[speaker001:] So... we can read that... and just put the towel on the table.... Right. If you'd like to tell me... how many... how many sixths you think there would be in a whole one.
[Kerry:] erm...
[John:] How many fourths would there be in a whole one?
[Kerry:] Erm...
[John:] How many... how many halves?
[Kerry:] Halves... erm... two.
[John:] Right two so... is you shared it out between two people you get a half, one, twoth, one over two. If you shared it out between three people how many so they all got the same... how many would they get?... Can you show me how much they'd get?...
[Kerry:] Yes.
[John:] If you shared it out between three.
[Kerry:] Mm.... Should I put it together first and then
[John:] That's it...
[Kerry:] Three.
[John:] So... which piece if there were just three of us, you and me and the dog
[Kerry:] [LAUGHTER]
[John:] sharing out a pizza... how big a piece would we get.
[Kerry:] A third.
[John:] A third. So share it out between three you get a third. If you share it out between four people how much would we get each?
[Kerry:] A quarter.
[John:] Good a quarter. Share it out between six people?
[Kerry:] A sixth.
[John:] A sixth good. Share it out between ten people?
[Kerry:] A twelfth.
[John:] How about
[Kerry:] Mm
[John:] Ah okay share it out between twelve people.
[Kerry:] A twelfth.
[John:] Have a guess share it out between ten people.
[Kerry:] A tenth.
[John:] That's it. Share it out between twenty people....
[Kerry:] A twentieth.
[John:] Good er share it out between five hundred people.... Or between a hundred people.
[Kerry:] A hundredth.
[John:] A hundredth. Share it out between a thousand people.
[Kerry:] A thousandth.
[John:] That's it. So you've got it haven't you you know that's that's all it means. All a third means is that's what you get if you share one between three so they all get the same. Er what does a sixth mean?
[Kerry:] That... there are six people there are six of us could have a maybe
[John:] Between six people and they're gonna get the same that's all a sixth means. And which one of those is a sixth? That's it okay. What does a twelfth mean?
[Kerry:] Erm... that if there was twelve people they'd all get the same piece each.
[John:] That's it that's all there is to fractions. And which one's a twelfth. That one.... Well I think you're doing very well on the fractions. Okay we'll leave that for a minute and we'll have a look so you can forget all about it right then I'll ask you later when you've forgotten okay. Let's have a look at erm what you did with the the numbers then.
[Kerry:] I've done I've done... the ten one.
[John:] Okay. Erm now do you know any of these? You know five add five don't you.
[Kerry:] Yeah.
[John:] Erm I'll turn that over... erm right and I'll say a number and you tell me what number you'd have to add to it to make it up to ten. Erm seven.
[Kerry:] Erm... four. Oh seven and two seven and three.
[John:] Seven add three good. Erm nine add?
[Kerry:] Oh nine... erm one.
[John:] Good. One add?
[Kerry:] Nothing.
[John:] One one add what would
[Kerry:] Oh zero.
[John:] One add what would make ten
[Kerry:] Oh one add nine.
[John:] That's it one add nine. We'd write a one and a zero
[Kerry:] Yes.
[John:] but we'd have to add another if we only had one penny we'd have to add another nine to get ten P. you're doing well on these. Eight add?
[Kerry:] Eight add... two.
[John:] Good... erm let's think of a hard one six add?
[Kerry:] Six add... four.
[John:] Good. Four add?
[Kerry:] Four add... eight.
[John:] Six add four. Six add four makes ten.
[Kerry:] So four add six.
[John:] Good. Four add six makes ten. Erm you did eight didn't you what was that? Eight add?
[Kerry:] Eight add... three er eight add two. [LAUGHTER]
[John:] Good eight add two. So two add what would make ten?
[Kerry:] Two add... eight.
[John:] Good. So have a look at the ones you've done here... right. Five add five
[Kerry:] Five. Nine add one.
[John:] let's see You know five add five don't you.
[Kerry:] Yeah.
[John:] Nine add one you know that one that's that's not hard. So if someone says one add?
[Kerry:] Nine.
[John:] you could work that one out. So you only have to learn half of these you don't have to learn all of them cos you can always switch it round. If you Just what you were doing what you worked out isn't it. So... eight add two eight... nine ten. It's just eight add two. So what would two add eight
[Kerry:] Two add eight.
[John:] What would that come to?
[Kerry:] Ten.
[John:] Yeah. Erm seven... eight nine ten.
[Kerry:] Nine ten. Three.
[John:] Do you think I'll tell you not to count on your fingers?... Well it's better if you can do it in your head it means okay you're a bit cleverer cos you can do it in your head. But if you can't do it in your head... what you going to do? You've got to use your fingers haven't you or get some pennies out and count them. Or write it down and put little dots and count up the dots or something it's a erm a lot of the Who tells you not to count on your fingers?
[Kerry:] Me headmaster or sometimes me teacher.
[John:] Mm sometimes the teacher but more the headmaster.
[Kerry:] Yeah.
[John:] Mm.... Don't like getting into... disputes into arguments with schools but in our lessons I don't mind if you count on your fingers. After a while... you get when you first start the first time you ever ride a two wheeler and you have someone holding it or you have some stabilizers on till you know what you're doing. And then when you're okay when you've been riding round a bit you take them off. And you're, Ooh stabilizers. you say to the other kids, Ooh... you don't need stabilizers. But when you first started when you're not quite sure what's happening you can't be expected to be perfect the first time you have a go at something can you. So use your fingers write down bits and more and more you'll be able to start doing it in your head then. Erm I reckon you could probably So if you keep practising these. You can practise them on our fingers. So if I say seven add you could go [whispering] eight, nine, ten [] three.
[Kerry:] Three.
[John:] Yeah and after a while you won't need to do that. You'll know them then and you won't need to use your fingers but while you're learning I don't see why you know why you can't use them do you. And if they say you can't at school well alright close you eyes and count, pretend there are some fingers there like that. That's good. That's very good numbers that add up to twelve okay. Erm... that's that's really good again you'd only have to learn up to six add six wouldn't you.
[Kerry:] Yeah.
[John:] Cos five add seven... seven add five would come to twelve. Now
[Kerry:] Twenty four.
[John:] add up to twenty four okay and right okay
[Kerry:] And there's thirty six there.
[John:] So you had a lot of practice adding there. Now what I want you to do... I want to just have a look at it now and I want you to... play with it over the holiday on your own. Have you got you your pennies?
[Kerry:] Yeah I'll go and get them.
[John:] Okay let's have a look at those.... Okay so...
[Kerry:] [LAUGHTER]
[John:] Right Cor! Gracious they're a weight aren't they.... They really are a weight. Okay you've got a fortune in here.... What have we got Can you sort out... ooh just the pennies.
[Kerry:] Yeah....
[John:] Okay how many have we got there roughly?
[Kerry:] Erm... two three four five six seven six seven eight... nine ten eleven twelve
[John:] Okay stop at twelve for a minute.... And keep those that's it keep those pennies separate. Now... let's put some of these back
[Kerry:] seven eight nine ten
[John:] just sort out another set of twelve.
[Kerry:] eleven.
[John:] Okay.
[Kerry:] Stand these up.
[John:] Another set of you just sort out another set of twelve pennies then we'll.
[Kerry:] Twelve....
[John:] Okay.
[Kerry:] Yeah. Twelve... six seven... eight eight nine... ten... eleven...
[John:] Okay that's lovely....
[Kerry:] Six seven eight nine ten eleven
[John:] So how many have you got altogether? Could you do it without counting them? You've got two sets of twelve.... How much would that come to.
[Kerry:] Two times twelve...
[John:] Could you do it by... adding up... on... paper?...
[Kerry:] Erm...
[John:] It was twelve add twelve wasn't it?
[Kerry:] Oh yeah.
[John:] Two ti two times twelve... is that the same as two add twelve?
[Kerry:] Yeah.
[John:] Yeah. Two sets of twelve so we could say... two times it or we could add twelve to twelve. Which which would be easier do you think?
[Kerry:] Erm... me tables' d be much quicker.
[John:] If you knew your twelve times or your two times up to twelve that would be quicker but if you don't...
[Kerry:] I've done the answer. [LAUGHTER]
[John:] Oh brilliant now how did you do it?
[Kerry:] Mm used me two times table.
[John:] You used your two times table good. So you had you had twelve pennies in one pile and twelve in another and you're doing twelve add twelve now you could have done... counted the whole lot couldn't you? One two three four That's take ages.
[Kerry:] [LAUGHTER]
[John:] Or you could take a bit of a short cut say well we've already got twelve there thirteen fourteen fifteen sixteen and so on. But that's a quicker way. That's really all we're doing we're just sort of counting how many would we have if we have twelve add twelve. Now if I'd said... how about if you had erm... sixty add sixty do you think you could do that?
[Kerry:] Sixty er
[John:] Have a have a go at that it's sixty add sixty.... Now is it easier if you write you them one under the other do you think? Yeah? Yeah most people find it a lot easier if you write them one underneath the other one.
[Kerry:] ...
[John:] Right good yeah that's correct. A hundred and twenty. Now that's much easier to do it on paper than if I say well the only way to find is let's get sixty pennies out, you count sixty I'll count another sixty then we'll see how many we've got. So it's just a quick way of doing counting really. A quick way of doing adding. When we do adding up, if we add two numbers together, we'll always get another number. Yeah? You've been doing quite a bit with... things that add up to ten haven't you and you've been doing things like seven add three... comes to ten and... three add seven... can you read my figures?
[Kerry:] Yeah.
[John:] Three add seven makes ten. It always gives you another number another counting number that you could use for counting your pennies. Now these counting numbers they're okay aren't they you know where you are with those no problem. So adding is okay when we add that's no problem. Now what about when we take away?... It goes a bit weird so we'll leave that for a while let's have a look at erm... what happens when we're doing times.... What happens when we're doing times now you did two sets of twelve didn't you?
[Kerry:] Yeah.
[John:] And you did that with your two times table so because times means the same as... sets of... or lots of.... It doesn't make any difference whether you say two times twelve,
[Kerry:] [sneeze]
[John:] two lots of twelve, two sets of twelve, two piles of twelve does it it's all the same. So times... multiplication... is the fancy word for it but times is good enough.... That'll always give you another counting number wouldn't it... because it's the same as adding really.... Say there we are you can add twelve add twelve or you can do two times
[Kerry:] Twelve.
[John:] two times twelve. Okay sixty add sixty or you could do
[Kerry:] Sixty you could do six times six two sixes.
[John:] You could do... two times sixty. That's it two times sixty. If if you had erm... eight eight add eight... eight add eight add eight....
[Kerry:] Eight.
[John:] How can you do it?
[Kerry:] Erm
[John:] Using your tables....
[Kerry:] Three times eight.
[John:] Three times eight or eight times times three doesn't matter which way you do it, it'd come to the same thing. Three times eight's better that's the the right way to do it. So really when you're doing times when you're doing your tables you're just doing adding aren't you. Adding lots of different... l lots of things that are the same. So times is okay. Three times four or four times three they just give us counting numbers again. Nice numbers that are easy to work with we can count out the pennies, count on our fingers, let you. Okay you can sort those out but when we get to take aways it goes a little bit odd doesn't it. So let's see, you've got... just check and see if you've got ten in that pile....
[Kerry:] Yeah.
[John:] Okay so if I do ten take away seven what do you think that will come to?
[Kerry:] Ten take away seven is... three.
[John:] Good now how did you get it?
[Kerry:] Erm
[John:] How did you work it out.... Cos you did that in your head you didn't use your fingers or anything how did you do it?
[Kerry:] Er... I u used like I did with the adds and
[John:] Alright.
[Kerry:] and then and then I s and then in me head I did erm seven... take away ten and then I worked it out and it turned out to be three. I had I had eight nine ten left in me head to make three.
[John:] Mm good so if you know what adds up to make ten
[Kerry:] Ten.
[John:] if you know seven add three make ten then you can work it out just in your head. Ten take away seven makes three. Okay so we can do things like that and we get counting numbers and we're quite happy with those. So it works sometimes take away but sometimes you get things like... ooh let's see... er I'm making a mess of this you can write it out nicely. Seven
[Kerry:] Take away
[John:] take away ten.
[Kerry:] ten.
[John:] So I'll say there we are you've got seven pennies there now take ten away.
[Kerry:] You can't. [LAUGHTER]
[John:] You can't... you can't and that's what people thought for thousands of years lots of years. They thought... you can't do it. But we we have these have you come across negative numbers?... Directed numbers?... On the number line?
[Kerry:] Erm yeah.
[John:] Yeah what did you think of them? A bit confusing. They can be very confusing if you don't know what it's about. Let's say I owed you erm... ten P. And I said, Oh well there we are... take it If I gave you a pound
[Kerry:] Yeah.
[John:] and said take that ten P out of that how much change would you give me?
[Kerry:] Erm ten pence out of a pound ninety pence.
[John:] Good you're very quick on money. Now if I said you know that ten P I owe you well there you are take it out of that seven pence.... And keep the change.
[Kerry:] [LAUGHTER]
[John:] How much more would you want?
[Kerry:] Erm three pence.
[John:] Three pence. So we call it minus three. We call it minus three I still owe you
[Kerry:] Three pence.
[John:] still owe you three. Okay if you try to take you've still got three to come
[Kerry:] Mm.
[John:] that means. Erm... we'll look at that then we'll look at the nu we'll have a look at the number line and we'll look at temperatures. Have you done do you remember looking at those. Do you ever watch the weather forecast and it says especially last or a few months ago say it'll be minus three tonight?
[Kerry:] Er... no.
[John:] No well it's... nought zero that's the temperature where water freezes. And if it's about four it's up here the normal four. So it'd go went down one it'd go to three, went down again it'd go to two. Went down another one what would it go to?
[Kerry:] One.
[John:] And then if it went down another one?
[Kerry:] Zero.
[John:] And if it goes down another one?
[Kerry:] [LAUGHTER] Erm
[John:] It's gone below zero. You just say it's gone to minus one.
[Kerry:] Minus one.
[John:] And then if it went down another one?
[Kerry:] Minus two.
[John:] And another one?
[Kerry:] Minus three.
[John:] Aha you've got it. Okay that's all that's all these minus numbers are about. Negative numbers, directed numbers all sorts of funny names for them and people get very confused about them but we'll sort those out we'll have a look at the number line which is a good way of doing it. So take aways sometimes they work and sometimes they give you a nice counting number and sometimes they give you this thing. Ooh what's this. Really it means we can't do it so we'll we make it up we've made up these funny numbers so that it'll always work. Cos we don't we don't like to say in maths we don't like to say we can't do it. And the same happens with sharing sometimes doesn't it erm... how many have you got there let's see?
[Kerry:] Seven....
[John:] Right there's twelve I'd like you to share that out between three people please.
[Kerry:] Three people.
[John:] Twelve shared out between Three people.
[Kerry:] ...
[John:] Okay we'll leave these out like that so we can see how many we're getting. That's it that's very good... okay.... and how many would they get each?
[Kerry:] Four pence each.
[John:] They'd get four each. Twelve twelve anything it could be twelve
[Kerry:] Mm.
[John:] twelve... cups of tea. Right twelve shared out between they'll get four each. Now how about this one then? Okay... there's three let's pretend they're pizzas say three pizzas share that out between twelve people.
[Kerry:] Er... twelve people
[John:] Mm.... Most people say say you can't do it you can't do that can you go on. Hey with twelve people and only three pi
[Kerry:] You'd have to cut it into twelfths.
[John:] Yes go on.
[Kerry:] You cut it into twelfths and then... you erm...
[John:] Good so if we cut the first into twelfth what how many pieces would they get out of that's be twelve pieces altogether okay.... And they'd get one of those each wouldn't they.
[Kerry:] Yeah.
[John:] And then what would we do with so that's the first pizza that's dealt with and they got a piece like that out of the first one. What would they do out of the second pizza?
[Kerry:] Erm
[John:] What would we do with that?
[Kerry:] Cut it into another twelve.
[John:] Cut it into twelfths again. Give them another piece. There they are with another twelfth for you.
[Kerry:] Another twelfth.
[John:] And the same for the last one brilliant. So they'd finish up with three pieces like that. Three twelfths and we know what three twelfths looks like. Three twelfths' d be one two three
[Kerry:] Two three
[John:] would be?
[Kerry:] Er a fourth.
[John:] A fourth a quarter.... So they're going to finish u they should finish up with a quarter so again this sharing sometimes it works okay and we just get a normal counting number. Say well that's okay. And sometimes we go, ooh no we've got fractions.... That doesn't matter. That's interesting isn't it. Twelve shared out between three you get four. Three shared out between twelve you get a fourth.
[Kerry:] Three between twelve you get a quarter.
[John:] Or a quarter as you say. How about this one how about twelve shared out between four how many would they get each?
[Kerry:] Twelve shared out... er...
[John:] Try those share those twelve out between four people.
[Kerry:] Mm one... two three... You get three pence each.
[John:] You get three pence each. Cos when we shared it out between three it was like if you just stand up and have a look along there. Okay?
[Kerry:] Mm.
[John:] There you are well you stand there that's a person standing there.
[Kerry:] Yeah.
[John:] And the dog can stand there and then that's there's the three people and they get four each. But if you look at it from this way four people standing there they'll get three each. So twelve shared out between four... they get three.
[Kerry:] Three.
[John:] Right how about four shared out between twelve people? How would you do that?
[Kerry:] Four shared out between...
[John:] What will that come to? That's that's not going to be as easy as the last one. How would you do it then?
[Kerry:] Er... Use them as pizzas maybe?
[John:] Yeah brilliant and what would you do with the first one?
[Kerry:] Erm cut it into twelve.
[John:] Cut it into twelve so they get one twelfth from the first one.... Carry on you tell me what
[Kerry:] Another twelve another twelve from the
[John:] Yeah.
[Kerry:] second one. And another twelfth for the third one and another twelfth from the fourth.
[John:] So how many twelfths would they get altogether?
[Kerry:] Erm four erm
[John:] Four they'd get four twelfths. Well that was three wasn't it?
[Kerry:] Yeah.
[John:] And another one... that's four... and that would make... how many how many twelfths in that?
[Kerry:] Erm... three three....
[John:] One two three
[Kerry:] Two three four.
[John:] Four.
[Kerry:] Four.
[John:] Four twelfths.... So four well that's interesting isn't it? Look four shared out between twelve
[Kerry:] Between twelve.
[John:] You get four twelfths.
[Kerry:] Four twelfths.
[John:] That's that's just another way of writing it. That's just the same thing it's not really answer you just say four shared out between twelve. And the same here three shared out between twelve it came to three over twelve didn't it?
[Kerry:] Yeah.
[John:] And that was the way you did it first. Your idea cut it into twelfths. Brilliant... and that came to the same as one quarter. And four twelfths came to the same as? One third.
[Kerry:] One third.
[John:] So twelve shared out between three no problem there we get four. Three shared out between twelves it comes to?
[Kerry:] Between twelve comes to a quarter.
[John:] One fourth a quarter. That was four that's one fourth. Mm. Four shared out between twelve
[Kerry:] Between twelve.
[John:] Sorry twelve shared between four?
[Kerry:] Between four is three.
[John:] But?
[Kerry:] Twelve divided by
[John:] Four.
[Kerry:] Four divided by twelve
[John:] That's it four shared out between twelve people
[Kerry:] Twelve comes to one third.
[John:] One over three. That was four and that's one over four. This was three and that's one over three.... Mm. How about this one? What would six shared out between two people give you?...
[Kerry:] Shared out... erm
[John:] How many twos make six?...
[Kerry:] Mm.
[John:] Two two whats would make six?
[Kerry:] Three.
[John:] Two threes are six so what we'll do is we'll say let's say how would you make six? You'd make it with two two lots of three.
[Kerry:] Three.
[John:] like that two lots of three. So six shared out between two we've shared it between two people they'd get three each. So the sharing's a bit like doing the times only the other way round isn't it like doing it backwards. That's the answer now what was the question. Yeah so sh six shared out between two is?
[Kerry:] Three.
[John:] Three. Have a guess at two shared out between six? Just have a guess at it.
[Kerry:] Two shared out
[John:] From what was happening here. We did twelve shared out between four was three. Four shared out between twelve was one over three. Have a guess.
[Kerry:] Two.
[John:] Er two shared out between six people. Here we are there's your two pi two pizzas now share that out between the six of us.
[Kerry:] Cut it into twelfths
[John:] Yeah we could use twelfths we could use we definitely use no no that'd be good. Right that'll work very well. Erm let's say... you and erm... and who's the other girl?
[Kerry:] Natalie and
[John:] And
[Kerry:] Gemma
[John:] And Natalie.
[Kerry:] and Joanne.
[John:] Joanne Okay well let's say you and Joanne and Jemma. You could share that one.... And I'll share the other pizza with your mum and is that your auntie so
[Kerry:] Yeah.
[John:] with your mum and your auntie. Okay so how many will you get when you share that with... Gemma and Natalie and you?
[Kerry:] Mm
[John:] How many people are there?...
[Kerry:] Three
[John:] Three
[Kerry:] Yeah.
[John:] so you're gonna get one shared out between three which is?...
[Kerry:] Three three is
[John:] You just you just write it like that one over three. A third a third. So it comes to a third. Let's see if we can do it a different way. Now you suggested you had a very good idea you said we could cut it up into twelfths. Okay... cut the first one up into twelve twelfths. Okay now there are six of us... how many twelfths will we get there are twelve of them. Twelve twelfths out of that out of that first pizza.
[Kerry:] Mm.
[John:] We didn't really need to cut it up into so many small pieces i would work but we'd get two of these each cos we've got twelve little pieces now and there are only six of us to share it out so we'd say, Oh well have er we'll we'll have two pieces each two twelfths.
[Kerry:] that'd be er a sixth.
[John:] Good. That'd be a sixth. Okay so we could do that in the first place we could say one pizza there well we've got two pizzas but we'll let's just concentrate on one, share it between six people.
[Kerry:] We'll we get sixths.
[John:] We'll all get one sixth that's dealt with one pizza what about the next pizza?
[Kerry:] Erm cut it up again.
[John:] Exactly same with that cut it into sixths. So we get another sixth. So how many sixths would we have altogether?
[Kerry:] Erm
[John:] As there are two pizzas.
[Kerry:] Two.
[John:] Two sixths oh well there's one sixth for you let's find the other one. That's how much that would be your share if we shared six pizzas between two of us and it's going to be the same as I said when i said well you share with your mum and Natalie.... Because two sixths is the same as?
[Kerry:] Erm fo a quarter third.
[John:] A third. That one's the quarter it's the one with the corner on. Okay it's a half of a half. It takes two of those to make a half. And there's the third same as two sixths. So it doesn't matter whether we look at it as whether you'd get a third or whether you say you'd get two sixths well it doesn't matter cos it's the same size it's just it's cut into two pieces or the way you wanted to do it which was a good way with the first pizza. Cut it into twelfths.
[Kerry:] Into twelfths.
[John:] And how many would you get you'd get two twelfths.
[Kerry:] Two twelfths.
[John:] Right... you'd get two twelfths out of the second pizza as well there's another two twelfths so you'd have four twelfths all together. So it doesn't matter which way you do it whether you get four twelfths, two sixths, or one third, they're all the same they all comes to the same thing. So four twelfths, two sixths, one s one third. If you share two between three of you... which is what we've just done... right?
[Kerry:] Yeah.
[John:] Let's just write down here I think what we've got hey? What did we do? We shared out... share out two... between six. Two shared out between six... is... So that's one of the answers that we got. Two sixths. You did it by twelfths and we got... four twelfths and the other answer we got was one third. So if we sort of put in here one one third what does it mean? Well it means just one shared out between three of you doesn't it? What does four twelfths mean?
[Kerry:] Means shared out between... four of us.
[John:] The the people always go under the table okay.
[Kerry:] shared it between twelve of us.
[John:] That's right and how many did we share out? It goes on top of the table.
[Kerry:] A quarter four.
[John:] Four when they're on top of the table it's just a number four okay. So that was four shared out between?
[Kerry:] Twelve.
[John:] Twelve of us. So it doesn't these are all the same all comes to the same amount doesn't it. You get the same piece of pizza whether it's two shared out between six, four shared out between twelve or one shared out between three... or... twenty four shared out between a lot of people.
[Kerry:] [LAUGHTER]
[John:] We could maybe work it out. So we've had a look at some of the numbers now haven't we and some of the things you can do with them. Adding up that's no problem you never get any surprises do we we all get another we always get sometimes it's hard but we always finish up with another counting number. Times sets of and lots of, that's the sam it's like counting in threes or counting in let's add another three, add another three add another three. Okay or add another six. So it's a bit like counting and we keep getting the same counting numbers that we're happy with. Take away what happened there? Well sometimes it works. When doesn't it work? When do we get these funny numbers?
[Kerry:] When... erm you have a lower number.
[John:] Very good very mathematical. Yes yes yeah when the first number is smaller than the second one. When you try and take away more than you've got. If I say there you are there's there's two P take five P out of that. Can't do that. It's when you you tend to say first thing you say is can't do that then you think, Oh well we get the we have to do it just playing silly game we get these funny numbers. It's just a game so that we can so that they can't say there caught you out. You have to say you can't do that I'll make up a new game to play. So they make up this game with negative numbers but it works very well it's very useful. Erm we need things like that for... windows and building bridges and things like that. Sharing sometimes no problem. When when do we get the problems with the sharing when does it go into fractions?
[Kerry:] Erm... when you have a lower number.
[John:] Right very good yes. When the number that we're sharing out when that's less than the number of people. And there's another there's a really awkward one. Do you want to go for it yes let's try it.
[Kerry:] [LAUGHTER]
[John:] A really awkward one you can get in sharing.... Let's say if we had... erm... six shared out between four okay?... One two three four five
[Kerry:] Six.
[John:] six. Okay... share it out between four mm. How many are we going to get? Well let's do it. Right give them one each to start with and then you've got two left over.
[Kerry:] [LAUGHTER]
[John:] Mm put them in your pocket. What are we going to do?... It's awkward isn't it.
[Kerry:] Yeah....
[John:] Well let's say there was Joanne and Natalie sitting there and you and me say.... That's one for Joanne, one for Natalie, one for Kerry... Now what would you do with the two that you've got left over?
[Kerry:] Er
[John:] What could you do?... If we were sitting together here and Joanne and N Natalie were sitting over there and we've got these two pennies?
[Kerry:] We could maybe... if we have Joanne, Gemma, Natalie, me, you
[John:] Mhm. No we've just got the four of us. Just got the four of us.
[Kerry:] Erm...
[John:] How about... forgot about one of the pennies for a minute this one if we shared that out between two of us. How if you get one each and then you get a half share in that.
[Kerry:] Mm.
[John:] So how much would you get out of this bit? What fraction would you get out of this if it was shared between two of us?
[Kerry:] A twelfth.
[John:] Just just between the two of us.
[Kerry:] Erm a sixth.
[John:] So it's it's one one pizza. Your mum brings the pizzas in she brings six pizzas in right great big ones. And she said Oh I thought there was supposed to be six of you here today, some didn't turn up. Okay so we've got six pizzas only four of us. So she goes round right there's a whole for you, and one for, one for you, one for you and she says, And you won't want any more will you? And everyone says, Ooh yes yes lovely pizza this yes. Oh so she's got to share it out evenly. So she could say How could she do it how would you do it?
[Kerry:] Erm
[John:] If you were the mum and you brought these pizzas in and there was four people sitting there... when you've got six pizzas and they all want the same size. Now we've done one each and we've got two now to share out between
[Kerry:] erm
[John:] these four people.
[Kerry:] Cut it into
[John:] Cut it into what size pieces would we cut it into?
[Kerry:] A twelfth.
[John:] Yeah we could cut it into twelfths but there are only two people so they're gonna finish up with lots of little bits aren't they if we cut it
[Kerry:] Yeah.
[John:] into twelfths. What do you
[Kerry:] Could cut it into er...
[John:] What could we cut it into?...
[Kerry:] Oh half.
[John:] Right good so we could just cut it into a half. We could say well there's our... it's a half for you and a half for you... and we cut the other one and they get a half each. If we if they weren't as quick as you are like that working that out what you could try is say well... I've given them one each there's the four people one two three four right you've all got a whole one so you can start eating that while I sort out how I'm gonna share this out. Now... this is the fifth pizza now how am I gonna share it out. Oh well there are four of them there so why not give them all... and I'll cut this pizza into
[Kerry:] Erm... quarters
[John:] Into quarters exactly cut it into four. So there they are while you're eating that another quarter each. And what shall we do with the last pizza so that
[Kerry:] Erm cut it into half again and
[John:] Cut it into?
[Kerry:] erm quarters.
[John:] Quarters again yeah and give them another quarter out of this so they get... they've got a whole one each and then we've got two left over. Now out of that two we'll say well share it out between the four of you... take a quarter each. Out of this one... take a quarter each so how many quarters would they get?
[Kerry:] Erm two quarters.
[John:] Two two quarters. There's two pizzas shared out between four so they're going to get? Two quarters. I think you're doing very well on this by the we're getting through an awful lot here it's usually even with very much older children they take a lot longer to get this.... So sharing out two six shared out between four what you'd normally write if you can't do fractions you'd say once remainder two wouldn't you.
[Kerry:] Mm.
[John:] You'd say once and two left over. You say well what are we going to do with those two left over? Well hide them. [LAUGHTER] But now we want them all shared out so... instead of saying one remainder two we writ it like this now. Six divided by four is one and... two left over we won't get two whole pizzas each we'll get
[Kerry:] Mm.
[John:] two... quarters two quarters. And what does two quarters come to?
[Kerry:] A whole?
[John:] one quarter
[Kerry:] A half.
[John:] is a half okay. Which is what you said earlier when you were working them out you said, Oh so they get one and a half each. one and a half. Now those I think and quite a lot of other people do are probably the most awkward ones. They're not hard once you understand what you're doing how you get it because you're sharing out but they're probably the most awkward when you've got mixed whole numbers counting numbers and fractions all in together. Erm then they get a bit awkward. So what I'd like you to do... when you get some... get a cardboard cutout.
[Kerry:] Yeah.
[John:] okay when you get those cut out you can just play with them just get used to the sizes and the shapes and erm... make sure that you ask someone. [tape ends]
[Kerry:] the erm...
[John:] Right so if someone holds up this piece and you hold up this piece to your mum and you say what sort of fraction is this? She says I don't know. You'll have to wait and ask John when he comes. Well let's work it out. How how could you work out?
[Kerry:] Erm...
[John:] Now this is this is the answer really what was the question. this is what we finished up with? Now what were we doing to finish up with a piece like that? We had a pizza and we were going to share it out between how many people?
[Kerry:] Erm... three.
[John:] Three so good you should find that three pieces just like that... the same size as that... would all... just fit together to make a whole. Right so that must be?
[Kerry:] A quarter oh a third.
[John:] A third. [LAUGHTER]
[Kerry:] [LAUGHTER]
[John:] Nearly you were going right all the way along there. right so that must be a third okay and... someone holds this up and says, What's that?
[Kerry:] A sixth.
[John:] Good. And just check it to make sure. Go all the way round and make sure you need six like that.... How did we get this piece. What were we doing to get that?
[Kerry:] Erm got the corner
[John:] Mhm.
[Kerry:] It's a fourth a quarter.
[John:] That's it it's a quarter. We were sharing it out between four so we got we we always say a quarter I think I think it's a good idea the way the Americans say a fourth cos you can it ties it up with the four shared out between four people. And you could do the same for the
[Kerry:] A twelfth....
[John:] Take you all day going all round with a twelfth wouldn't it. There's a slightly quicker way. You're happy with the sixth aren't you. There's a sixth. That was shared out between six people. If there were twice as many people
[Kerry:] You'd get
[John:] Just go on.
[Kerry:] two out of the s
[John:] You's have to get two pieces out of every sixth you'd have to cut that down the middle.
[Kerry:] So you'd just You'd just put the sixth if you know that there's two twelfth you just... like that and then the twelve and then you could count round like that
[John:] Right you could you can count round any way you like and the quickest way the easiest way that you're sure works that's the best for you.
[Kerry:] Is to work out how many sixths how many twelfths are in sixth
[John:] Right.
[Kerry:] and come round.
[John:] Right now I want you to do a bit of adding up okay. Erm... what would a third add a sixth make?
[Kerry:] A third add a sixth... put three add six down and then maybe
[John:] One one third just write down one third add one sixth.
[Kerry:] One third add one sixth.
[John:] Now I'll tell you the tell you the trick of what goes on here. You can't when you've got the numbers just like this it doesn't seem to work out so we've got to go back to find out what it means. Erm well... you could change them both into
[Kerry:] Sixths.
[John:] Into sixths very good. How many sixths there?
[Kerry:] Two.
[John:] And how many here?
[Kerry:] One.
[John:] So right so that's brilliant so underneath that third... how many sixths is it
[Kerry:] Two.
[John:] Two. So you could just write two sixths instead of that and it's the same. It doesn't matter whether it's one pizza shared out between three of us or as we tried earlier two shared out between six of us. You still finish up with the same amount. One third, two sixths, four twelfths all the same thing. Add one sixth okay. So just copy that one down underneath. Er two sixths add one sixth is going to come to how many sixths would you have?
[Kerry:] Three.
[John:] Three sixths okay so. You can just put your add in there as well. That's it. Equals three sixths. And three sixths makes?
[Kerry:] A half.
[John:] Okay. You could put there equals a half. Three shared out between six... we'd get a half. We could put ourselves in three lots of two and your mum came in with the three pizzas we'd get one between us so we get a half. Those two get one between none none for people peeping through the door though. Okay. I think we're getting very very well.... What about a a very awkward take away then if you're doing so well how about this there we are. A third take away a quarter.
[Kerry:] Quarter. Er
[John:] Let's see what it does come to? What do you think it comes to?
[Kerry:] Erm... comes to a twelfth.
[John:] Yep very good... it comes to a twelfth. Now we've got to make that's what really happens that's real. This is just playing games with the numbers to see if we can get the right answer. So how are we going to get the right answer? Well any suggestion if you'd like to write it down one third take away a quarter.... Mm any ideas?
[Kerry:] Erm... see how many quarters we've got there.
[John:] Mm have any quarters I mean you'd get one and a bit. Anything else we could try to see what're in a third?
[Kerry:] How many twelfths.
[John:] That sounds like a brilliant idea. Okay and how many twelfths?
[Kerry:] Er...
[John:] Instead of finding out how many twelfths in a third we could find out how many twelfths in two sixths couldn't we that'd be a bit easier.
[Kerry:] Four.
[John:] Four okay so underneath the one third you can write four twelfths.
[Kerry:] Just pick up my top
[John:] Okay.... Right mind you don't stand on it. Where's it gone? Where's it one. Patterned carpets are hard aren't they... to find things in.... Oh well I won't move in case I tread on. Oh you've got it.
[Kerry:] [LAUGHTER] It was by the door.
[John:] Right and how many twelfths in the quarter?
[Kerry:] Erm one two three....
[John:] So it's four twelfths
[Kerry:] A third and third three twelfths and a fourth.
[John:] That's it so it's four twelfths take away three twelfths.
[Kerry:] Three twelfths equals
[John:] How many twelfths would you have left if you started off with four twelfths then you took away three twelfths?
[Kerry:] Er one.
[John:] One twelfth left. And that's what we got with this. So that idea of yours change them all into twelfths... it's a brilliant one. That's that's the way we do fractions that's the way you do adding up fractions or taking away fractions you change them to the same. Okay.... Changed... if that's one third it's four twelfths one, two, three, four.
[Kerry:] Three, four.
[John:] How about this one? One th you try this one on your own. One third take away one twelfth.
[Kerry:] One... third... one third take away
[John:] Take away one twelfth.
[Kerry:] one twelfth.... Er... so you take away twelve?
[John:] Well what are you going to do with that one third what are you going to change that into?
[Kerry:] Erm twelfths so that'd be... four twelve twelfths.
[John:] Four twelfths good.
[Kerry:] That's fours twelfths and
[John:] Hang on... hang on you've just written a quarter you said four twelfths.
[Kerry:] Oh.
[John:] Okay four twelfths take away
[Kerry:] Take away one twelfth.
[John:] Take away one twelfth okay just write that down that you've got to take away the one twelfth.
[Kerry:] One twelfth erm One twelfth
[John:] Right so four twelfths and then you take away one twelfth. There's the four twelfths take away one twelfth. How many twelfths do we have left? We had four took away one twelfth
[Kerry:] three.
[John:] Three twelfths left. Equals three twelfths. And three twelfths is the same as?...
[Kerry:] A quarter.
[John:] A quarter.... So we can say that many that equals a quarter.... Right now have you done cancelling fractions?
[Kerry:] No.
[John:] No. Cancelling fractions is when somebody ha gives you somebody says erm you say, How much pizza did you get? three twelfths. three twelfths make it a bit more simple oh well it's just the same as three three twelfths is
[Kerry:] Same as a quarter.
[John:] A quarter. Okay if they said they got four twelfths.
[Kerry:] same as a third.
[John:] Same as a third exactly. If they said they got six twelfths?
[Kerry:] same as a half.
[John:] Very good okay try this one. A hard one nine twelfths.
[Kerry:] Twelfths same as a whole.
[John:] Twelve twelfths would make a whole wouldn't it. Now... nine twelfths
[Kerry:] Twelfths.
[John:] What would six twelfths be?
[Kerry:] Six er erm qua a half and a sixth.
[John:] A half A half good and then you'd have but we started off with nine twelfths so we'd have three other twelfths and three twelfths is the same as?
[Kerry:] A quarter.
[John:] Okay so nine twelfths would be enough to make make a half out of the six twelfths.
[Kerry:] two sixths.
[John:] Make a half... we'd make a half out of the six twelfths and then we'd have three left over make a quarter so it'd be a half add a quarter that's what nine twelfths would come to. There's the half it'd be the same as a half add a quarter. What does a half add a quarter come to?
[Kerry:] Erm
[John:] Well we usually change them into the same thing don't we if we're going to add them. So if we change them all into quarters how many quarters would there be in a half?
[Kerry:] Two.
[John:] Two. Two quarters add one quarter how many quarters altogether?
[Kerry:] So three.
[John:] Three quarters three quarters. Okay I think you're doing very very well on the fractions actually how do you feel? Do you think... you know what they're about don't you.
[Kerry:] Yes.
[John:] You're getting the hang of it. Now you need quite a bit of practice. You're understanding them now very well erm if you don't practise them a bit well this is what happens. You next time you come to do it you'll be doing you'll remember nearly as much as we're doing today but perhaps some odd little bits you'll think, ooh now how did we do that I can't quite work out. Cos we've done a lot haven't we. We've done a lot today. So some odd bits you might think, I'm not quite sure how you work that out. Not quite sure how you do that. So you might have to try and a try and find out again. Play with the fractions.
[Kerry:] Last night mister mister does those fractions
[John:] Okay now some people you mention fractions and they scream and run and, Ah no no hate fractions. and it's cos they don't understand them but you're understanding them I think very well now so you're going to like them. You get someone with a sharp knife
[Kerry:] Yeah.
[John:] to cut that out.
[Kerry:] Mm.
[John:] And then you can have your own fractions and you can just play with them and erm I'll give you some sums to do with your own fractions. Now we we'll have done some of them there and I don't want you to look there okay I want you to just try it
[Kerry:] I've got another book in me in me room. Quite a big book that I could use for doing me homework.
[John:] With fractions okay if you like to get that and I'll...... Right
[speaker001:] Do you take sugar in our coffee?
[John:] Er no sugar no milk.
[speaker001:] No sugar no milk
[John:] okay just the coffee that's lovely she's just gone to get a book for some homework. She's just popped up to get a book for some homework.... Aha right okay that's lovely. Now you haven't got any schoolbooks with you have you
[Kerry:] No.
[John:] the work that you're doing at school. No because when you when you are back at school erm...
[Kerry:] We bought a sheet home fractions on.
[John:] Did you could you could you find it fairly quickly do you think?
[Kerry:] Yeah.
[John:] Okay great. I'll write some of these out for you....
[Kerry:] Er... there
[John:] Aha let's have a look.... Mhm. Right so you don't know... you're not too sure about centimetres and millimetres hey?
[Kerry:] No.
[John:] We'll look at that some time.... Do you know how to multiply by ten normally?
[Kerry:] Yeah... but I got a bit stuck on that one
[John:] Mm it's a decimal thirty six point nine. How about this one? Fifty nine divided by ten. How many would you have left over? Oh lovely thanks very much.
[speaker001:] Okay.
[Kerry:] Erm
[John:] How much how much would you have left over here?...
[Kerry:] Ten er
[John:] Are you any good with money? I think you are. Sixty pence... sixty pence divided by ten... how many tens?
[Kerry:] It's divided by... ten...
[John:] How many ten Ps could you get out of sixty pence?
[Kerry:] Six.
[John:] That was quick it's the same yeah. Now if you only had fifty nine pence
[Kerry:] Fifty nine pence.
[John:] How many ten Ps could you get out of it?
[Kerry:] Er five and then nine
[John:] And nine left over. Okay so that one's five remainder nine isn't it you can change that one later. Okay. What decimal fraction of the circle is shaded?
[Kerry:] Shaded. Erm one two three four five six erm four...
[John:] From six whats how many what are these pieces. How many pieces to go all the way round. One two three four five six seven
[Kerry:] Three four five six seven eight nine ten
[John:] Right so they're tenths. So this was so they had a pizza sort of shared it out between ten people.... Okay so it's not just six that's that's shaded it's six tenths six out of ten okay. So that one'll be six six over ten. And that's a decimal fraction okay. And we'll have to change that to... we'll write it as six over ten then we'll write it as point six. We'll have a look at decimals because you need to... need to know what you're doing with decimals but decimals are fractions and until you I mean I think you're very happy with fractions now you're probably ready to go on to decimals. Erm we are I think do you. We'll sort them out cos they're just they're easy really. They're erm... they're just fractions where the bottom is always tens or hundreds or something like that so they're easier than some of the other fractions. So we'll have a look at those. Now which of these fractions, three tenths, point five, a quarter, point two. Well you can't... which is the largest?...
[Kerry:] Erm...
[John:] I think you need to know that nought point five... is five tenth five out of ten which is a half. So that's quite a big one so we don't don't bother about any of these the ones that have got tenths or decimals in we'll have a look at that.... The difference between okay. Now are you supposed to be doing all of these?
[Kerry:] No this sheet's from ages ago I found it in me desk when I was tidying it and er I asked me teacher if it
[John:] Mhm.
[Kerry:] was any good and she went, If you want to take it home and
[John:] Mm okay cos I see I'd like to know whether you're supposed to be doing decimals and things at the moment. It doesn't matter if we do it a little bit before you do it at school because when you do it you'll understand then and you can get a lot from it you can ask
[Kerry:] I think we're doing decimals in schools... at the moment.
[John:] You are okay. Well we'll have a look at that then. Erm now this is this this is very tricky these are... erm... mm aren't they? Hey some of these John's got forty pence and Paul's got two fifths of it. Hey and a cyclists speed... She bought a book for one seventy five... she gets seven fives
[Kerry:] to the rest of the rest of the
[John:] How would she do that then? How much would seven five come to? Seven five Ps.
[Kerry:] Seven... five Ps...
[John:] Let's have a look at number five... If she did something like this how much has she got to start to give. One seventy five
[Kerry:] One seventy five.
[John:] okay. Now she's going to give five Ps.... Seven five Ps. You've got a lot of really useful money here haven't you so you can you can work these out. Two three four five six... seven
[Kerry:] Four five six... seven.
[John:] Right seven five Ps how much will that come to?
[Kerry:] Erm ten twenty thirty five.
[John:] Thirty five okay.... Thirty five so we better take thirty five off cos she's already got thirty five hasn't she?
[Kerry:] Mm.
[John:] And how much would she have left if you took thirty five pence away away from one pound seventy five. How much would she have?
[Kerry:] Er...
[John:] You can just do it like a normal take away.
[Kerry:] It's thirty five...
[John:] From
[Kerry:] take away...
[John:] Forget about the pound thi seventy five take away the thirty five
[Kerry:] Seventy five take away thirty five.
[John:] So... she'd have one pound forty left so that's in five Ps.... In five Ps... thirty five. So you got one forty left how many tens would she need... to make one forty?
[Kerry:] One forty erm
[John:] One pound forty....
[Kerry:] Fourteen.
[John:] Good yeah fourteen great. Very good okay that's good. So that's how to do that one we could have a look at that. Mm... a week later than Christmas Day... Do you know about angles making right angles?
[Kerry:] Mm
[John:] No.... You maybe you've done it but... have forgotten. That's a right angle when it's like a like the corner of a square. A right angle ninety degrees. And have you done area and perimeter? How long is it all the way round something?
[Kerry:] Erm
[John:] No possibly not doesn't matter.
[Kerry:] I'm not too sure.
[John:] Now we'll we'll we'll concentrate on some see with maths you have to do things in certain Are we supposed to be doing maths today are we supposed to be doing English?...
[Kerry:] I'm not too sure....
[John:] Well we'll conc best to concentrate on the just on the fractions. Erm
[Kerry:] But you said you were gonna bring me some erm these special tables.
[John:] Did I... ooh well I haven't I'm sorry to say. Erm... right... er... now definitely by the time I see you next time... if not before... erm I'll get them okay. If I've got to print them off from my computer and the computer's... er not exactly in bits but it's just taken apart a bit at the moment so I need to put it back together again and print them off. So I'll do that very soon.... Now let's sort you out some fractions.... So... before adding... or taking away... fractions okay. Before adding or taking away we get the number on the bottom to be the same right.... And how do we do that? It's easy enough saying it isn't it.... Okay erm I'm just trying to think what I'm doing later.... I'll get those fractions those multiplication tables printed out and get you a copy in the next few days okay.... The bottom's the same on both fractions. How d how do we make sure that the number on the bottom is the same?...
[Kerry:] Erm
[John:] How did we do it when we doing some of these back here?... For example when we had erm... When you were doing these tricky things. Like a third take away a quarter how did you do it?...
[Kerry:] Three... You put the fractions
[John:] Okay so you change the fractions you change the one third and you change the one quarter into into what?
[Kerry:] Twelfths.
[John:] Into twelfths in this case you change them into twelfths to see how many twelfths it would be. And erm with these... you changed them both into sixths didn't you could have changed them both into twelfths and it would have work but then we'll get an answer that needs... we would have got... sixth twelfths... well it still comes to a half. But it's just a bit more awkward to work out what six twelfths is maybe. So I'll give you some here to do. Some of them will be the same ones that we've already done so don't look at the don't look at these... just try them on your own try and remember how you did them. And if you get stuck go back and have a look how you did them here. So... I'm going to do... erm... a half add a third... okay... and... a third add a quarter... and... a half take away a third... okay and I'll give you another one to do... How about this one. I'll leave you to sort out you're own own way of doing this.... Two thirds add a quarter. Okay? I haven't told you how to d I've told you how to change one third we've looked at that haven't we and we and we've worked out sort of how many twelfths would be in it and things like that. I'll leave you to work out on your own. Don't worry if you can't do it if you can't any of these any of these exercises that I give you by the way it's not like homework it's just for you to play with them to get the do them at your own pace. So that you feel happy with it so that you, Oh yeah now I understand what he's talking about. Now I can do it myself. That's the idea cos... when it's the exam I can't come in and do it for you or show you how to do it. You'll be doing it on your own so that's what I want you to do to get so you can do it on your own. Try those erm... and with the with the coins... what I'd like you to do now is not find out all the things that add up to twelve. Find out what numbers times what other numbers would make twelve. So can you g tell me any numbers that you could any two numbers you could multiply together to make twelve.
[Kerry:] Er... erm... eleven and one.
[John:] Those are adding.
[Kerry:] Oh.
[John:] Okay good yeah they are that's good that would add together to make twelve but how about... some number times another number....
[Kerry:] One times... twelve.
[John:] Good okay so twelve we could have one times twelve... right....
[Kerry:] Five times two.
[John:] well let's see. Let's get twelve coins this is the easy way to do it I think. One two three... one two three four five six seven eight... nine ten... how many more do we need?...
[Kerry:] Er.
[John:] I want twelve I've got ten there. How many more do I need
[Kerry:] three
[John:] Another... I've got ten
[Kerry:] Two.
[John:] eleven
[Kerry:] Twelve.
[John:] twelve okay so it needs another two. So there we are we've got one lot of twelve... or we might be able to have two lots of what see what you can make with it for two lots.
[Kerry:] Two lots of mm.... Two lots of... five. Six.
[John:] Okay so we could make one lot of twelve... we could make two lots of six. See if you could make three lots of something....
[Kerry:] Three lots of four.
[John:] Aha. Three lot of four. Okay... and could you make four lots of something.... You've already you're doing very good.
[Kerry:] Four lots of three.
[John:] [LAUGHTER] Four lots of three I haven't got time to write that down that was very quick. Good four lots of three and could you make five lots of anything?
[Kerry:] Erm
[John:] No.
[Kerry:] No.
[John:] You could make five lots of two but you'd two left over so it wouldn't go evenly okay. So you can't do five lots okay that was you that was trying five that didn't work so try six what will happen there.
[Kerry:] Er...
[John:] So you're going you got... okay now we've got six lots of
[Kerry:] Twos.
[John:] Two okay six lots of two.... Six times two. And then you could have twelve lots of...
[Kerry:] One.
[John:] Twelve lots of one.... Right... so I think that you've done twelve right just now showed me how to do it. I want you to do the same for twenty four... and you won't get it all on one line there'll be a lot of them and then try it for thirty six... and when you're really happy with twenty four... when you're happy with twelve and you can write all those out quite happily without looking at this... try twenty four see if you know see if threes' ll go fives' ll go and sevens and everything else. And then try it with thirty six. And then I don't particularly want you to start yet but if you do get time or if you're just interested and you don't want to stop and you want to keep going... try it with sixty.... Sixty pennies put them out. Make sure you don't put them straight on the table though. Newspaper's fine cos you can slide them about or a towel like this. Now... of what we've been doing today with fractions was there any of it that you're not quite sure of and you think, But could you just tell me about that bit again.
[Kerry:] Er...
[John:] How do you feel about it you feel fairly happy with it?
[Kerry:] Yeah.
[John:] We've done a lot today you know we've done a lot of things about fractions and a lot of things about adding, subtracting,... times, sharing quite a lot. So if you don't remember all of it. Don't worry and always ask me if there's something that we did last time and I start ta
[Kerry:] [sneeze]
[John:] I start talking about it as though you know
[Kerry:] [sneeze]
[John:] and you're if you think, Ooh I'm I'm not quite sure what he means by that. always ask me never never just let it go and think, Oh well perhaps I'll understand it later. Cos you've probably found that already with maths haven't you that once there's a little bit you don't understand they start putting more and more on that... you need to know that little bit for and you... you don't know it and you're getting more and more lost and then it gets a bit late then.
[Kerry:] It was only it was only that erm you know erm when you said the sixty pen pence it was the one that was the only one that I seemed to get stuck on. Okay well I'm not too bothered about adding those up. Adding up to ten fine, adding up to twelve that's good that's useful, adding up to sixty one... don't bother doing that again better concentrating on these. Seeing what things' ll multiply together to make twenty four thirty six and sixty. Okay.the don't look at these... just try them Yeah.
[John:] So it's just coming up to five to that's okay. Erm... now would you like to write something for me. Yeah if you can write erm... don't think of it as as homework you might like to writ it in book or something. When when I've when I've gone if you just write about what you think about the lessons. Whether it's a good idea me coming here, what are the good things, what are the bad things. What are the things that you'd like it if it was a bit different you'd like it better if it was... a bit more of this and not so much of something else in it okay.
[Kerry:] Mm.
[John:] Erm... and I'll have a look at that and see how your how your writing's doing.
[Kerry:] Okay.
[John:] Okay is that alright. Oh hi.... So... And don't forget to put the good things and what are the very good things.... the things that could be better and the things you'd like more or less of....
[Kerry:] I think there could be more of
[John:] Erm what thin would you like to do more fractions, more counting or you you think whatever it is that you'd like to do more of or is there anything you think we do too much of and we don't you don't want to do as much....
[Kerry:] [sneeze]
[John:] Oh dear.... those. Now... what did you think about this lesson was it a bit boring at some time or you think, Oh or did it go too quickly No. You'd like to spend a bit more time doing things and not do so much in one go?
[Kerry:] Er... it went alright really.
[John:] Okay. If you think we're doing too much you can sort of say, Ooh hang on. Because I want to do as much as we can during the holiday so that when you go back you you're up there with the rest of them okay. Erm if I try and do too much you might see you might be forgetting as much as you learn mightn't you and that's why it's important for you to do these do these exercises. Okay erm if you want to call your mum I'll just
[Kerry:] Yeah.
[John:] show her what you're doing there so that
[Kerry:] Okay.
[John:] she'll know as well. Or you can show her okay....
[speaker001:] Hi.
[John:] Hi I'll just just show you what er well Kerry'll 'll show you she knows what er what we're what you're going to do over the next day or so don't you.
[speaker001:] Yeah.
[John:] We're just playing with twelve pennies and she's making patterns out of them to make multiplication tables
[speaker001:] Mhm.
[John:] really. So she's trying to find out well the ones these are all one that Kerry suggested. Okay you could have one set one set of twelve. Okay that's how you could make up twelve coins one set of twelve. And then what's the next thing you tried? You tried putting them in two two sets of how many. So she tries that and what does that make?
[Kerry:] Erm two sets of six.
[John:] Okay and then carry on... Okay so now you've made three sets of
[Kerry:] Sets of four.
[John:] Three sets of four okay and you can just turn that round and look at it that way now. You've got four sets of three.
[Kerry:] Four sets of
[John:] Okay and... you made six sets of
[Kerry:] Twelve.
[John:] Six sets of two.... Right didn't you.
[Kerry:] Erm
[John:] So... that's it just go along the bottom one two three four five six okay, And then you won't move those and what can you do there? That's it six sets of two. And you tried five didn't you
[Kerry:] Yeah.
[John:] tried sets of five... but it nearly but you two two left over so that's no good
[speaker001:] Mm.
[John:] It doesn't go exactly into twelve. So five won't go. But we can find all the things that'll go into twelve. Well Kerry's going to do the same thing for twenty four. And then when she's really happy with twelve and with twenty four she's going to try thirty six all the different sets of one times another to make thirty six.
[speaker001:] Mhm.
[John:] And sixty is a bit much I think but if she you know if you want to go on and you're really happy you can do anything you like with these thirty six and twenty four... no problem there then go on and try sixty. You'll need a as I said put er put some paper on the or some newspaper won't scratch it.
[speaker001:] Oh she'll be in the kitchen Yeah
[John:] Okay kitchen table's ideal for sorting your money out on. So try that and the fractions. Be best cut out with a sharp knife that something like a Stanley knife
[speaker001:] Yeah.
[John:] rather than scissors. But just cut it out and then she'll just use the back and... she'll play about with some... helping to get some answers to these fractions
[speaker001:] Mhm.
[John:] and then just generally play with it say, Oh I wonder what would happen if you put two thirds together, how many twelfths would that be or what about if you had a third and you wanted to take a quarter away, if you cut a quarter off it. What would you have left?
[Kerry:] A twelfth.
[John:] Brilliant yes really good. She's really coming on well
[speaker001:] Mm.
[John:] with the fractions. You you like them don't you cos you're understanding them now. It's all about understanding if you understand something you can like it.
[speaker001:] Yeah.
[John:] But if you don't understand it and you're lost you just get to hate it you think, Oh no I can't stand that. So it's it's getting but you're coming along very well aren't you. I didn't bring the erm multiplication table that I promised either so I was late and I didn't bring that. I'll go and stand in the corner I think for being naughty. But erm I'll get that to you in the next... couple of days or so. Now what did we say about the next lesson? We wanted to g get one or two in during the holiday really I think
[speaker001:] Mm.
[John:] what... you see the idea is to get Kerry getting as much benefit from school as possible so you're not having to pay me
[speaker001:] No.
[John:] to do the lessons that Kerry is understanding it so she can. Once she's c more or less caught up doesn't have to exactly catch up just have some idea of the basic stuff that they're talking about
[speaker001:] Yeah.
[John:] and then you can just when the teacher says that, you know what questions to ask at least. if you don't if you're just lost you feel daft don't you. So you don't ask and you get sort of so that you understand less and less and eventually you think, Oh I don't feel like going to school today it's fractions again. Yeah so... just to get you so you understand about fractions, you know what's going on and you can ask intelligent questions and your teacher'll think, Oh she knows what she's talking about. She doesn't know how to do it but she knows what to ask and how to get there. So... erm where are we bank holiday Monday next week... I think you probably probably got enough to play with Tuesday. [tape ends]