We'll do you at the moment I'm in me too, rainy gray London. Whereabouts in London are you battersy? Oh, nice. Very nice. We were in batsy just yesterday buying a cake. I don't know if you've ever been to the the two love bake house and Battersea. It's just near, it's like underneath the railway arches. Oh no, we do very good gluten free cake. It's a recommendation, if ever you fancy it, a gluten free cake. The two house bake house. To love bake house in batsy. Well, I'm quite close. I'm over in in Richmond, you know, it's just like a little, a little further southwest. All right, well, let's get to it. So but you've got you're eleven years old now and you're at for a sandal manner, okay. And your application, school application, so you've been out of there. See the throat ants and growso? Good. So you've got an offer for rugby and you're preparing for their own. Okay, great. Okay, nice. All right, well, we may as well talk a little bit about maths. Are there any topics in maths that you feel you could benefit from help on? Are there any that spring into mind now? That's absolutely fun. I don't know. Yeah. Well, why don't in that case, I think because it would just be really useful for me to do a little, maybe an eleven plus test, and we can just gauge which areas need work, if there are any, and maybe there won't be any, and we can push right onto some 13 plus stuff, some slightly more challenging stuff. So let's get up one of these papers. I'm going to say, let's do something relatively challenging. Why don't we go for a dollar? Eleven plus first. And. Will work Yeah okay Yeah it is a it's a relatively tricky pay for this and we'll see how much of it you can do so I got a feeling calculate Yeah non calculates paper now how we we won't what I'm going to suggest just for the for the benefit of us using the time most effectively questions like these I'm going to assume that you can do those that just kind of facing you might need some paper Yeah. Well, I'm I'm going to say I'm going to trust that you can do those. And I'm going to say, let's skip on to question three. 6.48 divided by six. How would you do that? If you want to use paper, use paper if you want to draw on the screen. So 65 by six is one and 48 diviby six is eight. So thatbe 1.08. Perfect. Very, very nicely. We're know going, though this is just a way of me keeping track of how many Marks was going oring. So writing down the missing terms in each of the sequences below. So itbe 39, 15, 21, 27, 33 very, very good indeed. No problems there. And. Okay, b will be three, two, 16, eight, four, two, one. Very nice and see. This one. Okay. Es sounds quite hard. Two. I don't think I know. Okay, well maybe if we just track what's happening so what what's going on here? What are we how do how are we getting from eleven to 32 plus 32? How are we getting from this to 116-16? Okay I get it now. So plus eight minus four plus okay there's eight minus four plus two minus sorry 122 and 121. Lovely. Very, very nicely done and family view. 12 6:24. Times two times three times four times by that will be 126 is some hundred and 20 times seven is嗯。5:40. 5000, Yeah, it means he might be right. So seven, 700 times seven is 490. Sorry, 700 times seven is 4920 times seven is eight. Say absolutely right. 5000 and perfect. Very, very. And six circle the factors of 90. So it will be nine, eleven or 99. Sorry, any others? Wait, wait. 中。Three. Oh, I didn't see. I just looked at the first six. 33. Yeah, that's that's three. So Yeah, very, very nice. And it's quite. Are you familiar with the sort of prime factorization technique? You know if you have 99 like this, splilike three, three. Yeah, exactly. 33. Yeah. And so all of the combinations of these prime factors are factors of 99. Three is a factor three times. Three is a factor. Three times eleven is also a factor. Good. And obviously three times eleven times three is the number itself. Good. I'm going to assume that you can do all of this. I'm getting a sense quickly that you're actually quite good at matths Leo. So eight in a survey of children it survey a group of children sorry, what asked how many films they had seen last week, no one in the group had seen more than four films. And the results are shown in the pie chart below. Work out the percentage of children who had seen exactly three films. Okay, so the whole thing is 260 divide by four and 90 and divide by two is 45. That means divided by eight. So thatbe and and 100 divided by eight is what's that? 12.5%, 12.5% is absolutely correct. Fantastic stuff, Leo. Work at the fraction of children that had seen no felgiving your answer in lowest. Oh sorry, I sorry. Let let me see cloyeah sorry, do you want to big a? Yeah, we can drag it. He. In 45 plus 5:19 90 plus like 90, plus 30, plus 120. And the line in the middle I think is like the half line. So so therebe 180-30-45 will be 100 and well, so 135-100 and -30 will be 105. Therebe 105 degree 100. So let's say 30 is like a portion and it's like, Oh, three, there's twelve of them. So 40 plus 40 equals 90 and plus that will be three portions. I'm adding the one and the four, that will be four portions. So that will be so the one and then plus two. Two have 135, which is. 135 is 120. Four, five, 8.5 and so the rest will be zero, one, which will be 3.5%. So if it's if it's like three, five, twelve, that won't work because I decimal so you can ponabout two that will be seven over 24 work very, very good. Seven over 20, that is what they want. A fraction in its lowest accident. And they say nine of the children who were surveyed had seen exactly one film, and another nine had seen exactly four films. And they would need to complete the table. Now tell me if it's too small, it's just so that we can see the pie chart and the question, there's fine time. Time. Okay. Take to show the number in zero to. The school. Okay, that's. If 13 is 45 and it's nine, so thatbe 45 diviby nine is. Five. So if a person works like that, I'm on a movie theyadd like five degree. So 30, divide by five will be six. So two will be six. Very, very nice. Absolutely right. It will be fixed. Zero will be 20 plus one, 21 and and two is. Oh. 20. Four plus 3:27. Very very nicely done in the 27. Yes. And waswith the cake, I think I put it in the bin. So. Calculate 0.35 plus four fifths, plus 37 over 100. Very, very good though. Yeah, but I'm not like basically exchange the decimal to the fraction. So thatbe 35 over 100 plus if you make the five also, so 100 you have to go five times 20 thatbe 100 over four times 20 will be 80, plus 37 over 100. So that will be. 115 over hundred plus 37 over hundred, which is. Let me think. 152 is indeed 152 over 100 and that will be one and 50 200 and that will be 5026 over 50. That will be 13 over 25. That be one and 13 over 25. Be good. And just just have a look at the question what in terms of what they want your answer left as? So I think you've set it up perfectly actually to do this part here, leaving your answer as a. Oh deciso, what would your answer therefore be? So that be, and if I don't, and if I don't like, do all the simplifying, that be one and 52 over 100. So that will be 1.52. Very good. It's 1.52. Absolutely right. Another three Marks. Briliant, I'm writing 21 over 70 as a decimal. Okay. But this is. Okay. So I mean, Yeah. So this thing. Chat part. New. I think I know. Oh, fantastic. Ce me? There. I don't know. Okay, well you know some some we can we can practice different versions of this this question I think is relatively easy. It's only two Marks. So if we just try to simplify 21 over 70I mean what would 21 over 70 simplify to? Oh, thatbe three with ten Yep, three over ten is a decimal. There's also 30 of 100 so I'll 0.3, 0.3, exactly. So sometimes that's what you can do if you're ever in a trickiest situation where you find that you can't simplify. So if you have something like, I don't know, five over eleven and they ask you for that, maybe as a decimal to three decimal places, let's say, remember, you can always just think of fractions as divisions. If you think about the division sign, I mean, it's a fraction, right? There's a line, there's a middle line, there's a thing on the top and the thing on the bottom. And that's not a coincidence. They are the same thing. Five over eleven means five divided by eleven. So if you think of it that way, you can just go, okay, well, let's do it that. Let's do five divided by eleven. Give ourselves a couple of zeros to play with and I'm going to go, okay. So there are zero elth and five remainder five. There are 4:11s and 50 remainder six because eleven times four is 44. There are 5:11s in 60 remainder five because that's 55. And we can see that we're now caught in a loop where it's going to go four, five, four, five, on and on, no on forever and ever. So we can write that like that and we can do it that way. So that's actually a really nice way of if ever you're stuck, of converting from pertures to Decis. Yeah. So but good. Let's go to question ten. Simon and Fiona are sharing a cupboard. If Simon's things take up two thths of the space and Fiona's things take up two sevenths of the space, well, fraction of the cupboard is empty. Okay so we'll be empty. So now just like add them together. Nice. But five times seven equals 30 52 times five is ten and seven times two is 14. That will be 24. So that will be 24 over 35 and 24 over 35 that be six. I'm eleven over 35. Very, very nice. Eleven over 35. The remainder of fantastic work. Three Marks. Great. And eleven rounding 16 hundred and 19 to the nearest ten, I'll be 1620. It was indeed in 2017 to the nearest hundred. Thatbe 2000. Yeah, fantastic. So a little bit of plotting here. Question twelve, we've got A, B, C and d are four points in a grid. A is at 51, b is at 11, c is at 13. D is at five, four. They want you to plot these points and then state what kind of quadrilathas been formed. Okay? So it gave me a and b will be one, one, which is, wait, let me all way, the itbe about here. No, I, A, check. Behere and c 13 here d 545 no here no here, no here Oh my Yeah about there and Yeah I think that's it now if I. Will be itbe about like that. Yeah, I know it's good enough. It's. Kind of a quadrilateral is though what type of. Irregular qurilateral. I know that's like I like that. I don't think that's the thing. Well, I mean, it is a thing for some reason. There are loads of different types of quadrilatals and maths that you have to learn. And then like once you get Yeah and then once you get beyond four sides, everybody loses interest. Like I don't know how many different types of Pentagon there are a five sided shape or a six sided shape. So you know once you get above four, there are just sort of regular and irregular. But with if we just go over all of the different types of quadrilatch, or can you can you name, you just named kites, which is fantastic. So we've got a square rectangle. Those are the obvious ones. We've got kite, which is sort of like two isosceles triangles, like one above the other type thing looks like a kite. Unsurprisingly, I'll say there is Rubus rumbus. What's a Rubus? It's like this. It basically looks like. It does it does kind of look like that. Yeah, if we're being really, really pedantic, I mean, what's the definition of a Ronbus? It's like. It's like. I don't know. A diagonal square or like a it's a diagonal square that's I love that definition. Yeah, I agree. It is like a diagonal square. So really importantly, all of the sides have to be the same length. It's a kind of puover square. I don't know if mine are actually, I don't look quite equal but some something kind of I think that was rubbish actually that's something like that where all of the sides are the same length. Good. And actually, with the rumbuses that we tried and failed to draw, what would we call these shapes here? The one that you've drawn is a good example of it. The one that I've drawn is a pretty good example of it because those lengths are not definitely not all equal. Two of the pairs are slightly longer than the other. Sorry, one pair of sides are slightly longer than the other pair of sides. What would we call that shape? Shape? I mean, the shapes that we've drawn that are not quite rases begins with A P. I know it. It's like it's a. Okay, I know it's sure. I always like getting my with the Rubus and the people. So. Parparallelogram, absolutely right. So what was your definition of what's the difference between a parallelogram and a rombus? Like one of those have from different backlines. The others like Yeah, exactly. A parallelogram is like A, I don't know, it's like a diagonal square and then a Rubus like a diagonal rectangle rectangle. That's a really, really nice way of thinking about it. Absolutely right. They are both similar in that they have two pairs of parallel lines. So the the shape that we have here is the final remaining one that you generally need to learn, which is something that looks like I mean, most typically it's drawn to look something like this. Wait side and that have like an don't know trapezium trapezium. So what's your definition of a trapesium? What makes the trapezium a trapezium? So theybe like. It's like a social triangle, but actually not really. So it's a triangle and it's like head got cut off. Yeah, kind of yes, I like that definition a lot. Another way of thinking about it, if parallelograms have two pairs of parallel sides, wrong. Buses do as well, especially rectangles and squares do as well. But if we just clathese two together, parallelograms and trapezians, for the sake of understanding the differences, parallelograms have two pairs of parallel sides, trapezioms have one pair. And it's as simple as that. The trapezium is just a four sided shape with one pair, the parallel side. So that's why you can, you can get trapezium that look really weird. Like I could draw a trapezium that looks, let me try and do this better. You know this here technically, is it trapezia? Even though it's not it's it's not what we used to say. Yeah. That is that a trapezium? Well, you have to ask yourself, where are the parallel side? So here, even though it doesn't really look like it, those two lines are going at the same angle, this line here and this line here. And as long as there's one pair that makes a trapezia, Oh, okay, okay, let me draw another one. So this one, I'll don't make it like this. Yes, exactly. Like pretty much Yeah, pretty much like if you if you're saying that these this line, I mean, that's the old triangle, that's all triangle. That's my triangle. It's not a triangle. Yeah, if if that top line was kind of really like maybe wejust move it slightly like that and this one like that, then you've got Yeah, for sure tripiece. So Yeah, just the one pair of parallel lines. That's what makes the tripesium, and that's why this is a tripesium. It's spun on its you look like this, but we can see these two lines are parallel yet. So that's all you're looking out for though. It's quite a simple definition, actually a really helpful one. They say, see the side length of each small square in the grid is 1 cm. Work out the area of quadrilateral abcd. So you can just work out that you can count it actually. So the bottom two times four will be eight. And the top one put the small bit to the you put the smallest bit to the biggest bit, that will be one. And you put the small bit and the big bit together, that will be another one. So that will be eight plus two is ten. Very, very nice and absolutely right. Not the way you did that. As you venture towards 13 plus, you're gonna to be given questions which I'll ask you. The area of tripeziums without a grid. And there's actually a form I don't know if you've come across if you come across a trapezium area formula before, I'm not really sure. I think I've like heard it. It's a useful one to have up your sleeve. So I'll just give you an example here. If we say that this is 12 cm at the bottom, maybe this is 2 cm. Let's say the height of this tripesium is. What is that? I don't know. 15. The area of a trapesian formula. Which you could have applied to this question, if you want to, is a plus b, where a and b are the parallel sites. So in this case, a and b doesn't matter which is a and which is b, but they're these guys here exactly over two. Times height, so absolutely right 14 over two. Times 15. And that's going to give you. Seven times 15. I get it, I get it, I get it. So basically I know how this works now it was like a for speed diviby two is like an average of those so that be like one side of the rectangle and the other one will be the height because like it's one of them. Yeah that's a really clever way of thinking about it, Leo. Absolutely. You've gone you've gone deeper than most people go. Absolutely right. And you can see that this, it works here the way you did it was perfect. But if we did it this way, we've got 32 and we can see that the heights, it's the kind of perpendicular height. So I'm gonna to call that the heights because it's sort of you know it's the perpendicular distance, the parallel sides, that's a height of four and Yeah two plus three, five divided by 22.52 point five times four tech we get exactly the same I have a question so it's like a the Thesium looks like about like no sorry let me do another one what do another one quickly your time you can it's a bit weird to get it takes a while to get used so you can you have to sort of drag and then delete if you can you see the like select tool Yeah okay Yeah I see this one and then you just Press back space what if this thing is about like. How do you work on with particular hias this like. Yeah so for a starter you want to know what your parallel sides are. So with this one here I would I'm struggling actually to see which the parallel sides are but let's let's make to parallel. Let's say let's just drag that up there and this here so that we we do have a pair of parallel sides there and there. So the height is the perpendicular distance between those two parallel sides. So the height in this case is going to be like that kind of going at a slight angle because we want there to be a nice 90 degree angle there. Between the parallel sides. But like I have another like another question like the height from here and the height of the usual just like different. Well, it is different. It's going at a different angle. But if you think about it in terms, I mean that it's different here as well in that it's going sideways, which is a weird way to think about height. But of course, if we flipped it round eleven, yes. It would be the the vertical height and the numbers would remain the same. So what the really important thing is is not the the way the height is going or the angle that it's going, but it's that there's a 90 degree angle between the height and the perpendicular lines. Can you see that? Nice 90 degree angle there. Got a nice, actually, the line ujeris better than mine. Really nice 90 degree angle there. But like I have the question, so go for it. Let's say, the ones, the shape I draw is like the one off the the power allel line is like let me think, Oh, say about 36. So therebe three, six and then pipe from like here to here and satisyet, let me say let slihow like eight. And but if I like closely measure from like this line, I've just stored one across that line. If I calculated it, that will be like 8.3 or something. So I calculated it, that will be three plus six. I'll be nine divitwo, 4.5. And 4.5 times eight is four, and that be 36. But if I use the 4.5 times, like what did I say? 8.3? I can't remember. That would be like bigger than 36. Yeah. So the question is what I'm slightly lost as to what the question is though. I just want to say that like if I like these three labs, I've drathey're like different length because let's like this, this, like of this line, and for example, this is like diagonal, and this one will be different, obviously different to this one. Yes, you're right, but those lines are not parallel. And if they are parallel, if we have two lines which are exactly parallel, I'm just gonna to copy and paste that. Now these distances are equal. That distance there is exactly the same as this distance though. Why is that the case? Because you know, even though you've got one going up, the others is going up in exactly the same by exactly the same rates. So it wouldn't matter where you put the line, it's always going to be the same length if the lines are parallel. If they're not parallel, they're not going to be the same length. A question. Sorry. All right, good. Let's go on to question 13. A little bit of transformations here. Rothe angle through 180 about the. Something like this before yes, in school had like this, we use the trading paper. Like you put the trading paper on there and then you like go the shape and then put pencil onto the door and then like spin it. Okay. Well, look, I think the rules have changed this because when I was at school you weren't allowed. That was like cheating. Do it that way. But I think you're allowed to bring tracing paper into exam stars. That, right? Were you allowed to bring tracing paper? I don't know because like I never tried. Okay, well, I'll tell you what. Here's here's how you do it. If you weren't allowed to trace a paper, and we might do a class on this because it does can take a little longer than sort of five minutes to learn. If you imagine if let's just ignore the question for a second like this. No, like there. Let me select and delete it. Yeah. I mean, that's that is one of the corners. So going to have a go at crack at it. If you think you know how to do it, just go ahead. Okay. Dear, I was. Okay, about. Yeah, Yeah, lovely. Very, very nice indeed. Absolutely perfect. Just whilst we're on the topic, what about if they said instead of 180 degrees, which you did absolutely brilliantly, let's pretend that the question asked you to rotate the triangle 90 degrees anclockwise to know how you would do that without using the tracing paper. Without the tracing paper. You just have to like basically look like this. Thatbe. Like. Like Yeah, Yeah, very nicely done. Very good. Absolutely brilliant. You're one of the rare few that can do those sorts of questions in your head. Very impressive, Leo, Yeah, Yeah. No, you've got it. You've got it. That's fantastic. All right, working out the perimeter of this shape here. Okay. You can just like add them together. But the hardest one I think is the one that's not labeled, which is like like here, this one, Yeah if I can work that out, I would be like pretty simple, just like that. And this one, like actually this one's not really hard. You guys just go like eleven minus three minus six, so be two. So that one will be two. Yeah. No, that one. Okay, I so you just have to go 17 minus seven. So therebe the length of right here about, but I'll be 1010 and 40Minten. So you can work out that this bit, which is this bit as. Now if you worked it out for pretty simple eleven plus, like eleven plus 17, 28 and 28 plus 14 is. 4242 plus three, 4545 plus four, 4949 plus six and 5555 plus seven, 6262 plus two will be 6464. Very, very nicely done. Brilliant. Okay, Yeah, go on. So I'm holding. Here you just have to like. Wait, basically get rid of this bit so that if you get rid of that bit, the perimeter will be the same as. This one, I think like it will be like this wherethis one goes up and this one goes like, right. So that will be eleven plus 17 will be 28, 28 times, two will be 40, that will be 56. And now you just have to get the cut off bit, which is. Which is four times like four times two I'll be 88 plus two will be eleven so I'll be Yeah I don't think that work but like I think I know what you're Yeah so that be six so that be six plus eight therebe 14 and 14 plus. 14 plus 56 will be 60. Wait, so Yeah, I think wait, let me just calculquickly calculate 56. My brain is like not really working. 56 plus six plus some 8:14 star that will be 70. Yeah. Yeah, so I think we've slightly overshot. I think I know exactly what you're talking about, which is really good. You know we can say in a way we don't even need to work out the two do because we know that that length and that length and that length all add up to eleven. They have to so we can just sort of go eleven times two. It's 22. And likewise, we know that eleven times 22 is not 22, sorry, eleven times two. And likewise, we know that. The reason why I get slightly complicated is we know that this length and this length is also 17. So 17. I think this is what you are driving at correctly if I'm wrong. Yes, we just have to account for these little guys here, which every 56 and then you do my like the 17 minus seven we're ten and 14 minus ten because four. So there's these two equals four. Theybe plus 8:50 she six was able to 64. Yeah that's what I was trying to say. Like not saying like working now. Well, obviously somehow I didn't get it because I think I might get one wrong. Yeah, Yeah, Yeah, Yeah, Yeah, no. But it's a really good understanding of the question. Really, really good because sometimes you can be given like not enough information. And it relies on that understanding that all of those vertical sides equal the other vertical side. Good, let's go on to 15 as if we can do a bit of this before the end of the class. The example below shows a quick way to work out the difference between two square numbers. So it's a 19 squared -16 squared is the same thing as 19 plus 16 times 19-16, which is equal to 35 times three which is equal to 105 and then they want you to kind of experiment with that idea. So using the same method without a calculator, work out 17 squared -13 squared. So okay, that would be 17-13 times. So 17 plus 13 yeso that will be like four times. Four times 30 therebe 120, very good. But let me like actually use a calculator to work that. Where's my calculator? Yeah, so. Wait, wait, I just did the wrong thing. Yeah, that's 120. That's right. Let me let me try the top one. I'll be 105, four. Whoever said that this methwas so smart. Well, I mean, have you come across I agree, actually, it's very clever. Have you come across double brackets before? Like would you know how to expand? Yeah, Yeah, Yeah. This you know how to do that. Okay. So I mean, let's just take an example. Oh, wait a minute. I'm pretty sure he did, Diane. Then we tried to work it out, but like I'm not really cool, something like x plus three times x plus one. If you were asked to expand out those brackets, Bruce, x squared plus x times three, x plus three, plus three, x plus three. Absolutely right. And that would simplify, we can simplify the middle to x squared plus. One x plus three x, you give us four x, so four x in the middle and that's it. So if we think of that, that's how to do foil. You did it brilliantly. It's kind of multiplications like this expanding out. So if we think about why, why does this work? Like is it was it just fluke that this person came up with this idea? No, actually, it wasn't. If we think about it in terms of this, we're gonna to write this down in kind of a weird way. So we're going to do we're going to expand the brackets, but rather than working out what the numbers are, I'm just going to say 19 times 19 as 19 squared. I'm going to say 19 times -16. It's going to be -19 times 16. Maybe what I'll put them in little brackets like that. Then I've got 16 times 19. So that's plus 16 times 19. Then finally, I've got 16 times -16, which is -16 squared. Just move this over. And you can see now that this bit in the middle, we've got a -19 times 16 and we've got a plus 16 times 19. So these are the same numbers and they just cancel each other out. And what are we left with? We're left with 19 squared -16 squared and that's why it was the one who didn't still quite it's still still quite smart. Absolutely. She would do Yeah let's do b and then I think we're probably going to call it call it a day. Do I go on be now? Yeah okay. So. Answering a calculate 888-112. 晏。I'll be 776. And hundred and 88 plus 112. I think that should be like I don't know, a thousand. You've 776 times a thousand. No, no. Is 776000 brilliant and that's how it is done. Really, really good, Leo. Okay, so this is giving me a really, really good sense of your level. I think we're gonna be able to plow on and actually have a look at some of the more challenging areas of 13 plus is what I would suggest. I think your fundamentals are really secure. There's no point in us endlessly going over eleven plus stuff. So I think we're going to we're going to depart from eleven plus and have a look at 13 plus soon if you decide to continue lessons. But if you don't, that's fine also. And it was a pleasure to have met you. And I hope the sun shines on Battersea this afternoon. I mean, Yeah, there is like sunshine, Oh, not really sunshines, but poking through the clouds. All right, Leo, take care of yourself. Bye. Take care.