Video: Missing numbers

﻿So I wonder how you solve these problems from the last lesson. This is Mrs. Parry, we're back again, we're looking at fractions. I've just completed the first one's for you. I thought it'd be quite interesting to have a quick look at how we could have solved them. You were given three options. The first option was to use the proportional relationship. So we were looking at this relationship. And you could have done that for any of these. Your second method was to have a look at the scaling relationships, so going across the equivalent fractions. And again, you could have done that with any of these. And then the third relationship, your third solution was to look at your times tables. And again, you could have done that for any of these. Well done for getting those answers. If you're not sure about any of them, take them back to your teacher or to your adult in the house and talk about why my answers are different to yours. Let's look in depth now at the next one. This one seem to be trickier to me than the previous ones. I think the reason for that is because the, the denominators aren't in a sequence. So we had to really, really keep thinking about the proportional relationship within or we needed to be looking at the scaling relationship across. Let's start by looking at the very, very first empty number box here and deciding how we'd deal with that one. That's right. I looked and I noticed that there was a scaling relationship of times eight for the numerator and then I remembered I needed to do the same to the denominator. And that gave me the answer 40. And that was where you start it. So when I looked at the next fraction that I was dealing with. I had a quick look here and I looked to see if I could find a way to find that relationship, but I decided I was better of going back to my starting fraction. Once I was back at the starting fraction, I could see a relationship between these two. Did you see it? I know cause they're equivalent fractions. So we're looking at fractions that have got the same value, but have got a different appearance. So if I've multiplied the denominator by three, then I'm going to have to do the same to the numerator, and that's going to give me an answer of six. Great, we're getting on really, really well here. Let's look and see the relationship. Yeah, I've gone back to the starting fraction again. Let's look at the relationship between five and 35. I bet you saw that it was multiplying by seven. So we did the same to the numerator and that gave us a new equivalent fraction of 14/35. So 14/35 is in fact the same value as 2/5, but it's got a different appearance. And on, okay. So let's have a quick look down here. We've got to change, haven't we? When we moved to this next fraction cause this next pair of fractions, we're missing the denominators, which means we've got to look for relationships with our numerators. Now my first thought was I could go back to my starting fraction. Can you see that? Yeah, me too. So what I would do for that one is if my starting fraction needs to be scaled up by 14 for the numerator, I need to do the same for my denominator. And that gets me enough answer of my new fraction being 28/70. That's interesting. It's got the same relationship, 28/70 is 2/5. Great. But then I had a quick look and I thought, well, I could have used the next door fraction because 14 to 28 is the scale factor two. So I could have doubled 35 to get to 70. It doesn't matter which fraction you use because they're all equivalent. Okay. Okay, here we go. I wonder if when you got these final three fractions, you started to get a little bit worried because there are lots and lots of parts in these ones, aren't there? Of course we didn't need to worry because we know that they are all equivalent to 2/5. So the quick look at how we could have solved this denominator. Of course we've been given the numerator, so we need to look to the numerator and find a relationship. We could have gone back to our starting. Our starting numerator was two and I know that if I go up a factor of 16, I will go from two to 32 in my numerator. That means I'd have to multiply five by 16 to get to 80. Also had a quick look and I realised that this fraction could have helped me because if I scale up by two, 16 to get to 32, then I could scale up by two from 40 to get to 80. So two solutions to get the same fraction here. And it was the same for this one. I could see a relationship between 15 and 75. I could also see a relationship with this denominator five and 75. I wonder which one you chose to do. Let's just finish our home learning practise session from the last lesson, by looking at how we could have solved this final one. 92, Hmm. What I needed to do for this was I needed to look at 92 and I needed to work out how I would have scaled up from two to get to 92. I used division for that, cause it was 92 divided by two makes 46. So that meant that to go from two, all the way to 92, remember I'm scaling up by 46. If I did that to the numerator, then we know I needed to do that to the denominator as well. Five times 46. I could have used my fingers. Might've gone wrong though cause that's quite a lot of counting up in fives. I also could have got out of pencil and paper, but I chose to use a mental method. Five times 46 is the same as 10 times 46 and then half it. 10, 46 is 460, then half it is 230. I wonder which method you used. Wow, these look less complicated than the last one, don't they? We've moved on to new learning now. And in this slide, we are going to be looking at how you find a numerator, a missing numerator in an equivalent fraction. Let's have a look. I'm starting at the bottom for change cause it's quite fun to change. So our fraction has a proportional relationship of, that's right. Five. We've been given the denominator here, five. And we know that one is 1/5 of five. That means we need to do the same for this equivalent fraction. We've been given denominator of 10. If we divide that by five, we're going to get our new answer of two. 2/10 is an equivalent fraction for 1/5, they have the same value, but to different appearance. Remember we've got to keep the proportional relationship the same when we do the other two questions. Pause the video and have a go at it now. Welcome back. I hope you got the same answers as me. Okay. Let's move on to the next slide where we're going to look at the missing denominators. Here is our missing denominator. We know we've got to keep this new fraction as the same proportion as this one, because we're looking for an equivalent fraction which is a fraction of the same value but a different appearance. So our relationship here is from six to 12, that proportional relationship is, that's right. We scaled up to top by two, haven't we? We going to have to do the same here. That means we're going to want to scale up by a factor of two. One times two is two. Could we have done it by dividing? Yeah, we could have done, couldn't we? We could have started if we looked at this relationship. So this was six divided by six is one. And we did needed to do the same here, 12 divided by six is two. You knew what you were going to get on this slide, didn't you? In the last ones we've had missing numerators, we've had missing denominators, so in this one we're going to get both. I wonder if you expected them to still be equivalent fractions. And I wonder if you also thought that we might change where we put our fraction that we've got both the numerator and the denominator. It doesn't matter which side of the equal side it is, does it? Because we know that these are equivalent fractions. So have a go, think really carefully are you scaling up or down to find our missing numerator and our missing denominator. Did you get the same answers as me? Well done. You've really learned well. Well this is an unusual problem, isn't it? Because I've got two missing boxes. Says to me, hey could the missing digits be? That's more than one answer. I'm going to solve it? I think what I'm going to do first of all is I'm just going to see if I made one of the numerators one. Let's have a look. Still doesn't give me the answer to the second numerator. So I guess what I need to do is I need to be looking at the relationship between my denominators. What scale factor would I need to go from 11 to 88? Yeah, I bet you've got that one now. We scaled it up like eight, didn't we? So if we did that to the denominator, we going to have to do the same to the numerator, aren't we? Little picture there of the image. Can you see, this is in elevenths and each one of these boxes top here. Yep, there's 88 of them. So if I've done the scaling up for the denominator, I'm going to have to scale up by the same amount for the numerator. Mhh, is that the only way to solve it? No, I don't think so either. Let's look at the next slide. Okay. So we're back to the same problem. We've got the two empty numerator boxes, but what I've done this time is I've changed my image down here and I've given me 2/11. My scale factor is still going to be the same. This is just going to be a scale factor of eight. So if I've gone for 2/11, then yeah, two times eight is 16/88. I don't think that's the end of this. I think I could find other solutions to this problem. Why don't you have a go with it now and then show your teacher all the different ways that you've done. That would be a really interesting challenge. So here's one and it really, really clearly tells you in the question that you need to find as many ways as you can to solve this problem. The difference from the last one. Yep. That's a good question. Can you see this time we've got missing denominators, but we're still looking at equivalent fractions. What I want you to do is I want you to pause the video and I want you to see how many different ways you can do this. Off you go. Welcome back. Now, I've got my notes down here and I came up with lots of different ways. First of all, I thought to myself, okay, I'm going to try 3/6. Yep, that would work. And, ooh, I also had a go at, I had to do 6/12. Then I had another look and I thought, yep, 3/4 and I would need to scale up my denominator if it was quarters. Then the new one would need to be eight. So for those ones I was working in proper fractions. I just had a bit of fun playing with improper fractions. My I thought I could have three 1/2 and six 1/2. I wonder how many you found. Was there a number that you could find that was a total number or could it just have gone on forever? Talk to your teacher about that one. I really, really liked this problem. We've got two more problems and then we're going to be moving on to our independent activity before the next lesson. Let's start by reading this question. Okay. Can you circle the fraction which is equivalent to the fraction card? So let's start by looking at the fraction card. Our fraction card is 4/7. I'm just going to have a quick think about what that number actually means. It's a whole that's divided into seven equal parts, that's what the denominator means. And we've got four of those equal parts, 4/7. It's less than a whole and it's just a little bit more than 1/2. That thinking about the first fraction is going to really help me solve which ones of these four could be an equivalent. I'm going to start here because I quite like the look of this one. It's got the same digits, but they mean something completely different, don't they? Because in this one, when I mean quarters, it means that my whole is divided into four equal parts and I've got seven of those equal parts. That's more than a whole. So it can't possibly be 7/4. Let's come down here. I quite like in the look of this one, because I've got 8/14 and as I'm looking at it, I'm thinking sevenths and fourteenths, they do have a relationship, don't they? Yeah, it's a, it's a scale of two. So seven to 14 I've got to multiply by two. If I've done that to the denominator, I need to do it to the numerator as well. Four, yeah. Four scaled up by two is eight. So that one is a definite. I wonder if any of the others are also equivalent to 4/7. Let's have a quick look. I'm looking now here. It's denominator of eight, seven. Do you like I can use my times tables. I don't know but that's not going to be in the same family of fractions, does it? So that means that 5/8 even though it is just a little bit more than 1/2, it's not in the same family of fractions. It's not going to be an equivalent. And the same is true of this one. Okay. I think there is only one answer to this and it is I'm right. 8/14. Did you get that one right too? Okay. So we are on our final problem for today before we move on to a practise activity for the next lesson. Let's have a look at our questions, shall we? Show what each fraction on the number line is by converting to eighths? Oh, I like that. I like that bit because what that's telling me is that each of the fractions above is in the eighths family of fractions. Let's have a look. We can check it by using our times tables knowledge, couldn't we? Because we're on eighths. So eight, 16, 24. Oh there's no 32. 40, 48, yeah and 72. They are all in the eight times table. Right now I've checked that, I'm happy for you to have a go on your own. What I'd like you to do is I'd like you to find an equivalent fraction with them all in eighths and I'd like you to put them on the number line. Which one's going to be the smallest, and which one's going to be the biggest fraction? Okay. We'll come back. What we're looking for is where you've put these on the number line. Yep, 9/24 is equivalent to 3/8. Wow that's a hard one to say, isn't it? 36/48 is equivalent to 6/8. I quite like the way that, that is equivalent to 6/8 cause I've got a picture in my mind of what 6/8 looks like, but I find 36/48 quite hard. Oh, did you spot 12/16, 36/48 and 6/8 are all fractions that have the same value, but a different appearance. 10/14 is the same value as 2/8 but a different appearance. Now this one, I wonder if this one, with this really big number here in the denominator, I wonder if you've decided it's a smaller fraction or if it's a larger fraction. Yeah, I know we don't just look at the number in the denominator, do we? We need to look at the whole of the fraction, the numerator and the denominator. And when we do that is equivalent to 1/8. Well done, you've done really, really good learning today. Now before you go, have a look at how I'm going to take you through an activity that's going to help you with your practise one. Okay. So this is going to be a challenge that's going to help prepare you for your next lesson. I want you to look at this calculation and I want you to see, yeah, it's different to the ones we've been doing, isn't it? Because up until now, we've been looking at equivalent fractions only and this time the calculation is a subtraction. Okay. So a little bit of technical language. We're looking at a minuend of 2/14 and a subtrahend of 1/7. What I'd like you to do is I'd like you to look at these fractions. Yeah. Have you seen them before? We've looked at them a few times in this last couple of lessons. You're right. They are equivalent fractions. Ah, so what I want us to do, is I want us to think if we turn these into integers, if the minuend and the subtrahend was the same. Let's just imagine that our number was three. Three takeaway three would leave us with zero, wouldn't it? That's right. So what we're asking here is, is it the same when we deal with fractions? Yeah, of course it is. Of course it is cause fractions are numbers. That's going to help you to look at the final slide which is our practise activity so that you're ready for your next lesson. Have fun.

Lesson summary: Missing numbers

In this lesson, we practise using both vertical and horizontal relationships in fractions to find missing numbers.

Maths

Missing numbers

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Lesson summary: Missing numbers

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