Hi. Hi, Vivian. How are you? Are you okay? I can't hear you. Can you hear? Hello? There you are. Okay. Alright, so do you want to start with this one? I'm just getting some final questions for you. For some reason, they don't want to come up. I right I might just get them on my phone, but you start with this one. I think I. To. Look for look for them on my phone, but you start here. Okay okay. Okay, I found it now for the. Still hard to write, you want to write, do you want to write on paper and you want to write on paper and. Yeah, I think I did fly that tly. Nourish, perfect, lish. 谢谢我们。Yeah. Okay, lovely great work. Alright right next. Can I go to the bathroom course? Okay, sorry. Two PaaS five. Hello. Yeah, nice. Okay, right. That one is a little bit small, but let's go with this one. Is this an irregular shape? I, Yeah, Yeah, it's an irregular shape. Okay, let's use a straight slide. I went, do we sign this? Can help me raise the first guys show, but you need to do it like I don't that. Okay, thank you. 问题是说one。Nice. There is only one odd number here. Nice. No, this is not talking. Oh, no. Nice, very nice. Okay. Do we have one more of those? We do. Okay. Nice. Okay lovely. So just one more. Okay. Oh 11. I'm just mitrying here, not giving the right answer. It seems like it works. But it's a good policy, isn't it? I think it's a good policy to just throw numbers in sometimes and see what works. Yeah. That's the first time I write. Yeah Yeah. I think sometimes it's good to just try and then right. So sorry, some of some of these sorry, for some reason they put yellow writing. For the question, but it's it's abcde and then it says that yellow says what is the approximate cost of the path? Okay, Yeah, I think I can read it. Just put around a bbag will cover. So how did you figure that out? How many how how many? What did you said? I can't. How many so how did you figure that out? How many meters squared have we got? Let's just check. Did you do fifth 29? I did. I did. 28 times 500 140 okay so we got your voice ices a bit is it Oh Yeah was Yeah it's gone a bit crackly I don't know why yours was a bit crackly then as well okay well let me just type we got so we got 14m²Yeah. Yep, so 28 bags times five. Yeah, nice. Yeah, yes, okay. All right. Well, look, I think you can pretty much get all of those. So let's do a bit more. Did, did we did we do this? The other day. Yes, I think so. Okay. So could you just expand that? Okay, that's the five men of us. 嗯，哪个member？Three plus six, which as. Plus five x. Very nice. Okay. So how have you learned this yet? Back to ise three x plus nine. So that is it. And. Okay wait. Yes, which equals three times that. That's not. I'm not really sure if I've learned, Ned, this one, if I gave you this. Yeah I haven't learned this one. I know. Okay. But look, what could you your look what could you put in the bracket so that nine comes out basically back to Ising. These are in fact triple equals identity. It's exactly the same for all cases. Yeah have you seen that triple equals? No ple triple equals is the sign for an identity. Okay? It's nothing complicated. It's like an extra strength equals. It means for all the numbers in the universe, for all the numbers in the universe, this would equal this. Always it's an identity because we're saying those two things are in fact the same thing, just written in a different format, right? As in there is no dithis, is not one thing is equal to another. Like how much is x? This is three x plus nine. Will always be, will always factorize to three with a bracket x plus three. Can you see why that would be the case? Because when this happens, the multiplication, to get it out of the bracket, we have three times x and three times three, which is three x and nine. Hence. Six x plus two will always be. Two times three x plus one. Can you see why triple equals? Those two are the same expression. In fact, just one is written in brackets. Yeah, okay. Because when you do two times three x, you get 62 times one is two. So so here, what are we looking for? We're looking for the highest common factor, yes, yes, of both items. Highest common factor of your whole expression. Yeah, Yeah, Yeah. So whatever the highest common factor is, you can put it there. So let's just do one of these. Can you factorize this? 早味。Oh, this happened. Never mind. Okay, okay, so then so look, that was that's a very basic one, but look, use the same principle of the highest common factor, okay? Okay. What if I asked you to factorize that? Is it? Do straight line tool, yes. A B. But I see. Right. And then we see, in fact, Vivian, do we have the highest common factor outside the bracket? Or is there a common factor still inside the two terms of the expression? Is there something common to both? Yeah but there should be a factor. And for two I think is Yeah but don't forget a although it's an unknown algebraic value, it's a value right? Yeah Yeah it's it's an unknown quantity which has been given the letter a, but a is here and the same a is here. So in fact a is a factor of both terms. Two a times two b would give you four A, B. Does that make sense to you? Okay. Yeah, Yeah. And two a times c would give you two ac. So letters can be factors. Yes. Okay, in your algebra. So so this is this is partly factorized Yeah fully factorized. So if they say please factorize fully, it means there's probably more letters, more more things you can factorize out Yeah and this can go quite complex. Let's go to this. How could I factorize that one fully? Basically look at both terms. Okay but that this this b and D B and d are not added together. Oh wait啊啊啊。They're multiplied together. Yeah and what about this tweet? There makes sense. So basically I think you're starting to get the hang of that hang of it, right? You're just drawing out the common factors of each term Yeah and if you draw them all out, you're gonna to get the highest common factor three times a times. Y whatever a and y happen to be is the highest common factor. Yeah. Okay, Yeah. So let's do let's do one more. What's the highest? So what's that factorized? Nice. Yeah. Yeah, excellent. Okay, so great with stuff. Let's try a bit of quadratic factorization. How do you think this would work? Facto ised. So it's more t times t plus T T plus t. And you might throw yourself by saying t plus t actually, because it's actually t times, it is t plus t, but you might throw yourself without saying t times two. It was the bracket. Yeah. Nice. So the common factor, which is in fact the highest common factor of both those is Yeah and if we back to rise out the t, we are left with a single tee in the front of the bracket. Nice. So same goes for for this. How would we factorize that? The two times two or two x two x squared sorry okay. Come x. Two x. Nice. Is there something else you can factorize out? Maybe this. Very nice. Yes. Okay. So let's just go a little bit more complicated and take some quadratic terms into it. Okay. So two. Okay, I'm just going to. Oh, there's a Searight. No. It's like. This so that's it. Baby squared. Like. Two c squared no two. The middle one. Sorry, I think you were right first time. You were right first time, and then you corrected yourself. See. Even too icy, but though like there's no squin this one. Yeah so but anyway, it' S B squared. It' S B squared and then it's c squared there. So they're not the same squared anyway, right? So Yeah, so it's complicated, it's good. You have to just look at what you've got. Everything divides by two, so that's fine. Everything divides by c, so that's fine. But here you would have A C left when you divide by c. Yeah. And then Yeah and then so everything else is not common. Yeah Yeah because I thought it was abc squred and ac squared. Ok. 对。哎be square。Less. Three b. Yeah. There you go. Yeah, yes, Yeah Yeah okay. So it's so Yeah so sometimes you can't always factorize a huge amount out. Yeah and that's just the way it goes. The important thing is to make sure that you factorize out as many items that are common to all and keeping the ones. Obviously you've still got quite a long expression in the bracket, but that's just the way it goes. Yeah, Yeah, okay. Okay, nice job. All right, so look, this is what we have, right? So let's just go back to to this. In fact, let's let's change skill and what we'll do is we'll do a bit more tomorrow. Yeah because you're so advanced already on the on the eleven plus items, I think what we've been doing there is a little bit of advanced factorization, okay, so that you can understand how those how those things work. So let's just do and you understand you understand don't you? Highest common factor and lowest common multiple? Yeah, yes. Yes. Yeah, Yeah. Okay. And then just to check, you were also happy with Venn diagrams. Weren't you with those? Yes, I think so. Yeah, Yeah, okay. All right. So we've we're already on quite a few of the topic areas that you would be covering for your year seven maths. Yeah. So if we've got Venn diagrams and we've got higher highest contracftor locome multiple, let's go to some square root numbers. Okay. Sorry if I gave you this, you recognize it. Yes, what time? Okay, so we say the square root of 16 is four. Yeah, Yeah, that's squared. Okay, this the square root is of 16 is four or the square root of 16 is four squared. Four okay okay four okay all so this is so we've basically got a backwards and forwards Yeah. So that's identity. Yeah. So basically the square root of 25 is always five. The square root of 16 is always four. Yeah. Yeah, so then what if I said. What about this one? You've you've probably not studied it before, have you? Yeah should we decimal or something? Yeah, okay. Because we know what what do we know about it? It's going to be between. Square roofs is going to be between 45, isn't it? So we know for a fact that it's between 45. So four point, in fact, do you have a calculator? Wait towards okay okay. Okay, I got it right. What's 4.5 times? 4.5 then? It is 20.25, right? So we know it's less than 4.5, right? What do you want to try then? Right? So that's too big. 4:24. Times it equals 19.36. Okay, so we did this the other day with the perimeter, didn't we in the area? Yeah, Yeah. So we so we need to just check. Can you just check 4.45? Okay, 44, it equals 19.80, 25. Right? So because 4.45 is too small and 4.5 is too big, however, this is too small. So how much is it our answer to one decimal place? One doesn't face be four points. I don't know five or four it's this to one decimal place, right? Because this is too small. This is too small but this to one decimal place is still 4.5. Yes, yes, Yeah. So we know it's 4.4 something. However, Yeah, it could be right, but to one decimal place, if 4.45 is also too small, we know to one decimal place it's is 4.5. Yeah okay. Okay. Can you put it into your actual calculator? What what answer do you get when you put that in square root of 20? Wait this calculator is a little snow and please work. Wait, I can't find a square root symbol now. Oh, there's No Okay, don't way I'll use mine. It's just to show you square root of square root of four point, square root of 20. Is that okay? 4.4, seven, two, one, three, five. So right. Yeah, that's it because there's not the base. Yeah. So it's not very satisfying, is it? Four, seven, two, one, three, five, nine, five, five. Okay. And it goes on and on and on forever. So actually we want to use square root 20 instead because it's neater. Okay, Yeah, but we want to simplify it. Simplify it. Okay. Square root of 20 is the same as square root of Four Times Square root of five Yeah, okay. So what is the square root of four third of two, right? So what we can do is simplify out square root four, call it the number two. And factorize it out. Do you see what I just did? Basically, I just factorized two away from the square root. Yeah. Okay. Yeah, and you know that square root five can be done in that way, don't you? No itgo on like Yeah the only ones we can do must be these right? What would be the next one square root of. Nine square root, 16 square right? So we had 16 and 25. Yeah these are the only ones that could come out. Yeah Yeah. Yes. Okay. So can we try and simplify square root of 80. What could I call square root of 80? About nine with eight and ten eight times ten. Okay, so it's. They are not very simple, are 't they? No, but if I be, I could I could do this though, right? I could I could do this. Okay. So I could use your, I could use your eight times ten like that, couldn't I? Oh, Yeah. But is there a simpler way of doing it? Is there a simpler way? What could I choose instead? Four times 20. Okay, then what would that be? That will be two. Square 20. Okay. And so then actually Vivian can I go further? Because I got 20 now, which we just did up here. Oh Yeah, four, five. Yep. Yeyeah p four fine. And it's two, it's four or five. Nice. Really nice. Yeah. So actually, Yeah, it's the same it's the same as doing this, but it really doesn't matter. We're just playing around now. It could be that. Yeah, Yeah. So we just this is just a different factorization to oops, I've moved your camera for some reason. This is just a different factorization of 80, but it gets us to the same place, right? Okay, Yeah, Yeah. Okay, great work. Yes. What about this one? Hello 108. For. Yes, could be. 隔逼啊看到。Square b four times. 春。Seven, it's not the simplest way. Two and. 27. And don't think there's any learn. Which. 27 is what times table? Is it in the four times table? No, I said in a three times 93. Times my end. Oh, there's another one to be sold. So it's equals six and. Very nice. Yeah Yeah Yeah and just to see, you know you can be flexible, doesn't have to always be the same. It doesn't really matter as long as you fully factorize, as long as you go Yeah as long as you go as far as you can, we see we get the same answer. Yeah. Okay, Yeah, excellent. Okay. Look, really good. So no, that's really advanced work. Look, I don't look, this is the thing with you, Vivian. I think you've got more than enough to answer the eleven plus at the moment. Some students will know this as well as you, okay? But they will be the very advanced they will be the very advanced students, but that's okay. That means you're a very advanced student as well. Okay. Yeah. So, so okay. So then I just wanna know before we finish, do you know how to do this type of stuff? Okay, I'm just, I'm just kind of, what am I doing? Have you seen this kind of, I'm just coming up with an example off the top of my head. If you saw this, have you seen it before? For example, x equals. Have you seen that before? I think I've seen these but okay, so we will can do it. Okay, so I will just put that on the board because we've got a lesson in the morning. So I'm just going to remind myself we're going to start with that. Okay. Linear simultaneous. Okay, so I'm just writing a load of some words on your chat for us to do this tomorrow morning. Linear simultaneous equations is it's called yes, we'll start with that tomorrow. All right. Have a great rest of your day, and I will see you in the morning. Okay. Goodbye. Bye.