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?

Finding non-unit fractions of quantities

Key Stage 2

Maths

Fractions

Which of these fractions are non-unit fractions?

Which of these pictures represent a non-unit fraction?

A non-unit fraction is when the denominator is greater than the numerator

A non-unit fraction is when the denominator is more than 1

A non-unit fraction is when the numerator is more than 1

What is the definition of a 'non-unit' fraction?

What non-unit fraction of this shape is not coloured in?

Elizabeth ate 5 parts of a chocolate bar. The chocolate bar was split into 20 equal parts. What non-unit fraction of the chocolate bar did Elizabeth not eat?

﻿Hello, it's Mr Etherton here, and welcome back to another exciting day of our maths learning. Let's have a look at what we're going to be finding out today. So today is lesson two of week two, and it's our seventh lesson looking at fractions. Today we are going to be finding the non-unit fractions of a given quantity. So, let's have a look at what we're going to actually be learning. So we're going to revisit what a non-unit fraction is, and then I'm going to introduce to you a strategy, the bar modelling strategy on how you might calculate non-unit fractions of amounts. Finally, we're going to be working backwards to apply this knowledge, to use the value of the parts to help us calculate the total value of that quantity. So we've got some tricky learning, but I know we're going to do it amazingly. So, let's get our equipment ready. Today, you will need a pencil, a piece of paper or an exercise book, and if you have any counters, cubes or small counting toys, these might help you with some sharing. So if you need to get your equipment, pause the video now and get that ready. Brilliant, the first thing I would like you to do is complete our introductory knowledge quiz. So if you need to do this, please pause the video now, but if you have already done this, then continue watching our video so that we can get started. Fantastic, so a quick warm up here for you, what I would like you to do is I want you to write down or draw as many non-unit fractions as you can. This is yesterday's learning, so here are some pictures to help you if you can't quite remember what a non-unit fraction is, maybe you might be able to use these pictures to help you work it out. So when I say go, pause the video for 20 seconds, and write down those non-unit fractions. Go! Okay, welcome back, let's have a quick look through our answers. So what non-unit fractions did you write down? If we have a look at these pictures, my circle here has been cut open to nine equal parts, that's my denominator, and three parts have been coloured making 3/9. Here, I've got my rectangle cut into 8 equal parts and five have been coloured making 5/8, and over here, I've got a circle again cut into eight equal parts and two have been coloured, so 2/8. 3/9, 5/8 and 2/8 are all non-unit fractions, that's because the numerator is more than one, so the top number is more than one making it a non-unit fraction. You might have had some other answers such as 2/7, 7/10, 3/4, as long as your numerator was more than one then it was a non-unit fraction, great job. Let's continue and have a look at today's learning. So here are some of our star words, my turn, your turn, repeat after me. Non-unit fraction. Quantity. Whole. Divide. Denominator. Multiply and numerator. Fantastic, let's have a quick look at some of those words. A non-unit fractions, we've already spoken about those in our warmup, our fractions where the numerator is more than one, these are the fractions we're going to be working with today. A quantity, this might link back to last week's learning. We're going to be looking at quantities, which is another word for amounts or a value. Our next words, whole, divide, denominator, multiply and numerator, I've put those in that order because this is going to be the order of our process,Okay? So the whole, meaning the value of the entire thing, dividing, another word so we could say sharing, the denominator is the bottom number in our fraction, multiply thinking how many groups we're going to need, groups of something, and the numerator is our top number in our fraction. So let's have a quick look at our learning. So, what strategy can we use to find fractions of a quantity? So I have a question here, which I'm going to read out. I want you to think about, what calculation am I trying to work out? So, there are 12 pods on the London Eye, 1/4 of the pods are empty, how many pods are empty altogether? What calculation am I trying to work out? Well, let's have a look at this together. So first of all, I'm going to think about my whole, so in this question, the value of my whole was 12, I have 12 pods on the London Eye. I need to find out how many of those pods are empty. I don't know the value yet, but I do know the fraction. So it's saying that for every four pods, one is empty. So if I take my 12 pods and share them equally into four groups, then the value of one group is going to tell me how many pods are empty. So what I am trying to work out is 1/4 of 12. I know you find this a little bit tricky, so I'm going to teach you a strategy that is going to help us with finding different fractions of quantities. This method that I'm going to be teaching you today is called the bar modelling strategy, and it's going to look a little bit similar to something you might do in school, or it might be something completely new. So if it is something new, I want to see you endeavouring showing resilience to try your very best. So here, I've got my question again, 1/4 of 12, and here are some key questions to help me work it out. What is the whole? How many equal parts are there and how many equal parts do we want? So the first thing I'm going to do, and you can do this as well when you're doing your own working out, you're going to need a pen or pencil, and I'm going to draw a bar, which is a rectangle. So if I draw my bar with my pen, it might look like this. From my question, the first thing I need to think about is the value of the whole, what is the whole? And I know that the whole is 12, there are 12 pods on the London Eye. So I put that number 12 above my bar to represent the value of the entire thing. And Working through the next steps, how many equal parts are there? Or from our learning, I know that the denominator tells me how many equal groups I need to split my whole into, so I'm going to split it into four equal groups, one, two, three, four. And because that is a fraction, each part has a value, so the fraction of the first part is 1/4, the next part is also 1/4, the next part is also 1/4 and the next part is also 1/4, okay? But all of that together makes the whole. To help me, using my pen again, I'm going to draw some dots and share out the value of my whole, so I'm going to share out 12 dots into my parts. So let's have a look at how that might look. So one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, and I want you, when you're doing your own working out to also share out those dots into those parts. So having my parts equal, I've got three dots in here, three dots in this part, three dots in this part and another three dots in this part. So yes, they are all equal and in each part I have a value of three. So this is showing me, okay, that one part is equal to three. That was looking at my denominator. Now I'm going to look at how many equal parts do we want? And remembering from our previous learning, our numerator tells us how many parts we want. So I only want 1/4, so I'm only going to take one of those parts. This has given me my answer. 1/4 of 12 is equal to three, 1/4 parts of 12 is equal to three. So that is our bar modelling strategy, drawing the bar, sharing out your dots and finding the value of each part. But we're going to build on that a little bit now, okay. So very similar question, but this time it says 3/4 of the pods are full, how many pods are full? So again, 12 pods, but this time three quarters of them are full. So I'm going to use exactly the same strategy, so with my pen, first of all, I'm going to draw my bar, and there we go. And the first question I need to think about is what is the whole? I know that I'm working with 12 pods again, so I write that above and I divide my whole into four equal parts, 'cause quarters of four parts, and my denominator tells me this. So four equal parts, one, two, three, four, and the value of each of those parts was a 1/4. Again, using my pen, I'm going to share out my whole, share out 12 dots between my four parts, one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, are all the groups equal? Yes, they are, there are three dots in each part. But it's different now, because I'm longer working with 1/4, my question says, I need 3/4. So we've found the whole, we've divided it by the denominator. But now I need to look at how many equal parts do we want, and my numerator tells me this. So I want three of these parts. So I'm going to circle three of those parts, 'cause that's how many I need 3/4. To help me with my maths, I'm now going to take the value of one parts of three, and I'm going to multiply it by my numerator, so I'm going to see three, lots of three. And if I do my working out, three parts are equal to nine, count the dots one, two, three, four, five, six, seven, eight, nine, 3/4 of 12 is equal to nine. So that last bit is very, very important that we remember to multiply a value of one part by the numerator, or look at the numerator and have that many groups. Now, is your turn. So just like I've explained, you are going to need your pencil and a piece of paper, 'cause you are going to need to draw your bar. Have a look at those key questions, what I call the steps to success. Can you try and find the answer to 2/5 of 30. Pause the video now to complete this activity. Brilliant, welcome back, year three, really good job, 'cause that is quite tricky let's have a look through our answers. So, you should have drawn your bar, you should have remembered that the whole the value is 30, and our denominator, we're splitting it into five equal parts. So with my 30, you should have shared out your dots, one, two, three, four, five, six, seven, eight, nine, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30. Are all the groups equal? Yes, there are six in each part. Is my answer six, 2/5 of 30 is six, what do you think? Well done to everyone that said no, well done if you remembered that you now have to look at the numerator to see how many of those groups you need. So we needed two of those groups, 2/5 groups, 2/5. So I have a look at my working out, I can either multiply the value of one part by two, so two times six is equal to 12, or I can do some repeated addition, six add six is equal to 12. So altogether 2/5 of 30 is equal to 12. Well done if you did get 12 for your answer, if you didn't get 12 as your answer, I would like you to spend some time now, having a go at this question here, 4/6 of 21. If you're confident with your learning, then you can continue playing the video, but if you want another little practise, then hit pause now. Welcome back year three, let's have a quick look. So 4/7 of 21 should have been the same thing, 21 split into seven groups, three in each group, and then we're looking at four groups here, so four times three is equal to 12, so 4/7 of 21 is equal to 12, well done. Right, at the beginning of our lesson, I did say we were going to explore looking at this strategy backwards. So this time we going to look at this question here, if I know the parts, can I find the value of the whole? So here is my word problem, let's have a read, Mike has 4/6 of a packet of sweets. He has eight sweets altogether. How many sweets make the whole? Here is eight sweets. Mr. Overton's having a think now about what information I know. I know that Mike has eight sweets, but I know that this isn't the whole packet, this was only 4/6 of the packet, I know the whole would be 6/6. So I know 4/6 is smaller than 6/6, so my answer must be getting bigger. So I'm going to look for an answer bigger than eight sweets, okay? So I'm going to use my bar model to help me thinking about the key information, following those same steps to success. So with my pen, draw my bar. Right, the first thing I need to think is what is the value of my whole? I don't know the value of my whole, all I know is that Mike had eight sweets, but this was only 4/6 of the packet. And remember, fractions are a part of the whole, so this is smaller than the actual whole. So this is what I'm trying to work out, I'm trying to work out the value of the whole bar. So I do know though that Mike has 4/6, so the packet of sweets must have been cut into six equal parts, one, two, three, four, five, six, and out of those six parts, I know that Mike only has four parts, 'cause remember the numerator tells us how many parts he has, so he only has 4/6 parts. And the total of this 4/6 is eight, so I'm now going to share my eight sweets, but only between the four parts Mike has. So here we go, well, a 4/6 is eight, then what would the value of 1/6 be? Let's have a look by sharing out my sweets, so one sweet, two, three, four, five, six, seven, eight. We've shared out Mike's eight sweets between the four equal groups that he has, and the value of those parts are two. To be able to work this question out, I need to find out the value of one part, 1/6, and I can see here that the value of 1/6 is equal to two. This is now going to help me complete the rest of my bar model. If all of these parts are equal to two, then I know that the remaining two parts are also going to be equal to two. Now I have the value of my whole, I can see in this bar model, how many sweets there were to start with in the packet. So I've got six equal groups and the value of each group is two, so the total amount of sweets that he had was 12. I could also do repeated addition two, add two, add two, add two, add two is 12, but the whole bar now is equal to 12. That's how many sweets make the whole packet. What I would like you to do now is if you're feeling confident, I would like you to have a go at this same strategy. You going to need to use your bar model, to draw out your bar and work out how many equal groups there are? How many groups does Amy have to start with? Share out what she has? Can you use that information to find the whole? If you want a few prompts with this activity, on the right hand corner of the screen I've put a little steps to success box, with steps one to eight, this might be able to help you. So when you're ready, pause the video to complete this activity. Brilliant, well done year three, let's have a quick look at our answers. So I use my pen, I drew my bar, that was step number one. Do we know the value of the whole? No, we don't, all we know is that Amy has 15 bricks altogether. So this is what we are trying to work out. I do know from my denominator that the whole was split into four equal parts. How many parts do we have in the question? So this is our numerator, I know that I have three, well Amy has three parts. And the value of those three parts are 15 bricks, so I needed to share my 15 bricks between those three parts. So if 3/4 is 15, then what is 1/4? So let's share our 15. And the value of each of our parts was five, well done if you knew that 1/4 was equal to five, and this information now tells me that the remaining 1/4 it's value is also five. So here, I can work out the value of the whole bar or how many bricks made the whole box, by doing four groups times five or five, add five, add five, add five, so the answer, how many bricks make the whole box? The answer was 20. Well done if you managed to work through that, it is quite tricky. We now going to be doing some more work on this tomorrow, but what I would like you to have a go at now, is have a go at your main activity. So your main activity is to continue finding out how to find non-unit fractions of a given amount. So when you're ready, pause the video now to start your independent activity, and we'll go through the answers afterwards. Brilliant work year three, let's have a look through some of the answers to our independent task. I'm not going to use a bar model to help you with this task, well to go through the answers, okay. I will explain what we would have done, but I'm going to use some more numbers to help me. Okay, you did have the rules available on your slides, so let's see if you got the answers correct. So number one was find 3/5 of 25, so with your bar, we would have had 25 as the whole, split it into five equal groups, and we would have found that one group was equal to five, and then we would have taken that value and multiplied it by the numerator, so three of those groups was equal to 15, 3/5 of 25 is 15. Number two, find 2/7 of 14. So the whole bar would have been 14, we would have split that into seven equal groups, 14 divided by seven, so each group would have been worth two, and then I would have taken that value, the value of one part, and I know that I needed two parts. So two times two is equal to four, 2/7 of 14 are equal to four. Next, calculate 6/8 of 32. So 32 was my whole using my bar, split it into eight equal parts, share out my 32, and the value of one parts 1/8 was four, but I needed to know how many were in 6/8. So I'm going to multiply that four by six to give me the answer 24, 6/8 of 32 is equal to 24. And finally, for part one, Helen has 60 beanbags. She gives her friend 5/10 of them. How many beanbags did Helen's friend receive? So the whole again with my bar was 60. I should have divided that into 10 equal groups, and that would have shown me that the value of one group was equal to six, but I needed to know the value of five groups. So five lots of six were equals to 30. You might have also known that 5/10 is equivalent to a half, so you could have also done half of 60, which is also 30, well done. Right, the answers to part B now. So this was working backwards and we would have needed a bar model again, to help us with our working out. So this is 3/4 of a set of beanbags, how many were in the whole set? So I'm going to count my bean bags, I know that I have 12 bean bags, but that was only 3/4, okay. So I needed to have my whole, didn't know the value of that yet, all I knew the value of were the three parts and the value of those three parts was 12, okay. So I'm going to share my 12 into those three parts and to find the value of 1/4 was four, and I could have used that to work out the value of the value of one whole. So four quarters, four times four, that was 16 beanbags in the whole set. And our final question, if I know that 4/10 is 16, what is the value of the whole? So I would have drawn my bar, I don't know what my whole is just yet, but I do know that it was split into 10 parts, and I know the value of four of those parts. Four parts was equal to 16, so take that 16 and split them between the four parts that I already know to find that 1/10, one part was equal to four and I needed to have a look at what the whole value was, so the 10 parts that made the whole 10 tenths, so four times 10 is equal to 40. Well done if you put 40 as your answer, that was the value of our whole. Really good learning today, year three, great job. So to complete today's learning, I would like you to now do the final knowledge quiz to prove what you have learnt in today's lesson. Pause the video, when you're ready to complete that, but do come back for our final slide. Brilliant, welcome back year three, I hope you've managed to complete that final knowledge quiz to have a look at how you've done today with your learning. So that's it for today's learning, we hopefully now would have been able to use our bar modelling strategy to find non-unit fractions of a given quantity. Tomorrow, do come back, we are going to be looking at this again, because it is quite tricky and a really, really important thing we need to learn in year three, okay? So, I'll see you back here tomorrow for some more exciting maths learning. Goodbye.

Finding non-unit fractions of quantities

Finding non-unit fractions of quantities

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