1 Teacher: okay. guys. sh sh sh guys can you get the title date and objective down and I'll work out exactly whose supposed to be here and who we, we are waiting for.
2 Student: can I sit over there
3 Teacher: no
4 ((Other Interaction))
5 Teacher: okay guys listen up. I'm assuming that if youre not here now, if they're not here now they're not coming. okay. so we'll start without them, there's a lot of people missing.
6 Students: ((inaudible))
7 Teacher: no Tuesday I had, only had six
8 Student: seven
9 Teacher: we've got a few more, seven sorry.
10 Student: are they at the rugby pitch sir
11 Student: ((inaudible))
12 Teacher: yes the rugby ((inaudible))
13 Student: that's discrimination ((inaudible))
14 Student: ((inaudible)) universe
15 Teacher: perhaps its the boys rugby ((inaudible))
16 Student: sir on Tuesday was there like one person per table
17 Teacher: no we went to the computer room. okay today then. I did plan to do this, and I'm going to carry on cus we need to keep ticking things over, so. your title today is direct and indirect proportion. okay. er we're going to look at some practical examples of proportion, what proportion is etcetera and you need to just understand it and be able to work out which is which, whether it is direct or indirect.
18 ((Other Interaction))
19 Teacher: it's going to be a lot quieter in here today but, that's not a bad thing. have you done that SNAME.
20 Student: yeah
21 Teacher: and the date
22 Student: yep
23 Teacher: my board went on go slow this morning so I've had to write most of it and it's a bit there's a jump on my board I'm not very happy about.
24 Student: why does it do that then
25 Teacher: what
26 Student: jump
27 Teacher: dont know, there's a line on the board. er so. I'm just going to start straight away today cus I want to talk through some of it to start off with. direct and indirect proportion. okay what do I mean by that, what do I mean, if I said to you two quantities are in direct proportion, what do I mean by that. if I said two things are in direct proportion, what do I mean. have a guess. okay in fact talk to the people on your table first
28 ((Other Interaction))
29 Teacher: okay so. indirect, direct, what do you reckon indirect and direct. yep
30 Student: a direct answer
31 Teacher: a direct answer, what do we mean by that though
32 Student: well it's definite
33 Teacher: it's definite, good. what do we mean by direct proportion and indirect proportion. I've heard of something like fractions going on down here, something about going opposite ways. what do I mean by, if two things, if we're saying two things are in direct proportion. what do I mean. you're a lot quieter than the people who normally respond to me. yes
34 Student: they're directly the same size
35 Teacher: they're directly the same size. what were you saying SNAME?
36 Student: I was saying it's like um a cake, you split it in half and they'll be like your proportions, and then if it's indirect you'll split one half into, into two quarters
37 Teacher: so proportion, you're on about proportion as in like splitting into the same proportion
38 Student: yeah
39 Teacher: yeah okay SNAME what were you on about
40 Student: um like direct and indirect are opposites so something to do with opposites
41 Teacher: something to do with opposites and which one do you reckon is opposite
42 Student: um indirect
43 Teacher: indirect. okay. direct proportion, link it in to what you know about correlation as well, positive correlation think about that. what happens as one thing increases what happens to the other thing.
44 Student: it decreases
45 Teacher: for direct proportion. if you think of positive correlation
46 Student: increases
47 Teacher: increases. okay if two quantities in direct proportion, as one increases the other will also increase. okay. for indirect, what will happen then
48 Student: it will decrease
49 Teacher: it will decrease.
50 Student: oh
51 Student: is that higher or lower
52 Teacher: okay as one goes up it will decrease and that's what you were saying weren't you that's actually what you were saying when I heard you a minute ago. so for the first one, give me an example of something that increases and makes something else increase. or two quantities that increase together
53 Student: five and five
54 Teacher: what five and five. what do you mean by five and five. they're just numbers, they don't increase or decrease, they're just five. what do you mean. okay what about, SNAME try and think about two different things, like if I said to you if I said to you about the amount, the distance I run and how tired I feel, are they in direct proportion, as one increases does the other increase
55 Students: yeah
56 Teacher: yeah. yeah. so they're in direct proportion. it's probably not an ideal example, but they are in direct proportion cus as one thing happens the other happens. okay. give me another example of something that increases as something else does. more basic if you need to, I'm happy with that. yep
57 Student: shoe size and height
58 Teacher: generally shoe size and height they're not necessarily linked in as tightly as we're talking about in direct proportion but they do have positive correlation, they do increase as one increases.
59 Student: a man's nose and ears
60 Student: ha ha ha
61 Student: no because they never stop growing do they
62 Student: yeah
63 Student: they never stop growing
64 Student: age in ears
65 Teacher: is that true?
66 Students: yeah ((inaudible)) remember ((inaudible))
67 Student: that's why that's why you get the really old people with the really big ears
68 Teacher: is it the same with nose hair and ear hair as well
69 Student: I wonder how long SNAMEs going to be then
70 Teacher: it's not fair to say something about SNAME when he's not here
71 Student: well well it's kind, it's nicer to say it now when he's not here to hear it
72 Teacher: so we're talking about things increasing together. SNAME I'll take your word for that one. er what about the opposite then, give me an example of something increasing while something else decreases
73 Student: erm
74 Student: erm the amount of distance travelled in like a vehicle, and the amount of fuel left
75 Teacher: yeah the amount of distance travelled, the amount of fuel left yeah that's indirect
76 Student: the amount of like how long you use a pen and the ink, like how
77 Teacher: left
78 Student: yeah
79 Teacher: very similar yeah so the amount you use a pen and the ink left yeah. that would be there yep
80 Student: erm, more paper comes out of the printer, no this is for the direct one
81 Teacher: this is for the direct one carry on
82 Student: yeah more paper comes out as you're printing but more words come out as well on the to the paper
83 Teacher: you'd hope
84 Student: yeah, if you've got enough ink
85 Teacher: yeah as the words will print onto both pages
86 Student: as as you print
87 Student: assuming that there's ink
88 Teacher: yeah when you're printing out a word document, you always leave blank pages at the end by mistake and it just prints out blank
89 Student: yeah
90 Student: ah that's happened with me
91 Student: but then, but then that, that comes as indirect cus the ink has stopped, but the paper keeps coming
92 Teacher: what so the more paper you print out the less words
93 Student: yes
94 Students: ((inaudible)) ha ha
95 Student: yeah because you might get might get might get like you get
96 Student: ((inaudible))
97 Student: what if you just get bored of typing and then like er it can't be that bad, I'll just print it
98 Student: ((inaudible)) control p
99 Teacher: so you're saying in your work that the longer you type, the less it makes sense is that what you're saying
100 Student: ha ha
101 Student: yeah
102 Student: yeah a bit
103 Teacher: that's kind of, that's indirect proportion isn't it. the longer SNAME types the less sense his work actually makes yeah?
104 Student: that's true actually
105 Student: well let's hope ((inaudible))
106 Teacher: that's fair because he gets tired
107 Student: yeah
108 Teacher: okay fair enough. okay. they're more, we've got to be careful, they're more correlations, they show a pattern. when we're talking about direct and indirect proportion we can link it in with numbers, we can link it in to definite things. remember when we did, remember when we did correlation guys. we're talking about it being a general pattern, when we're talking about proportion now, we're talking about a definite, there is a definite pattern, there's a definite way to calculate things out. so. ((inaudible)) look at the question on the board. okay. six girls take four days to paint a fence, how many days will it take eight girls to paint the same fence. my first question, are we talking about indirect or direct proportion. as the number of girls increases, does the number of days it would take increase or decrease
109 Students: increase decrease
110 Teacher: decrease. so which are we talking about
111 Student: well it's ((inaudible))
112 Student: indirect
113 Teacher: indirect we're talking about indirect
114 Student: that depends though
115 Student: it takes three days
116 Student: yeah because they they might ((inaudible))
117 Student: cus some people might get in the way
118 Student: and they might get the other girls talking so they do less painting
119 Student: yes
120 Teacher: you know what women are like they just talk
121 Student: yeah exactly
122 Teacher: but there's less women here so we're okay, er let's say that doesn't happen let's say they don't talk let's say they just spread out, and they take a little bit each and they work at the same rate are we talking about indirect or direct
123 Student: but sir that will never happen
124 Teacher: but it's going to in this modelling situation
125 Student: how do you know, there might be some girls that hate each other, they're just oh they're not there just, just get on with your work
126 Teacher: yep they might do so indirect or direct. I've already written it up so you should be able to tell me
127 Student: indirect
128 Teacher: indirect as one increases the other decreases how would we work it out then guys how would you work it out
129 Student: er
130 Teacher: six girls paint a fence in four days, how many days would it take eight girls
131 Student: if you twice the girls
132 Student: three days
133 Student: twelve days
134 Student: three days no
135 Student: three
136 Student: no two and a half days
137 Student: three
138 Student: what was that
139 Student: three
140 Student: ah
141 Student: ((inaudible))
142 Student: I'd say three and a half
143 Student: they'd need two days three days
144 Student: two
145 Student: three
146 Student: two and half
147 Teacher: okay how long would it take if I said to you then well actually I'm going to take them all away and leave one girl on her own how long would it take her to paint it on her own
148 Student: eight days
149 Student: ten ten days
150 Teacher: why ten days
151 Student: no it would be sixteen days
152 Student: eight
153 Student: nine
154 Student: cus ((inaudible)) of them left
155 Student: sixteen days
156 Teacher: think about it
157 Student: then add five to the four
158 Student: twenty-four days
159 Student: no it would be six times four
160 Teacher: sorry
161 Student: twenty-four days
162 Teacher: good
163 Student: twenty-four days?
164 Student: yes because you do six, you do er six times four
165 Student: no
166 Teacher: work out how many sort of days work there is, if six girls are each working for four days, there's twenty-four days of work on that fence isn't there yeah so one girl would take twenty-four days so how many days would eight girls take
167 Student: they'd take eight times as long
168 Teacher: hands up
169 Student: three
170 Teacher: three
171 Student: I said three
172 Teacher: yeah do you know why you said three
173 Student: yeah
174 Teacher: go on then
175 Student: cus if six girls take four days
176 Teacher: mm mm
177 Student: and then like if three girls took erm twelve days yeah
178 Teacher: good
179 Student: then that'll be like because I've doubled it but then like you take two people away, like divide six by three and then you have two and then like take one day no what am I on about. well you get what I'm saying, you probably don't but I, I get what I'm saying
180 Teacher: well ((inaudible))
181 Teacher: okay no so long as you do SNAME that's fine somebody needs to right so if its indirect, generally guys if its indirect we times up to work out how many days or whatever it is and then we divide to work through. let's have a look at another one this one down here. four men laid three hundred metres of pipe in five days how much pipe can be laid in eight days are we talking direct or indirect
182 Student: direct
183 Teacher: direct why
184 Student: cus the pipe will go up when the days will
185 Teacher: because the length of the pipe will go up as the length of days go up good okay well done so five days in five days we can lay three hundred metres so how much could you lay in one day
186 Student: sixty
187 Teacher: sixty metres good because its direct we both know they're going up, if you divide one you're going to need to divide the other so in eight days, what would we get
188 Student: five hundred, four hundred and ((inaudible))
189 Teacher: yep
190 Student: four hundred and eighty
191 Teacher: brilliant well done guys four hundred and eighty metres. and it makes sense because the lengths gone up when the number of days have gone up so check that at the end. the other one was different right let's do the last one what about that one just do that okay six shirts take two hours to dry on a washing line how long will it take to dry three shirts should be a question mark at the end
192 Student: what?
193 Student: what?
194 Student: they'd be the same wouldn't they
195 Student: oh that is easy
196 Student: another trick question
197 Student: one hour
198 Teacher: one hour
199 Student: no that's a trick question
200 Student: ((inaudible))
201 Student: that's a trick question
202 Student: it'll take two hours
203 Student: it'll take two hours
204 Student: oh
205 Student: it will take one hour
206 Student: one hour because
207 Student: it will take one hour
208 Student: no it wouldn't it would take two because they've all got to dry ((inaudible))
209 Student: no it wouldn't
210 Student: ((inaudible))
211 Student: there all t-shirts aren't they
212 Student: it doesn't matter how many's on the line
213 Student: yeah
214 Student: it's all gonna take two
215 Teacher: good okay? you've got to be aware of the
216 Student: ((inaudible))
217 Student: trick question that's not nice
218 Teacher: things sometimes appear phrased like a direct indirect, indirect proportion question it's not always like that sometimes changing the amount won't actually change the time. six shirts taking two hours to dry each shirt is taking two hours to dry so three shirts are still going to take two hours to dry
219 Student: even twelve shirts would take two hours to dry if the washing line was big enough
220 Teacher: yeah
221 Student: I get that now
222 Student: big enough ha ha
223 Teacher: yeah? same way as if I said you lot took fifty minutes to complete a lesson, if I bought the others back we'd still take fifty minutes to to complete the lesson despite the fact that there's more people yes it still works out exactly the same so guys today what I want you to do is, we're going to go to the books in a minute. I want you to actually go through these questions, I want you to think about indirect or direct and then try and work it out. be careful there might be trick questions okay. we are going to talk through them. okay in a bit. but what I want you to do is actually talk to the people on your table as well to help you solve the questions okay so if you turn to page twenty-seven. should be enough books for everyone
224 ((Other Interaction))
225 Teacher: start on page twenty-seven talk through the questions it does say you can use a calculator to work it out most of these however you shouldn't need one
226 ((Other Interaction))
227 Teacher: okay Im going to just let you finish the question you're on just because I want to talk through the first few make sure we're doing it we're getting it exactly right.
228 ((Other Interaction))
229 Teacher: okay let's go through guys look this way okay just want to go through the first five very very quickly make sure we're on target and we understand what we're doing properly the first one, somebody tell me how to do it I want to know if it's indirect or direct and how you worked it out SNAME
230 Student: its mm direct
231 Teacher: it is direct how did you work it out
232 Student: I divided twenty-eight by five
233 Teacher: which was
234 Student: five point six actually
235 Teacher: so five pounds sixty
236 Student: yeah and then I timesed that by seven
237 Teacher: and then you did five pounds sixty times seven which gave you?
238 Student: thirty-nine twenty
239 Teacher: thirty-nine pounds twenty direct because the more you work the more you get paid, or at least it should be that way er work it out by dividing first and then timesing it up. question two. a girl walks three miles an hour, how long does it take to walk five miles SNAME
240 Student: isn't miles isn't here
241 Student: one hour forty minutes
242 Teacher: one hour forty minutes how did you work it out was it indirect or direct
243 Student: it was
244 Student: indirect
245 Student: does that say one hour forty miles
246 Student: yeah it would it's direct
247 Teacher: it's direct
248 Student: the amount of time the amount of distance increases as the amount of time increases
249 Teacher: good cus the longer you go the longer it takes so it's direct again
250 Student: sir does that say one hour forty miles
251 Student: sir why's it say pounds and then one hour forty minutes
252 Student: ha ha ha
253 Teacher: I don't know don't ask me silly questions right I don't know why it says that er direct proportion okay twenty minutes a mile work it out get it right question three question three, SNAME indirect or direct
254 Student: indirect
255 Teacher: indirect why
256 Student: because the more men there are the less days there are
257 Teacher: more men there are the less days it takes. good. so four men take five days. one man would take how many days
258 Student: twenty
259 Teacher: good so ten men would only take two days
260 Student: that was a lot like your question that you had
261 Teacher: it's very quite a lot of them are going to be similar aren't they yeah quite a lot of them are going to be very similar question four let's just quickly talk about whether they're indirect or direct my board is behaving really funny travelling at eight miles an hour a boy takes five hours how long will he take at twelve miles an hour is that indirect or direct
262 Student: indirect
263 Teacher: why
264 Student: because don't know
265 Student: ooh
266 Teacher: you're right I just want to know why
267 Student: cus the amount the speed it goes the time goes down yeah
268 Teacher: yeah the faster the speed the actual time decreases okay what I want you to do before we finish. look down, we've still got a bit of time I want you to look down the questions. I want you to pick guys I want you to pick four more questions to do. there are a lot okay I don't want you to do
269 Student: sir what was the answer to number four
270 Teacher: I didn't tell you, I didn't tell you that because some other people didn't understand okay I want you to pick five more questions to do and I want you to spot at least one trick question
271 Student: is there one in there
272 Teacher: there is at least one in there okay so I want you to do four questions
273 Student: I found one
274 Teacher: I said four earlier or I said five
275 Student: you said five
276 Teacher: I said both haven't I
277 Student: I've I've found one of the
278 Teacher: okay I want you to answer four or five
279 Student: one of the ((inaudible))
280 Teacher: more questions of your choosing and find me one trick question
281 Student: I've found the trick
282 Teacher: okay there is probably more than one trick question in there
283 Student: I've found one
284 Student: I've might I might just do them all
285 Teacher: okay you've got about six minutes to finish four or five more questions yeah you can choose whichever ones you want and then we'll finish up guys
286 ((Other Interaction))
287 Teacher: okay trick questions guys which ones are your tricks first
288 Student: twenty
289 Student: seven
290 Student: seven sixteen twenty twenty-four
291 Teacher: hands up. hands up SNAME I don't want you shouting out yes
292 Student: twenty
293 Teacher: twenty is a trick question why is it a trick question
294 Student: is it because um if it took her fifteen minutes to walk there it wouldn't take two, two women any less time or any more time to walk the same distance
295 Teacher: yeah if you're walking a distance, and you're walking with somebody else
296 Student: unless they stopped and started talking
297 Teacher: unless they stopped and started talking why, whenever we increase the number of women we talk about talking I don't know right just I don't know why I don't know what you're trying to say er yes SNAME
298 Student: twenty-four
299 Teacher: twenty-four why twenty-four
300 Student: because two girls can see twenty miles three girls can see twenty miles ((inaudible))
301 Teacher: because what
302 Student: ((inaudible))
303 Teacher: ((inaudible)) yeah so it's all about seeing distance that's not going to increase trick question SNAME did you find one
304 Student: no
305 Student: box of eggs
306 Student: not unless they stood ((inaudible))
307 Teacher: box of eggs which one's that
308 Student: er it's that one
309 Student: its that one
310 Student: it takes six minutes to boil
311 Student: hard boiled eggs, it takes six minutes to boil three hard boiled eggs in a pan, how long does it take to hard-boil two
312 Teacher: good
313 Student: at the same time
314 Teacher: cus if you're using the same pan it'll boil at the same speed and there's the one about the phone number isn't there
315 Student: yes it's here
316 Student: yeah
317 Teacher: yeah if it takes what's the question say?
318 Student: if it takes it takes twelve minutes seconds
319 Student: twelve seconds to dial a twelve-digit number
320 Teacher: twelve seconds to dial a twelve-digit number of a friend that's
321 Student: two hundred miles away and twelve minutes is how long would it take to dial twelve digits who is ten miles away
322 Teacher: it would be the same but then the next question says a six-digit number
323 Students: yep
324 Teacher: yeah and that's quite it's quite that's a really easy question, because it's one second per number
325 Student: it would take six seconds
326 Teacher: it would take six seconds good okay
327 Student: but how would you know if it if it was nine nine nine nine
328 Student: hey look it's batman
329 Teacher: final thing guys SNAME lift your head off the table please final thing, before we do we've still go ten minutes here it's going really er so before last thing I just want you to tell me give me somebody tell me what direct proportion is and give me an example yes
330 Student: is it when if something increases if one proportion increases then another will increase as well
331 Teacher: give me an example?
332 Student: if it's hot outside, the hotter it is the more you sweat
333 Teacher: good okay we're trying though to talk more about things that are tightly, tightly fit together like the more you work the more more you earn because that actually goes up by the same amount but no good yes
334 Student: is it like the more water you put in your kettle the longer it takes to boil
335 Teacher: yeah that would work wouldn't it
336 Students: yeah
337 Teacher: the more water you put in a kettle the longer it takes to boil good indirect proportion then, tell me what indirect proportion is and tell me an example SNAME
338 Student: erm indirect proportion is like when something gets higher but the other thing gets lower
339 Teacher: good
340 Student: but they don't go at the same rate
341 Teacher: good they go in opposite directions
342 Student: so basically er like SNAME said with the er further you go the less petrol you've got in the ((inaudible))
343 Teacher: the further you go the less petrol you've got in your tank good last thing then
344 Student: the less there is in the bottle
345 Teacher: last thing then. I just want you to think about this. er a square room of side two metres. takes one hundred tiles for the floor. okay. er how many tiles would be needed for a square room, square room even, of side four metres. if it takes a hundred tiles, to tile a two metre square room, they're not very big tiles, two metre square room takes a hundred tiles, and if I double the size of the room, how many, how many tiles would it take to tile the floor SNAME.
346 Student: two hundred
347 Teacher: two hundred SNAME.
348 Student: two hundred
349 Teacher: SNAME,
350 Student: two hundred
351 Teacher: two hundred?
352 Student: four hundred
353 Student: I believe two hundred
354 Teacher: why four hundred why two hundred
355 Student: copied me then
356 Student: ah yeah it's four hundred
357 Student: because you just double it
358 Student: because ((inaudible)) two hundred and then ((inaudible)) two hundred so
359 Student: ((inaudible))
360 Teacher: why two hundred? I want you to think about it, and I want you to tell me why you think it's two hundred
361 Student: how many tiles will be needed for a square room of side four
362 Teacher: okay let's SNAME
363 Student: yeah it's four hundred
364 Student: it's a trick
365 Student: I don't get it
366 Teacher: I can't get
367 Student: yes?
368 Student: ((inaudible))
369 Teacher: it says page one of eight, yet it won't turn onto any of the other pages. okay here's my room, two metres by two metres there's a hundred tiles okay? if I draw a four by four room how many times bigger is it
370 Student: four times
371 Student: twice,
372 Teacher: why twice, why twice bigger why four times bigger
373 Student: because twice, because
374 Student: it's doubled
375 Student: it's doubled yeah
376 Student: it's
377 Student: basically just doubling it
378 Student: yeah but it's four times bigger because
379 Student: that's a lot more than four times isn't it,
380 Teacher: SNAME what were you going to say
381 Student: well you see if all sides are four metres
382 Teacher: yeah
383 Student: then it's going to be two metres in each of there's going to be two metres left in each of those if you double it
384 Student: what? ((inaudible))
385 Teacher: okay I can fit one there if it was the proper size it would fit there I'd fit one there I'd fit one there because I've doubled that dimension and I've doubled that dimension,
386 Student: yeah
387 Teacher: how many times bigger is it?
388 Student: four
389 Teacher: four so that actually works out as how many tiles
390 Student: four hundred
391 Student: four hundred just like I said
392 Teacher: four hundred tiles
393 Student: just like me and SNAME said
394 Teacher: that's why I ask you why SNAME didn't I
395 Student: ha ha ha
396 Teacher: because it different from working it out and guessing it okay four hundred tiles it's still we can still say this is direct proportion because as one's increasing the other's increasing, but it doesn't necessarily increase in a linear way okay remember we talked about linear being a straight line doesn't increase in a linear way okay? if I talk to you about volume if I had a cube, two by two by two and I increase that to four by four by four, okay how many of those cubes could you fit in that cube?
397 Student: four
398 Students: eight
399 Student: two
400 Teacher: eight good, why eight
401 Student: because it's eight times bigger because it's um just like with that
402 Teacher: we've increased two dimensions doubled two that's two times two is four,
403 Student: but then you've got to times it to get,
404 Student: and you've increased three dimensions
405 Teacher: and we've increased three, dimensions, good
406 Student: eight
407 Teacher: so two times two times two is eight good so if we're talking about area or volume yeah, then we need to actually think about how many different dimensions that goes back to a question that always comes up on exam papers and stuff and people get it wrong okay, if there are a hundred centimetres in one metre how many centimetres are there in one metre squared how many centimetres squared are there in one metre squared?
408 Student: no
409 Student: fifty
410 Teacher: doing what we just did, two dimensions, we've increased it a hundred times that way, increased it a hundred times that way
411 Student: now we're going to increase it a hundred times
412 Student: now we
413 Student: it is ten thousand
414 Student: that one times that one
415 Teacher: good ten thousand one hundred there, one hundred there, times them together ten thousand centimetres squared. okay I was going to go on to do a lesson about er converting between area but we'll leave that for the moment we're going to go on to something totally different tomorrow. so. finish off today guys. can you just pile your books in the centre of your table. if you borrowed a calculator can you put that in this box on your way out.
