ths, three-10ths is halfway between the two.

Four-fifths, where's that? Fingers ready, goods and ooh, three-20ths, three-20ths but I've divided my rectangle into five parts, 10 parts, if it were 20 parts, where would three-20ths fall? It's falling between two-20ths and four-20ths, two-20ths, one-10th, four-20ths, two-10ths, three-20ths would be here, halfway between one-10th, two-20ths and two-10ths, four-20ths and of course two-20ths, one-10th, four-20ths, two-10ths, one-fifth, equivalent relationships there.

Fantastic ordering of those fractions along the number line, using some equivalent fractions understanding to help you.

Now we're able to look at these fractions and say things like three-20ths is less than one-fifth or three-10ths is greater than one-fifth.

What sentences could you say? Say one to me, give me a greater than sentence.

Under less than sentence.

Give me a greater than where the denominators are the same, five-10ths is greater than three-10ths, good and give me a less than sentence, where the denominators are the same.

Two-fifths is less than four-fifths, well done.

Keep those sentences in your mind with this next slides.

Find one-fifth and one-quarter, what do you notice? Get your fingers ready on the number line, where would one-fifth be? Good and one-quarter? Fantastic so here and here, what do you notice? Use the greater or less than sentences.

One-fifth is less than one-quarter.

One-quarter is greater than one-fifth, interesting, especially when you look at those denominators, five and four, five as a whole number is greater than four as a whole number but one-fifth is less than one-quarter.

The numerators were the same, they were both unit fractions there.

Those are things that I noticed, I wonder if you did as well.

Next, find three-fifths and three-quarters? Again what do you notice? Okay fingers ready, where is three-fifths? Good and three-quarters? Well done so what do you notice this time? Can you use the greater than sentence first? One, two, three, three-quarters is greater than three-fifths.

The less than sentence, three-fifths is less than three-quarters.

What do you notice? Same numerator, denominators are different.

Five is normally greater than four as whole numbers, but as fractions, three-fifths is less than three-quarters just like one-fifth is less than one-quarter.

I wonder if the relationship would be the same if we had two of each of them or four of each of them, I think it would be, can you find now four-fifth and 75-100ths? What do you notice? Let me give you a second, find four-fifths? Where is it going to be? Visualising a number line divided into five equal parts or connections, four-fifths, how many 10ths? Eight-10ths, four-fifths, that's where it would be.

How about 75-100ths? So a number line divided into 100 equal parts, 75 of them, where would it be? Right there, 75-100ths, don't you notice something about that as a fraction? I mean, it is a fraction but with it as in terms of an equivalent fraction, is equal to three-quarters, yeah.

Four-fifths is less than or greater than three-quarters, greater than 75-100ths, say the less than sentence, 75-100ths is less than four-fifths.

I'd like you to pause now and have a go at completing your activity, as soon as you're ready, come back and we'll look at some of the solutions together.

So we had these fractions to order along the number line and we needed to be able to explain our decisions.

As we're going through the solutions I'm going to be asking you about any patterns or connections that you've noticed.

So let me see what you managed first of all, hold up your paper, perhaps you've just listed the fractions in order from smallest to largest, maybe you've drawn a version of the number line as well, let me have a look.

Hold up actually, if you've listed in order, keep it still.

Okay and now hold up if you've joined the number line and you've placed them on a number line, good, hold up if you've done something completely different to those two, but you're confident you've got them in order.

Okay, well done.

So just look out for my arrows now I'm going to draw arrows from each fraction to their location.

One-fifth equal to two-10ths, one-eighth, I might come back to that one.

One-quarter, a quarter of the way along equal to how many 100ths? 25-100ths, 25-100ths along the number line, one-quarter, one-10th nice, divided into 10 equal parts.

One-10th would be here, one-20th, divide, well actually this number line is divided into a hundred equal parts, 10 equal parts and 20 equal parts.

Those small divisions on top of the number line, one-20th, half, one-half, one-half of the way along, how many 10ths? Five-10ths.

How many 100ths? 50-100ths.

How many 20ths? 10-20ths, there we go.

Okay one-eighth, well I've got that one too.

So I need to visualise the number line divided into eight equal parts or can I think about the connection half, one-quarter, one-eighth, whenever one-quarter is, well one-eighth is going to be halfway between zero and one-quarter, which is there.

Now one-quarter is 25-100ths, 25, half of 25, 12 and a half so it's looking to be that, bit of a challenge with that one.

In order though, this is how they look from smallest to largest.

What patterns do you notice? Numerators are the same denominators getting smaller, but the fractions value is getting bigger so that the larger denominators have the smaller value.

The smaller denominators have the larger value when the numerators are the same.

Next, again look out for my arrows as I order these five-20ths.

If I know where one-20th is, I can find where five-20ths are.

Five-eighths, if I know where one-eighth is, I can find five-eighths, can also think five-eighths, it's one-eighth more than four-eighths.

If four-eighths is halfway and one-eighths we worked out was 12 and a half 100ths, which sounds a bit funny but will help us adding on from halfway from 50 adding on 12 and a half, we would be around about there.

Five-10ths, wonderful, much easier than five-eighths.

Halfway, five-100ths, again we can see, we can visualise the hundred equal parts, we want five of them and 50-100ths, we've already marked it equal to five-10ths, equal to four-eighths in order with five-10ths and 50-100ths, one above the other.

The numerators were the same, the denominators were different.

Next one, so again let me show you the arrows for where each of them would be, seven-eighths.

So I'm using here my knowledge of eight-eighths being one it's, seven-eighths is one-eighth less than one, it's 12 and a half less than one than 100, 12.

5 less than 100, thinking about those 100ths that one eighth is equal to so I can position it there.

Three-quarters I can visualise where that would be again, one-quarter less than four-quarters.

One-quarter less than one, one-half halfway nice.

Four-fifths okay I can think well where's one-fifth.

I need four of them or is one-fifth less than one whole, there, I'll show you again because it's a bit tricky to see I think, there is, good.

99-100ths could count along to find 99.

I could count back 100th from one from 100 100ths there nine-10ths, I could find one-10th count along nine-10ths or what could I do? Count back one-10th.

Well, I wonder now they've been ordered what patterns have we noticed here? Each of these fractions is one of their equal parts, less than a whole.

If you would like to share any of your fantastic learning from this lesson with Oak National, please ask your parents or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Fantastic lesson everyone.

Thank you for your contributions and all of your brilliant learning from start to finish.

You should have very big smiles on your faces right now just like I do.

If you have any more learning lined up for the day, I hope that you enjoy it just as much.

Please have a breakfast though, you've worked really hard and you certainly deserve one.

I look forward to seeing you again soon for some more maths, until then look after yourselves, bye for now.