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 |

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

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] |