[John:] Okay... now if I write something down... [whispering] []...
[Kelly:] write an essay about
[John:] when you, when you pass not if
[Kelly:] Yeah.
[John:] When you pass. Erm right I'll just write this down.... Okay if you'd like to try that. Add that up.... six point eight plus nought point O two.... Good yeah that's great.... Right that's brilliant I think you can both do decimals. yeah that's very good I mean a lot of
[Kelly:] We done them in second year.
[John:] a lot of sixteen year olds are still having trouble with decimals like that and they're adding them in the wrong place. What is the most important point when you're adding decimals?
[Kelly:] Keep the decimal in a line.
[Claire:] Keep the decimal in a line.
[John:] That's it line that up and you can't go wrong. Right who wants to tell me what a pie chart is?
[Claire:] It's a chart in the shape of a circle.
[John:] In the shape of a circle. And why do we bother doing one?...
[Kelly:] So... it... [whispering] []... it can show you things how m many one piece and
[John:] Okay have you got anything to add to that?
[Claire:] It's like fractions, it's like
[John:] Right yes it's like fractions it can show you things and it can show you it as a sort of fraction. Erm on your computer okay. What sort of things have you seen pie charts used for?
[Claire:] In my maths in school we just finished them on the last day. We erm had a
[John:] Right.
[Claire:] but it just shows it erm twelve hours of a baby's life. And we had a round pie chart and it was split into all different hours.
[John:] Okay. So was it split into twelve sections for the twelve hours?
[Claire:] No it was just the round circle and that was twelv
[John:] That was, that was twelve hours and and how was that
[Claire:] Yeah we put twenty four hours and then coloured in half
[John:] Okay so you had twenty four hours all the way round Right okay erm what other things could you use a pie chart for?
[Kelly:] In geography we had one because erm there was a farmer and what he does and there's like a big section for sleeping, a smaller s section for eating
[John:] Okay.
[Kelly:] and the cleaning the pigs and stuff like that.
[John:] Right so you can use it for almost anything to show but it, it's showing it as a fraction of the whole thing. So it might be a fraction of a day a fraction of twelve hours a fraction of one hour. Erm a fraction of money is another... thing they use it for. Erm how much pocket money do you get, about three hundred and sixty each?
[Claire:] [LAUGHTER] one pound
[Kelly:] I don't really get pocket money but if I see something in the shops in, in, this toy or something my mum, mum'll buy it for me and say that's your pocket money for this week.
[John:] Okay so let's say if you got three pound sixty a week pocket money. Why do I pick three pound sixty or three hundred and sixty pennies?... Any ideas?
[Kelly:] Cos three hundred and sixty is a full turn.
[John:] Right three hundred and sixty degrees. So if we drew a pie chart how many degrees would be the same as one penny?
[Kelly:] One.
[John:] Are you happy with that?... Do you know, do you know about three hundred and sixty degrees goes all the way round? Ah okay when we do pie charts we're measuring angles aren't we? You, we're doing fractions if you like so you could draw a half and that would be a half of three hundred and sixty. Half of all the way round so how many would that be?...
[Claire:] Erm
[John:] What's half of three sixty?...
[Claire:] One pound eighty.
[John:] Right and it'd be a hundred and eighty degrees all the way round and that would represent one pound eighty if three hun three pound sixty was all the way round. And what about a quarter of the way round, what would that be?... Do you know how to divide three sixty by four?... Quite a big number could you divide thirty six by four?... How many fours in thirty six?... Okay? Could you have done, could you do half of thirty six?...
[Claire:] Mm....
[John:] Okay what would half of thirty six be?
[Claire:] Eighteen.
[John:] And then what would half of eighteen be?
[Claire:] It's er eight is it
[Kelly:] Nine.
[Claire:] Nine.
[John:] Nine so we're looking at three hundred and sixty.... Trying to divide it by four. Well that's a bit awkward so pretend it's thirty six times ten. Leave the ten alone we'll bring that back in later. Half of thirty six would be eighteen. So half of three sixty could be eighteen times ten. Half of eighteen is nine so half of one eighty would be nine times ten so ninety degrees is a quarter of a turn a quarter of the way round. And er look at, look at these again
[Claire:] In school we didn't really do the actual pie charts but we used compasses.
[John:] Yeah.
[Kelly:] To measure angles.
[Claire:] We had all different kinds of
[John:] One of these to make an angle?
[Kelly:] Yeah.
[John:] Yeah that's a protractor.
[Kelly:] Protractor that's it.
[John:] Protrac have you seen one of those, have you used one?
[Kelly:] Yeah.
[Claire:] Yeah.
[John:] Right that's for measuring angles so we could measure these angles before we s before we start on the money
[Kelly:] Yeah.
[John:] where it all goes to. Perhaps we could just have a look at what sort of angles we've got here. So let's say... that that represented your, your three pound sixty, the complete circle. And you spent quite a bit of it, that, say on sweets.... Okay so you could draw that and you'd draw the same angle and we could measure that angle... see what it is. Well what fraction is that?
[Kelly:] A third.
[Claire:] Third.
[John:] So what angle, anyone, Claire have a guess at what angle that will be or how would wor how would you work out what angle that is?... How did we work out what a half was?
[Claire:] It's erm divide thirty six by three and then
[John:] Right so we divide thirty six by three and what does that come to?
[Claire:] Tw
[Kelly:] Twel
[Claire:] twelve.
[John:] Twelve. So three hundred
[Claire:] And you times that by ten.
[John:] So that would be?
[Kelly:] One hundred and twenty.
[Claire:] One hundred and twenty.
[John:] So a third of this should be a hundred and twenty and we just measure that and see. Yes it does come to a hundred and twenty well that's good. I'd be looking a bit daft if it didn't. A quarter should be ninety. Well that's the angle on the
[Kelly:] Ninety.
[John:] square or a rectangle isn't it that's ninety degrees no need to check that really we can see that's ninety. It's ninety. What about this one? What fraction is that?
[Kelly:] A sixth.
[Claire:] Sixth.
[John:] And what angle will it be?... How will we work out the angle?
[Kelly:] Sixty?
[Claire:] Sixty yeah
[John:] Right good sixty. How did you do it?
[Kelly:] Divide thirty six by six is six and times it by ten.
[John:] Right so that's sixty and what's this fraction?
[Kelly:] A twelfth.
[Claire:] Twelfth.
[John:] And what will that be?
[Kelly:] Mm a twelfth.
[John:] What, what, what angle will it be?
[Claire:] A twelfth....
[John:] So how many twelves in thirty six?
[Claire:] Three.
[Kelly:] Three.
[John:] So that's going to be three times ten that'll be?
[Claire:] Thirty.
[Kelly:] Thirty.
[John:] Thirty degrees. We'll just check that see if it's right. Yeah that's fine. Okay you have to get the point just on
[Claire:] Yeah.
[John:] the hole there. Measure that and have a look and it comes just on the thirty.
[Claire:] Yeah.
[John:] Okay. So we could do thirds, sixth, quarter, twelfth, we could do a half. What would a half be again? What angle would a half be?... Half of three sixty.
[Kelly:] One eighty.
[John:] Okay one eighty. Right so let's decide how we're going to spend, what I'd like you to do, erm what sort of things do you spend your pocket money on?
[Claire:] Sweets.
[John:] Sweets. Is that what you spend most of it on probably?
[Claire:] Yeah.
[Kelly:] Yeah.
[John:] Okay so sweets. What else do you spend your pocket money on?
[Claire:] Sometimes if I see little, a little or little toys for my brothers
[John:] So presents okay presents for other people. Anything else?... Anything else you spend your money on?
[Claire:] Save it up.
[John:] Save it okay so saving is some of it and anything else?...
[Kelly:] like little rubbers
[John:] Okay the rubbers.
[Kelly:] Stationery.
[John:] Stationery good word. How do you spell stationery? Can you both write that down.... When it means pens and pencils and papers and rubbers and... Okay now what have you got there?
[Claire:] I don't think that's right.
[John:] Why don't you think that's right? Mm, what do you think Kelly? Do you think that looks right?...
[Kelly:] No.
[John:] No.... Okay what do you think about Claire what do you think of... Kelly's does that look better?
[Claire:] Yeah.
[John:] Can you both spell station?... Okay that's station. [LAUGHTER] do you want to swap back []? You can both write station.... There are lots of words are built up from other words aren't they?... Station and now underneath that write stationery.... That's it. That's fine now that's how you spell stationary if something's not moving okay. The wheels were stationary. With an A.... It's not moving but when it's papers and pencils and stuff like that
[Claire:] Is it E?
[John:] Exactly yeah it's stationery with an E. So write that one and then later on when I've gone if you can make up some sentences with stationary and stationery. We both just say stationary so you can't tell by the sound of it how you spell it? If you could make up a sentence with those. So stationery is one of the things so we've got erm... what else might you spend money on?... Okay so I, what I'd like you to do now is both write down if you had three pound sixty a week, how much would you spend on sweets, on presents, on stationery and how much would save
[Kelly:] I'd save most of mine.
[John:] So both write down you'd save most of it. What half of it or more than half or?
[Kelly:] Half of it
[John:] Okay. Well write, write down how much you'd save and how much you'd spend on sweets, how much you'd spend on presents, how much on stationery....
[Kelly:] Spend... on sweets......
[John:] So how much would you spend on sweets?... One pound on sweets okay.
[Claire:] I spend sixty pence on sweets.
[John:] Sixty pence on sweets okay and say say what you're spending that on, on sweets okay. And what about presents and stationery? Both make your own mind up what you'd want to do.... And how much would you spend on presents?... Mm?... You wouldn't spend any. Okay that's fine you put presents none....
[Claire:] Does it have to be a exact amount
[John:] Just what you what you think you'd...
[Claire:] on presents
[Kelly:] presents
[John:] Okay.
[Kelly:] But if I'm up at the shop and I see a little card or something
[John:] Okay.
[Kelly:] About a pound....
[John:] Okay. And would you spend anything on stationery?...
[Kelly:] Yeah....
[John:] Okay and have you added yours up?... Just put total, good, that's good.... stationery right.... So if you'd like to add them up now see what you've got.... Is that one pound?
[Kelly:] Yeah.
[John:] Mm.
[Claire:] ...
[John:] So adds up very nicely to three sixty and Kelly spent more than she had. So you've got to, you'll have to change something won't you?
[Kelly:] Ninety pence
[John:] Okay ninety pence yeah that's a good one. So ninety, ninety pence on the, on the presents there.... change that one there. So... we'll draw a pie chart now which one shall we do first? Whose shall we do first?...
[Kelly:] Claire's
[John:] Okay we'll do Claire's first.... The first thing we need it as a circle.... Mark the centre of it go all the way round with that. Now... what fraction are you s are you going to save?
[Claire:] S save a half of it.
[John:] Yeah so it's a hundred and eighty degrees. A hundred and eighty out of three hundred and sixty you could save a half of it. Well that's no problem. Could you d would you like to draw... Would you like to draw half?... Okay.
[Claire:] Just write save?
[John:] Write save in there.... Now what's your next thing that you're going to do?
[Claire:] Sweets.
[John:] Sweets one pound so... one hundred out of three sixty. So that's a hundred degrees out of three hundred and sixty degrees. Now if you can mark off a hundred degrees. You know how to use the protractor?
[Claire:] Yeah.
[John:] Good.... Now where's, where's the hundred? Ah okay what we usually do is make sure it's not upside down. And on this one there's a nought on the inside and a nought on the outside so we work with the nought on the outside and we'll go round that way, clockwise, the way the numbers go.
[Claire:] Yeah.
[John:] Nought ten twenty thirty forty. Okay so we start from nought and go round. So where are we going to, where are you going to put it? Down here say. Do don't be afraid to turn your paper round. So make sure that dot... is on the centre there. Is it on the c let's have a look. Let's get that in there.... Okay and then you can move it round to line it, is that lined up okay?
[Claire:] Yeah
[John:] Where you are?
[Claire:] Yeah.
[John:] Okay and then on the outside... circle there we mark a hundred degrees.... Okay and join that one up.... And then
[Claire:] With this part this bit?
[John:] Ah well... have a guess. Can you remember how much ninety degrees is?... Ninety degrees is that nice square angle you found on a
[Kelly:] A right angle.
[John:] square or a rectangle. special name for it as Kelly says a right angle, right. So that must be the hundred and that must be the eighty. So... that's for sweets... and what's this for?... Good and you've both spelt it correctly stationery. Okay so that's Claire's... chart. That shows, so you can look at that and you can see how she's spending her money....
[Claire:] But it doesn't tell you. It just unless you've actually got a protractor.
[John:] Doesn't doesn't tell you how much
[Claire:] Much you spend.
[John:] No but it's still helpful like that cos you can see, well it looks as if, without measuring it accurately, it looks as if she spends half of it she actually saves half of it. Okay. so it looks as if she saves half of her money... and then spends a bit more than a quarter. Out of what's left a bit more than half of what's left goes on sweets and a bit less than half goes on stationery. So even if you didn't have a protractor, I mean if you wanted to be really fussy and find out exactly you could measure it and say, ooh that's actually, it's not eighty that's seventy nine and this is a hundred and one so she spends a pound and a penny on sweets and she saves seventy nine. You don't normally need to get it that accurately do you? You just want a quick glance at it to see what she, oh well half of it's saved and then a bit more than a quarter.
[Claire:] ... is it... probability
[John:] Yes.
[Claire:] guess yeah that's it.
[John:] Guess okay. A bit more than a quarter on sweets and a bit less than a quarter on stationery. And if you wanted to find out exactly you could measure it. Now somewhere on there we should say what the total is because we could look at this and we could say, well she saves erm half of it but does she, how much does she get? Well perhaps she only gets two pence a week pocket money and she saves one penny. Or perhaps she gets two hundred pounds a week pocket money right? Or two million pounds a week pocket money. We don't know so I think lea at least you need the total on. And I know it's not, not saying there's anything wrong with it, just hadn't got round to writing it.... So we could say total, total is three pound sixty or something like that.
[Claire:] Just write total.
[John:] Yeah total is three pound sixty.... Right so do you want to have a go at doing your one Kelly?
[Kelly:] Okay.......
[John:] And oh we'll ask your dad what sort of computer he's got....
[Kelly:] I save about a half of it.
[John:] Okay...
[speaker003:] Hi.
[John:] Hello Claire says she's been doing pie charts on your computer.
[speaker003:] Yes it's only a, it's a Amstrad.
[John:] Er what sort is it? I B M compatible?
[speaker003:] No it's not no. It's the original one which was er what was it called? Six One Two Eight Plus. It's, it's only got a three inch disk drive on it.
[John:] Ah it hasn't got three and a half it's the Amstrad three inch?
[speaker003:] Yeah.
[John:] Okay.
[speaker003:] Are you doing pie charts, what are you doing that on?
[John:] Right. Because I've got some stuff for I B M compatible that she could play with.
[speaker003:] I'm looking to upgrade it soon so
[John:] Mm.
[speaker003:] hopefully it'll be alright then
[John:] Don't I mean don't, don't buy it just for this it's just that if you had it handy
[speaker003:] Yeah.
[John:] it's a shame not to use it. But er
[speaker003:] I'm goin I'm gonna upgrade it for business you know. You can't get no software for the Amstrad it's really hard to come by.
[John:] It is, it is. There is some very cheap stuff about for things like the Fifteen Twelve and Sixteen Forty.
[speaker003:] Mm the P C Ws then?
[John:] Erm no the P C rather than the P C the P C W is just a, a dedicated word processor that's all it does. But very good sort of cheap way into computers.
[speaker003:] We couldn't load save it could we?
[John:] Okay well she's just working out how she'd spend three pound sixty pocket money
[speaker003:] Very easily I would think. [LAUGHTER]
[John:] No she's going to save half of it. Oh yes please er black no sugar
[speaker003:] before I
[John:] Right you're a bit stuck. So let's see how, how is it going. What, see what, see if Claire can help. Let's sh explain to Claire what you're doing and Right.
[Kelly:] I think I'm right but I'm not sure. Well that's the your nought isn't it?
[John:] Mhm.
[Kelly:] And then that was right.
[John:] Right good.
[Kelly:] And then I needed my ninety pence
[John:] Right.
[Kelly:] for my present so
[John:] Ah okay right.
[Kelly:] do I go from that nought or that nought?
[John:] Don't mark the nought on. Now this is, this is very, this is very good, this the reason you're stopping here because... have you done bearings? No you probably wouldn't have done but you'll do
[Claire:] Yeah I had a homework sheet.
[John:] Okay we'll have a look at bearings as well while we're doing the, see you can see how fractions, angles and pie charts and bearings and lots of things all come together and if you understand the main part of it then you can, you can learn all the other things by yourself. And when you see them you can think, ah that would be same as what I was doing in that one, and you can work it out for yourselves. So yeah don't, you don't need the nought there but it was good thinking you put it in, putting it in. Erm it's just ninety degrees from here or from there depends on where you want to put it. So you've got one mark there okay? Okay well you could take it from here and take it round that way. But it'd be simpler to keep taking it round clockwise. So
[Kelly:] So where should I it from?
[John:] Well if it was me to keep it balanced I usually put the bigger ones near the bottom or on one side so that the small bit are at the top and the big bits are at the bottom and artistically it looks a bit better balanced but it doesn't really matter for the maths where you put it.
[Kelly:] So shall I keep from there and just do the ninety there?
[John:] Well you can't do it from there because that would mean you're spending you've got one ninety pence here and you're spending ninety pence of it on one thing and sixty pence of the same money on another thing. So it would have to start from where the last one finished each time....
[Kelly:] ... to
[Claire:] to ninety
[Kelly:] ninety
[Claire:] to ninety
[John:] Ninety.
[Kelly:] ninety from there...
[John:] Okay and then if it all adds up... how much should you have left over?
[Kelly:] Thirty
[Claire:] ...
[Kelly:] Yeah.
[John:] Okay.... Well that was easy wasn't it eh? No problems there for either of you so let's make it awkward. Now you don't really get three pound sixty do you Claire? How much do you get?
[Claire:] A pound but I get
[John:] A pound so let's say you just get a pound. And let's say erm... let's say you get one pound fifty Kelly. I know you don't, don't have a definite pocket money well let's say you get one pound fifty. So... so we look at Claire's pound now. What I want you to do is try and work out if you spent the same, not the same amount of money but
[Claire:] The same sort of thing.
[John:] You spent the same
[Claire:] Erm...
[John:] same
[Claire:] Try and get the same fractions
[John:] Good the same fraction. So what was happening here you were saving half of it.... Right?
[Claire:] So I'd save fifty pence yeah.
[John:] So you'd save fifty pence. And then you'd have fifty hundredths and it's still look like a half. So if you kept these same ratios... same fractions... even if you got ten pound or a hundred pounds or ten pence it would still look like that. The only thing that would change would be the total at the top. Don't forget to put the total on it. Total... the total is
[speaker003:] Claire.
[John:] three pound sixty.
[Claire:] Yeah?
[John:] Are you stuck. Oh well you [LAUGHTER] do have to stay out there sorry []. Okay.
[speaker003:] No sugar.
[John:] That, that's great thanks very much.... So that's for total pocket money three hundred and sixty.. Got an have we got another mat? We'll take that mat out of the way... So what if you did get a pound, if you did get a pound... Claire would you, would you still save half of it or do you think you might save a bit less than half?
[Claire:] A bit less.
[John:] Okay I'd like you to, if, if you work out Kelly one pound fifty. If you, if you had one pound fifty how much you'd spend on these different things. Okay? And Claire if you work out if you had a pound how much you'd spend... on each different one just as you did here....
[Claire:] ...
[John:] I mean you might decide you won't save anything if you only got a pound or you won't buy any presents or you won't buy any sweets. Give up sweets for Lent or something....
[Kelly:] Make it easy for us.
[John:] Ah [LAUGHTER] go on.
[Kelly:] ...
[John:] Now can you see the way Claire's setting it out?... So that all her figures are going to be all in one column so you can check them easily, you can add them up easily, you can find the total. This is very nice the way you've written it out. You would save fifty pence and then Or you can just yeah you can just use the sort of line you can see through there. Erm... you could just, you don't need to write, it's very nice writing you don't need to write it all out now you could put spending and a colon... right and then, or I would spend colon
[Kelly:] Shall I just put a line?
[John:] Oh no no leave, leave that erm you could just write sweets and how much would, just keep the figures underneath each other cos it makes it easier to follow.
[Kelly:] Sweets....
[John:] Well there's a bit of changing and messing about here to get it just right innit? Right this time you'd save forty P.... Erm is that... presants?... presents.... Prese it's awkward this spelling but it's, it's presents.... Okay?... Now I'd like you to have a think about them as fractions.... Forty pence out of a pound what would that, roughly is it about half or about a quarter or what?...
[Claire:] About... nearly a half.
[John:] Right so it's a bit less than a half. And what about ten P out of a pound?... A tenth.... Right. Okay well that looks as if that adds up nicely.... Ooh lovely that's lined up.
[Kelly:] ...
[John:] That was strange starting to add up from the centre you don't usually do that.
[Kelly:] No.
[John:] Okay that's good that adds up now what sort of fraction, what sort of fraction are you spending on stationery?... Fifty pence out of one pound fifty is that about a tenth or about a hundredth or about half or what, what sort of fraction?
[Kelly:] A third.
[John:] Do you agree?
[Claire:] A half. Fifty pence
[John:] Fifty pence out of one fifty.
[Claire:] A third
[John:] Yeah you're both happy with a third.
[Claire:] Yeah
[John:] You were thinking fifty pence in a half of a pound. Right
[speaker003:] ...
[John:] I knew I had three fifty pence okay. So that's how much Kelly's got to spend. Three of those and she spends one of them she spends one of them on stationery and she saves one of them. So she's spending a third on stationery, she's saving a third and the other third has got to be split up between
[Kelly:] Sweets and presents.
[John:] presents. Erm thirty pence out of a hundred and fifty, any idea of what that would be fraction?
[Claire:] ... mm
[John:] What do you think?... Yeah it's a fifth. How did you work it out? If you're dealing with big numbers it's quite hard isn't it? Okay how do you, how would you do it?
[Kelly:] Five times three is fifteen times it by ten.
[John:] Right so the first thing you do if we're dealing with a hundred and fifty. Well that's a bit big that's not in any of my times tables. Let's forget about the
[Kelly:] Mm.
[John:] hundred and fifty forget about that nought and just think about the fifteen. When we've worked that out don't forget to put the ten back on multiplying by ten putting the nought on okay? So if I said three out of fifteen. Three shared out between fifteen people is one over five one fifth. Right so how would you like to have a go at drawing your pie chart? Mm?
[Kelly:] Okay.
[John:] Now what I want you to do is is to just, just talk about it erm okay fit it on there looks like a good idea. yeah it'll fit on nicely. Oh very good, good, watch that it's very easy to get it the wrong way round.... you just think how is she going to do it how would you do it if you were doing Kelly's one?... It's usually a good idea to do the biggest ones first... get those out of the way.
[Kelly:] The two fifties.
[John:] Right.
[Kelly:] Er two halfs two thirds.
[John:] Do a third for each of them.
[Kelly:] Two fifties....
[John:] Erm do this one in, do this one in pencil....
[Kelly:] In case I get it wrong?
[John:] In ca w you don't think she's going to get it wrong do you?... So you, do think she's going to get it wrong ooh? Do you think you're going to get it wrong? Go on have a go.
[Kelly:] I don't know.
[John:] It doesn't matter whether you get it right or wrong it doesn't come into it really.
[Kelly:] The two big ones.
[John:] Okay.... Okay... Right okay what's this, what's this hundred degrees for? What does it mean?...
[Kelly:] I've spent two fifties. I spent a hundred.
[John:] Aha.
[Kelly:] Oh I know what I didn't do.
[John:] Right what do you think about this then?
[Claire:] It's cos you've only got one fifty three pound sixty.
[John:] Right. If you'd had three pound sixty to spend then fifty would be fifty degrees. Yeah that would be right. Now when I said you were very good at it I said what's fifty as a fraction of one fifty?
[Claire:] A third.
[John:] A third so on here it's got to look like
[Kelly:] A third.
[John:] a third.... Okay.... Right it's got to look like a third. So how are you going to make it look like a third?...
[Kelly:] With your protractor.
[John:] Okay.
[Kelly:] Measure your protra measure
[John:] Okay you could measure a third. But you won't always have these... so you could measuring it's a good way. You could do it roughly but we want this accurately. How are we going to do it?
[Kelly:] Erm if you the circle with the
[John:] Right.
[Kelly:] then you could... mea see what the erm...
[John:] Go on.... Go on you've got the right idea don't be afraid to say it.
[Kelly:] Mm
[John:] Well try and explain it, you don't have to get the right words.
[Kelly:] circle
[John:] Okay.
[Kelly:] then you could... you could and then you could measure it and see if three of them
[John:] Right you could see, you could have a guess at it and see if three went round exactly.
[Kelly:] Yeah I was just I was just trying to do that
[John:] Okay that's a good guess or as you said Kelly you could just use your, your fraction here as and mark it off cos you know that's a third or you could measure the angle on the fraction and see what it comes to oh yes Go on. Right you could put that centre point there on that and you could draw them. But I but you wouldn't normally have that. They're all really good ways of doing it. But I'd like you to try and calculate it....
[Kelly:] ... Is that one third?
[John:] Did you try one fifty?... Good guess. What, what are you trying to do? How are you trying to calculate this?
[Kelly:] Well do one fifty
[John:] Mm.
[Kelly:] my fifty
[John:] Mm.
[Kelly:] and then my other fifty.
[John:] So you did three times fifty?
[Kelly:] Yeah.
[John:] Erm that doesn't that doesn't help much. Any ideas Claire how we can sort this out, how we can find out what is exactly one third of the way round this circle?... How far is it all the way round the circle?
[Claire:] Three hundred and sixty.
[John:] Three hundred and sixty degrees.
[Claire:] Half a
[John:] How many degrees would it be to go a third of the way round the circle?
[Claire:] One hundred and twenty.
[John:] Right okay. So although this is fifty pence when you show it on here the fir so the first thing we've got to do is change this fifty pence to get away from fifty pence or thirty pence or twenty and change it into a fraction. What fraction of one pound fifty is it?
[Kelly:] Er
[John:] A third.
[Kelly:] A third.
[John:] So as a fraction you can just write, this is if you just write, that's erm he over here you can put a heading fraction erm you can go back to your pen now.... Fraction of total. Right that's okay. Now would you like to do the same for yours, work out what fraction of a total yours are.... Okay and then underneath that you'll put your, your forty pence. An so on so fifty pence is fifty over one fifty isn't it? That's what fraction it is. Fifty out of one fifty. fifty over one fifty.... And have you done cancelling fractions?... No okay.
[Kelly:] Yeah I think
[John:] Well what does that come to?
[Kelly:] Three a third.
[John:] A third okay.
[Kelly:] So
[John:] Equals a third.... Erm here, I should have told you, here if you can put... fraction of circle.... erm let's see fraction of that's fraction of okay fraction of total and then here you can put circle. So fraction of a total is fifty over one fifty. And it's going to be a third of three sixty isn't it? A third times three sixty. Times is the same as of.
[Kelly:] For the thirty?
[John:] For the, for the fifty. Still working on this one.... Erm yeah see
[Kelly:] One third of
[John:] you're going to go one third of the way round. If you go all the way round you go three hundred sixty degrees.
[Kelly:] Sixty degrees.
[John:] Alright to go a third of the way round you'll go one third of and we know how to write of.
[Kelly:] Times.
[John:] That's it one third of three hundred and sixty.... and we can work out what that comes to.... And then you can do the same for all the others. Erm do you think it would be an idea if we made a sort of table out of this?...
[Kelly:] Yeah.
[John:] Yes so this i I mean this is what maths is, is about, you start doing something and then... [tape ends]... So how we going to lay this out?...
[Kelly:] In an actual table.
[John:] some columns.... Something like this say.... Okay. Probably got more columns than I need there. You could normally draw So let's have a look at erm... the previous one no we'll look at, we'll look at Kelly's here and if I do something like... save... so we put here total... is one pound fifty. How much are we going to save? How much are you saving?
[Kelly:] Fifty pence.
[John:] Fifty pence.... Fifty pence and sweets thirty pence...
[Kelly:] Presents.
[John:] Presents
[Kelly:] Twenty pence.
[John:] twenty pence.
[Kelly:] Stationery fifty pence.
[John:] Stationery good.... Stationery fifty
[Kelly:] Fif
[John:] pence well that's quite a bit.... Fifty P and there you have the total one fifty. Now fraction of total... fraction of total... So this is going to come to fifty over one fifty. This' ll be thirty
[Kelly:] Thirty.
[John:] over one fifty.
[Kelly:] Twenty over one fifty.
[John:] And?
[Kelly:] Fifty over one fifty.
[John:] Well we worked out that that comes to one third. Thirty over one. ooh that's a hard one this one comes to one third. So that's three fifteenths right?
[Kelly:] Yeah.
[John:] Thirty over one fifty will be the same as three over fifteen which comes to?
[Kelly:] Five.
[John:] One fifth.
[Kelly:] Fifth one fifth.
[John:] One over five one fifth. Are you happy with that one over five?
[Kelly:] Yeah.
[John:] One over five. And what will twenty out of one fifty be? Well we can divide the top by ten and the bottom by ten... and we'll get two fifteenths.
[Kelly:] Yes.
[John:] Can't do any more than that. So fraction of a circle... fraction of a circle this is going to be one third times three sixty or we could say number of degrees here, fraction of a circle as number of degrees. So that's a third of three sixty degrees and that's a third of three sixty okay?... Going to be a fifth of three sixty. And two fifteenths
[Kelly:] [whispering] Fifteenths... of three sixty [].
[John:] of three sixty.... Okay so let's see, okay things that I bought, right how much and now we need quite a bit sort of across there if we can, if we can get it. So er... if you make another one here you can put this as a fraction of the total. Right and then there as a fraction of the circle. And we'll put one down one down yes okay down there. Right so this' ll be a fraction of total... Okay...
[Claire:] Do you want me to write it?
[John:] Erm yeah if you can do one something like that. Have another, have a, have one of these with lines on perhaps.... That's, that's okay isn't it? You can, you can write it out again afterwards to make sense of it and you can both get together and write it out and sort of do pretty tables. It's better than my scribble. So something like that. Er now... so what fraction of the total, forty out of a pound. So the fraction will be... you spend forty pence out of a hundred pence. Are you a bit worried about this?
[Claire:] Mm.
[John:] [whispering] Well it's dead easy fractions []. Don't forget a fraction is the answer to a division and they're saying what's erm forty divided by a hundred right? And we pretend we know the answer all we do is we write the sum out again and we say forty divided by a hundred is forty divided by a hundred. Only now it looks like a fraction. It still means the same thing. Forty divided by a hundred.... Good.
[Claire:] [whispering] Stationery fifty pence [].
[John:] Now this one... can you make that a er a more useful fraction? If you had ten out of a hundred you can cancel it have you done cancelling?... No well if you had ten pounds shared between a hundred of us we'd all get the same amount if we had one pound shared between ten of us. Cos we could put it into lots of ten. Couldn't we, we could put the, we could put the money into lots of ten and we could put the people into lots of ten. So let's say if we had ten pounds on the table and a hundred people underneath.
[Kelly:] I done it wrong.
[John:] Erm that's fifty out of one fifty that's right.
[Kelly:] Yeah but I, I done that one underneath
[John:] just do a thirty out of one fifty there.
[Kelly:] Shall I do me fifty?
[John:] Let's see keep, keep it on the same line if you can. Can you? Yes that's fine.
[Kelly:] Fifty over one fifty
[John:] So we look at this ten pound we're going to put that ten pound on the table we might put a ten pound note or we might say we'll have ten one pound coins. Right ten p ten times one pound and underneath we can tell all the people to get into lots of ten. Don't all just stand together can you make ten lots of ten okay. And then you could say, well you lot of ten there, you group of ten, you can have that one pound. And the other group of ten have another ten pounds, and so you'd get, each group of ten would have one pound shared out between the ten of you. Okay now this isn't a very good example to show you how fractions cancel because we get this ten all over the place. So let's look at one of, let's look at the one that Kelly's working on there where she's got fifty pounds shared out between a hundred and fifty people. Right we'll say oh well they both end in a nought don't they so what number will divide into them. What number would go into fifty and the same number go into a hundred and fifty?
[Claire:] Ten.
[John:] Ten so that fifty we'll write it as five times ten or ten times five doesn't matter let's write it as ten times five. And this one we'll write as ten times fifteen. So what have we done, we've put the money into ten lots of five pound now okay so we got fifty pounds let's say we had it in five pound notes. So we put ten five pound notes round this very big table and then we're saying now you've a hundred and fifty people I don't know how you managed to get into this room. But a hundred and fifty of you can you all get into two groups and there'll be fifteen in each group of you. So this group of fifteen here that's your five pound between you and then we'll go onto the second group of fifteen people and they could have the second five pound and the third and the fourth and so on. Up to the, the tenth group of fifteen people well that's your ten pound that's your five pound the tenth five pound. So they say, oh okay we've sorted this out a bit now each group just has five pound to share out between fifteen of them. That's a bit easier what number will divide into both of these?
[Claire:] Five.
[John:] Five right so we'll put them in five groups of five lots of one pound on the table. We'll change these, this five pound note into pound coins. Five lots of one pound and the people, we'll put them into five sets of... there were fifteen of them so we'll make
[Claire:] Three.
[John:] five sets of three. Right okay set number one that's, that's Claire's set... three of you share that first pound. Second set... Kelly's set you three share that pound. Third one share that, fourth share that. Fifth set the last set you three you group of three people will share that last pound. So now... they've got it sorted out to one pound between three of them. And we got to there from starting off with fifty pounds between a hundred and fifty of them which was quite hard to handle but by making it smaller this is called cancelling fraction when you... take... really we're dividing this side we say, well we've got ten on the top and ten on, ten times five on the top ten times fifteen on the bottom. Well if we put the money into sets, lots of ten and the people into lots of ten we could cancel those tens out and it would just come down to five over fifteen. Okay and then as you saw five'll go into it so we can cancel the fives out and it's just one over three. So how much will they get? They'll get one pound shared between three. And maybe at that point we say, oh oh okay we can't share it out any more it doesn't work out very well. Perhaps we, we all have erm thirty three pence each and we give a penny to Oxfam, or we'll toss up or we'll, thirty three pence each and one penny left over so we'll have a third of that penny each we'll cut it up. Right so have you worked out what those come to? How many degrees it is.... You can you can sort of just go over that line and put equals so many degrees. So what would a third of three sixty come to? So you're working out what your fractions are so forty over a hundred is four times ten lots of four over ten lots of ten. Well we can forget about those cos they're in sets of ten. Four tenths okay. Erm... how many twos in that well we can think of that as two times two over two times five. We can cancel those twos again. Two fifths.
[Claire:] Is that right? Am I doing that right?
[John:] That's brilliant. Yeah that's great.... That's going to be two fifths. How about the ten over a hundred what will that come to?
[Claire:] Erm they both end in nought so ten goes into both of them.
[John:] Right good so you could just So this is ten times one and this is ten times ten we could cancel those out and we get
[Claire:] One tenth.
[John:] one tenth brilliant. So that's one tenth and that's one tenth and then what I'd like you to do is work it out as a fraction what fraction of how many degrees would it be if you had a tenth of three hundred and sixty degrees, how many degrees would that come to?...
[Claire:] So would it be ten divided by three hundred and sixty?
[John:] It'd be, it would be... one tenth... of don't forget that's of, one tenth of three hundred and sixty.
[Claire:] so you're just dividing
[John:] You're dividing it by ten or you're of-ing, times-ing, multiplying it by one tenth, it's the same thing. Multiply it by one tenth or divide it by ten. What is a tenth of three sixty? Right you can cancel it like this you multi can you multiply fractions? So we've got one... one over ten... times... thirty six times ten. We can cancel that ten with that ten and what does it comes to?
[Claire:] Thir mm thirty six.
[John:] It just comes to thirty six good. A fifth of three hundred and sixty. Ooh a fifth is awkward isn't it? How many tenths would there be in a fifth?...
[Claire:] How many tenths in a fifth?
[John:] Mm.
[Claire:] ...
[John:] Share out, share out something between erm ten people... okay say share out a pound. How much would we get each? If we shared out, let's say you share out erm... ten pence... between ten people how much do we get?
[Claire:] Two one.
[John:] Yeah so we get one and the you're going on to the next one. Share it out between five people you get two.
[Claire:] Twenty pence.
[John:] You get two pence.
[Claire:] So do I divide that by five and then times it by ten?
[John:] Excellent....... So... you're trying to find out one fifth well you just divide it by five it's the easy way to do it. But well it's one way to do it you can use a calculator or... you could say what would, could you work out a tenth of three sixty?
[Claire:] A tenth of three sixty?
[John:] Mm what's ten times six?
[Claire:] Sixty.
[John:] Ten times erm nine?
[Claire:] Ninety.
[John:] So ten times something gave us three sixty ten times what?
[Claire:] Thirty six.
[John:] So a tenth of three sixty must be?...
[Claire:] Thirty six.
[John:] Thirty six so that was one way of working out a tenth of it but we want a fifth.... a fifth would be two tenths.... When you get a fifth of something you get twice as much as when you get a tenth. It's probably simpler not to, not to worry about that that's just a quick a bit of a short cut way of doing it. You just divide three sixty by five and see what you get.
[Claire:] I know.
[John:] Good do you remember a long time ago doing factor trees and I gave you three sixty to do?
[Claire:] Yeah.
[John:] Can you see now why it's useful? Why it comes in handy to know all the things that you could multiply together to know three hundred and sixty. Can you remember any of them? Did you do that?
[Kelly:] No.
[John:] No.... The factors of three hundred and sixty. So let's have a look.
[Claire:] Ten times thirty six.
[John:] Two fifths you get a hundred and forty four. Is that right? Ooh I don't know. Do you want to, do you want to check it on the calculator?... So if you multiply a hundred and forty four by
[Claire:] By...
[John:] Okay try... tr just, just try this one erm divide, divide your three sixty by seventy two let's see what you get....
[Claire:] [whispering] [] Five... five times seventy two by two.
[John:] Right....
[Claire:] A hundred and forty four.
[John:] Good so they all look, they all look fine.... Okay I reckon you can start drawing your one now can't you?...
[Claire:] Seventy two.
[John:] Right.
[Claire:] Do you want to show you how I done it?
[John:] Go on.
[Claire:] Well I went back up to the first one and I said you need three one hundred and twenties to get to three hundred and sixty so
[John:] Yes.
[Claire:] what do you need five of to get to
[John:] That's it.
[Claire:] three hundred and sixty. Seventy two.
[John:] What do you need five of.... Seventy two. You need ten thirty sixes. So you could cut it up you cut your, your circle up into ten equal pieces, cut your pizza, your pie into ten equal slices and they'd all be thirty six degrees. Then you'd say well here's our pie we're going to share it out between ten people tonight. Oh half of them haven't turned up we're only going to share it between five of us. Well we'll get two pieces two of those thirty six pieces that those one tenth
[Claire:] Add the two thirty sixes.
[John:] Seventy two okay. Right that one you've already done up here haven't you?
[Claire:] Yeah.
[John:] So that one's okay. And don't forget to put your little squi little circle at the top for degrees, seventy two degrees. Good, total one pound. Right off you go.... Okay Right now how are you going to do this one, two fifteenths?... If I said to you, what's erm what's three quarters of twenty? How would you work it out?
[Kelly:] Three quarters of twenty?
[John:] Mhm.
[Kelly:] twenty.
[John:] Mm what does three quarters look like?
[Kelly:] three quarters.
[John:] It's got a quarters missing.
[Kelly:] Looks like a
[John:] So how would you, how would you find three quarters of twenty?...
[Kelly:] ...
[John:] Could you find a quarter of twenty?
[Kelly:] Ten?...
[John:] What's half of twenty?...
[Kelly:] Half of twenty, ten.
[John:] Right what's a quarter of twenty?
[Kelly:] Five.
[John:] Okay... what's three quarters?
[Kelly:] Fifteen.
[John:] Okay so that's how you, that's how you'd do three quarters you'd say well I could find a quarter of it and then cut it all up into quarters and then I'll take three pieces, three quarters. So how would you find two fifteenths?...
[Kelly:] Well we've just said if Well we've just said
[John:] We've said find three quarters by finding one quarter first and then you take three times it. So how would you find two fifteenths? What would be the first thing you'd do?
[Kelly:] one fifteenth.
[John:] Right so find one fifteenth of that and then
[Kelly:] three hundred and sixty.
[John:] So how many fifteens would you get in three hundred and sixty?... So one fifteenth of three hundred and sixty is going to be three hundred and sixty and then in front of that you'll want one fifteenth of... and this times thing is quite handy when we're multiplying fractions together we'll just get three sixty over fifteen. Okay. Oh that looks good. Have you checked at all the angles?
[Claire:] Yeah.
[John:] Including the last one that just happened.
[Claire:] Yeah.
[John:] Erm now they should both be thirty six do they look, do they look like thirty six? They look pretty good to me.... Erm looks a little, just a little bit more.... And that one's... that one's thirty isn't it?
[Claire:] Mm.
[John:] These two should be the same and these should be a hundred and forty four.
[Claire:] Mm.
[John:] About a hundred and forty five but that's fair enough that's near enough. That's good. Erm if you look at that it looks as if you spend a bit more on presents than stationery. Cos it's a little bit bigger cos it didn't, it didn't work out completely right, you did a hundred and forty five. It's very hard to do just one degree but that's very good that's, that's good enough, that's what people can see. That's great that's good. Yeah yeah erm you could write just outside it here like save and you could say that you save forty pence.
[Claire:] Save forty pence underneath or
[John:] Yeah. Erm ou outside here put forty pence.... Right how are you going to do that three hundred and sixty divided by fifteen?... Try a bit of cancelling first. Okay three hundred and sixty over, let's, let's do three sixty over fifteen. Can you think of any factors of fifteen? Two numbers that would multiply together to make three.
[Kelly:] ...
[John:] This is getting hard Good, good getting hard this isn't it when you've been having a holiday and you thought you were gonna have a nice play and we're doing all this hard work. Now some factors of three sixty. Well three would be a nice one to have. Will three go into three sixty?
[Kelly:] Yeah.
[John:] Okay three whats would make three sixty?... Three times what?...
[Kelly:] Three times a hundred and twenty.
[John:] Three times a hundred and twenty. Okay and then we'll write that again. Erm we could write that as, instead of the hundred and twenty we could have twelve times ten couldn't we? Three times twelve times ten. That makes, that makes three sixty over three times five and then we can cancel. Okay see what we're cancelling.... Okay so... three times twelve times ten over three times five. Well there's a three on the top so we can just divide by three on the top and that's, how many threes in three? One.
[Kelly:] One.
[Claire:] One.
[John:] Divide by three on the bottom how many threes in? One.... How many fives in five?
[Kelly:] One.
[John:] One. How many fives in ten?
[Claire:] Two.
[Kelly:] Two.
[John:] Two right so on the bottom now we've just got one times one which is one and on the top we've got one times twelve times two what does that come to?
[Kelly:] [whispering] [] is twenty four.
[John:] Okay twenty four over one what does that mean? It's twenty four shared out between one person, they get the lot. It's not really a fraction it's just twenty four okay. So now you've worked out what one fifteenth is right? One fifteenth equals twenty four degrees.... So two fifteenths [whispering] [] two times twenty four degrees equals forty eight degrees okay. Now on the angle that you did there the degrees can you add those up and just before you start drawing it you should always add them up and make sure they all come to three sixty cos if it comes to four hundred it's going to go right round and a bit further than once round. If it comes to less than three hundred and sixty you're gonna have a little bit left over that you didn't spend on at all. So it's a good thing to check. If you'd like to add yours up... try them in your head if you have trouble then you can use the calculator.
[Kelly:] [whispering] Try them in my head []
[John:] Okay good. Right good and you should always check that before you draw it just in case your pie chart comes out and put, put that up in the air a bit I'll just show you that, those are good there, but up in the air like that
[Kelly:] Mm.
[John:] .... Quite small and up there cos otherwise you're go it's going to look a bit like three thousand six hundred isn't it? Looks like another nought as you say. Okay looks great. So now you're ready to draw your. Okay so a hundred and twenty. What do you think about this? Do you think it's quite hard? There's quite a lot to it isn't there? A lot of things going to here....
[Kelly:] Shall I do it on that piece of paper so I don't get mixed up on
[John:] No no don't, well it doesn't matter, anywhere you like. Here do it on, do it on that one that's good so you keep it together. What you could do with is labelling these so that, which one of them is the first question, sort of pie chart A if you like then pie chart, pie chart A and again if you've got the total on, on your pie chart then you, you won't get confused will you?... What do you think of it? Do you think it's pretty hard?
[Kelly:] I don't.
[John:] There's a lot in it, there's, a but it's a good exercise because if you can do all these different bits
[Kelly:] Right.
[John:] then you can do almost anything in maths. Erm and you could start making up your own and playing with them on the computer.... and you'll you know it does it itself you just, you, with the computer you just say well I had four pounds and I spent a pound on that and two pound on this thirty pence on that and it goes pow does it by magic. it do what it's doing
[Kelly:] pie charts and graphs
[John:] and bar charts and graphs it's doing all this. It's got some arithmetic in the program that works out all the angles and then it draws them. That looks good. And you don't need to mark the one twenty on I mean you can do if you like. Erm you could perhaps put erm one side here what the one twenty comes to, it was, how much erm fifty pence. and don't forget to mark on it what that was, that was save....
[Kelly:] Shall I put like
[John:] Mm no that's okay and somewhere what the total was. Well the total is always three sixty all the way round but was this when you had a million pound pocket money or when you only got four pence a week. So you have sort of
[Kelly:] When I got one
[John:] total one fifty.... Okay good now this is probably the first real go at doing pie charts that you've had isn't it? The other ones you've been doing have been pretty easy. Well that's, that's fine you've got to start with the easy ones and at your age you wouldn't, you wouldn't normally be doing them this hard at all, this is for sixteen year olds who are doing their, their plot paper on G C S E maths so you expect to find, oh hang on this is a bit hard there's a bit of work in this, but I think you're capable of doing it. You, you might think, ooh I don't really know what I'm doing at the moment er perhaps I couldn't do it on my own. But if you practise it you will be able to. You'll be able to do these on your own.
[Kelly:] did you say move your nought to there then do your
[John:] You're going to, you're going to measure an angle now of another, how much do you want to do?
[Kelly:] I'm doing my seventy two.
[John:] Seventy two so you'll start from, that bit's, that's gone now if you like if somebody came along and they cut out that piece of cake.
[Kelly:] So you put them
[John:] So you as you say put your nought there you've got to start from where you finished off last time and carry round again.... And... would you two like, do you think you'd like to work through these again together doi just doing the same ones
[Kelly:] Yeah.
[John:] to see and talk about it between the two of you and see how you got on with it. Now it's quite likely that next time I come we can spend quite a bit of time doing this same thing again yeah cos there's a lot in it there's angles using a protractor adding things up to check they come to the total that the angles come to three sixty and there's this thing about fractions there's cancelling fractions and then there's working with quite big numbers three hundred and sixty what's two fifteenths of three hundred and sixty mm that's quite hard. A lot in it er but you can learn a lot from it and eventually you'll be able to do any sort of these pie charts, if somebody says well you've got four pound eighty to spend, and somebody spends three quarters on this and a tenths on that, two fifteenths on something else and you can add them all up and do a nice chart. What do you think of it? Do you think it's hard?
[Kelly:] Yeah.
[John:] Yeah it is hard, it's hard and... and i when, when Kelly's done this one we'll have a little bit of a break okay? And... you might both like to talk to each other now about what you found easy what you found hard because Kelly found some bits hard, you thought oh it's obvious, didn't you? You found some bits hard and Kelly thought ooh that's obvious. Okay it's easy if you know how to do it, it is obvious when you know how to do it but if you don't know how to do it it's not that easy and it's definitely not obvious.
[Kelly:] [LAUGHTER] I'm stuck [].
[John:] Right are you stuck? What have you got here then?
[Kelly:] It's supposed to go like
[John:] Right no no you've got a one twenty and a on a one twenty and a one twenty and then you've got a forty eight, forty eight and a seventy two. That looks right. How m and this is wha you worked all the way round now how much have you got left over? You should have this one twenty left over so just check that and make sure that you have cos if you haven't something's gone wrong and you have to start again but you
[Kelly:] Yeah.
[John:] absolutely spot on.
[Kelly:] Well I lo I I looked at the fifty and then
[John:] And you thought, ooh it's going to be fifty degrees because of because we started off with a very easy number three pound sixty. That was why I chose it. Three hundred and sixty pennies one penny for every degree. Oh this is easy anyone can do this. Right but then we go on to working out fractions, what's two fifteenths of a pound. Oh don't know. So, but three sixty, it's a lovely number cos it's got so many factors. Okay so what I'd like you to do now a little bit of revision... which, which way shall we do it first of all no just talk about it both of you what you found easy and what you found hard. What you can both agree on, oh that was easy, or both think ooh that was hard. If I'm, try and tell me the steps that you went through to work out how you were going to draw your pie charts. For the, for the, for the first one where it was just three pound sixty that was pretty easy wasn't it? How did you do that?
[Kelly:] The three pound sixty
[Claire:] It's
[Kelly:] Do you mean that one?
[Claire:] If you save half of it
[John:] Yeah.
[Claire:] it's one pound eighty and it's just gonna be half
[John:] Well why, why w it's just half okay so that was easy you didn't have to work out how many degrees, it was just a half, it's half way round the circle.
[Claire:] It'd be a hundred and eighty degrees.
[John:] Right now what about this one where it was erm you spent... one pound.
[Claire:] It'd be, you'd put your nought here
[John:] Right.
[Claire:] and then a hundred.
[John:] And it was just a hundred degrees?... Mm why was it a hundred degrees?
[Claire:] Cos it's a penny for each degree.
[John:] Right because we've picked that three sixty a penny for each degree makes it easy then no problem none of this messing about with fractions and all the cancelling and ooh dear, which is where all the hard part is that's where all the hard work is this doing the fractions. So no real problems with that one?
[Claire:] No.
[John:] Now we go on to the second one.
[Claire:] Is that the one we've just been doing?
[John:] This one you've just been doing now. What did you think of that? [LAUGHTER]
[Claire:] It was hard.
[John:] It was hard wasn't it? No no two ways about it that was really hard. So what was the hardest part about it?
[Claire:] Mm.
[Kelly:] Hardest part.... Mine was erm because it's not with the nought on the end so you can just find that number
[John:] Right.
[Kelly:] find
[John:] So once you knew wh how many degrees it was for each slice of the pie in your pie chart no problem to use your protractor and mark off forty eight degrees, a hundred and forty four, seventy two, thirty six
[Kelly:] You'd have to find
[John:] Finding s okay so there was a little bit of it was a little bit awkward to get it to the nearest degree there. That was a bit awkward but erm... calculating how many degrees it was.
[Kelly:] It was quite easy.
[John:] Was it was it quite easy? You both had quite a few once a, well once you know how to do it it's easy. But working out how to do it wasn't that easy was it, it wasn't a very easy thing to do that, no. Erm I think we'll go over... the working out, how to work out the fraction so there's two stages really. What fraction of the total is it. Okay and let's say it comes to a third or it comes to two fifteenths. So that's that's not too bad that but that, that's hard enough. And it doesn't stop there because when you've worked that out now you've got to wo you've got this biggish number three sixty, Urgh! Or how, what's a fifteenth of three hundred and sixty? Urgh what's a tenth of three hundred and sixty? Or what's a fifth of it? Or worse still what's three fifths of it? Or two fifteenths? So that's, it's pretty awkward. Erm we'll have a look at that in a minute. Now what I want you to do now I want you to draw a factor tree... of three hundred and sixty.
[Kelly:] Right now.
[John:] Right now okay. Have you done a factor tree?...
[Kelly:] [whispering] Three sixty [].
[John:] Can you explain to Claire how to do a factor tree?...
[Kelly:] Should I do it on the back of that?
[John:] Erm on a new bit of paper you know have some of, have some of these okay have some of those.
[Kelly:] Just put a little square there. And put three hundred and sixty inside it....
[John:] Okay now while you're explaining is it all right if I just use your toilet?
[Claire:] Yeah erm go to, when you're at the top of the stairs first on the right.
[John:] Okay
[Kelly:] And then bring a little line coming down from your right hand side.
[John:] [in the distance] Hello I'm just coming up to use your loo if it's okay. []
[Kelly:] Done that yet? A bit
[Claire:] Yeah.
[Kelly:] bigger.... And then the factor is you've got to find all different things... that
[Claire:] Yeah.
[Kelly:] bring a little line coming there into it and I'll make that into a little square. No bring another line coming down like that.... That's it. And then put a square onto e the end of that.... And put a times in between them.... And now put... mm now think of something that you could times that adds up to three hundred and sixty.
[Claire:] thirty six by ten.
[Kelly:] Go on put that then.
[Claire:] Thirty six times ten.
[Kelly:] That equals that.
[Claire:] Three times twelve.
[Kelly:] So bring this down
[Claire:] From this one cos erm er three times twelve would equal thirty six.... [LAUGHTER]
[Kelly:] It's just like a family tree.
[Claire:] Oh ask John [whispering] say it was ages ago []
[speaker003:] [whispering] []
[Kelly:] Oh it's ages ago since I done these. Erm we've done one...
[John:] Right so do you understand it all?
[Claire:] No.
[John:] No. No what bits
[Kelly:] I remember
[John:] Hasn't Kelly explained it properly?
[Kelly:] I remember.
[John:] That's good that's a good start. Okay I'll ex I'll explain to Claire. Now what we do, oh the dog wanted to know all about it.
[Kelly:] To explain it better I should have done what adds up to thirty six then up to three hundred and sixty shouldn't I?
[John:] Adds up to?
[Kelly:] Times.
[John:] Times, so all you do you can start anywhere you like.
[Kelly:] Yeah.
[John:] We pick two factors two numbers that would make you multiply them together and they would make three sixty. And the obvious ones look like thirty six and ten. Now I usually but the small number first, doesn't matter. So erm they're okay so we could have ten times thirty six. Now... and then we could do the same with... the ten now
[Kelly:] Yeah then all the things that times ten.
[John:] So what would make the ten? We put two boxes under the ten What would make ten and put the small one first.
[Kelly:] Two times five
[Claire:] Two times five.
[John:] Okay good yeah two times five.... Two times five and what about the thirty six can you think of two numbers that would make thirty six when you multiply them together?
[Kelly:] Six times six.
[Claire:] Yeah.
[John:] Okay six times six. Could have had three times twelve it doesn't matter which ones Okay well you put three times twelve that's what you were going to say so, if Claire puts six times six you put three times twelve and I'll put four times nine just to be awkward.
[Kelly:] [LAUGHTER]
[Claire:] [LAUGHTER]
[John:] There we are we all have different ones but we should all finish up with the same answer. Right so let's see on Kelly's then you've got three times twelve. Can you get any other factors from three apart from one and itself?... No
[Kelly:] No.
[John:] so that's the, that's the end of that we don't split that box up any more. What about the twelve? What would you split that up into?... [tape ends]... Okay. So two times six, can you go any further with the two?
[Kelly:] No.
[John:] That's it okay that's finished. What about the six? Can you see what Claire's doing?... So she's split the twelve up into a two times six. Now what about the six?
[Kelly:] Should I split the six up?
[John:] Erm well yours is different so we'll look at yours in a minute.... So what happens to your... six?
[Claire:] It's two times three.
[John:] Right good. Two times three.... Okay... it can't go any further with the two or with the three. So let's have a look at Claire's. What's Claire got?... So you've got two times five. You can't go a can't s split the five down any more can you or the two so you've finished there. What about the six what c that first six what could you split that up into?
[Kelly:] Two times three.
[John:] Right that'll make two times three.... Okay and if you bring that one down a little bit then it'll collide with these. Okay.
[Kelly:] Mm this far.
[John:] And that six is going to make?... Same as this six.
[Kelly:] Two times three.
[John:] Two times three okay. And I'll do mine... so I had three sixty and I split it as a ten times thirty six and then I had two times five for that ten okay can't go any further there. Now I've got four times nine. Well what can I split this four up, what can I split that up into?
[Kelly:] Two times two.
[John:] Okay so I'll make that two times two.
[Kelly:] Can't go any further with that.
[John:] And wha can't go any further with that and what about the nine?
[Kelly:] Could do three times three.
[John:] Three times three okay and that's that. So we've all finished our trees now I'm going to write out what I've got on mine and I'm going to pick the smallest numbers first. So I've got a two there I'll put a tick on that so I've got two times I've got another two so I always put my smallest ones on the left so I can find them quickly. Another two there... another two here.... And then I've got some threes. I've got a three... another three and that's
[Kelly:] A four.
[John:] A five I don't count, I only count the ends when I got to the point where I couldn't go any further. And there was a five there. So who wa who's good at calculating?
[Kelly:] Me.
[Claire:] Me.
[John:] You do you work that I'll tell you what you work that I'll work my own out. No two times two times two
[Kelly:] Two times two times two
[John:] times three
[Kelly:] times... three
[John:] times three... times five... and what's that come to?
[Kelly:] Three hundred and sixty.
[John:] Okay oh that's a very, so that's... all of those multiplied together are, would make three hundred and sixty.
[Kelly:] Sixty.
[John:] Now if you'd like to check... what Claire has got. Let's see what Claire's got first of all. Erm can we find the smallest. We'll both have a look at this, all have a look at it and find the smallest.
[Claire:] Two.
[Kelly:] Two.
[John:] So there's a two....
[Kelly:] Times
[John:] Okay there's another two if you like to carry
[Kelly:] Mm two
[John:] if you'd like to carry on from there Claire. So and just put on each one as you find it. There's a two there's another two.
[Claire:] And then three.
[John:] Right... there's another three
[Claire:] Then five.
[John:] and there's a five.... Okay so I got, what did I get? Underneath there.... Two times two times two times three times three times five. So we've, we've got the same one. And if you like to check yours now just okay. If you like to check your...
[Kelly:] That's two... two times... John?
[John:] Mhm.
[Kelly:] There do I go two then times two?
[John:] Right so you've got, got a tick on that two and now look for, are there any other twos?
[Kelly:] Oh God yeah times two
[John:] Have a look see if you got any other twos.
[Kelly:] times two
[John:] And put a tick on each one as you get it so that's one two three okay.
[Kelly:] times three.
[John:] Times three.
[Kelly:] times three
[John:] Okay see if you can make
[Kelly:] times five.
[John:] what other things you could make just by multiplying these together now.
[Kelly:] Done that.
[John:] Okay and you we all get the same and it comes to three sixty. Cos mine came to three sixty. So what numbers could you make just by taking just a few of these... and
[Kelly:] Should you should we put brackets
[John:] You could put brackets round that would be good.
[Claire:] So what are we doing?
[John:] So if you put brackets round say three of those twos what would that, what number would that make? Two times two times two.
[Kelly:] Six.
[John:] Now would it? Two times
[Kelly:] Eight.
[John:] Eight
[Claire:] Eight.
[John:] okay. Erm and you could put brackets round the three times three see. Just, just round the three times three okay.
[Kelly:] And then the three times five.
[John:] And what would that make?
[Kelly:] Nine.
[Claire:] Nine.
[John:] So you could have, we'd know that eight, if you'd like to check that eight times nine times five
[Claire:] Eight times nine times five.
[John:] that should come to three sixty.
[Claire:] Yeah.
[John:] Okay.... Now what I'd like you to do is to look at these numbers this is a bit like erm have you seen Countdown? Carol Vorderman... where you have to make... numbers? You have to make a total out of the numbers? No okay what you need to do, what I want you to do now is... just pick some of these numbers and multiply them together so that you get forty five.
[Kelly:] Forty five?
[John:] Mhm.
[speaker003:] [whispering] []
[John:] Good thanks. Yes that was very good that's excellent. Cover, it cover it up just in case Kelly's tempted to look over that way.... Right now good.... Right h how did you do what you did Claire? How did you do it, why did you go for it that way?
[Claire:] Because... five times three is fifteen and if you times fifteen by three it'll be forty five.
[John:] Mm but did you know that already? Okay well Claire seemed to go straight for the answer straight, right away. She's not really quite sure why but she knew that was the way and it was, it was the right, was the right things to go for. But that doesn't help if you don't know how to do it? So let's see if we can think of a way of doing it. Could we use a factor tree to find out... we're trying to find out which of these when you multiply them together would give you forty five....
[Kelly:] Would give you forty five?
[John:] Mm....
[Kelly:] five in it.
[John:] So let's get, is that what you did Claire, there's going to be a five in it?
[Claire:] Yeah.
[John:] Forty five is in your five times tables.
[Claire:] At first I looked at that nine and then I went five.
[John:] Right so you spotted that right away. And you got a nine there times a five would make forty five. Well if you don't spot that it's no h it's no help really you can't just think, Oh well I'll just sit there until it comes into my head. So you're gonna have to think of another way. If there'd been a much
[Claire:] whenever you get three times three.
[John:] Well erm I mean I might have said Right if it ends in a five then five is one of its factors. So let's do a little Ah if it ends in ten what could you say about one of its factors? Sorry [LAUGHTER] if it ends in nought [].
[Kelly:] Yes. ten.
[John:] Ten is one of its factor. But if it ended in, if ten is one of its factors then there's a num another number that must be one of its factors.
[Kelly:] Five.
[John:] Five must be a factor and two must be a factor. Right cos they go into ten. So if it ends in a nought or it ends in a five then five goes into it. But we could have dome a little tree for forty five. We could done forty five how are we going to split that up? Well it ends in a five so we know that five goes into it. So we'll have five times and then
[Kelly:] And then you think what comes down there.
[John:] work out what is it. Five nines okay. Five nines and then... how can we, how can we split the nine up?... Three times three.
[Kelly:] Yeah. [dog barking]
[John:] Okay. Right now what do we need to make up our forty five? Five times three times three. Have we got that here yes here's a five and a three so we could make forty five. How could you make, how could you make, I'd like you to both have a look at those now and see how you could make, quiet. How, how you could make ninety?
[Claire:] Benji.
[Kelly:] Ninety?
[John:] Mhm.
[Kelly:] Ninety.
[John:] Okay but we want to do it, good that's it but we want to do it by times lots of these numbers times together.... You've already worked out, was good cos you've worked out how to make forty five haven't you? So how would you change that forty five into a ninety now?
[Kelly:] ... Forty five into your ninety
[John:] You could do that much, do the three times three times five and that gives you forty five but we're looking for ninety. So what have you got to do to it now to make it into a ninety? That's it times two. So two times three times three times five will give you ninety.... Why are we doing all these things? Anyone got any idea why we're looking at all these interesting factors of three hundred and sixty?
[Claire:] Well I was just gonna say because all the numbers go into three hundred and sixty.
[John:] Yeah but why are we so interested in three hundred and sixty? Right because it's a complete circle, a full turn all the way round a hundred percent of your pie chart.
[Kelly:] Mm.
[John:] That's the total. Is it time already?... Oh it's not far off actually only about five minutes to go. [LAUGHTER] Right okay well while we're interested in
[speaker003:] Hi.
[John:] We've g we've got five minutes haven't we? Right cos I know you've got to get off you've got to be there for six have you?
[speaker003:] Yeah.
[John:] You're going to be worn out with all this aren't you? Now don't worry abo if you forget all of this... by next time. If you've forgotten, if you think you've forgotten you won't really forget it. But it's the sort of thing that we want to go over a few times. Yeah and especially on the fractions and the different types of fractions but you just find o found out what makes ninety haven't you?... Two times three times three times five makes ninety so what have you got left over? Two times two. So we could write this as four times ninety. Okay? Four time so if someone says what's a quarter of all the way round you can look at all of these and you can think, well four times ninet four times what would be all the way round? Four times ninety, so a fourth of the way round, a quarter the way round must be?
[Kelly:] Ninety.
[John:] Ninety. So... how about if you'd both like to find out what a thirtieth... of the way round is using the fra the factors there.
[Kelly:] A thirtieth?
[John:] Or try, you did a fifteenth earlier didn't you? What would a fifteenth of the way round be?
[Kelly:] A fifteenth?
[John:] But I don't look, don't look
[Kelly:] Seventy two.
[John:] Okay.
[Kelly:] [LAUGHTER]
[John:] Right. Well this is, this is what we'd do. We'd have a look, anyone ideas? Anyone got any ideas? We're trying to come u
[Kelly:] find fifteenth
[John:] We'd go on.
[Kelly:] Find fif find thirty in there.
[John:] It's fin okay if we're looking for a thirtieth we'd find thirty in there. Right if we were looking for a fifteenth, say we were looking for a fifteenth... what would make
[Kelly:] Times it by two.
[John:] what would make fifteen out of this lot we've got here?
[Claire:] Five times three.
[Kelly:] Five times three.
[John:] Right so five times three would make fifteen and what have we got left over? Two times two is four times two is eight times three is twenty four.... Okay is that right? Two ti eight, do you want to check that on the calculator? Twenty four times fifteen....
[Kelly:] Three hundred and sixty.
[John:] Right so if you get to know if you drew... do it through the week don't worry about the pie charts don't worry about the fractions. We'll go over those again. Just play with these what num what numbers would make three sixty? So once you've got all those you can say well four times ninety or two times one eighty okay fifteen times twenty four. And you work all of those out so that you just play with them just get to know them so that you're happy with them. And you could both write something maybe about your grading maybe a little bit about what was good, what was hard, what was easy, what was boring... about this cos I think there was a lot of hard work, there wasn't much play in it today was there? A lot of hard work to get you working during the holidays. But erm we'll have a look at it next time and we'll, you know, play with it a bit more and we'll get on with doing some more pie charts okay? Now I think we'd better finish on time so you can go and stand in the, the wet and [breathes in] breathe in get some fresh air into your lungs and get all psyched up ready for your grading. Right and I'll explain to Claire about what I want both of you to do... for next week. And Claire can make, you can make some
[Kelly:] sleeping Claire's gonna sleep in my tent
[John:] Right okay. Yeah so I'll tell you roughly what I want you to do and you can make a few notes and then you can tell Kelly. So first of all I think Kelly had better get off
[Kelly:] Okay thank you.
[John:] and get to her grading. Oh you're welcome, you're welcome. Did you think it was hard?
[Kelly:] Yeah.
[John:] It was it was very, it was very... sixteen year olds find this hard when they're doing the, the high level stuff but it's no good giving you the easy stuff cos you're both very bright, both very clever and it's no good saying, well what, does anyone know what one add two is is it?
[Kelly:] No.
[John:] No.
[Kelly:] turn that off?
[John:] No just leave it on it's okay....
[Kelly:] Thank you.
[John:] You're very welcome and I hope you do very well at your grading. I'm sure you will.
[Kelly:] Bye thanks John.
[John:] Okay bye. ... Right erm... I'll keep those. You're going to need to have a look at fractions a bit but that's just for you. I'm just going to have a look at this cancelling fractions don't worry about that. Cos you're thinking, oh dear this is a bit I'm not sure I could do this on my own. Don't worry cos we'll help you with it. So I'd like you and Claire
[Claire:] You mean Kelly.
[John:] and Kelly as well to talk about... what you were doing today. What were the hard bits? What were the easy bits? So the hard bits and the easy bits.... The... interesting parts, don't s don't worry don't rush I'll, I'll catch up.... The interesting parts and the have a guess.... And the boring parts okay.... And... and then I'd like both of you separately to say... which bits you'd like to go over again and which bits you'd like us to spend more time... doing more and more examples of. Okay so which bits should we spend more time on?... Which, I say which bits should we spend more time on which topic which topics should we spend more time on? Topics... should we spend more time on? And you I think, oh you want more time on fractions, Kelly might think, well she doesn't she wants more time on doing the degrees.... Erm... and then... what would you like to writ would you like to write about this? About what this lesson was like about?
[Claire:] Yeah.
[John:] Yeah if you write about that... and Kelly can write about her grading. Okay but the, you can, you can do what you thought and what Kelly thought in your essay. Okay have you got you haven't got any work to do over the holiday have you?
[Claire:] Erm I've got a project
[John:] You've got a project to do okay just do what you thought. You don't need to put what Kelly thought.
[Claire:] Okay.
[John:] Erm Yes if you've got time do it but don't, with all of, it don't feel you've got to do it, that it's homework and I'm going to get annoyed if you don't do it. It's not like that it's just that I think it'll help you to write it down... and to think about it and to talk, talk to Kelly about it.... And I'd like you to both... spend quite a bit of time just playing with the numbers that make up three sixty. See how many different ways you could make three sixty. You can use your factor tree and then you can combine them in sets and say we're gonna have two times five times three. See what that comes to. And times what would be left over. So now I don't want a factor tree I just want how many different lots of two numbers just two numbers that make three sixty like ten by thirty six or twenty by eighteen all the different things. And then you'll be able to work out a twentieth or an eighteenth or a fiftieth or a quarter.... Okay all the different, any two, all the two numbers so that when you multiply them together they make three sixty.... So one way we could write it we could sort of use algebra couldn't we? We could say something like, the first number... times... second number... equals... three sixty. And you find out how many different numbers could you fit in there? And you could use the calculator if you like try it, try it first with the, all the different ones that you've got out of the factor tree.... Most things.... Thank you very much.... Erm... I'll just sort this out. Yes if she's coming out you mean you don't, you don't have to do it all tonight she wan might want to be talking about erm... her grading a lot so you can't expect her to do any work until she's got that out of her system she might want to go on for an hour or so. I'll just have a quick word with your dad.
[Claire:] [shouting] Dad! Dad []!
[John:] Okay