AU4 RATIOS
This eighth grade mathematics lesson focuses on developing student understanding of ratios. It is the fourth lesson in a seven-lesson unit of work focused on ratio and rates. This is a "double lesson" of 69 minutes duration. There are 30 students in the class.
| Time | Caption |
|---|---|
| 00:00:01 | Okay. We're finishing off where- we're going to continue from where we were, last class. So you need to try to be reasonably quick about taking- Twelve? |
| 00:00:19 | You'll need your books so we'll put today's date. And the heading. |
| 00:00:40 | B:10th September, 1999 Dividing a Given Quantity in a Given Ratio |
| 00:01:05 | Is that a microphone Miss? |
| 00:01:06 | Yeah. |
| 00:01:07 | (inaudible) |
| 00:01:09 | No I don't think so. |
| 00:01:18 | The exercise we're referring to in the textbook is ten-o-four. Page two two two. We won't necessarily need that straight away but you will need it shortly. |
| 00:01:48 | Count 12 each and give me the rest back. Count out 12 each and give me the rest back. Or hand the rest back to the people behind you. Twelve each please. |
| 00:02:09 | Miss (inaudible). |
| 00:02:11 | Yeah (inaudible). |
| 00:02:18 | Mm... Why is (inaudible)? |
| 00:02:20 | (inaudible) |
| 00:02:21 | Oh okay. Take 12 each and give me the rest back. Better still, take 12 each and hand the rest back- over to these girls. |
| 00:02:36 | Twelve each please. |
| 00:02:56 | Six seven eight nine 10 11 12. |
| 00:03:13 | Hand them back (inaudible). Okay. Twelve each. |
| 00:03:22 | Lindsey you can take any spares and put them in the box and bring the box to the front, okay? |
| 00:03:28 | All right. Now let's just go over what we did yesterday. Yesterday you had to divide your 12 into different ratios. Let's do one of those again. Or two of them. |
| 00:03:44 | Let's divide the 12 you have in the ratio, uh... five to seven. Divide them into ratio five to seven. Thank you. |
| 00:04:09 | So that means that you're going to separate them into two groups on your table with how many in the first group? |
| 00:04:17 | Five. |
| 00:04:18 | Five and seven in the second one. Okay. What if I say I want them divided into ratio one to two? |
| 00:04:29 | (inaudible) |
| 00:04:36 | No. Six in each would be? |
| 00:04:38 | Fourteen. |
| 00:04:40 | Six to six which would be? One to one. |
| 00:04:44 | Eight in one group and four in the other. |
| 00:04:48 | Eight in one group. Which group? |
| 00:04:51 | In the two. |
| 00:04:52 | Groups, so you really should have told me four to eight because remember with ratio the order is important. |
| 00:05:03 | Now I want you, for what we're moving onto today, to actually make them equal piles. So I want how many piles altogether really? |
| 00:05:17 | Two. |
| 00:05:18 | No. |
| 00:05:19 | Three. |
| 00:05:20 | Three piles all together and I want you to stack them up so you have three piles. One on your left, and two on your right. Stack them up so you have one on your left and two on your right. |
| 00:05:56 | One two three four five... six seven eight nine 10 11 12. |
| 00:06:05 | All right. So what we actually have there- Danny doesn't seem to, but the rest of us should have. Is when we- |
| 00:06:21 | We have three piles worth 12 and you have created one pile of four and two piles of eight. Okay? |
| 00:06:40 | How did you get two piles of eight? |
| 00:06:42 | Two piles. Two piles of four to equal eight. All right. So you created three stacks of blocks. All right. |
| 00:06:55 | For the next lot of questions we're not going to maybe use all 12 blocks. |
| 00:07:01 | What we're going to do is consider it almost as if it was an empty box. |
| 00:07:06 | So we're going to just create, use this box as one pile so in this particular case, if I said to you I want the ratio of one to two you would have one empty box to two empty boxes. |
| 00:07:24 | So you would have the ratio or the way you're- one is to two. All right? |
| 00:07:35 | Okay, so I want you to see if you can create for me a ratio of one to three. A ratio of one to three. How many blocks have you got? |
| 00:07:54 | Three |
| 00:07:55 | Twelve. |
| 00:07:56 | Altogether, four. So you actually would have four shares or four boxes, four piles that you need to create. All right? |
| 00:08:10 | Okay. What about the ratio two to five? Two to five. That means on your left hand you would have? |
| 00:08:23 | Two. |
| 00:08:24 | Two blocks which are empty boxes and on your right hand you've got? |
| 00:08:30 | Five. |
| 00:08:31 | Five which means that you have used- for a ratio of two to five you have used? Seven boxes. Two here and five there. Right? Follow that? |
| 00:08:52 | Yeah. |
| 00:08:54 | Okay. What about eight to three? The ratio of eight to three. |
| 00:09:19 | If you've used eight to three you should have eight empty boxes on your? |
| 00:09:25 | Left. |
| 00:09:26 | Left hand side and three empty boxes on your right hand side which means you have used? |
| 00:09:33 | Eleven. |
| 00:09:34 | Eleven. |
| 00:09:35 | Eleven boxes, shares, piles, whatever you want to call it. Any kind of grouped word. Okay. |
| 00:09:46 | What if I want to divide money up? You have to use your imagination here. Smarties later. Money now. |
| 00:09:57 | Money. |
| 00:09:58 | I want you to divide 200 dollars in the ratio one to three. |
| 00:10:11 | So create for me the ratio one to three again. Right. So you have? One box on the left, three boxes on the right. Now the whole idea- Dylan. |
| 00:10:37 | The whole idea about dividing things up in a ratio is that you have equal piles in each of your four- equal amounts in each of your four boxes. |
| 00:10:56 | So what will go in one box if you have to fill four boxes equally. Ashley? |
| 00:11:04 | Fifty dollars. |
| 00:11:05 | Fifty dollars. So four shares is equal to 200 and so one empty box or share has 50, so the ratio one to three will equal 50 to 150. Yes? Okay. |
| 00:11:38 | So you write this down please. It's best if you write the question since it's an example, so write divide 200 dollars. Divide 200 dollars. Right. Two hundred dollars. |
| 00:11:57 | Divide 200 dollars in the ratio one to three. I (inaudible) forgotten your (inaudible). |
| 00:12:09 | (inaudible) |
| 00:12:12 | Mm. Then copy down four shares equals 200 dollars. One share is 50. One to three is 50 to 150. |
| 00:12:23 | Four shares is equal- |
| 00:12:25 | Now if we're going to be very good, people, with this, |
| 00:12:30 | then we ought to write an English statement at the end of it, so we should say something like the first person gets 50 and the second- |
| 00:12:50 | That's presuming that was a story about people, the second person could have been companies I suppose, gets 150. |
| 00:13:05 | Okay, so you really ought to put some English in at the end to actually answer what the question was. |
| 00:13:15 | (inaudible) |
| 00:13:22 | Right? Finished? Okay, next one then was... the next one that we had, we recreate a ratio of two to five. |
| 00:13:40 | So recreate your ratio of two to five. Which was? How many blocks required? |
| 00:13:54 | Seven. |
| 00:13:55 | Seven. It's starting to seem really easy now, isn't it? Okay, and I actually want you to divide 210 dollars. |
| 00:14:04 | Two hundred and ten dollars between those seven boxes in the ratio two to five. |
| 00:14:28 | I want you to divide 210 dollars into those seven boxes but in the ratio two to five. So firstly you have to figure out how much is in one box. |
| 00:14:47 | Just a minute girls, we'll just let the others have a think first. |
| 00:14:57 | Danny. You don't need a calculator to do that. |
| 00:15:03 | You told me to get it out Miss. |
| 00:15:04 | Well you don't need a calculator to do that. What is it Tanya? One box in each box. Would it be equal to 30? I think it would. How would you find 30? |
| 00:15:17 | Seven divided by (inaudible). |
| 00:15:19 | Three. |
| 00:15:20 | Seven. Twenty-one divided by? Seven is three. Two hundred and ten divided by seven is 30. |
| 00:15:28 | (inaudible) |
| 00:15:33 | Yep. Okay. So two boxes, 60, five boxes, 150, so the first person gets? Sixty dollars and the second person gets- 150 dollars. Write that down. |
| 00:15:58 | Write what down? |
| 00:16:00 | Write down the English. So the first person 60 and the second person gets? A hundred and fifty again. |
| 00:16:18 | Okay let's do one more of that. Let's do eight to three and this time I want to divide 66 dollars. |
| 00:16:51 | Worked it out Mark? |
| 00:16:55 | (inaudible) |
| 00:16:59 | You can't give me one number for an answer if you're going to give me a ratio, because you've gotta give me? |
| 00:17:03 | A number for this share and a number for that share don't you. So- |
| 00:17:07 | Yeah. |
| 00:17:11 | Oh, you're telling me what one share is worth. Is that what you're saying? So 11 shares is 66 so you're saying one share. Okay. |
| 00:17:23 | So what you really wanted to say to me was? Is one share six and the answer to that would be yes. |
| 00:17:28 | So the eight would be- |
| 00:17:30 | Nicole? |
| 00:17:31 | Yes. |
| 00:17:33 | So what would the ratio eight to three be? |
| 00:17:39 | Eighteen. |
| 00:17:41 | Eight to three would equal? |
| 00:17:43 | Do you follow what's going on? |
| 00:17:44 | Forty-eight. |
| 00:17:45 | Yeah. Forty-eight to 18. |
| 00:17:51 | Just that you missed a couple of the classes so I didn't know whether you had caught on. Forty-eight to 18. Six times eight and six times three. |
| 00:18:04 | So, you're right, the first person gets 48 dollars and the second person gets 18 dollars. All right. |
| 00:18:15 | Now, I want you to see if you can make up your own question, but before you do that... |
| 00:18:24 | If you want to make up an easy question you can find a bit of a relationship between the ratio and the amount. |
| 00:18:33 | Have another little look at the numbers that I chose and see if you can see a pattern. |
| 00:18:55 | I'm not speaking about a pattern from this ratio to that ratio to that ratio. I'm speaking about a pattern between ratios and amounts. |
| 00:19:03 | Because I deliberately picked these numbers so that they would be relatively easy to work out. |
| 00:19:14 | So what numbers am I actually speaking of? I'm speaking of one to three which is 200. |
| 00:19:21 | Eight to three, which was 66 and two to five which I chose 210. Okay? Bobbie Jo? |
| 00:19:29 | Easily divisible by (inaudible). |
| 00:19:32 | Exactly. They are easily divisible by the? Total number of blocks you used to create them. Eight and three is 11, and 11 goes into? Sixty-six with no remainder. |
| 00:19:46 | One and three make? Four, and four goes into 200 nice and easily. No remainder. |
| 00:19:52 | Two and five make seven, and I deliberately chose a multiple of seven so you wouldn't have thir- 29 dollars and 43 cents or something like that. |
| 00:20:05 | Which would have been okay because you've got a calculator there. You could have handled it. But to start with I chose something easy for you to work out. |
| 00:20:15 | So I want you to create for your friend a question and then swap books and see if they can do it. |
| 00:20:24 | So it would be better if you tried to create one they could do in their head without a calculator. So try to maintain that relationship where the total number of boxes- |
| 00:20:35 | (inaudible) need a (inaudible). |
| 00:20:37 | No you don't need to restrict yourself to less than 12. You can have a ratio of 25 to one if you want or- |
| 00:20:46 | Forty- a hundred to one. |
| 00:20:48 | A hundred to one? Yeah. But then try and find a number that would be a multiple of a hundred and one. Two hundred and two. |
| 00:21:01 | (inaudible) |
| 00:21:02 | Yeah. All right. |
| 00:21:04 | (inaudible) |
| 00:21:06 | No. But he might beat you up if it's too hard. Then again, Byron is pretty good at conflict resolutions so you might be lucky. |
| 00:21:23 | You three swap, you know, between you. |
| 00:21:36 | (inaudible) This is good. This is better. Did you have, um, something to give me, a tear off slip off the bottom of that letter? |
| 00:21:45 | No. Okay. There is one so maybe you might want to bring it back so I just know that I've seen it. |
| 00:21:54 | Make up a question, swap it over. So the question just has to be divide something. Do you have to restrict yourself to dollars? |
| 00:22:00 | No. |
| 00:22:01 | No. |
| 00:22:02 | No. You can have any kind of quantity you like. Kilometers, liters. |
| 00:22:11 | He got eight. |
| 00:22:13 | Surfboards. |
| 00:22:32 | Well what's one box (inaudible)? So your question is to divide 55- five dollars or fif- |
| 00:22:40 | Five hundred dollars in the ratio four to six which would have been nice as two to three wouldn't it, because we like a simple ratio. |
| 00:22:51 | Okay. So you've got 10 boxes so how much is in one box? |
| 00:22:54 | Fifty. |
| 00:22:55 | Fifty. So you write 50 there. One box is 50 dollars. So four to six would be? Four lots of 50 and six lots of 50. Two hundred to 300. |
| 00:23:15 | And notice when you actually add those back up you still do get your 500. |
| 00:23:28 | Have you finished doing your friend's question yet? |
| 00:23:29 | No. |
| 00:23:33 | Come on. |
| 00:23:35 | Can one of you swap with Gary, please? So what are you dividing? Eighty-one dollars in the ratio six to three yeah that's good. That's really good. |
| 00:23:48 | So nine into 81 goes three times. (inaudible) Very good. Do you want a hand? |
| 00:24:08 | All right. |
| 00:24:10 | Do you want Gary to do yours for you? |
| 00:24:11 | (inaudible) |
| 00:24:12 | All right. |
| 00:24:22 | Okay. I prefer you to write somewhere five shares equals 50 while you're doing your working. Hmm? All right 100 dollars (inaudible) one to four. Yeah, okay. |
| 00:24:39 | But as I say, I'd still like to see somewhere five shares equals 100. Just to remind you that what you have to do is total up to start with. All right. |
| 00:24:53 | You right? Did you- have you swapped? |
| 00:24:56 | (inaudible) |
| 00:24:58 | Still? Okay. |
| 00:25:00 | Yeah, we both wrote (inaudible). |
| 00:25:01 | She had (inaudible) because I did 121 divided by 65. |
| 00:25:07 | One twenty-one divided in the ratio. You shouldn't really use the division sign like that because you're not dividing by, you're dividing in. |
| 00:25:18 | Eighty-one. How do you- |
| 00:25:19 | See? And that- and that line with the two dots means divide by not divide in. Does nine go into 121? |
| 00:25:30 | (inaudible) |
| 00:25:34 | Oh 65. Three. (inaudible) |
| 00:25:44 | They were supposed to make one up that you could do in here. In your head though- not with your calculator- not with- |
| 00:25:50 | I was just doing (inaudible). |
| 00:25:55 | What do you have to do? |
| 00:25:57 | She had to (inaudible). |
| 00:26:15 | Are we all right then? Is that just about enough time? How did you guys go? You got it right? Pardon? |
| 00:26:31 | (inaudible) |
| 00:26:33 | Yeah. |
| 00:26:34 | (inaudible) |
| 00:26:35 | No. I don't even know if I can find the marks out. |
| 00:26:48 | Okay. |
| 00:26:56 | Uh, let's see. (inaudible) Four is- 25. |
| 00:27:03 | Twenty-five (inaudible). |
| 00:27:11 | Twenty-five to one dividing them both- now wait a second, you're dividing them both by four aren't you? |
| 00:27:16 | So isn't it 50 to one? Are you making up the question or are you doing his question? |
| 00:27:29 | So what- so you have to divide 408 dollars in the ratio of 200 to four. Okay. So you actually have? Two hundred and four shares so one share's eight. |
| 00:27:44 | No, that can't be right. If 204 shares is two- 408 dollars, one share is only two dollars isn't it? |
| 00:27:56 | Because 408 divided by 204, is only two- so it should be 400 to eight. |
| 00:28:04 | (inaudible) eight (inaudible) |
| 00:28:09 | (inaudible) Miss, is that (inaudible)? |
| 00:28:14 | No. No. Let me finish this off first. Let's just start again here. Turn around. |
| 00:28:26 | What do we do when (inaudible)? |
| 00:28:29 | Just wait a second. You've got 408 dollars and you want 200 to four. |
| 00:28:34 | So 204 shares equals 408 dollars, one share is two dollars, 200 shares would be 400, two times 200. |
| 00:28:47 | And four shares would be two times four which is eight. All right? I'll help you in a minute Kelly. |
| 00:28:55 | Okay. Let's return to this question here. Two to five. But I want to change 210 to something else. Not dollars. |
| 00:29:12 | Enough now, thanks. Dan, Stephen. |
| 00:29:21 | Okay. I'll go with Smarties. You need to create for me a story to explain why I would want to divide Smarties in the ratio two to five. Nicole? |
| 00:29:37 | Because you only need certain- |
| 00:29:39 | Because (inaudible). |
| 00:29:43 | Wait a second. Nicole first. Thanks. |
| 00:29:45 | Because you might only like a certain color. |
| 00:29:49 | But that- how is that going to make a story? How is that going to make a story that says divide 210 Smarties into the ratio two to five. |
| 00:29:58 | One person might want color and one wants the other color. |
| 00:30:02 | And there's more of one color like the blue ones there's heaps of those, and the brown- no, and then there's a color (inaudible) red. |
| 00:30:11 | No. I can't- can't quite see. Bobbie Jo? |
| 00:30:15 | There's seven people (inaudible). |
| 00:30:20 | No. That's a different question isn't it? Dividing 210 Smarties between seven people is a different question. How many people have you actually got here? |
| 00:30:31 | Two. |
| 00:30:32 | Two. Only two people involved in this story. Only person A who gets two shares and person B who gets? |
| 00:30:44 | Five shares so you need to think of a story as to why two people would get different amounts of Smarties. Lindsey? |
| 00:30:51 | A. A. Um, (inaudible) to what person B (inaudible). |
| 00:30:57 | All right. So, I had some Smarties and person A stole some? |
| 00:31:03 | Yeah. Person B stole some from person A. |
| 00:31:08 | Person B pays- |
| 00:31:10 | Oh, okay. So I had some Smarties which I thought I was going to give equally between A and B, but B was greedy and stole some, so, they were now in the ratio two to five. |
| 00:31:27 | How many did he have? Okay. Think of another quantity. Not Smarties this time, something else. |
| 00:31:36 | Marbles. |
| 00:31:39 | Marbles, surfboards? |
| 00:31:43 | I think Smarties- |
| 00:31:44 | Let's move past the chocolate. Bodyboards. |
| 00:31:48 | Ah, Skittles. |
| 00:31:50 | Bodyboards. Can you make me up a story to divide bodyboards in the ratio. We have 210 bodyboards and we want them divided in the ratio two to five. |
| 00:32:02 | Eight? |
| 00:32:03 | No, no, no. If you think you've got a story put your hand up. Tanya? Sam. Pardon? |
| 00:32:20 | (inaudible) |
| 00:32:23 | Yes you do. What is it? |
| 00:32:24 | No she said- she said one's a pro surfboard, one's just a beginner. |
| 00:32:29 | Okay. So there's 210 surfboards where? On the beach? Bodyboards. |
| 00:32:39 | In a shop. |
| 00:32:40 | In a shop? |
| 00:32:42 | On the shore. |
| 00:32:43 | And a pro surfer and an amateur walk into the shop and they buy some boards in the ratio two to five which means that the amateur- |
| 00:32:57 | Who would be the amateur who do you think? A or B? |
| 00:32:59 | B. |
| 00:33:00 | A. |
| 00:33:01 | A would be the amateur and they get- how many boards would they have got? |
| 00:33:05 | Thirty. |
| 00:33:06 | Thirty. Sixty. Sixty boards and the other person bought 150. Might have been better to knock off a zero in that story perhaps, eh? Six boards and 15. |
| 00:33:17 | You wouldn't even need- you just need one. |
| 00:33:18 | Well. |
| 00:33:21 | Maybe they're getting very serious about bodyboarding. |
| 00:33:23 | Okay. I want you to write a story now about the ratio that you created for your friend to do. |
| 00:33:32 | Well make a new ratio if you don't want to write about that one. But make a ratio and a quantity and write down a story for that question. |
| 00:34:05 | I didn't get to work my ratio out Miss. |
| 00:34:08 | You can't work it out? |
| 00:34:10 | Divide 80 dollars in the ratio 23 to one. Twenty-three. Is it? So that's 24 boxes all together. |
| 00:34:21 | So 80 divided by 24... is 10, 80 over 24, they're both divide by eight, aren't they? So that would be 10 over three which would be three and a third. |
| 00:34:42 | So one box would have three and one-third. So 23 would have- 23 times three and a third. Can you work that out in your head? |
| 00:34:56 | Well, it'd be 23 wholes and 23 thirds. We divide 23 by three. Follow what I'm saying? |
| 00:35:06 | One box is three and a third. All right. So two boxes would be? |
| 00:35:16 | Six and two-thirds. Three boxes would be nine and three-thirds but three-thirds is another whole so three boxes we'd have, 10. |
| 00:35:26 | Okay. So 23 boxes has three and a third times 23. |
| 00:35:33 | All right. Which would be three times 23, which would be, uh, three times... 69 and 23 thirds. All right? |
| 00:35:49 | Yeah. |
| 00:35:51 | Now 23 thirds, how many wholes is that? Well 23 divided by three is seven remainder two, so you actually have 69 plus seven. |
| 00:36:03 | And it would be 76 and two thirds. Okay? |
| 00:36:16 | There were 11 boxes and 77 apples. Three were (inaudible) and eight (inaudible). |
| 00:36:27 | Three boxes. |
| 00:36:29 | (inaudible) |
| 00:36:31 | Yeah. |
| 00:36:32 | That would? |
| 00:36:33 | Yeah. Yes. You had 77 apples, that's what you're saying, and you packed them in the ratio and they went to market in a ratio of three to eight. How many went to market? |
| 00:36:52 | Three. (inaudible) |
| 00:36:55 | Three. |
| 00:36:56 | What happened to my story? |
| 00:36:58 | Yeah. Isn't that right? |
| 00:36:59 | Well I said that- |
| 00:37:01 | You had 77 apples and you packed them into boxes. All right. But you don't need to tell that in the story because that's what the person has to work out. |
| 00:37:11 | Seventy-seven apples- |
| 00:37:14 | (inaudible) In the ratio- and they went to market. In the ratio three- |
| 00:37:15 | And they were packed in two boxes. |
| 00:37:17 | (inaudible) in the ratio and they went to market in the ratio three (inaudible). |
| 00:37:27 | (inaudible) |
| 00:37:28 | No. Because that's what the person who does the question has to work out. |
| 00:37:37 | Have you finished? All right, Stephen. As soon as I've answered Ashley's question you can give me your story. Danny, you'll be second on the story list. And Laura third. |
| 00:38:06 | Yep. Maybe they didn't pay the same amount for the ticket. That would be why they would divide it in a different ratio. |
| 00:38:11 | Jessica needs help Miss. |
| 00:38:13 | Okay, a bit of quiet. Listening to Teague. |
| 00:38:15 | No, Jessica needs help first. (inaudible) story makes sense. |
| 00:38:19 | No. |
| 00:38:20 | No. We'll listen to your story and I'll help Jessica. |
| 00:38:22 | (inaudible) |
| 00:38:23 | Why not? |
| 00:38:25 | Because they thought they already had stories but then they read mine and realized they didn't (inaudible). |
| 00:38:30 | So you have a good story that you can- |
| 00:38:32 | No it's not good. |
| 00:38:33 | It is. |
| 00:38:34 | All right. Well, it'll do. |
| 00:38:38 | I'll read it for her. |
| 00:38:40 | Okay. |
| 00:38:41 | Okay two basketball players were comparing how many points they had in their NBL careers. They had a ratio of one to one. |
| 00:38:45 | Shh... Katie. |
| 00:38:47 | They jointly scored five thousand, fifty-five- |
| 00:38:49 | Sorry, Stephen you'll need to start again because you're not getting full attention. Come on now please. |
| 00:38:56 | Two basketball players were comparing how many plays they had in their NBL career. |
| 00:39:00 | They had a ratio of one to one. They both scored five fifty-five thousand six hundred forty-nine points. Together they equaled (inaudible). |
| 00:39:10 | One hundred and eleven thousand two hundred and ninety-eight. |
| 00:39:15 | Okay. Yeah, so that's a good story but where's the actual question if you were going to make it into a question for someone to do? |
| 00:39:22 | My question was, um, one to one equals- I mean, one for the ratio of one- equals 111,298. |
| 00:39:31 | Oh, okay. |
| 00:39:32 | So the 55,000 would actually be the answer so it would have been better left out of the question, wouldn't it? |
| 00:39:41 | So really your question would have boiled down to divide 111,000 in the ratio one to one. |
| 00:39:46 | Yeah. |
| 00:39:48 | Okay. Who else was there? Danny? |
| 00:39:52 | I haven't finished Miss. |
| 00:39:53 | All right well I'll give you- |
| 00:39:54 | (inaudible) either. |
| 00:39:55 | Well- you- let's just go with what you've got then, eh? |
| 00:40:03 | What- to say the story? |
| 00:40:04 | Yep. |
| 00:40:05 | We didn't have a story. It's just like- |
| 00:40:09 | Read me what you have. That'll be fine. |
| 00:40:11 | One to four? |
| 00:40:12 | Yeah. |
| 00:40:13 | (inaudible) person how much (inaudible). Emma has one blue candle and Laura has four red candles. That's my story. |
| 00:40:25 | Yeah, okay. So that's a ratio story. If Emma has one blue candle and Laura has four, what's the ratio of candles? |
| 00:40:37 | But it's not really a dividing something in a ratio story is it? Danny? |
| 00:40:42 | Yes. |
| 00:40:43 | Times up. Read me what you have please. |
| 00:40:52 | There was 30 lollies. One man got 10 lollies the other got 20, therefore the ratio was 10 to 20. |
| 00:41:01 | Okay. So if we wanted to create a question for somebody in the class to do, then your story would say, two men have 30 lollies and they want to divide them in the ratio one to two- |
| 00:41:14 | How much does each- man- get? All right? Anybody else got a good story? (inaudible)? |
| 00:41:24 | There is a Mars Bar competition and you can win a free Mars Bar. |
| 00:41:27 | Um, five in six are losers and the shop has 121 Mars Bars, how many Mars Bars are losers? |
| 00:41:34 | So the ratio of five to six is winners to losers. Yeah, that's a good question. Did you understand the question Colin? |
| 00:41:45 | Yep. |
| 00:41:52 | However, do you actually think the Mars Bar company would have a ratio of five to six of winners and losers? |
| 00:41:58 | No. Um, five are the losers and then the last one (inaudible). |
| 00:42:02 | The winners. So a ratio of losers to winners of five to six. Is that likely? |
| 00:42:09 | Probably not. |
| 00:42:10 | No. Because every time someone wins they have to pay for a prize for another Mars Bar. It's unlikely that the ratio would be five to six. |
| 00:42:19 | What would be a more realistic ratio if you were running the Mars Bar company |
| 00:42:24 | and you wanted to give a prize for a winner, what ratio of winners to losers? Let's do winners first to losers. |
| 00:42:30 | Give me a pen. |
| 00:42:31 | One to 10. |
| 00:42:32 | Emma? |
| 00:42:33 | One to six. |
| 00:42:34 | One to six. |
| 00:42:35 | One to five. |
| 00:42:36 | One to five. |
| 00:42:37 | Two to 10. |
| 00:42:38 | Two to 10. One to five. Same thing isn't it? |
| 00:42:43 | On that- on that ad thing they have one to six. |
| 00:42:46 | Do they? On the- on the ad- |
| 00:42:47 | Or was it four? |
| 00:42:48 | That was one to six. |
| 00:42:49 | That was one to three. It used to be- |
| 00:42:52 | So there's a- is there an ad? |
| 00:42:53 | Yeah. |
| 00:42:54 | From the Mars Bar company that says that they're going to- |
| 00:42:56 | Something might (inaudible). |
| 00:42:59 | Well, I must confess I would of thought it would of been more like one to 20 or 30. |
| 00:43:04 | (inaudible) |
| 00:43:08 | Okay. Good. All right. I want to show you one more way of writing these questions out before you start... and then you can have a choice of ways. |
| 00:43:23 | If the question- let's go back to our 210 dollars, so we have divide 210 in the ratio two is to five. |
| 00:43:36 | Now this is just an alternate way of setting out your working. It is not really any different in- in actual working philosophy. |
| 00:43:48 | If- or the first share will actually get two seventh's of the prize. Is that right? |
| 00:44:01 | Because you had seven piles that you had to divide the money in and the first person would actually get two out of seven of them. |
| 00:44:12 | So you could actually just find two sevenths of 210 which means that you have to multiply by two and divide by seven. |
| 00:44:22 | Easier if you divide by seven first. That's what you did before. You found 30 and multiplied by two and got? |
| 00:44:28 | Sixty. |
| 00:44:29 | Sixty and so what is the second share worth? |
| 00:44:34 | A hundred and fifty. |
| 00:44:35 | A hundred and fifty we already know because that's five-sevenths of 210, 150. So you've got two methods. |
| 00:44:47 | You can say, seven shares is 210 dollars. Work out one share and then two and five. |
| 00:44:55 | Or you can go straight to saying, if I have two shares out of seven, |
| 00:44:59 | I must have two sevenths of the money on the left hand side and I must have five sevenths of the money on the right hand side. |
| 00:45:13 | So, how would I set this one out where I had a ratio of eight to three. |
| 00:45:19 | I would of said the first person gets eight elevenths of 66 and the second person gets three elevenths of 66. |
| 00:45:32 | Here I would of said the first person gets one quarter of 200 and the other person gets three quarters of 200 dollars. |
| 00:45:44 | It has one small advantage, it's probably just a tad shorter in writing, but that's about the only advantage. |
| 00:45:55 | Which method do you like best? Let's take a sample. Let's have Nicole, Jessica, Daniel and Michelle. |
| 00:46:06 | Which method would you prefer the seven shares, one share, which I might add is basically what you call a unitary method because you go down to one and then back up to two and five. |
| 00:46:24 | Do you prefer the unitary method or the fraction method? |
| 00:46:28 | Unitary method. |
| 00:46:29 | Okay. Jessica? |
| 00:46:30 | Yeah, that one. |
| 00:46:31 | Unitary. Michelle? |
| 00:46:34 | The top one. |
| 00:46:35 | The top one. The unitary one. Who else? Was it Daniel was it you I was asking? |
| 00:46:39 | No. |
| 00:46:40 | Unitary or fraction? |
| 00:46:42 | Unitary. |
| 00:46:43 | Okay. That's fine. You'll find most people across the world do the unitary method but you might want to write it that way if you like. All right. Exercise ten-o-four. |
| 00:46:57 | When are we doing this? |
| 00:47:00 | After you've done ten-o-four. I want you to do question one and two. Just do every second one. |
| 00:47:16 | Can you share with him please? |
| 00:47:17 | All right then. |
| 00:47:26 | We're not going to do very much in question three just A, part one. You get started with that, I'll collect your 12 blocks. |
| 00:47:51 | What are you doing? |
| 00:47:52 | (inaudible) brought me lunch. |
| 00:48:06 | Get started now please. Otherwise you won't have time to do the Smartie question. |
| 00:48:18 | [BREAK BETWEEN TAPES] |
| 00:48:47 | Yeah. |
| 00:48:48 | That's what I'm doing, I'm just not writing- I'm just not writing it out with the times. I'm doing the times in my head. |
| 00:49:00 | Can you make sure that you are (inaudible) good person? |
| 00:49:03 | Yes. |
| 00:49:32 | Finish question one and two. |
| 00:49:46 | It's about seven questions. It will take you that long to do if you're quiet. |
| 00:49:58 | Do we have to write out the question Miss? |
| 00:50:00 | No. |
| 00:50:01 | Do we do every- every question? |
| 00:50:02 | In fact, I would excuse you from writing the story in question one, if- if you wanted to just say, divide 60 in the ratio of five to three, you could just write it as a ratio. |
| 00:50:16 | The way I've used here. You could just write, five to three equals- I would do your working. |
| 00:50:30 | No. That's- I don't want you to write five to three is 60. You've really got to write eight shares in 60. |
| 00:50:35 | All right? Because five to three is two separate numbers, so it can't equal one number. |
| 00:50:51 | The five share would be 10. And the three share would be? |
| 00:50:52 | Its ratio would be? |
| 00:50:53 | Right. |
| 00:50:54 | Six. |
| 00:51:00 | That's the ratio. This one's 10 to six. |
| 00:51:08 | Charles... is not well. He was away yesterday, too, wasn't he? |
| 00:51:33 | Who's got (inaudible). |
| 00:51:37 | You. |
| 00:51:38 | Me. |
| 00:51:39 | Yeah, I told her you (inaudible). |
| 00:51:43 | Don't encourage him. Go on, get on with your work. |
| 00:52:07 | Because we were going to do Smarties with the other stuff, so I thought, well I got them, I might as well use them. |
| 00:52:35 | Finished? |
| 00:52:37 | (inaudible) |
| 00:52:50 | He has three. |
| 00:52:59 | I'm handing around a sheet for the next activity. Should you work fast enough and well enough to get there. Otherwise, I might take the Smarties. |
| 00:53:08 | On the back of it- the back of it is not important. It's using up scrap paper. |
| 00:53:50 | Instead of slash we use dot-dot. |
| 00:53:52 | Oh, he told me to use the slash (inaudible). |
| 00:53:54 | Oh, dot-dot was right. Let's say you move back a little bit so, you're out of reach. |
| 00:54:05 | (inaudible) So you don't (inaudible)? |
| 00:54:09 | Yes, that's right. That's right. |
| 00:54:11 | I'd have to do (inaudible). |
| 00:54:13 | And? |
| 00:54:14 | And no (inaudible). |
| 00:54:15 | Four of them. |
| 00:54:17 | Four of them. |
| 00:54:26 | Which question is it? |
| 00:54:27 | Four twenty- |
| 00:54:28 | Divide 420 in the ratio of seven to one. |
| 00:54:30 | Okay. So how many lots do you have? |
| 00:54:35 | Four. |
| 00:54:36 | So what's in one lot? One share? |
| 00:54:40 | Thirty-four. |
| 00:54:41 | How did you work that out? |
| 00:54:44 | Four twenty divided by 12. |
| 00:54:46 | Thirty-five. |
| 00:54:47 | Four twenty divided by 12? |
| 00:54:48 | Okay. So, you've written down 12 shares equals 420. |
| 00:54:52 | One share equals 35, so then you'd have to just do seven times 35 and five times 35. |
| 00:55:01 | Three forty-five- (inaudible). They got the answer. |
| 00:55:10 | You right now then? |
| 00:55:11 | Yeah. (inaudible) How come you have to get that microphone (inaudible). |
| 00:55:19 | So they can listen to me talking to you. |
| 00:55:22 | So they can't hear us but they can hear you. |
| 00:55:23 | Probably. |
| 00:55:33 | Yes. |
| 00:55:54 | How can I use this to bribe my mom to get me some Smarties? |
| 00:55:56 | Okay, there's only 10 or so minutes to go. So what you can do is finish question one and two for homework. We'll do question three next class. |
| 00:56:12 | You can start on the Smarties sheet and that can be completed for homework as well. All right? |
| 00:56:26 | I'll need- I'll need a few- |
| 00:56:28 | So follow the instructions on the sheet. You can't eat the Smarties. |
| 00:56:33 | Oh. |
| 00:56:35 | Until you have completed question one. Now, hold it. Be sensible with them please. And I might point out that you- you need- no listen. Shh, be quiet. |
| 00:56:59 | Be quiet or I'll just forget about the whole thing. |
| 00:57:08 | You need to keep these sheets because the information you're collecting today we're going to be using when we get to the next topic or two topics down the road on statistics. |
| 00:57:55 | Everybody got a box? |
| 00:58:10 | (inaudible) |
| 00:58:11 | He does usually. |
| 00:58:16 | Okay, you make a prediction first. |
| 00:58:19 | My prediction is 12. |
| 00:58:23 | How many? |
| 00:58:33 | I said- my prediction is 12 and you got to (inaudible). It's twelve. |
| 00:58:38 | Okay. The table you have there has got color, tally and frequency. |
| 00:58:45 | You won't need the tally column because you only use the tally column when you've got lots to count, and you don't have very many. |
| 00:58:53 | So when you've opened your packet, count how many of each color you are and write that in the frequency column because frequency means? |
| 00:59:02 | How many. And you write two in the frequency. |
| 00:59:15 | I've got lots of blues. I've got five- |
| 00:59:17 | (inaudible) |
| 00:59:18 | Pardon? Who? |
| 00:59:24 | You got 51. |
| 00:59:26 | No. (inaudible) |
| 00:59:36 | I didn't realize you were (inaudible). |
| 00:59:47 | Uh, add it on the bottom, then. |
| 00:59:51 | Well then you can. |
| 00:59:57 | Well, how many blues have you got? None? Well, actually why don't we cross tally off and write frequency there. It'll be easier, won't it? |
| 01:00:05 | (inaudible) and just makes it even. |
| 01:00:08 | Okay, now you can- (inaudible) Miss? |
| 01:00:10 | How many? Well, the blue equals none, brown is one, red is three. |
| 01:00:18 | Are we done (inaudible) now Miss? |
| 01:00:20 | I'd like it complete. |
| 01:00:21 | What do you have to complete? Just the- |
| 01:00:22 | Tally's the working column and frequency's the answer. |
| 01:00:23 | Everything Miss? Oh, I'm hungry. |
| 01:00:28 | But we don't really need a work column so- |
| 01:00:29 | Look at these, they're very tempting. And now I've got to (inaudible). |
| 01:00:34 | Yes, I think so. |
| 01:00:49 | Miss, can we eat this after we just calculate the frequency? |
| 01:00:53 | Yes. |
| 01:01:01 | He's got 13. |
| 01:01:19 | What does it mean by frequency? |
| 01:01:20 | Frequency means how many. |
| 01:01:24 | How do you work out percentage? |
| 01:01:25 | That's what I'm about to do. Let's have a quick look at this. Let's presume that I only had a total of three, four, five, six Smarties, and I only had blue, red and green. |
| 01:01:43 | How would I work out the percentage of blue? |
| 01:01:46 | Well I have three out of six and to change a fraction to a percentage you must multiply by 100. That's a half so I really could just do that in my head, 50 percent. |
| 01:02:05 | How would I work out this fraction? That would be two out of six, which is a third. |
| 01:02:17 | It's thirty-three point three three. |
| 01:02:20 | Thirty-three point three for Peter. And one out of six... we've got 16, or so, isn't it? |
| 01:02:33 | Sixteen and two thirds? So, you're going to have a different number here to six, aren't you? |
| 01:02:48 | How many did you have, Sally? |
| 01:02:51 | Thirteen. What an awkward number, but never mind. How many did you have, Jessica? |
| 01:02:56 | Thirteen. |
| 01:02:57 | Thirteen? |
| 01:02:58 | Twelve. |
| 01:02:59 | Twelve. Anybody have 14? |
| 01:03:02 | I had 13. |
| 01:03:03 | Thirteen or 12. So your number here won't be six. It will be 12 or 13. |
| 01:03:11 | It's easier if you use your calculator in this case. Especially if you've got 13 because it's an awkward number. |
| 01:03:18 | Do you have to write down three over six times 100 (inaudible)? |
| 01:03:24 | Well, you were right. Something over 13 would be a good idea to do, so you remember how to do it. |
| 01:03:33 | How many? No, the tally is the working column for the frequency. |
| 01:03:39 | What if you have zero (inaudible)? |
| 01:03:47 | So, what have you got? Four blue out of 12. So you were right. Four, fraction 12, times 100. |
| 01:03:57 | Well, you're lucky because four out of 12 is a third, and a third of 100 is easy to work out. I already know a third is 33 and a third. |
| 01:04:10 | How would you work out like to continue working without a (inaudible)? |
| 01:04:14 | Ask (inaudible) for her calculator. |
| 01:04:21 | How are you going to continue working without a biro? |
| 01:04:26 | I'm not going to (inaudible) my calculator. |
| 01:04:32 | Calculator would be helpful, too. Did you happen to remember a calculator today? |
| 01:04:36 | It's broken. |
| 01:04:43 | Well, you've got your yearly exam coming up, you know, and in the third week or so next term. It might be an idea to get one before your yearly exam. |
| 01:05:01 | What for? |
| 01:05:03 | I didn't have any blues, any browns, one green- |
| 01:05:04 | No, that can't be right. |
| 01:05:06 | No oranges, four pinks- |
| 01:05:07 | This means- doesn't mean- percentage of total. It means what percent is blue out of the total. It's obviously nothing, nothing. |
| 01:05:16 | Now you have to do one, 12 times 100 to work out that color's percent. |
| 01:05:30 | (inaudible) |
| 01:05:40 | Well that's lucky for you, you don't have anything to- |
| 01:05:41 | (inaudible) |
| 01:05:44 | Yeah. Like pink, yeah, orange and black equal. |
| 01:05:49 | Do you know any (inaudible)? |
| 01:05:52 | Eight-thirds. |
| 01:05:55 | Good choice. |
| 01:05:57 | Do you know how to work this out? You do one, fraction 12 (inaudible) which is all right. |
| 01:06:06 | Three, fraction 12. Three, fraction 12, one, fraction 12- one (inaudible) fraction 12. Modify the (inaudible). |
| 01:06:31 | I'm not really up on Smarties. (inaudible) |
| 01:06:49 | Byron. What? |
| 01:06:55 | I've got 21, six seven. |
| 01:06:57 | Did you when you add them up make it six repeater and three repeater or just six and three? |
| 01:07:04 | Just six and three. |
| 01:07:05 | Oh, then that's where you- probably you've got a (inaudible)? |
| 01:07:11 | I got (inaudible) left (inaudible) nine-nine. |
| 01:07:15 | This is better than (inaudible). |
| 01:07:18 | Yeah, because he's knocked off the extra threes and sixes. So you expect him to be short. You don't really expect him to be long. |
| 01:07:29 | Is that a three or an eight? |
| 01:07:30 | Eight. Eight point three. |
| 01:07:35 | Oh, that's why you're over (inaudible). |
| 01:07:40 | Because (inaudible), that's a very small part, but point three three three three, but when you add up three of them, you've got a whole, haven't you. |
| 01:07:53 | Okay. Let's just reassess where we are. It's time to go. |
| 01:08:02 | You have for me... exercise ten-o-four, question one and two to work on. You have the assignment that I gave you which is due Friday. |
| 01:08:18 | Friday? |
| 01:08:19 | The one about the replica of the first fleet. |
| 01:08:22 | Oh that. |
| 01:08:28 | (inaudible) That's due Friday. If you do not need your Smarties packet please put it in the box on the way past. |
| 01:08:38 | If you are in Mister Anderson's class now, then perhaps you can stay behind in case we need some help. |
| 01:08:46 | Make sure you push your chairs in. (inaudible) they're back where they should be. |