| PS1SY | Ag4 | m | (John, age 50+, tutor) unspecified |
| PS1T0 | Ag0 | m | (Simon, age 9, student) unspecified |
| FMHPS000 | X | u | (No name, age unknown) unspecified |
| FMHPSUNK (respondent W0000) | X | u | (Unknown speaker, age unknown) other |
| FMHPSUGP (respondent W000M) | X | u | (Group of unknown speakers, age unknown) other |
| Unknown speaker (FMHPSUNK) |
[1] Okay. [2] ... Now what we'll do do you like pizza? |
| Simon (PS1T0) |
[3] Yeah. |
| John (PS1SY) |
[4] I've got some stale pizza here do you like stale pizza? [5] ... Do you we could make that into a whole pizza? [6] ... Okay right that's lovely. [7] Now do you know what any of these are? [8] Do you know what fraction that would be of a whole pizza? |
| Simon (PS1T0) |
[9] Er ... |
| John (PS1SY) |
[10] What fraction's that? [11] ... Well don't worry if you don't know. [12] How many of those would you need to make a whole pizza? |
| Simon (PS1T0) |
[13] Erm |
| John (PS1SY) |
[14] Let's have a look ... one ... two ... |
| Simon (PS1T0) |
[15] Three ... |
| John (PS1SY) |
[16] And this one here? ... |
| Simon (PS1T0) |
[17] erm four. |
| John (PS1SY) |
[18] So we need four of those to make a whole pizza so we call that ... a fourth well the Americans call it a fourth |
| Simon (PS1T0) |
[19] Fourth. |
| John (PS1SY) |
[20] we call we've got a special name for it we call it a quarter . |
| Simon (PS1T0) |
[21] Quarter. |
| John (PS1SY) |
[22] And we write it like this. [23] ... It's one on the top and there's the table and then |
| Simon (PS1T0) |
[24] Mhm. |
| John (PS1SY) |
[25] the fourth underneath. [26] One shared out that just means one shared between four. [27] Fra fractions are a bit of a cheat really because this is what we do we say ... [whispering] let's have a look at the page [] ... how much would you get if you had one and you shared it out between four and you just write well it's one shared out between four. [28] You haven't really got the answer at all you've just written it differently and that's all it means whatever you're sharing out goes on the top what ever number of people of people it's being shared out between go underneath. [29] Erm do you normally sit on the table stand on the table? |
| Simon (PS1T0) |
[30] No. |
| John (PS1SY) |
[31] No. [32] if your mum brought a pizza in would we put it under the table or on the table? |
| Simon (PS1T0) |
[33] On the table. |
| John (PS1SY) |
[34] On the table so whatever you're sharing out goes on top there's the table ... put some little legs on okay there's the table whatever you're sharing out goes on top and we're sitting here with our knees under the table okay so the people are underneath the table. [35] How about if we had one shared out between three people have a guess at what it would look like the fraction. |
| Simon (PS1T0) |
[36] One ... erm three. |
| John (PS1SY) |
[37] One over three that's a third. [38] Now can you show me here any are there any pieces there is there a piece there that would be a third? [39] So that you'd get move those round a bit so that you'd get Say that pizza came in like that and your mum sat down there said, Right we're having some pizza we're going to share this out between the three of us so we all get the same sized piece. [40] How big a piece would we get? |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[41] One of those? |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[42] How many how many pieces like that would you get out of it? [43] ... A lot I think cos this this bit's a quarter isn't it and we'd get that'd be enough if we cut it into quarters how many quarters would we get? |
| Simon (PS1T0) |
[44] Erm ... |
| John (PS1SY) |
[45] How many of those would we get? |
| Simon (PS1T0) |
[46] Erm [...] |
| John (PS1SY) |
[47] Right right that'd be that'd be the same as well wouldn't it that'd be another quarter. [48] How many ... How many quarters would we get out of this piece here? |
| Simon (PS1T0) |
[49] One two |
| John (PS1SY) |
[50] Two so so we'd get four quarters right four fourths if you like that's one fourth one quarter. [51] We'd get four fourths. [52] So if there are less people sharing it out are we going to get more pizza or are we going to get less? |
| Simon (PS1T0) |
[53] More. |
| John (PS1SY) |
[54] We're going to get more so it's going to be a bigger piece that that isn't it it's going to be bigger than the quarter. [55] Can you see any pieces that are bigger than the quarter? |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[56] That one okay. [57] So let's see if we could get three pieces like that out of a whole one? [58] ... Yeah cos these that'd make another one wouldn't it. |
| Simon (PS1T0) |
[59] Mm. |
| John (PS1SY) |
[60] Let's have a look. |
| Simon (PS1T0) |
[61] One |
| John (PS1SY) |
[62] One two |
| Simon (PS1T0) |
[63] two |
| John (PS1SY) |
[64] And this one do you want to put that on there. [65] ... And they'd be all the same size so if we had a piece like those two stuck together |
| Simon (PS1T0) |
[66] Three. |
| John (PS1SY) |
[67] that'd be that'd go round three people evenly so that'd be a third if we had these two pieces stuck together that'd be a third |
| Simon (PS1T0) |
[68] Yeah. |
| John (PS1SY) |
[69] and this one that's a third . |
| Simon (PS1T0) |
[70] Third. |
| John (PS1SY) |
[71] So one shared out between three people is a third. [72] Now what I'd like you to do is show me can you divide it up if we were going to eat this whole pizza between the two of us if it was one one shared out between two people how much would we get? |
| Simon (PS1T0) |
[73] Mm. [74] ... Erm [...] |
| John (PS1SY) |
[75] Show me again. |
| Simon (PS1T0) |
[76] Those |
| John (PS1SY) | [...] |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[77] Would that be it? |
| Simon (PS1T0) |
[78] Yeah. |
| John (PS1SY) |
[79] So that how big a what's that [...] ? |
| Simon (PS1T0) |
[80] Half. |
| John (PS1SY) |
[81] That's a half. [82] So one ... shared out between two people is just one [...] a half again okay. [83] Where do you think erm how would we write one shared out between six people? [84] How would we write it? |
| Simon (PS1T0) |
[85] One and the table and then the six. |
| John (PS1SY) |
[86] That's it ... so that's what a sixth looks like. [87] What does it mean? [88] Well it means we had one and we shared it out between six people. [89] Now any idea what one sixth would look like? [90] We found out what one shared out between three people is like that's a third. [91] If we shared it out between six people would we get more or would we get less? |
| Simon (PS1T0) |
[92] Less. |
| John (PS1SY) |
[93] We'd get less wouldn't we. |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[94] [...] erm how many of how many of these would we need to go all the way round? [95] ... It takes two of those [...] takes two of those to make a third to make [...] . |
| Simon (PS1T0) |
[96] Two. |
| John (PS1SY) |
[97] So how many thirds did we have? ... |
| Simon (PS1T0) |
[98] Three |
| John (PS1SY) |
[99] Three thirds that's it three thirds. [100] Now let's say let's say your mum came in and she said how many for this pizza and we said oh just the three of us and she cut it ... cut it up into three pieces three pieces all the same size. [101] Cut it into three thirds. [102] Show me how how big they'd be. [103] Show me which one's a third. [104] ... Right that one or those two stuck together would make a third. [105] Or these bits stuck together. [106] So we'd get one third and then just as we were going to eat it three other people came in. [107] And said, Oh can't we have some. [108] How would you share it out so we all got the same? [109] ... We you you've got let's say let's say there's your third you've got your third. [110] And I'm sitting next to you right. [111] And ... so there are six people all together there's your mum and your dad okay and then there's two friends over there and we're sitting here. [112] So mum and dad have half of that third they'd share it out between them so they got |
| Simon (PS1T0) |
[113] Mm. [114] Me and me friend'd have half of that one . |
| John (PS1SY) |
[115] Yeah yes. [116] So you'd need six |
| Simon (PS1T0) |
[117] Six. |
| John (PS1SY) |
[118] of these six pieces like that. [119] Now that's what's that Kerry if we get six like that make a whole one? |
| Simon (PS1T0) |
[120] A half oh |
| John (PS1SY) |
[121] If it needs six like that to make the whole one these this is one sixth. [122] Cos this is what you get if you have one shared out between six people so they all get the same okay. [123] So that's that's one sixth okay. [124] Now don't worry about this is it going do you think it's going a bit quickly? [125] Okay. [126] Do you think we're doing a lot all in one go? [127] Mm I'll just ... show you one last one and then we'll we'll we'll start this again and have a little look at the beginning. [128] Now let's say we've done that we thought there were three people here so you though you were getting a third right. [129] And then there were twice s many people there were six people. [130] So you had to share yours with someone else and you just got a sixth okay. [131] And then just as you were about to eat that another six people turned up so there were twelve altogether and you'd have to shar share that |
| Simon (PS1T0) |
[132] Yeah. |
| John (PS1SY) |
[133] with some one else. [134] Let me just get [...] down there. [135] [...] just get that little piece. [136] Now that's the piece that you'd get if there were twelve of you sharing out one pizza so what do you think that's called? [137] Have a guess doesn't matter if it's not right. |
| Simon (PS1T0) |
[138] A twelfth? |
| John (PS1SY) |
[139] A twelfth yes great that's a twelfth and how would we write it? |
| Simon (PS1T0) |
[140] One |
| John (PS1SY) |
[141] Shared out between twelve people equals what would it look like ? |
| Simon (PS1T0) |
[142] [...] equals one ... table [...] |
| John (PS1SY) |
[143] One and then th one on top of the table and underneath? |
| Simon (PS1T0) |
[144] Twelve. |
| John (PS1SY) |
[145] Twelve that's it. [146] So that's one twelfth and that's what it looks like. [147] How many twelfths would you need to make a sixth? |
| Simon (PS1T0) |
[148] Two. |
| John (PS1SY) |
[149] Good and how many sixths how many sixths would you need to make a third? |
| Simon (PS1T0) |
[150] Two. |
| John (PS1SY) |
[151] Erm how many ... how many twelfths would you need to make a quarter? [152] Think how many you'd need. |
| Simon (PS1T0) |
[153] That's one three. |
| John (PS1SY) |
[154] Three right so ... perhaps someone had divided this pizza up and all the extra people kept coming in and your mum was saying, Oh no I thought there were going to be three and now there's six of us. [155] Right cut it into six. [156] Oh no more turning up twelve of us cut it into twelfths. [157] Yeah and then she's already cut it up into twelfths like this and then she thinks about asking them who wants pizza and there's only four of them want pizza [...] after all this trouble. [158] So one pizza shared out between four people how much are they going to get each? [159] ... One shared out between four is? |
| Simon (PS1T0) |
[160] A fourth. |
| John (PS1SY) |
[161] A fourth or a special name for it a quarter |
| Simon (PS1T0) |
[162] Quarter. |
| John (PS1SY) |
[163] and that's what it looks like. [164] So we'd have that but she's already cut them all up into twelfths so how many twelfths how many twelfths would we get each? |
| Simon (PS1T0) |
[165] Three. |
| John (PS1SY) |
[166] Three so she'd say, Oh [...] you know mind I've cut it up a bit do you [...] you shouldn't it's still a quarter still a quarter you haven't lost a bit of it [...] but it's still a quarter [...] three twelfths is the same as a quarter. [167] [...] exactly the same isn't it you get the amount. [168] How about how about if she had erm say [...] just the two of us |
| John (PS1SY) |
[169] just the two of us |
| John (PS1SY) |
[170] and share one pizza between the two of us how much would you get each? |
| Simon (PS1T0) |
[171] Er ... |
| John (PS1SY) |
[172] So it's it's one shared out between two. |
| Simon (PS1T0) |
[173] Yeah a half. |
| John (PS1SY) |
[174] A half right. [175] So your mum's cut it up or you've cut it up this time just between the two of us and you've cut it into two halves you've got half there and I've got another half. [176] And then another two people come in so we've got four people all together. [177] How much are we going to get now if we share one between four people? [178] ... It'll be |
| Simon (PS1T0) |
[179] Thirds. |
| John (PS1SY) |
[180] one shared out between four |
| Simon (PS1T0) |
[181] Fourths. |
| John (PS1SY) |
[182] A fourth exactly a fourth. [183] So we'll get a fourth we get one of those how many fourth would you get out of a half? |
| Simon (PS1T0) |
[184] Two. |
| John (PS1SY) |
[185] Two you don't do you remember the special name for a |
| Simon (PS1T0) |
[186] Quarter. |
| John (PS1SY) |
[187] Quarter so how many quarters would you get out of a half? |
| Simon (PS1T0) |
[188] Two. |
| John (PS1SY) |
[189] Right and how many halves make a quarter? ... |
| Simon (PS1T0) |
[190] Mm one. |
| John (PS1SY) |
[191] How many oh I said that the wrong way round didn't I. |
| Simon (PS1T0) | [laugh] |
| John (PS1SY) |
[192] How many quarters make a half? |
| Simon (PS1T0) |
[193] Two. |
| John (PS1SY) |
[194] Two brilliant. [195] Very good okay. [196] Erm ... can you remember what size that is? |
| Simon (PS1T0) |
[197] It's a quarter. |
| John (PS1SY) |
[198] Let's have a look that one is a quarter and this one's a bit bigger. |
| Simon (PS1T0) |
[199] A sixth. |
| John (PS1SY) |
[200] So we must be shared now this is the interesting thing which do you think is bigger, a a sixth or a third. |
| Simon (PS1T0) |
[201] A third. |
| John (PS1SY) |
[202] Yeah in the the number on the bottom is bigger but that just means you've got to share it out between more people so do you get more or less if you share it between more people? |
| Simon (PS1T0) |
[203] Less. |
| John (PS1SY) |
[204] You get less. [205] So as the number on the bottom is getting bigger ... |
| Simon (PS1T0) |
[206] You get less . |
| John (PS1SY) |
[207] the fraction's getting smaller and smaller the piece you get is getting less and less. [208] That was all we got when it was a twelfth a little tiny piece like that. [209] [laugh] So that's a sixth and that's a third which is bigger? [210] ... Yeah which one's bigger? |
| Simon (PS1T0) |
[211] The the sixth. |
| John (PS1SY) |
[212] The |
| Simon (PS1T0) |
[213] Third. |
| John (PS1SY) |
[214] The thir it sounds as if the sixth should be bigger doesn't it cos it's got a six in it. [215] A third's only got a three in but the third is bigger. [216] How many sixths would you need to make up a third? [217] Try it. [218] ... Try this. |
| Simon (PS1T0) |
[219] Mm. [220] ... Erm two. |
| John (PS1SY) |
[221] Two so two sixths would make a third. [222] Now this is two sixths that we've use to make the third. [223] How many twelfths would make a sixth? [224] A sixth. [225] Okay here here's a sixth |
| Simon (PS1T0) |
[226] Mm. |
| John (PS1SY) |
[227] and how many twelfths would make a sixth? ... |
| Simon (PS1T0) |
[228] Two. |
| John (PS1SY) |
[229] Right very good. [230] Now a tricky one how many twelfths would make a third? [231] There's the third two sixths how many twelfths would you need? |
| Simon (PS1T0) |
[232] One ... two |
| John (PS1SY) |
[233] Two okay. |
| Simon (PS1T0) |
[234] three |
| John (PS1SY) |
[235] Yeah. |
| Simon (PS1T0) |
[236] four. |
| John (PS1SY) |
[237] Four so four twelfths'd make a third. [238] So if our mum had cut it up into twelve pieces and then only three people wanted pizza so she cut it up into twelve twelfths and then said who wants pizza and only three people wanted pizza she'd now have to put some of these twelfths back together again then and just three of us how many twelfths would we get? ... |
| Simon (PS1T0) |
[239] One two three four. |
| John (PS1SY) |
[240] Four so we'd get four twelfths. [241] Okay what do you think about fractions? |
| Simon (PS1T0) |
[242] They're hard when you know how to do them but like |
| John (PS1SY) |
[243] If you don't know what they mean i anything if you don't know how to do it it's hard but if you don't even know what they mean it's very hard to work out what's going on isn't it and what you're supposed to be doing. [244] Do you think you're getting a a better idea of what they mean what it's about. [245] It's just sharing out. [246] I mean if I said, Share six Mars bars between two of us. how many would we get each? ... |
| Simon (PS1T0) |
[247] Erm [...] |
| John (PS1SY) |
[248] Six Mars bars share them out between two of us. [249] There's six share it out between the two of us. |
| Simon (PS1T0) |
[250] Three each. |
| John (PS1SY) |
[251] Three each okay now if I said share erm ... if I said share ten pence between five people how many would they get each? [252] ... Well how many fives make ten? |
| Simon (PS1T0) |
[253] Two. |
| John (PS1SY) |
[254] [...] two each. [255] Now if I said share five pence between ten people what would you say about that? ... [...] a bit hard isn't it. [256] Mm. [257] So ... say we put the people into pairs into sets of two. [258] How many sets of two would those people make then if there were ten of them? [259] How many twos make ten? ... |
| Simon (PS1T0) |
[260] Five. |
| John (PS1SY) |
[261] Five good so we'd have all the people sitting round a table five sets or two. [262] Perhaps they could both sit on one chair between one chair between the two of them. [263] And then with the five pennies we could say well penny between you two, penny between you two, another penny between you two, between you two,an . [264] So that the five pence we shared it out and we've given each two each two people one penny between them. [265] How much would they have then? [266] If we had the penny between the two of us how much would we get each? |
| Simon (PS1T0) |
[267] Nothing. |
| John (PS1SY) |
[268] Nothing okay if we had the pizza between the two of us how much would we get each? [269] ... One shared out between two. [270] ... How much would we get each? |
| Simon (PS1T0) |
[271] Half. |
| John (PS1SY) |
[272] That's it okay. [273] Erm so if we had one penny shared out between two of us we get a half a penny each a half penny which they don't have any more they used to but they have them any more. [274] So fractions it's only sharing. [275] It's just like sharing I mean if we had two pizzas and we shared them between the two of us how many would |
| Simon (PS1T0) |
[276] [...] whole. |
| John (PS1SY) |
[277] We'd have a whole one. [278] If we had erm four pizzas and we shared them between the two of us how many would we get? [279] ... Four share it out between two of us |
| Simon (PS1T0) |
[280] Two. |
| John (PS1SY) |
[281] We'd get two each. |
| Simon (PS1T0) |
[282] Mhm. |
| John (PS1SY) |
[283] If we had six pizzas and we shared them out between two of us how |
| Simon (PS1T0) |
[284] [...] three pizzas each. |
| John (PS1SY) |
[285] We'd get three each so it's just fractions are just sharing. [286] It's just that what happens is ... we we've got less sometimes we have less pizzas than we've got people. [287] Okay so we've got one pizza share it out between the two of us we get? |
| Simon (PS1T0) |
[288] A half. |
| John (PS1SY) |
[289] Share it out between four of us how many would we get? |
| Simon (PS1T0) |
[290] A Twelfth. |
| John (PS1SY) |
[291] If we shared it out between twelve of us we'd get a twelfth. |
| Simon (PS1T0) |
[292] Get erm |
| John (PS1SY) |
[293] Share it out between four of us we get |
| Simon (PS1T0) |
[294] Quarter. |
| John (PS1SY) |
[295] A quarter yeah. [296] You could say a fourth it doesn't matter it's the same thing. [297] Erm if we shared it out between six of us? |
| Simon (PS1T0) |
[298] A sixth. |
| John (PS1SY) |
[299] How about if we shared it out between a tenth of us. [300] ... Have a guess go on. [301] ... If we share it out between four of us it's a fourth if we share it |
| Simon (PS1T0) |
[302] A tenth. |
| John (PS1SY) |
[303] A tenth yes brilliant very good. [304] How many fourths make up a whole ... how many fourths to make a whole one? ... |
| Simon (PS1T0) |
[305] Four. |
| John (PS1SY) |
[306] Four how many how many sixths make up a whole one? [307] Have a guess. [308] How many tenths make a whole one ... you got it right [...] said ten. |
| Simon (PS1T0) |
[309] Ten. |
| John (PS1SY) |
[310] How many how many sixths make a whole one? |
| Simon (PS1T0) |
[311] Six. |
| John (PS1SY) |
[312] Yeah good good. [313] How many twelfths make a whole one? |
| Simon (PS1T0) |
[314] Twelve. |
| John (PS1SY) |
[315] Very good erm alright go for an impossible one how many mm how many twentieths make a whole? |
| Simon (PS1T0) |
[316] Twenty. |
| John (PS1SY) |
[317] Yep. [318] I think you've got it haven't you. [319] How many hundredths make a whole one? |
| Simon (PS1T0) |
[320] A hundred. |
| John (PS1SY) |
[321] Yeah. [322] That's it. [323] Now which is bigger a sixth of a third? |
| Simon (PS1T0) |
[324] A third. |
| John (PS1SY) |
[325] Very good very good now a lot of people take a long time to get that. [326] They keep saying well a sixth must be bigger cos six is bigger. [327] [...] that's how many people you're sharing with so that's very good you got that very quickly. [328] Oh I'm very pleased I think you're going to like fractions aren't you. [329] If you if you don't understand things it gets very hard to like them cos you d just don't know what's going on do you? [330] Once you get to know a bit what's happening. [331] And you get good at doing it then it's, Hey I can do this. [332] Then you start liking it. [333] So do you think you're going to get on alright with fractions? [334] Yeah when we've had a look at fractions a bit erm we'll play with those and we'll find out things like what's half of a quarter things like that. [335] So what does that's when you start thinking about half of a quarter it gets very confusing [...] what do you mean do you mean half or a quarter? [336] Well what they mean when they say a half of a quarter is that we had a a quarter and we've shared it out between the two of it so we've got half to that each. [337] How much would we get? [338] Have a guess. [339] It's not one that we've met so far so it's a completely new one. |
| Simon (PS1T0) |
[340] A fifth? |
| John (PS1SY) |
[341] If we had there's a quarter. [342] How many of those to go all the way round? |
| Simon (PS1T0) |
[343] Erm |
| John (PS1SY) |
[344] How many quarters would make a whole one? ... |
| Simon (PS1T0) |
[345] Four. |
| John (PS1SY) |
[346] Four okay good. [347] If we cut each one of those into two pieces the same, how many of the new pieces would we need to go all the way round? |
| Simon (PS1T0) |
[348] Four oh |
| John (PS1SY) |
[349] We need we need four like that four quarters that's good and then for each one of those when we've cut it in two it would give us two of the new pieces so every one of those four would give us two new pieces how many would we have altogether then? [350] ... We'd have four lots of two wouldn't we do you know what that is four twos? [351] Or two fours? |
| Simon (PS1T0) |
[352] Two's two four eight. |
| John (PS1SY) |
[353] Eight so we'd have eight pieces all the same size and what would that be called have a guess? |
| Simon (PS1T0) |
[354] An eighth. |
| John (PS1SY) |
[355] That's it an eighth. [356] That's an eighth. [357] So two eighths would make a quarter. [358] Two quarters would make |
| Simon (PS1T0) |
[359] A ... third. |
| John (PS1SY) |
[360] A half. |
| Simon (PS1T0) |
[361] Oh. |
| John (PS1SY) |
[362] Would make a half and two halves would make |
| Simon (PS1T0) |
[363] A whole. |
| John (PS1SY) |
[364] That's it good. [365] That's very good. [366] Okay so [...] don't need to learn all the fractions but we need to we'll probably just go playing with these the ones we've got here. [367] Now which is bigger? [368] What's what size is this? |
| Simon (PS1T0) |
[369] A fourth. |
| John (PS1SY) |
[370] A fourth okay which is bigger a fourth or a sixth? |
| Simon (PS1T0) |
[371] A fourth. |
| John (PS1SY) |
[372] A fourth. [373] Now let's see how much bigger. [374] Well it's that much bigger isn't it. [375] Can you see any there that would just fit in that? [376] [...] Right so if we added together a sixth and a twelfth what will it make? [377] This one here what's this? |
| Simon (PS1T0) |
[378] A quarter. |
| John (PS1SY) |
[379] A quarter so a sixth and a twelfth makes a quarter |
| Simon (PS1T0) |
[380] Quarter. |
| John (PS1SY) |
[381] now this isn't I mean there are some funny rules with fractions aren't there sort of tricky things you have to do. [382] Not that tricky once you understand them. [383] And we didn't make them up. [384] Just to make it hard it's because this is how it really works when we're sharing out things. [385] So a quarter ... how many twelfths ion a quarter? |
| Simon (PS1T0) |
[386] Three. |
| John (PS1SY) |
[387] Three twelfths in a quarter. [388] That's what size is this piece go on say it. |
| Simon (PS1T0) |
[389] A sixth. |
| John (PS1SY) |
[390] A sixth how many twelfths would we need top make a sixth? |
| Simon (PS1T0) |
[391] Two. |
| John (PS1SY) |
[392] Two. [393] So if we had a sixth and a twelfth well the sixth is the same as two twelfth and another twelfth makes how many? [394] ... Two twelfths from there and then an extra twelfth how many have we got? [395] ... Two two twelfths there and then another twelfth. |
| (FMHPS000) |
[396] Excuse me would you like another drink? |
| John (PS1SY) |
[397] Erm I wouldn't mind actually I I can't drink milk actually [...] I'm it's okay I did say but yeah yeah yeah so so just black no sugar that'd be lovely thanks. |
| (FMHPS000) |
[398] Oh look I'm sorry [...] I'm sorry So black black okay. |
| John (PS1SY) |
[399] Now and so that's |
| Simon (PS1T0) |
[400] A sixth. |
| John (PS1SY) |
[401] two twelfths there. [402] That's sixth one sixth but you could make two twelfths out of that. [403] And another twelfth. [404] What would two apples plus one apple come to? |
| Simon (PS1T0) |
[405] Three. |
| John (PS1SY) |
[406] Three apples okay. [407] Have a guess what do you think two twelfths add one twelfth comes to how many twelfths would that come to? [408] Two and the an extra one two twelfths and an extra one twelfth how many twelfths would we have altogether? [409] Have a guess. [410] ... We've got two pears and then we had we had say two bananas and then another banana how many bananas would we have then . |
| Simon (PS1T0) |
[411] Three. |
| John (PS1SY) |
[412] If we had two pigs and another pig how many pigs would we have? |
| Simon (PS1T0) |
[413] Three. |
| John (PS1SY) |
[414] If we had two twelfths and another twelfth how many twelfths would we have altogether? |
| Simon (PS1T0) |
[415] Three twelfths. |
| John (PS1SY) |
[416] That's it three three twelfths. [417] And three twelfths is the same as a quarter isn't it. [418] We stuck three twelfths together we can make a quarter. [419] Do this is how we have to add up fractions. [420] If if I say well let's try and add up a sixth and a twelfth and most people want to add the six and the twelve together and things like that but you can't do it that way you'll have to change them both into something that's the same. [421] twelfths is a good one quite often and then we'll add up and find out how many twelfths we've got. [422] And then see what that how many that would make. [423] So three three twelfths that would make a quarter . |
| Simon (PS1T0) |
[424] A quarter. |
| John (PS1SY) |
[425] So a sixth plus one twelfth is |
| Simon (PS1T0) |
[426] A quarter. |
| John (PS1SY) |
[427] [...] good very good oh that's good. [428] Okay how about if we added here's a tricky one see if you can work out how we're going to do it. [429] A quarter add a sixth. [430] Now could you turn them all into twelfths? |
| Simon (PS1T0) |
[431] Yeah. |
| John (PS1SY) |
[432] Okay how many twelfths would there be in the quarter? [433] How many twelfths would there |
| Simon (PS1T0) |
[434] Three. |
| John (PS1SY) |
[435] Three twelfths good and how many twelfths would there be in the sixth? |
| Simon (PS1T0) |
[436] Two. |
| John (PS1SY) |
[437] So how many twelfths would we have altogether? |
| Simon (PS1T0) |
[438] Five. |
| John (PS1SY) |
[439] Five brilliant. [440] So we'd have five twelfths. [441] That's very good. [442] Thanks very much . |
| (FMHPS000) |
[443] Okay. |
| John (PS1SY) |
[444] Okay thanks. [445] So we'd have five twelfths. [446] Right erm now you're doing very well at this. [447] Let's try this one. [448] Quite a big one. [449] That one's this one's a quarter and remember what this one is? |
| Simon (PS1T0) |
[450] A third. |
| John (PS1SY) |
[451] A third good. [452] So if we added a third and a quarter could you turn them into twelfths? |
| Simon (PS1T0) |
[453] Yeah. |
| John (PS1SY) |
[454] Okay go on how many |
| Simon (PS1T0) |
[455] Three. |
| John (PS1SY) |
[456] Good. |
| Simon (PS1T0) |
[457] Two ... [...] |
| John (PS1SY) |
[458] [...] let's have a look at that [...] |
| Simon (PS1T0) |
[459] one |
| John (PS1SY) |
[460] [...] put it there. [461] How much is that bit there that we haven't haven't covered? |
| Simon (PS1T0) |
[462] A quarter. |
| John (PS1SY) |
[463] A quarter and how many twelfths in a quarter? |
| Simon (PS1T0) |
[464] Three. |
| John (PS1SY) |
[465] Three so there's three twelfths there and that one makes? |
| Simon (PS1T0) |
[466] Seven. |
| John (PS1SY) |
[467] Good. [468] So it's seven twelfths altogether so if we add a third to a quarter |
| Simon (PS1T0) |
[469] Third and a quarter |
| John (PS1SY) |
[470] Say add a third and a quarter can't do that don't know where to start. [471] Change them into twelfths |
| Simon (PS1T0) |
[472] Seven. |
| John (PS1SY) |
[473] and add the twelfths up seven twelfths. [474] Okay how about erm [...] this one? [475] Now this time we don't need to change them into twelfths could you add that's a half add a sixth? [476] Any idea what we could change this into so we could add them? |
| Simon (PS1T0) |
[477] erm |
| John (PS1SY) |
[478] What could we change that half into so that we could one sixth to it? [479] ... Go on have a guess. |
| Simon (PS1T0) |
[480] Twelfths or |
| John (PS1SY) |
[481] We could twe change it into twelfths yes and we could change the six into twelfths see what that would come to. [482] How many twelfths would we get in that? |
| Simon (PS1T0) |
[483] Two. |
| John (PS1SY) |
[484] Two in there and how many twelfths would we get out of the half? |
| Simon (PS1T0) |
[485] Seven erm |
| John (PS1SY) |
[486] We'd get |
| Simon (PS1T0) |
[487] t two |
| John (PS1SY) |
[488] Two out of that and then another two |
| Simon (PS1T0) |
[489] Two. |
| John (PS1SY) |
[490] would be four |
| Simon (PS1T0) |
[491] Four. |
| John (PS1SY) |
[492] and another two |
| Simon (PS1T0) |
[493] Would be six. |
| John (PS1SY) |
[494] Six so six twelfths makes a half. [495] Yeah. [496] Six twelfths and another |
| Simon (PS1T0) |
[497] Eight. |
| John (PS1SY) |
[498] two twelfths is eight |
| Simon (PS1T0) |
[499] Eight. |
| John (PS1SY) |
[500] twelfths right. [501] So if we add a half |
| Simon (PS1T0) |
[502] To a to a sixth. |
| John (PS1SY) |
[503] to a sixth we get eight twelfths . |
| Simon (PS1T0) |
[504] Eight. |
| John (PS1SY) |
[505] Okay. [506] Erm we could even do it without bothering with twelfths on this. [507] We could just change them into sixths. [508] How many sixths would we get out of a half? |
| Simon (PS1T0) |
[509] Two. |
| John (PS1SY) |
[510] [...] have a look. ... |
| Simon (PS1T0) |
[511] Three. |
| John (PS1SY) |
[512] [...] that's a half okay so three sixths add ... one sixth |
| Simon (PS1T0) |
[513] Sixth. |
| John (PS1SY) |
[514] how many would that be? |
| Simon (PS1T0) |
[515] Three four. |
| John (PS1SY) |
[516] Four sixths. [517] And four sixths comes to the same as two thirds. [518] One third and another third. |
| Simon (PS1T0) |
[519] Mm. |
| John (PS1SY) |
[520] Okay have you done cancelling fractions? |
| Simon (PS1T0) |
[521] No. |
| John (PS1SY) |
[522] No. [523] Okay have you done things like erm three twelfths is the same as a quarter? have you done that at school? |
| Simon (PS1T0) |
[524] I'm not too sure really. |
| John (PS1SY) |
[525] No well you may have done. [526] But this is the this is the secret with fractions this is the trick. [527] So that you can [...] do anything. [528] To be able to change them into different fractions. [529] So you you'll already know how to change a sixth into twelfths don't you? [530] How many twelfths does that make? |
| Simon (PS1T0) |
[531] Two. |
| John (PS1SY) |
[532] Two twelfths good. [533] And you know how to change a quarter into twelfths how many twelfths does that make? |
| Simon (PS1T0) |
[534] Three. |
| John (PS1SY) |
[535] Three twelfths good and can you remember how many twelfths you got out of a half? |
| Simon (PS1T0) |
[536] Mm ... [...] |
| John (PS1SY) | [...] |
| Simon (PS1T0) |
[537] one two three four five six. |
| John (PS1SY) |
[538] Six twelfths. [539] So what would a half add a twelfth come to? |
| Simon (PS1T0) |
[540] Seven. |
| John (PS1SY) |
[541] Seven twelfths very good. [542] You're doing all this in your head you know you're not writing any of it down are you? [543] Doing fractions in your head. [544] Adding them up I think that's very good. [545] I think that's excellent. [546] You could probably do take aways. [547] Take away fractions . |
| Simon (PS1T0) | [laugh] |
| John (PS1SY) |
[548] You don't think you could I think you could. [549] What would be a quarter take away a twelfth? [550] Cut that off. |
| Simon (PS1T0) |
[551] Two. |
| John (PS1SY) |
[552] Two twelfths. |
| Simon (PS1T0) | [laugh] |
| John (PS1SY) |
[553] And two twelfths is the same as? |
| Simon (PS1T0) |
[554] One quarter. |
| John (PS1SY) |
[555] One sixth yeah one sixth. [556] So you're doing take aways [...] in your head now. [557] A quarter take away a twelfth. [558] What about a sixth take away a twelfth what would that come to? |
| Simon (PS1T0) |
[559] One twelfth . |
| John (PS1SY) |
[560] One twelfth one twelfth. [561] How about one third take away one twelfth what would that come to? |
| Simon (PS1T0) |
[562] Mm. [563] ... Three. |
| John (PS1SY) |
[564] Three twelfths which is the same as |
| Simon (PS1T0) |
[565] Mm one fourth. |
| John (PS1SY) |
[566] A fourth. [567] Okay erm how about a half take away a twelfth? [568] How many would we have left over? |
| Simon (PS1T0) |
[569] Four five. |
| John (PS1SY) |
[570] Five five twelfths cos we started off with six twelfths take one twelfth away start off with six pigs and take one pig away got five pigs. [571] Start off with six twelfths and take one twelfth away you've got five twelfths. [572] I think you're very good at this. [573] What do you think? [574] Do you think you're getting you know you know what it's about don't you? [575] Yes. [576] Well I think that's very good. [577] Okay erm what I'd like you to do now is I'd like you to tell me what you think are the important things about fractions and ... anything important or interesting that you've learnt this afternoon. [578] ... What what was the most interesting thing? [579] Did |
| Simon (PS1T0) |
[580] Well |
| John (PS1SY) |
[581] you find any of it interesting? [582] ... Was it better than school or worse than school? |
| Simon (PS1T0) |
[583] Better [laugh] . |
| John (PS1SY) |
[584] Oh that's good [laugh] . [585] And what was good about it then? |
| Simon (PS1T0) |
[586] Working them out and ... then [...] . |
| John (PS1SY) |
[587] Good don't forget if I go too quickly or if I give you too much say, Ooh hang on. [588] and I probably won't stop I'll just tell you a different way. [589] Probably tell you the same thing a different way. [590] And Do you think you understand do you know what fractions are about? [591] ... How would suppose you have you got any brothers and sisters? |
| Simon (PS1T0) |
[592] One sister and me nanna. |
| John (PS1SY) |
[593] Okay and how old's she? |
| Simon (PS1T0) |
[594] Erm eight. |
| John (PS1SY) |
[595] Eight so if you had to explain to her about fractions, how could you tell her about what's what is it all |
| Simon (PS1T0) |
[596] Er |
| John (PS1SY) |
[597] about this fractions? |
| Simon (PS1T0) |
[598] It's the same if you're erm erm tell her the take aways and how many twelfths in like a whole and stuff like that. |
| John (PS1SY) |
[599] So it's all about sharing things out and it gets into this sort of fractions when we get when there's not enough to go round and we have to start cutting things up cutting the pizza up. [600] Okay erm now have you got any work to do during the holiday any homework |
| Simon (PS1T0) |
[601] No. |
| John (PS1SY) |
[602] or schoolwork? [603] None okay ... do you think the fractions were more interesting than erm what numbers add up to make ten? |
| Simon (PS1T0) |
[604] Mm. |
| John (PS1SY) |
[605] Mm. |
| Simon (PS1T0) |
[606] Yeah. |
| John (PS1SY) |
[607] And more interesting than tables. |
| Simon (PS1T0) |
[608] Yeah [laugh] . |
| John (PS1SY) |
[609] Yeah oh definitely hey. [610] Well sometimes when I was asking you things like erm ... say if I asked you how many quarters to make a whole one? [611] How many quarters make a whole one? ... |
| Simon (PS1T0) |
[612] Four. |
| John (PS1SY) |
[613] Four good. [614] And for every quarter we need three twelfths so we need four lots of three twelfths how many twelfths to make a whole one? ... |
| Simon (PS1T0) |
[615] Three erm ... |
| John (PS1SY) |
[616] Right now if you know your tables if you knew three fours or four threes it'd be a lot easier wouldn't it. [617] Now the trouble with fractions is if you don't know your tables it can be you can work it out you could get there but it'll take a long time if you do know your tables you just go, Yeah three fours are twelve. [618] Four threes twelve. [619] straight away like that. [620] If you don't know them it's going to take you a long time. [621] Now if you're doing fractions with the others and they know their tables what's going to happen? ... |
| Simon (PS1T0) |
[622] I'm gonna be slower than them. |
| John (PS1SY) |
[623] They're going to keep being first all the time and you'll be thinking, Hang on hang on I haven't worked that out. [624] You know you can do it you can do the fractions and once you've turned it into twelfths you can do it. [625] But you're going to be finding out they're all rushing off ahead and you haven't worked out how many twelfths there are in two thirds or things like that. [626] Once you work it out you can do it but you need your tables to do that. [627] So I'll get some tables for you for next time erm if |
| Simon (PS1T0) |
[628] Will I need to erm buy a maths book or anything to write in? |
| John (PS1SY) |
[629] No have you got any any sort of pad like this will do anything to write in. [630] But I do want you to write some things for next time. [631] Erm have you got a have you got pad or anything ? |
| Simon (PS1T0) |
[632] Yeah I've got got got this little book in here. |
| John (PS1SY) |
[633] Okay. ... |
| Simon (PS1T0) | [...] ... |
| John (PS1SY) |
[634] Right well the first thing I'd like to have you got counters or have you got a |
| Simon (PS1T0) |
[635] Counters? |
| John (PS1SY) |
[636] a big jar with pennies in or anything like that? |
| Simon (PS1T0) |
[637] Yeah. |
| John (PS1SY) |
[638] You have that's good. [639] If you get just pennies out right. [640] If you'd like to make a a little note of what I want you to do. [641] I'll tell you what it I I want you to do first and then you can write it down. [642] I want you to get ooh ... start of with twelve pennies okay. [643] Twelve pennies ... and then use them you know the way we were working out things like three times four makes twelve. [644] ... Set them out like this okay so that's three fours or four threes make twelve okay. [645] How else could we make twelve? [646] We could make |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[647] two sixes or six twos. [648] [...] twelve. [649] I'd like you to play with that and just with twelve pennies until you've found all the ways of arranging them like that. [650] So they can show what two numbers multiply together to make twelve. [651] Then I'd like you to try thirty six. |
| Simon (PS1T0) |
[652] Thirty six. |
| John (PS1SY) |
[653] Maybe maybe twenty four first okay. [654] So try twelve pennies and find all the numbers that will multiply together to make twelve and one you mentioned earlier which was very good cos a lot of people forget it was just twelve ones or one twelve. [655] Okay so try it with twelve first of all and then try it with twenty four |
| Simon (PS1T0) | [...] |
| John (PS1SY) |
[656] and see all sorts of numbers that will make twenty four. [657] So you could try it like this if we had twenty four we could see what happens if you make them into twos? [658] Would that work? [659] Yes that would work. [660] What happened if you make them into threes? [661] How many lots of three would you make? [662] You might find it works you might find you've got some left over in which case it doesn't work you can't make sets of three out of them. [663] And then try fours and fives and sixes. [664] Do you think fives would work with twenty four? |
| Simon (PS1T0) |
[665] Mm. |
| John (PS1SY) |
[666] Your five times table always end in a in what? |
| Simon (PS1T0) |
[667] Five. |
| John (PS1SY) |
[668] Or a nought don't they? |
| Simon (PS1T0) |
[669] Yeah. |
| John (PS1SY) |
[670] Does twenty four end in a five or a nought? |
| Simon (PS1T0) |
[671] No. [672] Ends in a four. |
| John (PS1SY) |
[673] No so it wouldn't so it wouldn't work wouldn't work with the fives. [674] So you try it with the sixes see if they work try it with the sevens try it with the eights see what works. [675] And find all the just just play with them and find out all the things and write down your answers. [676] What numbers would multiply together to make twelve? [677] What numbers would multiply together to make twenty four? and then try it again for thirty six okay. |
| Simon (PS1T0) |
[678] Yeah. |
| John (PS1SY) |
[679] So if you like to write that one down. [680] And then if you've done that by next time got all them all written down and you're quite happy and you want to go on and do some more try it with sixty pennies. |
| Simon (PS1T0) |
[681] Sixty. |
| John (PS1SY) |
[682] Sixty pennies okay. [683] Now have you had your tea yet? |
| Simon (PS1T0) |
[684] No. |
| John (PS1SY) |
[685] Have you just come in from school. [686] [...] What time do you get in [...] |
| Simon (PS1T0) |
[687] No I came home at half two today. |
| John (PS1SY) |
[688] Cos you'd finished early did you ? |
| Simon (PS1T0) |
[689] Yeah. |
| John (PS1SY) |
[690] Okay ... so you'd had a bit of a break that's good. [691] Erm the other thing I'd like you to do is adding up all all the numbers that make ten. [692] Okay do you want to make a note of that and do you remember how we did it? |
| Simon (PS1T0) |
[693] Erm yeah erm |
| John (PS1SY) |
[694] You could do it with your coins again if you like. [695] So ... we started with five add five didn't we? |
| Simon (PS1T0) |
[696] Yeah. |
| John (PS1SY) |
[697] Cos that was the first one that you know. [698] Five add five makes ten. [699] What did we do then? |
| Simon (PS1T0) |
[700] Mm. [701] ... We we took one out of there that made s six |
| John (PS1SY) |
[702] Six add. |
| Simon (PS1T0) |
[703] Six add four makes |
| John (PS1SY) |
[704] Right. [705] Six add four makes ten. [706] And what would four ad six make? |
| Simon (PS1T0) |
[707] S ten. |
| John (PS1SY) |
[708] Right so you worked out that you've only got to learn half of them. [709] Don't want to I want you to learn things but there's no point in learning everything twice is there or learning more than you need to at the moment. [710] Just learn we'll try and find some easy ways for you to learn it erm cos I think you're a good learner you've learnt a lot today haven't you? [tape ends] |