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.
3 Teacher: no
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.
7 Teacher: no Tuesday I had, only had six
9 Teacher: we've got a few more, seven sorry.
12 Teacher: yes the rugby ((inaudible))
15 Teacher: perhaps its the boys rugby ((inaudible))
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.
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.
21 Teacher: and the date
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.
25 Teacher: what
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
29 Teacher: okay so. indirect, direct, what do you reckon indirect and direct. yep
31 Teacher: a direct answer, what do we mean by that though
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
35 Teacher: they're directly the same size. what were you saying SNAME?
37 Teacher: so proportion, you're on about proportion as in like splitting into the same proportion
39 Teacher: yeah okay SNAME what were you on about
41 Teacher: something to do with opposites and which one do you reckon is opposite
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.
45 Teacher: for direct proportion. if you think of positive correlation
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
49 Teacher: it will decrease.
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
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
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
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.
65 Teacher: is that true?
68 Teacher: is it the same with nose hair and ear hair as well
70 Teacher: it's not fair to say something about SNAME when he's not here
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
75 Teacher: yeah the amount of distance travelled, the amount of fuel left yeah that's indirect
77 Teacher: left
79 Teacher: very similar yeah so the amount you use a pen and the ink left yeah. that would be there yep
81 Teacher: this is for the direct one carry on
83 Teacher: you'd hope
85 Teacher: yeah as the words will print onto both pages
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
92 Teacher: what so the more paper you print out the less words
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
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?
106 Teacher: that's fair because he gets tired
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
110 Teacher: decrease. so which are we talking about
113 Teacher: indirect we're talking about indirect
120 Teacher: you know what women are like they just talk
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
124 Teacher: but it's going to in this modelling situation
126 Teacher: yep they might do so indirect or direct. I've already written it up so you should be able to tell me
128 Teacher: indirect as one increases the other decreases how would we work it out then guys how would you work it out
130 Teacher: six girls paint a fence in four days, how many days would it take eight girls
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
150 Teacher: why ten days
156 Teacher: think about it
160 Teacher: sorry
162 Teacher: good
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
168 Teacher: hands up
170 Teacher: three
172 Teacher: yeah do you know why you said three
174 Teacher: go on then
176 Teacher: mm mm
178 Teacher: good
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
183 Teacher: direct why
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
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
189 Teacher: yep
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
198 Teacher: one hour
215 Teacher: good okay? you've got to be aware of the
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
220 Teacher: yeah
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
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
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.
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
231 Teacher: it is direct how did you work it out
233 Teacher: which was
235 Teacher: so five pounds sixty
237 Teacher: and then you did five pounds sixty times seven which gave you?
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
242 Teacher: one hour forty minutes how did you work it out was it indirect or direct
247 Teacher: it's direct
249 Teacher: good cus the longer you go the longer it takes so it's direct again
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
255 Teacher: indirect why
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
259 Teacher: good so ten men would only take two days
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
263 Teacher: why
266 Teacher: you're right I just want to know why
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
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
272 Teacher: there is at least one in there okay so I want you to do four questions
274 Teacher: I said four earlier or I said five
276 Teacher: I said both haven't I
278 Teacher: okay I want you to answer four or five
280 Teacher: more questions of your choosing and find me one trick question
282 Teacher: okay there is probably more than one trick question in there
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
287 Teacher: okay trick questions guys which ones are your tricks first
291 Teacher: hands up. hands up SNAME I don't want you shouting out yes
293 Teacher: twenty is a trick question why is it a trick question
295 Teacher: yeah if you're walking a distance, and you're walking with somebody else
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
299 Teacher: twenty-four why twenty-four
301 Teacher: because what
303 Teacher: ((inaudible)) yeah so it's all about seeing distance that's not going to increase trick question SNAME did you find one
307 Teacher: box of eggs which one's that
312 Teacher: good
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
317 Teacher: yeah if it takes what's the question say?
320 Teacher: twelve seconds to dial a twelve-digit number of a friend that's
322 Teacher: it would be the same but then the next question says a six-digit number
324 Teacher: yeah and that's quite it's quite that's a really easy question, because it's one second per number
326 Teacher: it would take six seconds good okay
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
331 Teacher: give me an example?
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
335 Teacher: yeah that would work wouldn't it
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
339 Teacher: good
341 Teacher: good they go in opposite directions
343 Teacher: the further you go the less petrol you've got in your tank good last thing then
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.
347 Teacher: two hundred SNAME.
349 Teacher: SNAME,
351 Teacher: two hundred?
354 Teacher: why four hundred why two hundred
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
362 Teacher: okay let's SNAME
366 Teacher: I can't get
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
372 Teacher: why twice, why twice bigger why four times bigger
380 Teacher: SNAME what were you going to say
382 Teacher: yeah
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,
387 Teacher: how many times bigger is it?
389 Teacher: four so that actually works out as how many tiles
392 Teacher: four hundred tiles
394 Teacher: that's why I ask you why SNAME didn't I
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?
400 Teacher: eight good, why eight
402 Teacher: we've increased two dimensions doubled two that's two times two is four,
405 Teacher: and we've increased three, dimensions, good
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?
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
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.
