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?

Consolidating finding non-unit fractions of quantities

Key Stage 2

Maths

Fractions

﻿Today, our learning outcome is going to be to be able to consolidate, finding non-unit fractions of a given quantity. So we're going to be focusing and building on yesterday's maths learning. Let's have a quick look at what we are going to be finding out, in today's learning. So, in this lesson we will consolidate the learning from lesson four, so last week, and lesson seven, yesterday's lesson. We'll be using our multiplication and division facts to become more confident with finding non-unit fractions of amounts. Today, we will only use the bar modelling strategy to represent our procedure. So know that yesterday we got our pens out, we drew our balls and shared out the dots. But today we're going to be using more numbers, our times tables to help with our working out. So, today what equipment will you need? You're going to need a pencil, you need a piece of paper or an exercise book to do you're working out. And if you can, you might want to access to a multiplication grid. This is going to help you with your times tables and division facts. Like I said, that's going to be very important today. We need to get confident with our procedure and not worry too much about those times tables. So, you might have a printed version of this multiplication grid, but you can also get one online. So when you're ready, pause the video to get your equipment. Great job, year three. The first thing I would like you to do is complete your introductory knowledge quiz. If you haven't done this already please can you pause the video and start that now. If you've already done that, continue watching. Amazing work here, three quick warmups. So, with our multiplication division facts are going to be super important today. So, let's see what you already know. Can you complete the multiplication and division triangles to show the relationship and inverse between these numbers? So, each triangle, 1, 2, 3, has three numbers inside, but one of them is missing. Can you find out what number is missing based on the division, or the multiplication equation? So, our two numbers at the bottom are usually our parts and we multiply those together to make our whole because the number at the top is our whole so we might work backwards. Then we divide our whole by one part and it always equals the other part. So, you might want to count in your times tables, counting your 3s, counting your 2s, or counting your 4s, to help you complete these number triangles. So, when you're ready, pause the video, off you go. Brilliant, well done year three, let's have a quick look through our warm up answers. So, I've got a multiplication grid on my screen. I'm going to be using that throughout our lesson to help us with our learning, okay? So, the first triangle we had the parts 9 and 3. They're the parts I would multiply those together. So, on my multiplication grid, I'm going to go across the top to my 9 times table. And I'm going to go down, so 2, 3, and I'm going to match it up. Okay, so 9 times 3 was equal to 27. 9 times 3 is equal to 27, but working backwards, 27 divided by 9 is equal to 3, or 27 divided by three is equal to 9. Number 2. So this time we're working backwards. 14 divided by 2. So, I'm using my 2 times tables to help so I'm going to go across to my 2s and I'm going to go down till I find 14, there's 14. And I'm going to look at the side. The other part would be the number 7. 7 times 2 is 14, or 14 divided by 7 is equal to 2, or 14 divided by 2 is equal to 7. And the third triangle, okay? So again, we have the whole 40 divided by 4 is equal to what? So looking at my 4s to help me 4 times table go across. I'm going to go all the way down to my whole, which was 40 there's 40. Go across to this side, 10 was my other part. 40 divided by 4 is equal to 10, or 10 times 4 is equal to 40 or 40 divided by 10 is equal to 4. So those multiplication and division facts are going to be really important on today's learning. Right, let's get started. Here are some of our star words for today. So my turn, your turn, repeat after me. Non unit fraction, quantity, whole, divide, denominator, multiply and numerator. Fantastic, let's quickly recap what these words mean. So non-unit fraction is a fraction where the numerator is more than one. A quantity, this is an amount or a set of objects, and we're going to be trying to find a fraction of this today. The whole, that's what we're going to be starting with some of our questions and remembering that the process is to divide into those equal groups. Here is our division sign that's going to be really important so we know what operation we are doing today. Following yesterday's process, we divide by the denominator. That's the bottom number of our fraction, and then we're going to multiply. This is our multiplication sign. So that's to see how many lots of a number we need. So it's going to get bigger after we multiply. And then our final word was numerator. And this is the top number in our fraction because we multiply our value of one part by a numerator. So, let's have a look at how our learning is going to look today. We're going to continue to find fractions of a non-unit fractions to be specific. And we're going to try and avoid doing the bar model to do our working out. What we are going to try and use is our multiplication grid. And all we need to do today is follow step 1, follow step 2, and we will get that answer. So, let's begin my question here. 2/3 of 15 is equal to something. If I think back to yesterday's learning the most steps to success, the first thing I needed to do was try and work out what is the value of the whole? Well, I can see from my question that the value of my whole is 15. So I'm going to take that number. That's my starting point. And I remember that when I was doing my bar model, I needed to cut it into equal parts and the denominator told me how many equal parts. So, I'm going to make sure that I do 15, shared into 3 equal parts. Mr. Edison's just said the word shared and another word for shared is divide. So, that's given me my first number sentence. So step 1, divide the whole, by the denominator. So my first number sentence is 15 divided by 3. I'm going to use my multiplication grid to help me. So, I'm looking within my 3 times tables. So I'm going to go across my 3s and I'm going to go down till find the value of the whole, 15, there we are. So the other part that's missing is 5. That's step one, whole divided by denominator. If I was going to do this with a bar model, which we're going to try and avoid today, it would look like this. Whole is 15, shared there out between my 3 groups, and one part is equal to 5, step one. Now, step two, is the tricky part. Because my question didn't want me to know the value of 1/3. It's asking me find the value of 2/3 and the numerator gives me this information. So, step number two, multiply the part by the numerator. So, I take my answer from step number one. So I take the value of one part, which is 5. And I now multiply times that by my numerator, which is 2, 5 lots of 2. We should know our 5 times is, we hopefully know our 2 times tables. But if not getting that multiplication grid out and have a look, 5 times table, 5 lots of 2, to the make 10. So my answer is 10. And if I look at my bar model, how would this look? There we go, 15, the whole shared into the different parts, the 3 different parts even, and I want 2 of those parts, 5 and 5, 5 times 2 make 10. 2/3 of 15 are equal to 10. Follow those two steps and hopefully we'll find an answer quicker than if we were going to use the bar modelling strategy, okay. So, it's now your term. Again, I would like you to try and avoid using the bar modelling strategy. I want you to follow those two steps, divide the whole by the denominator, and then multiply that answer by the numerator. Use your multiplication grid when you're ready, pause the video and you can begin. Amazing work year three, let's have a quick look at our answers to see if you've got it correct. So, divide the whole number. Step number one, divide the whole by the denominator. So my whole was 28 and I'm going to divide it by 4. 4 equal groups for a 1/4. 28 divided by 4, use my multiplication grid. I'm looking at my 4 times table, 4s find the whole 28 and the other part is 7 well done. So the first part 28 divided by 4 should be equal to 7. We then take that answer. That starts our next process to multiply that part by the numerator. Remember the numerator is 3. We want 3/4 of 28. So, I now do 7 times 3 use my multiplication grid find 7 and 3 down the side. Where do they meet? They meet at 21, 3 lots of 7 is 21. You could count in your 3s. 3, 6, 9, 12, 15, 18, 21, 7 lots of 3 are equal to 21. How would it look in our bar model? There we go. 3/4 of 28, 3 out of 4 equal parts, make 21. That should have been your answer. 3/4 of 28 is equal to 21. Step number one, divide the whole by the denominator and step number two, multiply that answer that part by the numerator. And here you can see that is our rule so today we're going to be working with the rules to help us. So when calculating the fraction of an amount, step one, divide whole by the denominator and step two, multiply the part by the numerator. I want you to repeat those after me now, my turn, your turn. So step one, divide the whole by the denominator. Step two, multiply the part by the numerator. And here at the side, we can see what those key words mean, whole, denominator and numerator. So, that's half of our learning today when we're trying to find a fraction of an amount. But yesterday we also looked at building on that and if we knew the value of a fraction already, how would we then find the value of the whole? It's a very similar process. Let's have a look at how this will be done so let's explore. Here is my question. If 2/3 of a number is 10, what is the value of the whole? Let me think about that more carefully. 2/3 of a number is 10. So, I need to find out what this number is. The information I know is that 2/3. So a part of that whole is equal to 10. I now need to find out what the whole is, 3/3. And that means that it's going to increase in value so, I'm expecting a number bigger than 10. So, for this strategy, the rule slightly changes. On the previous strategy, we divided by the denominator then multiplied by the numerator. But this strategy it's going to slightly change. So step number one. We are going to divide the fraction values that's this number here, by the numerator. So we've swapped it and we're not dividing by the denominator in this part, we dividing it by the numerator. So, I know that my numerator is 2 and that fraction value is 10. So my first fraction is, my first number sentence, sorry is 10 divided by 2. If I use my multiplication grid, I can use my go across to my 10. Well I'm going to have a look at my, sorry I'm going to have a look at my 2 times table 'cause that's what I'm looking at here. Find the value of 10 and I know that the part is 5, 10 divided by 2, is equal to 5. If I looked at this in my bar model, it would look like this. You might remember this from yesterday's law that we don't know that whole. But what we do now is that the number 10 is 2 of those 3 parts. So I've shared my 10, between those 2 parts and the answer to find the value of 1/3, one part is 5. There we go. And just like the previous rule, we then take the answer the value of one part. But this time it is that we multiply this part by the denominator, because that's going to tell us the value of the whole. This whole has been split into three parts. So we now need to multiply it by 3. So we're going to do 5 times 3. I can use my multiplication grid again here, go across to my 5, go down to my 3 on the side. And where do they meet? They meet at 15, 5 times 3 is equal to 15. And if I looked at my bar model, the whole, each 1/3 is equal to 5, so 3 1/3 the whole, would be equal to 5 times 3, 5, 5, 5, which make 15. That's my answer. If 2/3 of a number is 10, the value of the whole 3 1/3 is 15. That is, our working out, working backwards, okay? So, it is going to be your turn, now. What I would like you to do is have a go at the question at the top in the box. It says if 4/6 of a number is 8, the fraction value, what is the value of the whole? I've put the two rules there so that you can do some working out. Rule number one, divide the fraction value by the numerator. Then multiply that answer that part by the denominator to make the whole. So when you're ready, pause the video, use your multiplication grid to do your working out off we go. Brilliant, welcome back year three let's have a look through our answer see how we got on with that. So, what information do we know? We know the fraction value, we know that that is 4/6 of the whole. We're trying to find the value of 1/6, 6 so it's going to get bigger. So, the first thing I needed to do was divide that fraction value by the numerator. So 8 divided by 4. Hopefully we know our 4 times table. We might know those multiplication vision facts, but if not we'll go across to our multiplication grid, okay? So we're working with our 4 times table. So 4 is one part 8 is the fraction that we were working with the other part is 2. 8 divided by 4 is equal to 2. And this is how it would look with our bar model. We don't know the whole yet, but we know that 4 of the 6 parts make 8. So if we shared that 8 out equally between those 4 parts, the value of each part is 2. When we're working this way to try and find the value of the whole, after being given a fraction amount, you must always find the unit fraction. So we must always find the value of one part. So in this case, we must find the value of one set. We then take the answer and we're going to multiply that part by the denominator. This is going to help us know the value of every part, all six sets and that will give us our whole. So our denominator, sorry is 6. So, the number centres we were looking for was 2 times the denominator, times 6. If we don't know our 2 times table, then we can use our multiplication grid. So go across to our 2, on the 6 down the side, where do they meet? They meet at 12. 2 times 6 is equal to 12, and we can check that. Here is a completed bar model. All of my sets have the same value 2, so six sets the whole 6 equal groups would make 12. That is our answer. The value of the whole six sets is 12. Brilliant job well done fluent learning so far. Let's move on, okay? And just recap that rule. So the rule when calculating the whole after being given a fraction value. So, I want you to repeat after me. So, when calculating the whole after being given a fraction value, step number one, divide the fraction value by the numerator. Step number two, multiply the part by the denominator. Brilliant, thank you for repeating those after me. These rules are available on this video. So as you're working those out, you might want to come back and pause the video at this time so that you can access these rules, okay? If we look at these rules, they both follow very similar patterns. So on this side, when calculating the fraction of an amount, we have two steps. And when we are calculating the whole after being given a fraction value, there are also two steps. The first step is to always divide, always divide. And the next step is to always multiply. But what we are dividing by and what we are multiplying by changes. So, when calculating the fraction amount, we divide by the denominator, multiply the numerator. But when we've only been given a fraction value and we need to find that whole, it changes. We divide by the numerator and multiply by the denominator. So, two rules to help with our working out today, right? What you're going to do now is you are going to complete on main independent activity. I would prefer you to try and not use a bar model strategy to share out your dots today, because we're trying to look at those formulas, we're trying to look at those rules. If you would like to draw a bar model afterwards, to check your answers, that's absolutely fine. And remember, you can use your multiplication grid to help you. Today, the focus is on understanding that procedure, those rules, rather than worrying about our times tables. So, when you're ready, pause the video to complete your main activity and come back to this video to go through our answers. Brilliant, welcome back year three let's have a quick look through our answers. So, here were the two rules for the first part, divide the whole by the denominator, then multiply the answer by the numerator. So question one, find 2/5 of 15? So we have the whole, first of all, divided by the denominator, 5, makes 3. And then use that answer multiply it by the numerator 2 make 6. 2/5 of 15 is equal to 6. Question number two, find 3/4 of 32. So, we have 32 as our whole. We divide it by our denominator 4 into 1/4, and that gives us 8. We then take that answer and multiply it by the numerator so 8 times 3 is equal to 24. So 3/4 of 32 is equal to 24. And question number 3. Calculate 7/8 of 16. So 16 was our whole. We're going to divide it into 8 equal groups to give me the answer of 2, that's one group 1/8. And then we need to take that answer and multiply by 7, that's the numerator value to find 7/8, which make 14. 7/8 of 16 is equal to 14. And question number four, George has 40 pieces of lego. He gives his friend 8/10 of them. How many lego pieces did George's friend receive? So the working out. 40 was my whole. I'm going to divide it by the denominator 10 equal groups. Each group has a value of 4 and then take that number one part, multiply by the numerator 8 to give me the value of 8/10, and that gives me 32. George's friend received 32 lego pieces. And then part two was working backwards so we had the fraction value, but we needed to find the value of the whole. So, here were the rules. Step number one, divide the fraction value by the numerator, this time. Then number to multiply the value of one part by the denominator to find the whole. So, if I know that 3/7 is equal to 12, what is the value of the whole? So, I had the whole as 12. I divide by the numerator this time. So that would tell me the value of one part, which was 4. And then I'm going to take that part and multiply it by 7, the 7, 7s to give me the whole. So the whole was 28. The value of the whole is 28 full sentences. And finally, Sandra was given £50. This was 5/9 of her brother's money. How much money did Sandra's brother have? So, the fraction amount that we were given was £50. First, we divide that by our numerator to find 1/9, which gives me £10. And then I'm going to take that value one part, and I need to multiply that by 9, the denominator to give me the answer for 9, 1/9 and the whole was equal to £90. So Sandra's brother had £90 to start with. Really good work, because I know that is very, very tricky, especially learning from home. Finished today's lesson. What I would like you to do is complete our final knowledge quiz, to prove what you have learned in today's lesson. So pause the video to complete that now. Brilliant, thank you year three and have an amazing lesson. So, just a goodbye from me, well done and for completing today's learning. We should hopefully now be more confident with finding non-unit fractions of a given quantity. If we are doing this in the future, remember now you've got two strategies, you can use the bar modelling strategy, share that out, or you can remember those two rules to help you with your working out. Hopefully, I'll see you back here tomorrow for more exciting maths learning, goodbye.

Consolidating finding non-unit fractions of quantities

Consolidating finding non-unit fractions of quantities

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