Hello over Vivian. Hello, good morning. Can you hear me? Okay? Okay, hello, a second, are you all right? Yes, it's, I'm all right here. Good. Okay. Have you seen Venn diagrams before? Yes, yes, I think okay. Can you complete the Venn diagram with the pen? Okay, I use different colors to separate. I think I need to type. It's still hard to write. No, it's not. What role? I just need to connect it to my keyboard. Sorry, I. Just need to be connected to my keyboards because okay. Thank you. Just one. Just grbing something. Okay, nice. So one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, 13, 14 there are still some, wait a moment. One, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, 13, 14, it's just another 15, right? And to be fair, it's something every time I do this with someone, I realize, really, in fairness, there should be this. Yeah around the picture, right? Yeah like this. And then the only thing I would question is this. Oh, Oh, Oh, wait a moment, just need to tarsomewhere. There should be here, right? Yeah. Yeah because apart from one apart from one, no one as well doesn't count. Can a number be square and prime at the same time? I. So I don't think, no, it's impossible, isn't it? Because it means that it has to have a double factor of itself. Yeah in which case that would eliminate the only one that the factor of just one in itself. Yeah, okay. Yeah, nice. Let's. Do a little bit of. A substitution into mathematical expressions. A little bit of this is slightly harder level for ubivian. Okay, I just try them. Hey, nice. I think you get that fine. Yeah, that's all really nice. Okay. Have you tried? Do you recognize these? Yes. Okay, let's just check. Black, just Frithe expression. Yes. Are we're expanding, okay. I guess it's also impossible to write a home like a result. 15. If. You want, you can just go down. Downwards just do those eight. Okay. And do you recognize this type of expansion? Oh, wait. So it's a bit small. Let me just get. Do you recognize this type of expansion? What mean? I think so. I think so. Maybe I'll try. Might not be correct. Thank. This is a little harder at the I need to walk the house episode. Okay. Oh, there is. No, never mind. Okay. If you've not studied it, I can show you a number of ways. What do you think? Yeah because this might take a bit of time. Let's consider look, so Vivian, look, let's consider this. Okay, so so you did this, right? This is easy. Yeah, it's two k plus six. Yeah, but Yeah. Okay. So what is happening is we have two times k Yeah and two times six, two times three. Sorry. Yeah. Yeah. Okay. So then if you consider k plus five, if if we look at what's actually being going on here, this is also a multiplication. Yeah so is this something like K K plus 52 minus two k plus five? Almost look, what we've actually got is you could look at it like this. You've got the k times the k minus two and you've got the five times the k minus two. Yeah, Yeah. Because this is going on in the in a single bracket, two times k, two times three. In this one you've got K K times k and five times k and five times k, five times minus two and k times minus two. So can you expand it this way? 嗯，okay. Should be. The second part is easy, yes, okay, I don't add, write it by hand because some Marks is missing from a keyboard. A squared. Oh. This can be a little even more simplified than this. And it be. Okay. I think it can be even more when. Right in the middle. Yeah, I think k squared and five Ken can go together. It's actually these two can go together. Yes, Yeah, no, no, no you see what I've I'm roting writing please I'll just yes but then yes, but this would become three Yeah Oh Yeah I intended to be okay. Yeah cool. Yes all so we can think of it so we can think of it like that. We can think of it like we take it with x. Ups. Right? So we can think of it in this way. Oh Yeah, times final school Yeah. Okay, or we can think of it like this. When you get more fast at it, you can you can mentally what you're doing is four multiplications x times x Yeah x times minus four, two times x and two times minus four. Yeah. Yeah x times x, it can be in any order really two times x Yeah minus four times x and two times minus four, everything by every other thing. Yeah on the opposite side of the bracket. Yeah as as in each thing each thing in one bracket by the two things in the other bracket. Yeah Yeah some people do it like this. What we call grid method. And they would put x and plus to one of the brackets on the top of the gras of the table and the other bracket on the column rows of the table. Yeah and then they would put the answers in the middle x times x Yeah. Yes two times x. Yeah X X times minus four. Yeah and two times minus four. Yeah that's actually very useful when it gets to factorizing this this what we call grid method. Yeah do you want to just help right? If I just give them, I know it's I know it's difficult for you to write. So do you want na just tell me what the answers would be? And I'll write them down. Oh, sorry, that's meant to say x. It will be. X squared. 嗯，wait a moment. X. Minus five x. Five foot? 呃，X. This is plus I believe plus 70x -15 which will be minus two x. Right so when you get really fast at it, you can do plus three x minus five x Yeah and straight away right down. Minus two x Yeah okay, very nice. So good job. All right, let's do some questions from a paper. So do I wanted to check this? 嗯，this box the following number are first result. Oh back and fact five to get a second more first and second okay then starting final answer. 光探出来那一天。Okay the. Second, was this little hard multiple last meant that one of his result or maybe two will be zero. Okay. It's my way 13 and my way five or it's. Yeah it's I was 13 or I' M5. Nice 13, Yeah five. Nice. Yeah. Let me make these ones bigger. I'm just getting a worksheet for my. For if we run out of things to do. A group of 46 children are also to the. Subject. Out of 360 inches. A quarter a quarter Yeah. I'm just trying, sorry, then. Wow. Well. This is hard. So have you worked on pie chart angles? Yes, a bit. I don't really know why they wrote it like that. I think they're just trying to throw you. But what fraction is that? Latthree 19 nine 100 out of three. Oh Yeah, Yeah so Yeah, I know what you mean. You're you're saying that Yeah. 嗯。Yeah. Yeah 33 at 0.3% is rounded Yeah because 100 100 divided by three. Is that right? Yeah. Yeah. So it's one third of the pie chart. You agree? Yes, okay matthink. Itbe about. Let's think 1:16 1616 people hundred and Yeah 120 degree nice nice okay, so. The last one is 2020I think. So we've got a quarter. So what's that? Twelve? We've got twelve, 16. Yeah and 20. Yeah, nice. Your volume is your is. Did you say you're struggling to hear me? Yes and my voice is echoing and I can't hear what you say. Okay. If your voice is echoing, it's usually to do with your upload speed, I think to the lesson space. Okay. Do you want to just try? Is it still bad? Do you want to just try refreshing? Because mine mine sounds fine. Let's see. Is it okay now? It's fine for me anyway, but are you better few? Yes yes, yes, is not good now. Okay, if it is a cold rainy when I wear, then I wear a racoat it the warm rainy day, but I Carry an umbrella. If I wear my raincoat, then I also wear either gloves or a hat, but not both. If I Carry an umbrella, I always wear gloves and sometimes wear my hat as well. I never Carry an umbrella and wear my raincoat on the same day for each of the folding state, whether it is definitely force or uncertain, it is a warm rainday. I wear a raincoat and a hat. It. Is definitely false f okay. Yeah, it's a warm Raday. I Carry my umbrella, I wear hair. It is false. Htch. I think it's falnice. Yeah, okay, Yeah, all very nice. Let's try. Not that. Let's go to here. Okay, Addie is addicted to a new quiz. Skon her phone, she gets one diamond for getting the first question correct, two diamonds of getting a second question correct. Four time, I'm getting the third question correct. In fact, every time to answer the question correctly, the number of diamonds she receive, ves doubles receive 127 diamonds and total. How many questions did she answer correctly? Okay. Two 63. Eight. Wait to I'll think again. Ha, last is because the four times two meant to be equal to 128, but only 127. So she's probably one less than that no, because she's getting one plus two, plus four, plus eight Yeah. Oh, Oh, Oh, yes, I forgot. I forgot. Yeah. So how much is that up to? That's three, seven, 15, 31, 63. Oh Yeah, 127, Yeah 77. Which is interesting I think because this pattern, so you recognize this pattern obviously in the doubling Yeah one, two, four, eight, the powers of two Yeah, we call this the powers of two. Yeah Yep. What's interesting or for some people is these two are one less than this. These three are one less than this. Yeah. These are one less than this. These five are one less than this and so on and so on and so on. Yeah, Yeah. And so 127 is one less than 128. Oh, so no question nine. Oh excuse me, it's very early the morning here. Alright, okay, so question nine. U and calculation above, what is the value of n? This is big calculation fcing. I think you can do it as long as you calculate directly. A long calculation question, wait, is it a long calculation? Is it a long wait? Not a long wait moment? I don't. And finally divided by two. It be. This this 17Yeah so we're just trying to speed up our Yeah we're doing a speedy calculation there like that. Yeah. Yeah. Actually what I did is 32 times, 33 times, 34 divided by four, divided by a, divided by three, divided by eleven and divided by two. You did what? Sorry. And did 32 times 33 times 34, then divided by four, eight, three, eleven. Okay, so you did work it out. You did work it out. So we just want we just want na see the connection between this, right Vivian, the 32 is in fact the four times eight because Yeah so if you think about how timzing, how does tizing work? Yeah. Four times eight is just broken down, a broken down way of writing 32, right? So essentially the four times the eight is the same as the 32 and the three times the eleven is the same as the 33. So then immediately, Yeah but it's just about getting fast. Yeah so that you could look at that and you could answer it really fast Yeah without any need for kind of brain work. Yeah. Okay. What about what about question ten? Members favorite number is one. If you take away 500 from educate number, what if add 501, you get a whole digit. This is total of the digits and patri's favorite number. So it would be a three digit and it must be 21 aha. Good moment might not be good moment. And it should be less to be less than 500. Okay, that's interesting. And. 499. 499. It's 22. Nice. Nice. Okay, one more of those. This plan of a rectangle garden shows that it is fire industry, three smaller rectangles, the area of the flower bed is equal to let off the vegetable pack, and how the area of the grass flower bed is 2m wide, and the vegetable artitistics leayou the area of the grass. Peace. Two we've got two. Okay, let me just chat. Yep, hold on. Yeah, nice. Yeah, excellent. So look, I think actually let's do some something off something different to finish with which is the reverse mean Yeah. So you know you know how to find the mean, don't you? Yeah. Right. So let's just look at let's look for the last 15 minutes, let's look at the reverse mean. Okay okay. All right, here it is on your board. Let me just put it onto the blackboard. Right. Is it going to be annoying? Hopefully it won't be too. Sorry, the writing might not be clear. Let's just check. Is it going to be clear? Obviously it needs to be bigger. It's not very clear. So let me, let me try and zoom in on it right first, okay? Because I don't want you to hurt your eyes trying to read this. Just wait me right? Let me do it this way. Okay, you see that? Okay, that's better. That's clear enough. Okay, Pete has seven, a mean height of 116. So we took Pete by eight, the mean height. Okay, 707. No, 700, 800, 106 times seven equals equals. 800s and twelve. 812 and 128 equals 140 what by eight equal 100 100? 17.5 it nice. The mean height of seven pupils is 123 centimeone puil has of height 147 meleaves the group okay. So it's 423 times seven it be. 861-147 what's your be? 714 divided by six and then equals two. 190. Is it nice? There are twelve students in filth, the math group, the mean mark in a test is 76%. In false pols who lose only eight students, their mean mark is 84%. But the overall mean for 20 children, so it be 76 times twelve. It's 912. 912 and then it is 84 times eight times twelve and it equals 1000. I got zero. No, no, no. A four times eight equals 672. They added. Together. 1584 divided by 20. Yeah. 79.2. 79.2. Very nice. Yeah, okay. I'm finding I'm finding it hard to challenge you at the moment because look, this is for students. This is for students who are about six, 15, 16 years old. So I'm just, so I think you're look, I think you're doing really great stuff, Vivian. So I think we've got ten minutes. We might as well look at this, right? Take a look at these questions. These are designed to be quite a lot harder than what is expected of your level. But just see, like take a look at the first one. Does do you think it's something you could maybe try to start solving? Yes, yes. Okay. I think for the first question, we've learned it at school. Okay. So if you've learned the first one, take a look. Okay, let's take a look at d. Did you learn this in school? Not yet right? Okay, so what if I do this then you understand it right? Or or not. Yes, okay, I understand it. All right, so try it that way. Age. 23. Seven point wait. Up here for. And then eleven right so so we've got three x minus five is equal to 28Yeah. Yes, so three x is equal to 23. Sorry, big pardon, 33. Yes. Okay. So in this context in this context, what we're looking at is saying. Three x minus five divided by two must be greater than 40. Okay, so three x minus phi must be greater than 28. So three x must be greater than 33 and x must be greater than eleven. Okay, okay, okay. Right now question two is talking about number lines. Okay, so if we had so let's just do a very basic demonstration. If you haa number line zero, one, two, three, four, five, six, seven, eight, nine, okay, and then it doesn't look very good, sorry, it's a bit squashed, right? But then we've got down here, we've got minus one. Yeah, minus two, okay, it's a bit of a squashed up, not very well drawn number line, right? But you get the idea. In fact, let's just okay, let's just right, let's just put a space into it, right? Okay, okay, so just imagine this is a number line, right? Let's put an actual line on it. Boom. Yes, yes. Okay. In terms of representation, okay, because this second question says represent the solution on a number line. This this is the solution for part one x is greater than eleven. This is what it looks like as a solution on a number line, a circle above eleven. And an arrow pointing this way. Have you seen that before? No. Okay, this means numbers this way. Obviously bigger than eleven, bigger than eleven. Okay. Yeah and this is the marker at eleven. Yeah. So it's saying, okay, so not not this way basically Yeah or rather I should say not not this way. Yeah. Okay. And then Additionally Additionally, just so you know, right, this would be for these two. Crocodiles, I don't know if you call them crocodiles, I still call them crocodiles, right? Yeah and this. Is a different marker you use, which is for these two. Can you kind of tell why? It means it's either equal or it's either it's either equal or bigger or big equal and or smaller. Yeah, right. So basically this is saying eleven is not allowed. Yeah. Okay. Yeah and then so if we did this, then we're saying it is allowed like that. Okay, Yeah, okay, so now let's try now let's try and solve this then. Let's think. I think it is. Is lower than four is it okay? So so Yeah we would solve it like this minus five x Yeah is greater than -20. Yeah, okay, now something. So normally it would be that, right? Yeah. But there's a funny thing that happens when it's I don't really have time to explain it very, very well, but when there are negatives involved and we divide, actually you have to reverse the sign. Right, that's -20. Let's see why actually this is. X is less than four not x is more than four because if if x is right, Yeah I said. Okay I said x is because just imagine right if x is five right then because I think Yeah I said x is lower than four Oh you did say x is low for I beg upon okay, Yeah. Okay. All right so on the number line that would be this right? Yeah and then what do I need arrow pointing this way, this way. Yeah. Yeah. Okay, very nice. Look, I have to go to my next lesson. It's been an absolute pleasure. Vivian. I don't know if we have any more lessons or not because of your half term, but I think you've been doing some really, really good work and you've been really excellent at finding all the solutions. So congratulations and maybe see you at a future time. Okay. Bye. Okay. Thank you. Bye. What?