Comparing fractions with the same denominator

Key Stage 2

Maths

Fractions

If 2/4 of a number is 10, what is the value of the whole?

Rachael gave 8 crisps to her friend. This was 2/10 of the whole pack. How many crisps did Rachael start with?

George thinks he has the most sweets. He has 3/5 of 50 sweets, but his friend, Fred, has 5/10 of 50. True or False that George has the most sweets?

﻿Hello, this is Mr. Etherton here, welcome back to another exciting day of maths learning. Today, our learning outcome is to compare fractions with the same denominator. So what are we going to be learning about today? Let's find out a bit. So in this lesson, we will start to use pictorial representation to help identify and compare the size of fractions with the same denominator. That means we're going to be using some mathematical pictures to help us look at which fractions are bigger and which fractions are small. We will then apply this learning to think more abstractly about what procedure is used to compare fractions with the same denominators. So that is a rule to today's learnings, we'll be listing out for the rule. Let's get our equipment ready, so today all you'll need is a pencil, a piece of paper or an exercise book to do some working out. So please pause the video to get your equipment ready now. Fantastic. The first thing I would like you to do today is complete a introductory knowledge quiz. If you have already completed this then continue watching, but if you need to complete it before the start of lesson, pause the video now. Brilliant, let's get started with a quick warmup, okay. So would you rather have one quarter of these cakes or two quarters? Think then explain your choice to an adult or maybe someone that might be in the room with you. So look at how many cakes we have. Would you rather have a quarter of those cakes or two quarters of those cakes? Pause the video now think, explain, go! Really, let's have a quick look through our answers year three. This really depends on how hungry we might be or whether or not we like cake. If we're hungry, we might want a bigger fraction, if we aren't so hungry or don't like cake, we might want a smaller fraction. I can imagine that some of you might have gone back to the previous two days learning where we found fractions of amounts to help find our answers. So the fractions we were working with were one quarter and two quarters. Altogether I had eight cakes and because I'm working with quarters, I know that quarters have a denominator of four, meaning there are four equal groups. So I've split my cakes into four equal groups here. One, two, three, four, all representing one quarter. If I wanted one quarter of those cakes, I would receive two cakes. But if I wanted two quarters of those cakes, I would have received two groups, that was my numerator two, and I would take four cakes all together. Some of you might have done that working out and thought I'm hungry, I want two quarters. But today we're going to think about, did we really need to do the working out to find out if we wanted more cakes? So we're going to build on this through today's learning, using our pictures, using a rule to help us compare fractions. Let's have a look at our star words. So my turn, your turn, repeat after me. Same denominator, fraction, compare greater than, less than, is equal to. Fantastic, thank you for repeating after me. Let's have a quick look through some of these words. Same denominator. Today all the fractions you will be comparing will have the same denominator. This means that the bottom number in the fractions will be the same. That means the rules I teach you today only apply to fractions with the same denominator. When you progress through your maths and start comparing fractions with different denominators, there will be a different rule. We're working with fractions again, a part of a whole, today we're going to be comparing, so looking at two fractions and start to describe their relationship is one bigger than the other, smaller than the other, equal to. We've got our symbols, our signs here that we need to become more familiar with, we've got greater than we might say more than bigger than we've got less than we might say fewer than, smaller than, and we've got is equal to which means the same. So let's have a quick look at our learning. Let's learn. Today, I'm going to put a lot of the learning more on you so make sure you've got your pencil and pen and paper ready to join in with some of these tasks. So on the screen you can see eight different representations, A B, C, D, E, F, G and H. What I would like you to do is work out which of these can represent fractions with the same denominator? So have a look at a picture and work out what fraction of that picture is shaded in. So if I look at A, I know that the whole has been split into four equal parts, and one part is coloured in. So A represents one quarter. But do any of my other pictures represent one quarter? I want to start to group those fractions together that have the same denominator. So pause the video to complete this activity, and we'll have a look through our answers. Brilliant, year three, let's have a quick look through our answers and see how you group these fractions with the same denominator. So if we have a look through all of our fractions, hopefully we've managed to work out what fraction was shaded in, so A with together was one quarter. B we had three equal parts, two shaded in, making two-thirds. C we had two equal parts, one coloured in that was a half was coloured in, D we had three equal groups and one group was coloured in, a third was coloured in. We had E rectangles could four equal parts and three were shaded in, so three quarters, with the F we had a line here that split into four equal parts, one coloured in, one quarter. G this was a little bit tricky. We could have said that there were eight circles and four were coloured in, four-eighths, but these have been grouped into two groups that we're going to say that there were two groups, and one whole group was coloured in, so one half was coloured in and over here was a little bit trickier to see, but there were three equal groups and one group was shaded in showing one third. So we've managed to work out what fractions were represented, but how have we grouped them? Well, we needed to look at the denominators to see which were the same. So let's group them together. So representation C and G both represented a half because they had the denominator of two. B, D, and H were all representations of thirds and that denominator was three, three equal groups. And that leaves representations A, E and F, all representing quarters, four equal groups, so the denominators were four. Remember today's learning only focuses on fractions with the same denominators. So we're going to be only working with fractions within those groups, right? Let's continue. So let's learn. Shade one third of the shape and shade two-thirds of this shape. We're going to try and explore and compare by finding out which fraction is greater. So I'm going to do this example for you before we have a go together. So here I have a square and it's been cut actually into nine equal parts. But if I look here, I'm split it into three equal parts, four-thirds, because that what my denominator is telling me to do. It's also telling me to colour in one of those parts. So if I do that, I can see that I've shaded, one out of three equal parts of shape. I'm going to do the same here, it's the same shape, and I've got my third each column, but this time it's telling to shade in two of those parts. There we go. Look at the pictures on your screen, which fraction is greater one third or two-thirds. If you said the fraction two-thirds is greater, then you are correct. We can see from this picture that when we shade it in two-thirds, there were more parts coloured in. This shows that it is a greater, a larger fraction. If we look over here where we only had one-third shaded in then there was less of the whole taken, less of that fraction was shaded in making it smaller. So when we were already starting to compare fractions with the same denominators, we don't need to work out and share like you might have done in our warmup. We're going to start to look at our numerators and work out, which has a greater value. Which one wants me to take more parts. Two-thirds is bigger than one-third, because we're taking two of the parts over one of the parts. So what we're going to do now is I would like you to have a go at this example on the screen. Which fraction is smaller? On your piece of paper, you might want a ruler a for this activity as well. You need to try and draw two equal lines. I suggest drawing these lines, 10 centimetres long. Then you need to divide those lines with the intervals and we need 10 equal parts because we're working with tenths. Then for the first line, can you shade in two-tenths and for the second line can you shade in eight-tenths. Which fraction or which line will have less shaded in, which is smaller. Pause the video when you're ready to complete this activity. Brilliant job, year three. We'll have a quick look through this one together, see if we got the same answers. So we had our line split into 10 equal parts my denominator tells me that, and for my first line, how many parts, shout at the screen, how many parts have you coloured in? Amazing, if you said two that is correct. We should have shaded in two of those parts. Again, line number two is cut into 10 equal parts my denominator tells me that, but shout at the screen, how many parts of you shaded in? Amazing if you said eight, because our numerator tells us that we need eight-tenths. If I compare these lines, which were the same length, I can see that my blue line two-tenths is a lot smaller than the red line, eight-tenths over here. So if you have said that two-tenths is the smaller fraction, then you are correct. This is because we have coloured in less of the parts. We've only coloured in two out of 10, whereas on eight-tenths, we've coloured in eight out of 10. So again, when comparing fractions with the same denominator, we need to look at the numerator. We can see that two parts is going to be less than eight parts. So two-tenths is smaller than eight-tenths. Great work, let's continue with our learning. So now we're going to introduce some of those signs, symbols from our star words to help us compare. So what statements can we write to compare these fractions? So to start with, I'm going to see which of my symbols would fit correctly in my circle to compare one-third and two-thirds. If we remember from before, I can see that two-thirds has more and one-third is less. So my statement, if I already stopped to speak or talk it through, one-third would be less than two-thirds. And here I have the symbol for less than say, if I fill that in, before we do that, let's have a look. So like I've said, we could say one-third is less than two-thirds, but we could also work backwards and say that two-thirds are more than one-third, and I've chosen this less than symbol in the centre. And we can remember how to use these symbols because it's a bit like an arrow. The bit which joins together, the small side is where we put the smaller value, and where it is open, the bigger side, that is where our greater value is going to go, a bit like we always eat the biggest value, if we imagine it's maybe the mouth of a crocodile, we eat the largest value. So I'm eating two-thirds here because one-third is less than two-thirds or working backwards two-thirds is more than on- third. It's your turn now. So what I would like you to do is have a look at A an B on the screen. What statements can we write to compare the fractions? There are some pictures for A, for A we're looking at what fraction of the whole have been coloured in yellow, and for B, that is a picture and a word representation. Can you write the fractions, use the correct symbols to compare them, and can you write the statements to compare them too? So pause the video to complete this activity. Fantastic, well done year three. Let's have a quick look through our answers to see how we've been getting gone. So I'm going to look at A to start with, so I'm going to look at my first representation, and I knew that the whole was splitting to eight parts and six were coloured in, so six-eighths. And for the next picture, it was also cut into eights and there were five coloured in. Remember the rule when the denominators are the same, we look at the numerator to compare and I can see that more have been coloured in on six-eights. So the statement I might say is six-eighths is more than five-eighths, or I could work backwards and say, five-eighths is less than six-eighths. So which symbol is correct? Let's see if you've got it right. So we have the more than sign here to show that six-eighths is more than five-eighths and remember open end, the bigger end is always eating the biggest fraction. Let's have a look at B now, okay. So in the bag we have some lollipops and three-tenths of them are in there. So we had 10 equal groups and three were being used, and with my pictures of the lollipops, again, we had 10 lollipops and three of them were what we were using, so three-tenths, again. Both of my numerators are the same value here. One isn't bigger than the other. So the sign or symbol that needed to compare these two fractions was the equal to sign. So well done if you've managed to complete both of those tasks correctly, right? It's now time to complete your main activity, where you're going to compare fractions with the same denominators. Remember when the denominators are the same, we're looking at the numerator to help us compare. So pause the video now to complete your main activity, then play again and we shall go through those answers. Brilliant, thank you year three, I've been really impressed with how hard you've been working so far today. Let's have a look at our answers. So the task for part one was to complete the missing boxes in the table to compare the fractions. So the orange are the answers that we're going to go through, you can see them correctly as we go through those. So what representation here was four-sixths and over here we had five-sixths so the correct symbol here, we might say, one of our statements four-sixths is less than five-sixths. Four-sixths are less than five-sixths. We might however, be able to work backwards, and the statement would be true, if you said five-sixths are greater than four-sixths. So both statements are true, and this was the correct sign or symbol. Number two, four-eighths is what to oh, this picture here. They were eight equal parts, eight coloured in, eight one whole. So the answer here was four eighths is less than eight-eighths. That was statement number one we could have had, or we could have worked backwards and said that eight-eighths is more than four-eighths. We know this because denominator four a smaller than that, sorry, the numerator four my bad, is less than the numerator of eight. Number three, the picture here, we had seven equal parts and four were coloured. And I'd already given you the equal sign that we were looking for a fraction of the same value. So four out of seven, the answer should have been four-sevenths. Four-sevenths is equal to four-sevenths, and that was our statement to compare those two fractions. And finally little bit trickier, five-tenths, and I'd given you the statement, I'd said one-tenth is less than five-tenths. So we should have worked out but one-tenth was the fraction number two that we were looking for, because five more parts that we are taking we should have known that it was the more than sign because it's greater than one-tenth, okay. So double check those answers, pause the video if you need to go through this again, but we will continue on, right. Part number two, there were 30 strawberries in a bag. Aisha ate one-tenth of the strawberries, Khaled ate five-tenths of the strawberries. Who ate fewer strawberries? Hopefully we didn't need to go back to our learning from yesterday or finding fractions of amounts, because we already should have been able to look at those fractions. Aisha only ate one-tenth, one out of 10 equal parts, whereas Khaled took five out of 10 equal parts, five-tenths. So we should already know, that five-tenths is greater than one-tenth. So Khaled is going to take more strawberries. So the answer who eat fewer strawberries was Aisha cause she took a smaller fraction. We could work this out, we could have drawn a bar model shared out of 30 or drawn out strawberries. So Aisha would have taken one-tenth, which is three, Khaled would have taken five-tenths, which is 15, and we can see that Khaled has taken a lot more than Aisha, so Aisha ate fewer strawberries. And B this was an open task, so you could have drawn many different representations, so to draw your own mathematical pictures to compare fractions and use the correct symbol to compare that relationship. I've done an example here where I've said four quarters is more than three quarters, but you could have done many different representations in drawing. So maybe ask an adult if they can check through those four, right? We're almost at the end of our lesson now, what I would like you to do is complete the final knowledge quiz to prove what you have learned in today's lesson. So pause the video to complete that quiz now. Brilliant, welcome back. And finally it is time for me to just say a quick goodbye and then we will review what we've done. So goodbye from me. You should now be able to compare fractions with the same denominator and hopefully I will see you back here for more exciting math learning tomorrow. Bye.

Comparing fractions with the same denominator

Comparing fractions with the same denominator

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