Maths tutorial. Sample containing about 4448 words speech recorded in educational context

4 speakers recorded by respondent number C805

PS6M0 Ag4 m (Malcolm, age 50, tutor) unspecified
PS6M1 Ag0 f (No name, age 15, student) unspecified
KNDPSUNK (respondent W0000) X u (Unknown speaker, age unknown) other
KNDPSUGP (respondent W000M) X u (Group of unknown speakers, age unknown) other

1 recordings

  1. Tape 086902 recorded on unknown date. LocationNottinghamshire: Nottingham () Activity: Tutorial

Undivided text

Unknown speaker (KNDPSUNK) [1] [...] .
Malcolm (PS6M0) [2] Right.
(PS6M1) [3] That erm ... course work's gotta be in a week today.
Malcolm (PS6M0) [4] Yes.
[5] What've you Is er
(PS6M1) [6] I've got that other one to do yeah.
Malcolm (PS6M0) [7] What both sets of course work have gotta be in ?
(PS6M1) [8] Mm.
Malcolm (PS6M0) [9] Right in that case we'd better have a look at that now. ...
(PS6M1) [10] Is it in here?
[11] No it's in the other one. ...
Malcolm (PS6M0) [12] Have you got the other one written up?
(PS6M1) [13] Yeah it's just that erm ... It's just got [...] .
Malcolm (PS6M0) [14] Right.
[15] Yes.
(PS6M1) [16] And that's all.
Malcolm (PS6M0) [17] Lovely. ...
(PS6M1) [18] [...] .
Malcolm (PS6M0) [19] [whispering] Next one. []
[20] ... [...] should have plenty of work there, you should be okay
(PS6M1) [21] Mm.
Malcolm (PS6M0) [22] with that.
(PS6M1) [23] [...] that one. [cough]
Malcolm (PS6M0) [24] Which one are we going to do?
[25] Can't remember. ...
(PS6M1) [26] [cough] [...] [cough] volumes or polygons. ...
Malcolm (PS6M0) [27] [reading] Cheapo supermarkets produced dried peas in sealed polythene bags contained in er stored in wire bins blah blah [] ... Oh.
[28] [sigh] ... Was this one we were wanting to look at wasn't it?
(PS6M1) [29] Yeah. ...
Malcolm (PS6M0) [30] [reading] Draw accurately and name six polygons with sides three four five six seven and eight and nine sides.
[31] Three of these should be regular. [] ...
(PS6M1) [32] Mhm.
Malcolm (PS6M0) [33] Okay.
[34] So y can you remember how to erm produce er polygons, how to how to make them?
[35] How to make regular polygons?
(PS6M1) [36] No.
Malcolm (PS6M0) [37] Right.
[38] Now a regular polygon ... Where are we?
[39] Something to write with.
[40] ... A regular polygon ... has all its sides ... and ... all its angles ... equal. ...
(PS6M1) [41] Mhm.
Malcolm (PS6M0) [42] So if you start with three, ... that's
(PS6M1) [43] Mm.
Malcolm (PS6M0) [44] a triangle isn't it?
[45] It's the smallest polygon you can make cos if you've got two sides you can't join it up can you?
(PS6M1) [46] No.
Malcolm (PS6M0) [47] So you've three sides, ... all equal length, and all the angles have gotta be equal.
[48] Now the triangle add ups to how many degrees?
(PS6M1) [49] ... Hundred and eighty.
Malcolm (PS6M0) [50] Hundred and eighty.
[51] So if the three have gotta be equal you've a hundred and eighty divided by three which is sixty each.
(PS6M1) [52] Mhm. ...
Malcolm (PS6M0) [53] Er and then the next one's four.
[54] Now there are a lot of four-sided ones really, ...
(PS6M1) [55] Mm.
Malcolm (PS6M0) [56] erm cos if you start thinking about the four-sided ones there's the square which everybody ... knows about which is again is the regular polygon isn't it?
(PS6M1) [57] Mm.
Malcolm (PS6M0) [58] Cos it's got all four sides equal and four ninety degrees.
(PS6M1) [59] Mhm.
Malcolm (PS6M0) [60] Then if you can think about that as being stretched as it were,
(PS6M1) [61] Mm.
Malcolm (PS6M0) [62] you know keeping two of them fixed and the other two If you think about it being stretched you get a rectangle don't you?
(PS6M1) [63] Mhm. [cough] ...
Malcolm (PS6M0) [64] A K A an oblong.
[65] But again
(PS6M1) [66] Mm.
Malcolm (PS6M0) [67] ... it's not regular.
(PS6M1) [68] [...] no.
Malcolm (PS6M0) [69] But you can then think of that That's with the ... the sides ... two sides stretched but still parallel to one another aren't they?
(PS6M1) [70] Yeah.
Malcolm (PS6M0) [71] Now you c the angle's ninety.
[72] As soon as you destroy the ninety degree angle you get a parallelogram don't you? ...
(PS6M1) [73] Yeah. [laugh]
Malcolm (PS6M0) [74] [laugh] I'm gonna have to draw it there cos I wanted to ... Like that.
[75] You get the parallelogram.
(PS6M1) [76] Yep.
Malcolm (PS6M0) [77] Opposite sides parallel, but the angles aren't the same any more.
(PS6M1) [78] No.
Malcolm (PS6M0) [79] Now if you think about going this way, that was ... So [...] keeping the angles constant at ninety wasn't it?
(PS6M1) [80] Mm.
Malcolm (PS6M0) [81] Now this way you can keep the sides constant and destroy the angles.
(PS6M1) [82] Mm.
Malcolm (PS6M0) [83] And if you do that you end up with a rhombus ... which is a squashed
(PS6M1) [84] Mm.
Malcolm (PS6M0) [85] square.
[86] The four sides are the same length,
(PS6M1) [87] Mm.
Malcolm (PS6M0) [88] but the angles have gone.
[89] So that's a rhombus.
[90] ... And that's your quadrilaterals except for this one of course.
[91] ... [...] haven't finished yet with quadrilaterals.
[92] ... There's this one ... which
(PS6M1) [93] Yeah.
Malcolm (PS6M0) [94] is the kite.
(PS6M1) [95] Yeah. ...
Malcolm (PS6M0) [96] It's got pairs of equal sides, ...
(PS6M1) [97] Mm.
Malcolm (PS6M0) [98] but the two pairs of equal sides aren't opposite one another so you don't end up with the the either the rectangle
(PS6M1) [99] Mm
Malcolm (PS6M0) [100] or the parallelogram.
[101] If you think about this you can think of a kite as two isosceles triangles glued together.
(PS6M1) [102] Mm.
Malcolm (PS6M0) [103] Of different sizes.
[104] As you can think of a rhombus as two iso two same-sized isosceles
(PS6M1) [105] Yeah.
Malcolm (PS6M0) [106] triangles glued together.
[107] So it's line of symmetry there and that isn't a line of symmetry [...] .
[108] ... Okay?
[109] So there's your four. ...
(PS6M1) [110] Yeah.
Malcolm (PS6M0) [111] That's the regular one.
[112] You can get thr triangles isosceles triangles, ... right-angled triangle and
(PS6M1) [113] Mm
Malcolm (PS6M0) [114] scalene and so on.
[115] There's your four ... That's your quadrilaterals, except of course for this one.
[116] Any old size.
(PS6M1) [117] Mm.
Malcolm (PS6M0) [118] No no angles the same, no
(PS6M1) [119] Mm.
Malcolm (PS6M0) [120] no lengths the same, which is the quadrilateral.
[121] Which is the general one.
[122] [laugh] ... All right?
(PS6M1) [123] Mm.
Malcolm (PS6M0) [124] Now it is possible ... to draw these, and the the next one up is a pentagon isn't it?
[125] Can you remember?
[126] You've gotta remember these.
[127] You need to remember these anyway for your exam.
(PS6M1) [128] Mm.
Malcolm (PS6M0) [129] Well if we're gonna draw a pentagon ... It's easy enough, we want five sides, so everybody can draw a house end. ...
(PS6M1) [130] Mm.
Malcolm (PS6M0) [131] But it's not regular.
(PS6M1) [132] No.
Malcolm (PS6M0) [133] You can also draw this, and people tend to forget this one.
[134] Oh by the way, sorry, there's another one here.
[135] ... I tend to forget it, everybody else tends to forget it, it's an arrow, arrowhead, or something like that, ... is also a quadrilateral.
[136] It's got four sides.
(PS6M1) [137] Mm.
Malcolm (PS6M0) [138] So you can remem you can think about this.
[139] This is can happen here as well.
(PS6M1) [140] Mm.
Malcolm (PS6M0) [141] So you can actually get ... That's a pentagon ... isn't it?
[142] Five sides.
(PS6M1) [143] Mm.
Malcolm (PS6M0) [144] And you can stretch it and bend it wherever you want but that's th th
(PS6M1) [145] Mm.
Malcolm (PS6M0) [146] it's it's till a pentagon isn't it?
[147] It is possible of course erm to you know draw a line er c you know distort it, like that.
(PS6M1) [148] Mm.
Malcolm (PS6M0) [149] But if you want to draw the regular one ... You can sit and do this backwards and work out what the angles are.
[150] [...] . But if you think, all polygons can be drawn inside a circle.
(PS6M1) [151] Mm.
Malcolm (PS6M0) [152] So if you draw a circle ... You know you wanna split this up into five sides. ...
(PS6M1) [153] Mm.
Malcolm (PS6M0) [154] So, a circle is three hundred and sixty degrees isn't it?
[155] ... So if you wanna split that up into five segments you divide three hundred and sixty by five which gives you?
[156] Seventy two.
[157] Yeah?
(PS6M1) [158] Mm.
Malcolm (PS6M0) [159] Seventy two degrees, you want five sides.
[160] ... So if you start at the centre ... and draw a line and mark off seventy two degrees,
(PS6M1) [161] Mm.
Malcolm (PS6M0) [162] and then mark off another seventy two degrees and another seventy two degrees and another seventy two degrees and join the ends,
(PS6M1) [163] Yeah.
Malcolm (PS6M0) [164] you'll end up with a regular pentagon.
(PS6M1) [165] Sorry.
Malcolm (PS6M0) [166] Have you got ...
(PS6M1) [...]
Malcolm (PS6M0) [167] a compass and protractor to hand?
(PS6M1) [168] No.
[169] [...] I can go and get one. ...
Malcolm (PS6M0) [170] I don't need wonderful drawing instruments but [laugh] ... [break in recording]
Malcolm (PS6M0) [171] No no no.
[172] No, draw yourself a circle.
(PS6M1) [173] Oh.
Malcolm (PS6M0) [174] Try one of those.
[175] ... Right.
[176] Okay.
[177] Er put a line in from somewhere, there from the centre up to there, just to give yourself a start somewhere.
(PS6M1) [178] Mhm.
Malcolm (PS6M0) [179] Just draw that in.
[180] ... Straight line, yeah, use the edge of the protractor'll do.
(PS6M1) [181] Mhm. ...
Malcolm (PS6M0) [182] Now draw yourself seventy two degrees from that.
[183] Seventy two degrees seventy two seventy ... er all the way around.
[184] ... That's right.
[185] ... Join each end there, you end up with a pentagon.
[186] Just join join them up and see, what d'you get?
[187] ... Alright?
(PS6M1) [188] Mm.
Malcolm (PS6M0) [189] You get a very nice ... pentagon.
(PS6M1) [190] Mm. ...
Malcolm (PS6M0) [191] You can do the same thing for any of the others, so however man many sides you want, ...
(PS6M1) [192] Mm.
Malcolm (PS6M0) [193] you divide three hundred and sixty by that number of sides which gives you this angle here, ... the angle at the centre.
[194] Cos you just dividing three hund You just divide the three hundred and sixty up into seven eight or how many bits
(PS6M1) [195] Mm.
Malcolm (PS6M0) [196] it is.
[197] You've got a slight problem with things like seven cos what's three hundred and sixty divided by seven?
(PS6M1) [198] I don't know.
Malcolm (PS6M0) [199] Yes I don't know either! [laugh]
(PS6M1) [200] Fifty four point fifty one point four.
Malcolm (PS6M0) [201] Fifty one point four.
[202] Now if you're drawing fifty one point four, ...
(PS6M1) [203] Mm.
Malcolm (PS6M0) [204] you're going to have to ... erm
(PS6M1) [...]
Malcolm (PS6M0) [205] you know very
(PS6M1) [...]
Malcolm (PS6M0) [206] very careful with a protractor and the protractor you've got not it's not gonna really do a fifty one point
(PS6M1) [207] Mm.
Malcolm (PS6M0) [208] four, it's gonna be marginally out.
(PS6M1) [209] mm.
Malcolm (PS6M0) [210] Fifty one point five you'll f you'll manage ...
(PS6M1) [211] Mm.
Malcolm (PS6M0) [212] reasonably, particularly if you got a sharp pencil.
[213] So ... But six you can do.
[214] Can you do can you do a hexagon the other way, which is six sided?
[215] ... S you could do ... you could do a hexagon this way [...] actually draw a hexagon.
[216] Do another circle.
[217] ... Now, ... it's gotta Hexagon's got six sides hasn't it?
(PS6M1) [218] Mm.
Malcolm (PS6M0) [219] So you've gotta divide three hundred and sixty by six.
[220] What d'you come to? ...
(PS6M1) [221] Sixty.
Malcolm (PS6M0) [222] Sixty.
[223] So if you need sixty just draw it and I'll show you You'll remember the other way when I've sho when I've shown you it.
[224] Just draw that up.
[225] [break in recording] D'you remember drawing the flower pattern when you were a kid? [laugh] ...
(PS6M1) [226] No.
Malcolm (PS6M0) [227] Eh?
[228] Oh dear me!
[229] ... Can you remember? ...
(PS6M1) [230] Oh yeah [...] .
Malcolm (PS6M0) [231] Yes?
[232] ... That's right, just mark them off.
[233] Now this is n not quite ... accurate, because it doesn't quite go into it six times.
[234] It's just marginally off.
[235] But usually by the time you've taken in the errors of your compass and your pr your pencil and everything else it come out to be fairly close to.
[236] Do you remember doing that?
(PS6M1) [237] Yeah.
Malcolm (PS6M0) [238] That's right, well that's in that's it.
[239] That's all it is.
[240] And then join 'em up.
[241] But it only works for that particular ...
(PS6M1) [242] Mm.
Malcolm (PS6M0) [243] erm ... f ... figure for the hexagon.
[244] It actually doe it works for triangle, you can do a triangle as well cos of course if you realize you can put a line across there a line across there a line
(PS6M1) [245] Mm.
Malcolm (PS6M0) [246] across there, which'll give you the equilateral triangle.
[247] So you understand what you've got to do.
[248] You've only gotta pick out ... Does it say three regular ones?
[249] ... [reading] Three of these should
(PS6M1) [250] Mm.
Malcolm (PS6M0) [251] be regular. []
(PS6M1) [252] I've gotta draw six polygons, and then
Malcolm (PS6M0) [253] Yes.
[254] Yes.
(PS6M1) [...]
Malcolm (PS6M0) [255] Right.
[256] So the first polygon's a triangle.
[257] The next one's a quadrilat well is a quadrilateral or a square or whatever it is.
[258] Fifth one That one's a pentagon.
[259] That's a hexagon. ...
(PS6M1) [260] Mm.
Malcolm (PS6M0) [261] What's seven? ...
(PS6M1) [262] S ... What do you call it?
Malcolm (PS6M0) [263] Well that's the point.
[264] You've gotta know what you call it.
(PS6M1) [laugh]
Malcolm (PS6M0) [265] I think it's a heptagon.
(PS6M1) [266] [...] .
Malcolm (PS6M0) [267] I think so.
[268] There's also people who call it a septagon as well September seventh.
(PS6M1) [269] Oh.
Malcolm (PS6M0) [270] You know that.
[271] That sort of thing.
[272] Erm ... usually called a heptagon.
[273] You're gonna have to look it up, you're gonna find a
(PS6M1) [274] Mm.
Malcolm (PS6M0) [275] erm ... maths dictionary or something somewhere.
[276] Eight is the? ...
(PS6M1) [277] Erm ... the octagon isn't it ?
Malcolm (PS6M0) [278] It's the octagon yes.
[279] And nine's a nonagon.
(PS6M1) [280] Mm. [laugh]
Malcolm (PS6M0) [281] Well nine's non.
[282] Yeah?
(PS6M1) [283] Mm.
Malcolm (PS6M0) [284] N O is actually the the the November is actually
(PS6M1) [285] Mm.
Malcolm (PS6M0) [286] really the ninth month except they ... decided to stick a couple of m extra months in to get the twelve.
[287] It was originally September October November and December are seven eight nine ten.
(PS6M1) [288] Mm. ...
Malcolm (PS6M0) [289] Really.
[290] [laugh] Cos that's why they d You know it's it's sept
(PS6M1) [291] Mm.
Malcolm (PS6M0) [292] oct nov and dec, seven
(PS6M1) [293] Mm.
Malcolm (PS6M0) [294] eight nine ten.
[295] But
(PS6M1) [296] Yeah.
Malcolm (PS6M0) [297] they stuck a couple of months in the middle of the year
(PS6M1) [laugh]
Malcolm (PS6M0) [298] so that th instead of working properly
(PS6M1) [299] Mm.
Malcolm (PS6M0) [300] [laugh] they're now two out.
[301] Right.
[302] [reading] [...] polygon triangle as shown.
[303] Find first by measurement and then by calculation the sum of the internal angles. []
[304] Er ... right.
[305] If you got some ... There's a pentagon.
[306] ... It says divide 'em up.
[307] ... Sum [reading] Find first by measurement and then by calculation [] .
[308] Right.
[309] Okay.
[310] I'm gonna have to draw these with straight lines [...] with a ruler it's not gonna work is it?
[311] ... Can you draw one of these?
[312] Draw a pentagon with a with a ruler.
[313] ... Doesn't matter what it looks like as long as it's got five sides that join together without gaps.
[314] [laugh] ... So now you've gotta split it up into triangles by starting at one corner.
(PS6M1) [315] Mm.
Malcolm (PS6M0) [316] So pick a corner,
(PS6M1) [317] Mhm.
[318] Mm.
Malcolm (PS6M0) [319] and split em up, yeah?
[320] That'll do.
[321] ... Draw a line so you produce triangles.
[322] You've already got one there haven't you?
(PS6M1) [laugh]
Malcolm (PS6M0) [323] How many triangles have you got?
(PS6M1) [324] Three.
Malcolm (PS6M0) [325] You've got three haven't you?
(PS6M1) [326] Yeah.
Malcolm (PS6M0) [327] Five sides, three triangles.
[328] ... It wants the sum of the internal angles.
[329] Now the internals angle is that isn't it?
(PS6M1) [330] Mhm.
Malcolm (PS6M0) [331] And that and that and that and that.
[332] So can you measure those, ... write hem down and add them up.
[333] See how good you are at measuring ang how [laugh] how good that protractor is.
(PS6M1) [334] [laugh] [...] ... That one's ... sixty one isn't it .
Malcolm (PS6M0) [335] Yeah sixty one.
[336] ... Yes.
[337] ... That one's not far off ninety I think. ...
(PS6M1) [338] [...] smack on ninety.
Malcolm (PS6M0) [339] By jove! [laugh]
(PS6M1) [340] [laugh] ... Er that's
Malcolm (PS6M0) [341] Well what's your Just Long as long as you stick That's it. ...
(PS6M1) [342] One hundred and seven.
Malcolm (PS6M0) [343] Yeah.
[344] ... Next time I shall bring you a protractor that you can read.
(PS6M1) [345] [laugh] I bought I had one but I think someone nicked it.
Malcolm (PS6M0) [346] Yes.
[347] It tends to be the fate of protractors.
(PS6M1) [348] Mm.
[349] Hundred and five.
Malcolm (PS6M0) [350] Yes I'd call that a hun I'd go along with that at a hundred and five. ...
(PS6M1) [351] Hundred and ... nine.
Malcolm (PS6M0) [352] Hundred and nine all right then.
[353] Just tot 'em up and see what you what you the total comes to. ...
(PS6M1) [354] Four hundred and seventy two.
Malcolm (PS6M0) [355] Four hundred and sev Eh?
[356] ... You sure? [laugh]
(PS6M1) [357] [...] . ...
Malcolm (PS6M0) [358] That must be more than sixty three.
[359] ... Sixty one.
[360] Measure that one again please. ...
(PS6M1) [361] [...] . ...
Malcolm (PS6M0) [362] That's right. ...
(PS6M1) [363] [...] a hundred and twenty. [laugh]
Malcolm (PS6M0) [364] That's more like it yes.
[365] [laugh] ... That's much more like it. ...
(PS6M1) [366] Five hundred and thirty two.
Malcolm (PS6M0) [367] Five hundred and thirty two.
[368] Okay.
[369] Now, it says by calculation.
[370] Now, what do you know about the angles of a triangle?
(PS6M1) [371] Add up to a hundred and eighty degrees.
Malcolm (PS6M0) [372] Add up to a hundred and eighty degrees.
[373] So you've got a hundred and eighty degrees there haven't you?
[374] You've got that one plus these two gives you a hundred and eighty.
[375] You've got a hundred and eighty degrees there haven't you?
(PS6M1) [376] Mm.
Malcolm (PS6M0) [377] Cos these ... are these three add up to a hundred and eighty.
[378] And you've got a hundred and eighty degrees there.
[379] These three add up to a hundred and eighty.
[380] So all in all you've got ever angle covered here haven't you?
(PS6M1) [381] Mm.
Malcolm (PS6M0) [382] So it should come to three times one hundred and eighty.
(PS6M1) [383] Mm.
Malcolm (PS6M0) [384] Which is? ...
(PS6M1) [385] Five hundred and forty .
Malcolm (PS6M0) [386] Five hundred and forty.
[387] You're eight degrees out, which is not bad considering this the [laughing] rather poor nature of your erm protractor [] .
(PS6M1) [388] [laugh] .
Malcolm (PS6M0) [389] So when you do this properly
(PS6M1) [390] Mm.
Malcolm (PS6M0) [391] make sure you've got a reasonable size reasonable clear protractor
(PS6M1) [392] Mm.
Malcolm (PS6M0) [393] and draw a reasonable sized diagram.
[394] Now ...
(PS6M1) [395] Mm.
Malcolm (PS6M0) [396] Yeah.
[397] But of course the thing about it is that it works for any shape.
(PS6M1) [398] Mm.
Malcolm (PS6M0) [399] So no matter if you have ... and pick a corner.
[400] I'd rather pick this one because it makes life easier, ... you can see
(PS6M1) [401] Mm.
Malcolm (PS6M0) [402] because of this [...] idea here.
[403] Go like that, ... like that and like that, and you've got one two three four triangles.
[404] You should have six
(PS6M1) [405] Mm.
Malcolm (PS6M0) [406] sides, one two three four five six.
(PS6M1) [407] Mm.
Malcolm (PS6M0) [408] As long as you pick i If you pick your corner carefully,
(PS6M1) [409] Mm.
Malcolm (PS6M0) [410] you don't end up with problems.
[411] And if you draw your figure carefully as well if you did a erm
(PS6M1) [412] Mm.
Malcolm (PS6M0) [413] a hexagon like that with a ... going inwards rather than sticking outwards,
(PS6M1) [414] Mm.
Malcolm (PS6M0) [415] you'll erm ... you'll find you get nice easy ...
(PS6M1) [416] Mm.
Malcolm (PS6M0) [417] erm triangles that come out of that.
[418] Now then.
(PS6M1) [419] That's doing it by measurement and tha and that's doing it by calculation ain't it .
Malcolm (PS6M0) [420] That's right , that's doing by measurement and that's doing by cal Y actually I think ... dunno.
[421] ... My eyes aren't as good as yours but me me glasses aren't bad.
[422] Oh I can't No I can't see this on this ... protractor.
[423] No that's one of the problems.
(PS6M1) [424] Yeah. [...]
Malcolm (PS6M0) [425] That's really one of the problems.
[426] Get a decent one.
(PS6M1) [427] About ten P [...] .
Malcolm (PS6M0) [428] Well they're at least l you know ... they're hardly the m greatest thing for ... breaking the bank.
[429] So are you happy with what you're supposed to do with this to produce these results?
(PS6M1) [430] Yeah.
Malcolm (PS6M0) [431] Yes.
(PS6M1) [432] [...] that mea that measurement and back up again [...] .
Malcolm (PS6M0) [433] Yeah, yeah.
(PS6M1) [434] Yeah.
Malcolm (PS6M0) [435] [reading] Draw a graph ... draw a graph by plotting the internal angle sum [] , which is the sum of the internal angles, [laugh] in this case five hundred and forty,
(PS6M1) [436] Mhm.
Malcolm (PS6M0) [437] [reading] on the vertical axis [] , upwards,
(PS6M1) [438] Mm.
Malcolm (PS6M0) [439] [reading] the number of sides, N on the horizontal axis.
[440] Use your graph to find the sum of internal angles of an eleven-sided blah blah and twelve sided [] .
(PS6M1) [441] Mm, so you just carry it on do you?
Malcolm (PS6M0) [442] You just carry it on .
(PS6M1) [443] Mm.
Malcolm (PS6M0) [444] Just carry the graph on.
[445] [reading] Deduce a rule from your results so far that could be used to find the internal angle sum of a polygon with any number of sides. []
[446] You should know now.
[447] ... How many triangles?
(PS6M1) [448] ... Three.
Malcolm (PS6M0) [449] How many sides?
(PS6M1) [450] Five. ...
Malcolm (PS6M0) [451] I rest my case.
[452] ... [reading] Using your original polygon constructions [] ...
(PS6M1) [453] Mm.
Malcolm (PS6M0) [454] [reading] that the sum ... Show using your original polygon constructions that the sum of the external angles of a polygon is three hundred and sixty.
[455] ... Mm.
(PS6M1) [456] Mm.
Malcolm (PS6M0) [457] Now you think about walking round this.
[458] I've
(PS6M1) [459] Mm.
Malcolm (PS6M0) [460] started along here, I turn through that, I walk along here I turn through that angle I walk along here I turn through that angle I walk along here I turn through that angle, ... I walk along here and turn through that angle and I'm back where I started from.
(PS6M1) [461] Mm.
Malcolm (PS6M0) [462] Now in fact of course you've gone round in a? ...
(PS6M1) [463] Circle.
Malcolm (PS6M0) [464] In a circle.
[465] A circle is ... three hundred and sixty
(PS6M1) [466] Mm.
Malcolm (PS6M0) [467] degrees.
(PS6M1) [468] Mm. ...
Malcolm (PS6M0) [469] Which of course is what you were doing here.
(PS6M1) [470] Mm.
Malcolm (PS6M0) [471] Are you happy with that?
[472] Does that give
(PS6M1) [473] Mm.
Malcolm (PS6M0) [474] you a reasonable start?
(PS6M1) [475] Mm. [...] .
Malcolm (PS6M0) [476] Go on tell me
(PS6M1) [477] [...] mark this out in a table don't you?
Malcolm (PS6M0) [478] Yes.
[479] So y y the internal angles of the regular ones ... you can measure.
(PS6M1) [480] Mm.
Malcolm (PS6M0) [481] Don't when you're doing this This has six triangles in it hasn't it?
(PS6M1) [482] Mm.
Malcolm (PS6M0) [483] If you're doing it by calculation, you pick one corner and draw ... tr
(PS6M1) [484] Y
Malcolm (PS6M0) [485] the other triangles.
[486] Don't do this, cos it doesn't work that way.
[487] You need to have picked one vertex and just draw
(PS6M1) [488] Mm.
Malcolm (PS6M0) [489] the diagonals from that vertex to the other ones.
(PS6M1) [490] Yeah.
Malcolm (PS6M0) [491] Otherwise you end up with a some very very strange results.
(PS6M1) [492] Mm.
Malcolm (PS6M0) [493] Right?
(PS6M1) [494] Yep.
[495] That's that bit accomplished .
Malcolm (PS6M0) [496] That's that bit accomplished yes.
(PS6M1) [497] [...] just got that one to finish off. [...] .
Malcolm (PS6M0) [498] On the fourteenth.
(PS6M1) [499] Yeah I've got seven actually.
[500] Seven or eight.
[501] I'll just go and get them.
[502] I've got them upstairs.
Malcolm (PS6M0) [503] Right.
[504] [break in recording] Yeah.
[505] ... [...] . [laugh] ... That's right.
[506] ... Yeah, but you're as tidy as I am you are!
(PS6M1) [laugh]
Malcolm (PS6M0) [507] [laugh] Come on then.
(PS6M1) [508] That's nought .
Malcolm (PS6M0) [509] Nought , that's right.
(PS6M1) [510] That's three.
Malcolm (PS6M0) [511] Yes.
(PS6M1) [512] Six.
Malcolm (PS6M0) [513] Yep.
(PS6M1) [514] That's ... eight. [...]
Malcolm (PS6M0) [515] What's the sum of those three?
(PS6M1) [516] Nine.
Malcolm (PS6M0) [517] Nine that's better.
(PS6M1) [518] And that's ... eight ... twelve.
Malcolm (PS6M0) [519] Twelve is right. ...
(PS6M1) [520] [...] ... [...] minus two.
Malcolm (PS6M0) [521] Just write the minus two all the way across there cos it allows you to do the calculation much easier rather than trying to remember it. [laugh]
(PS6M1) [522] Mm.
Malcolm (PS6M0) [523] So nought minus two.
(PS6M1) [524] Minus two .
Malcolm (PS6M0) [525] Is Good.
[526] Well done.
(PS6M1) [527] [...] .
Malcolm (PS6M0) [528] Eh?
(PS6M1) [529] [...] ?
Malcolm (PS6M0) [530] Oh beg your pardon yes sorry.
[531] [laugh] You're right [laugh] .
(PS6M1) [532] [...] ... Seven.
Malcolm (PS6M0) [533] Mhm.
(PS6M1) [534] [...] .
Malcolm (PS6M0) [535] Yeah.
[536] If you're gonna draw that graph up what will you have to do?
(PS6M1) [537] [...] put it down below.
Malcolm (PS6M0) [538] You'd have to put it below.
[539] That's right.
(PS6M1) [540] Mm.
Malcolm (PS6M0) [541] Right now I don't wanna I'm gonna have to push you along a bit to ... to erm make sure you get this done.
[542] So I don't ... You know whilst I would have normally ... if I'd been teaching a class done about five or six examples of that, that's all you're gonna get.
(PS6M1) [543] [laugh] Right.
Malcolm (PS6M0) [544] To start with, anyway.
[545] So ... we're gonna up the ante a bit.
[546] We've got X Y equals X squared ... plus two X, which is what I was talking about before.
(PS6M1) [547] Mm.
Malcolm (PS6M0) [548] We'll still do it the same.
[549] Nought one two three four.
(PS6M1) [550] Mhm. ...
Malcolm (PS6M0) [551] We're gonna set it up again.
[552] We got X ... and nought one two three four, but now to start the calculation ... we're going to put X squared in first.
(PS6M1) [553] Mm.
Malcolm (PS6M0) [554] So we've got X squared, and then we're gonna put in two X.
[555] That term then that term.
[556] ... So, nought squared?
(PS6M1) [557] It's nought.
Malcolm (PS6M0) [558] It's nought.
[559] One squared?
(PS6M1) [...]
Malcolm (PS6M0) [560] No.
(PS6M1) [561] [laugh] .
Malcolm (PS6M0) [562] One times one.
(PS6M1) [563] Oh yeah one.
Malcolm (PS6M0) [564] One.
[565] Be very careful with that cos it's very very easy to do that.
[566] Yeah.
(PS6M1) [567] Four.
Malcolm (PS6M0) [568] Yep.
(PS6M1) [569] Six.
[570] Nine.
Malcolm (PS6M0) [571] [tut] How many ?
(PS6M1) [572] [...] ... Nine.
Malcolm (PS6M0) [573] Nine.
(PS6M1) [574] Twelve.
[575] No it's not twelve [...] .
Malcolm (PS6M0) [576] Don't do that!
(PS6M1) [577] [laugh] It's erm ... sixteen.
Malcolm (PS6M0) [578] It's sixteen.
[579] You must get over this business
(PS6M1) [580] Mm.
Malcolm (PS6M0) [581] ... of ... thinking about it in those terms, that way along, along
(PS6M1) [582] Mm.
Malcolm (PS6M0) [583] that line.
[584] Think about it from there to there.
(PS6M1) [585] Mm.
Malcolm (PS6M0) [586] What's the relation that to that not this to this.
(PS6M1) [587] Mm.
Malcolm (PS6M0) [588] It's really very erm bad this business.
[589] You know you got introduced to it when you were ... y very
(PS6M1) [590] Mm.
Malcolm (PS6M0) [591] small and the things you first hear are the things you remember.
(PS6M1) [592] Mm.
Malcolm (PS6M0) [593] [laugh] And it takes a terrible st struggle to get rid of it.
[594] Okay, so now we want two X. ...
(PS6M1) [595] Two.
[596] Er two X?
[597] Oh that's nought.
Malcolm (PS6M0) [598] It's nought, good.
(PS6M1) [599] S Two.
[600] [laugh] Four.
Malcolm (PS6M0) [601] Yes.
(PS6M1) [602] Six.
Malcolm (PS6M0) [603] Six.
(PS6M1) [604] Eight.
Malcolm (PS6M0) [605] Eight.
[606] And now we add 'em together.
[607] ... Well I'll do the first one for you cos I can do that.
(PS6M1) [608] [laugh] .
Malcolm (PS6M0) [609] [laugh] .
[610] ... Yes.
[611] What's the next one?
[612] That's a two.
(PS6M1) [613] Three.
Malcolm (PS6M0) [614] Three.
(PS6M1) [615] Eight.
Malcolm (PS6M0) [616] Eight.
(PS6M1) [617] Fifteen.
Malcolm (PS6M0) [618] Fifteen.
(PS6M1) [619] Erm
Malcolm (PS6M0) [620] Twenty four.
(PS6M1) [621] Mm. ...
Malcolm (PS6M0) [622] I'm the next one I'm gonna do I'm gonna spread it down below nought so we're getting into the negative numbers.
[623] But it w which will give you a better picture of this graph, but we gonna have to get ... a chunk on this.
[624] ... I'm also gonna open this up a bit.
[625] One ... two ... three ... four.
[626] Just for reasons that it'll draw better if I open it.
[627] ... I'm not gonna get it on. ... [...] . ...
Unknown speaker (KNDPSUNK) [628] Yeah you will.
Malcolm (PS6M0) [629] I'm not you know.
[630] Gotta get up to thirteen er up to twenty four.
(PS6M1) [631] Oh right. [laugh] ...
Malcolm (PS6M0) [632] I'm not gonna go that far.
[633] Blah blah blah.
[634] We'll get enough from this.
[635] So nought is nought which is alright.
[636] One ... two three four.
[637] One is gonna be three isn't it.
(PS6M1) [638] Mm.
Malcolm (PS6M0) [639] Which is there roughly.
[640] Two is going to be eight.
[641] ... Which is about there isn't it?
(PS6M1) [642] Mhm.
Malcolm (PS6M0) [643] Three is gonna be fifteen.
[644] ... Which is ... One of these days I'll do this on graph paper.
[645] I'll try fifteen rather than fourteen.
[646] What you've got is this.
[647] It's not a straight line.
[648] ... There's no way you can get a straight line through that
(PS6M1) [649] No.
Malcolm (PS6M0) [650] at all.
[651] So it's actually a curve ... like that.
(PS6M1) [652] Mm.
Malcolm (PS6M0) [653] Yeah? ... [whispering] [...] other side the same. []
[654] It's called a parabola.
[655] That's only one half of the parabola.
(PS6M1) [656] Mm.
Malcolm (PS6M0) [657] So what we'll do is to gi y Thing about this is you need the practice in in actually crunching
(PS6M1) [658] Yeah
Malcolm (PS6M0) [659] the numbers.
(PS6M1) [660] Mm.
Malcolm (PS6M0) [661] So what we'll do is we'll have ... It's also actually equals X squared plus erm we'll make it three X ... minus ... No I'll not be I'll not be nasty.
(PS6M1) [laugh]
Malcolm (PS6M0) [662] Plus one.
[663] We're gonna go from minus three to three.
(PS6M1) [664] Mm.
Malcolm (PS6M0) [665] Now again just in steps of one.
[666] Don't ...
(PS6M1) [667] Mm.
Malcolm (PS6M0) [668] you know try and [laughing] get [] [laugh] Sometimes in an examination they'll give you funny numbers like two point five but they tend to work 'em out for you.
(PS6M1) [669] Mm.
Malcolm (PS6M0) [670] So you get things in there that have already been worked out for you so you don't have to ... erm ... So minus three.
[671] The next one will be minus two won't it?
(PS6M1) [672] Yeah.
Malcolm (PS6M0) [673] Next one?
(PS6M1) [674] Minus one.
Malcolm (PS6M0) [675] Minus one.
(PS6M1) [676] Nothing.
Malcolm (PS6M0) [677] Nought.
(PS6M1) [678] One.
Malcolm (PS6M0) [679] One ...
(PS6M1) [680] [...] .
Malcolm (PS6M0) [681] two and three.
[682] ... So now we're gonna work out X squared.
[683] What's X squared then?
[684] ... What's minus three times minus three?
(PS6M1) [685] Six innit?
Malcolm (PS6M0) [686] No!
[687] Three threes are ?
(PS6M1) [...]
Malcolm (PS6M0) [688] Nine.
(PS6M1) [689] Nine.
Malcolm (PS6M0) [690] Yeah so minus times a minus is plus.
(PS6M1) [691] Mm.
Malcolm (PS6M0) [692] That'll be nine.
(PS6M1) [693] That'll be ... four.
[694] ... Two.
[695] And one.
Malcolm (PS6M0) [696] One.
(PS6M1) [laugh]
Malcolm (PS6M0) [697] [laugh] Well rethunk .
[698] Yes nought. [laugh]
(PS6M1) [699] One.
Malcolm (PS6M0) [700] One.
(PS6M1) [701] Four.
Malcolm (PS6M0) [702] Four.
(PS6M1) [703] Nine.
Malcolm (PS6M0) [704] Nine.
[705] Good.
[706] Now it gets hairy.
[707] But you may ... Whatever, ...
(PS6M1) [708] Mm.
Malcolm (PS6M0) [709] if you square a number you're gonna get a positive answer.
[710] It's gonna give you a plus every time.
[711] So if end up squaring a number and get a negative answer you've got it wrong!
(PS6M1) [712] [laugh] .
Malcolm (PS6M0) [713] But now of course three times minus three is minus nine.
(PS6M1) [714] Mm.
Malcolm (PS6M0) [715] Three times minus two is? ...
(PS6M1) [716] Minus six.
Malcolm (PS6M0) [717] Minus six.
[718] Minus three .
(PS6M1) [719] Three.
Malcolm (PS6M0) [720] Nothing,
(PS6M1) [721] Mhm.
Malcolm (PS6M0) [722] three, six
(PS6M1) [723] Six.
Malcolm (PS6M0) [724] and nine.
[725] Remember you're working from there to there.
(PS6M1) [726] Mhm.
Malcolm (PS6M0) [727] Now we want a plus one.
[728] ... Nine minus nine plus one.
(PS6M1) [729] Minus eight.
[730] No, add em all up?
Malcolm (PS6M0) [731] Add em all up.
(PS6M1) [732] Plus one.
Malcolm (PS6M0) [733] Plus one is good.
(PS6M1) [734] Sic ... [...] minus three.
Malcolm (PS6M0) [735] Minus ...
(PS6M1) [736] Two.
[737] Not two.
[738] ... Si
Malcolm (PS6M0) [739] Four ones
(PS6M1) [740] Four.
Malcolm (PS6M0) [741] five, take away six is minus one.
(PS6M1) [742] One yeah. ...
Malcolm (PS6M0) [743] Minus one again .
(PS6M1) [744] Minus one.
[745] ... One.
Malcolm (PS6M0) [746] One.
[747] ... Five.
[748] ... Eleven.
[749] ... Nineteen.
(PS6M1) [750] Mhm.
Malcolm (PS6M0) [751] You with that?
(PS6M1) [752] Yeah.
Malcolm (PS6M0) [753] Happy?
(PS6M1) [754] Yeah.
Malcolm (PS6M0) [755] I've not gone too fast?
(PS6M1) [756] No.
Malcolm (PS6M0) [757] Good.
[758] [whispering] That's okay. []
[759] So now of course we want minus three to plus three, so we want the axis down the middle. ...
(PS6M1) [760] Mm.
Malcolm (PS6M0) [761] Don't we?
[762] And also we've gotta go down to minus one, ... so we'll put it there and hope and pray we've got enough on this time.
[763] ... Nought, one, two, three, minus one, minus two, minus three.
[764] [sigh] Oh.
[765] [sigh] Yeah.
[766] We'll put in minus one there.
[767] [watch beeps] One, two, God is it that time? three, four, five, six, seven, eight, nine, ten, eleven, twelve.
[768] It's getting better.
(PS6M1) [769] [laugh] . ...
Malcolm (PS6M0) [770] Done it! [laugh]
(PS6M1) [laugh]
Malcolm (PS6M0) [771] Got it on.
[772] ... Right.
[773] Minus three is at one isn't it?
(PS6M1) [774] Mhm.
Malcolm (PS6M0) [775] Yeah.
[776] Minus two is at minus one .
(PS6M1) [777] Minus one.
[778] Mm.
Malcolm (PS6M0) [779] Which is unfortunate the way we've got it numbered but that'll do.
[780] Minus Yes?
(PS6M1) [781] Yeah. ...
Malcolm (PS6M0) [782] M minus one is at minus one, ... as well.
(PS6M1) [783] Mm.
Malcolm (PS6M0) [784] Nought is at one. ...
(PS6M1) [785] Mm.
Malcolm (PS6M0) [786] One is at five.
[787] ... Two is at eleven, ... which is about there isn't it?
(PS6M1) [788] Mm.
Malcolm (PS6M0) [789] Have I gone I've gone over slightly have I?
[790] [whispering] Never mind. []
(PS6M1) [laugh]
Malcolm (PS6M0) [791] And three is at nineteen.
[792] ... Now the thing about this is look y y This is alright, you can get this curve in here.
[793] ... Dow down there, and turn around so you can get through and get the curve.
[794] Now when you get down to one you do not suddenly t put a straight line across there.
(PS6M1) [795] Mm.
Malcolm (PS6M0) [796] You carry the curve on round ... come back like that.
(PS6M1) [797] Mhm.
Malcolm (PS6M0) [798] So in fact one of the things that you Cos usually you're given more points here so you can get a nice curve on both sides so you get a nice ... Don't go from there to there straight across.
(PS6M1) [799] Mhm. ...
Malcolm (PS6M0) [800] Cos you'll lose marks for that.
[801] You want a nice smooth curve.
[802] Does it?
(PS6M1) [803] Mhm. ...
Malcolm (PS6M0) [804] Yes.
(PS6M1) [805] Mm.
Malcolm (PS6M0) [806] We'll do other things, but it's gotta be done with that ... later.
[807] But what I'll do is I'll set you some work on stuff you need to revise and so forth.
[808] And we shall [tape change]