JP1 FINDING THE VALUE OF AN ANGLE
This eighth grade mathematics lesson focuses on two-dimensional geometry - in particular, parallel lines and angles. It is the third lesson in a sequence of seven lessons on this topic. The lesson is 50 minutes in duration. There are 31 students in the class.
| Time | Caption |
|---|---|
| 00:00:02 | [ Bell ] |
| 00:00:04 | How about today? |
| 00:00:08 | Good morning. |
| 00:00:09 | Stand up. |
| 00:00:14 | Bow. |
| 00:00:16 | Sit down. |
| 00:00:22 | Okay. It's supposed to be as usual so let's go on without being concerned about it. |
| 00:00:32 | Anyway your face might not be taped. |
| 00:00:34 | [ Laughter ] |
| 00:00:35 | Actually there is just going to be a black line across your face. |
| 00:00:37 | [ Laughter ] |
| 00:00:39 | Don't worry. |
| 00:00:45 | Okay. |
| 00:00:48 | Ahh. |
| 00:00:53 | Okay, yesterday was about the relationship between parallel lines. |
| 00:00:56 | We ended quickly yesterday by doing some problems. |
| 00:01:00 | Do you remember what they were? |
| 00:01:27 | The first written problem on the handout we hurried through it yesterday, |
| 00:01:31 | so we were not able to summarize it well at the end... |
| 00:01:35 | So today in between the parallel lines there is a line that is bent into an angle. |
| 00:01:43 | So first we will obtain that angle. |
| 00:01:46 | When I had you do the problems yesterday |
| 00:01:48 | we had three problem solving methods that were presented... |
| 00:01:51 | It's okay to use the method you think is the easiest. |
| 00:01:57 | Please try to do the problem. |
| 00:02:32 | After you have finished writing, please add an explanation. |
| 00:02:37 | My- my method is this and this way. |
| 00:02:39 | If you can also give an explanation that would be amazing. |
| 00:03:36 | This, right. |
| 00:03:38 | You're fast. |
| 00:03:54 | If you forgot how to solve it, it is okay to look at the previous handout. |
| 00:04:06 | (inaudible) let me borrow this for me. |
| 00:04:09 | Let me borrow this because he needs a pencil. |
| 00:04:13 | It's a little different... line... (inaudible). |
| 00:04:22 | Umm. Okay. |
| 00:04:26 | Are you done? Can I ask? How is it? |
| 00:04:32 | People who solved it? |
| 00:04:35 | Okay then... Arai. |
| 00:04:40 | Yes. |
| 00:04:42 | Okay, what did you do? |
| 00:04:43 | Fifty. The 50 degree. |
| 00:04:46 | The line around it. The line there extend it. |
| 00:04:50 | Okay. Did you extend it like this? |
| 00:04:53 | Bring that over there. |
| 00:04:56 | Uh- 50 degrees. Alternate interior angles of it. |
| 00:05:00 | There. That is 50 degrees so. |
| 00:05:04 | This? Okay. |
| 00:05:06 | The right angle is 30 degrees. |
| 00:05:09 | If you add it all up it becomes 180 degrees so. |
| 00:05:12 | A triangle. Yes. |
| 00:05:14 | Yes. The top part is 100 degrees. |
| 00:05:18 | The one before. A right angle is. |
| 00:05:18 | A right angle is. |
| 00:05:21 | Um, it becomes 180 degrees so. |
| 00:05:25 | Okay. Not a straight line? |
| 00:05:26 | Yes. A straight line becomes 180 degrees |
| 00:05:29 | So X is 80. |
| 00:05:32 | Okay. Is this okay? Here we go. Okay. |
| 00:05:35 | We can see he was a little tense. |
| 00:05:38 | Um, that was a clear method. People who did it using this method? |
| 00:05:45 | Oh... okay. |
| 00:05:48 | About five people? Okay, other methods. |
| 00:05:52 | Okay, Bunya. |
| 00:05:56 | Okay, please go ahead. |
| 00:05:58 | In the middle. |
| 00:06:00 | Draw a... parallel line. |
| 00:06:07 | Oops? Okay. |
| 00:06:08 | Then. Um, the top 50 degrees, the alternate interior angles of that. |
| 00:06:14 | Yes. |
| 00:06:15 | It is made there so. |
| 00:06:17 | Yes, well- Well, okay. |
| 00:06:21 | So it's 50 degrees. |
| 00:06:23 | The bottom is 30 degrees. |
| 00:06:25 | It can also be done in the same way. |
| 00:06:28 | Add those together it becomes 80 degrees. |
| 00:06:31 | Okay. That's good. |
| 00:06:32 | The method was to use the alternate interior angles of the parallel lines. |
| 00:06:37 | Good. |
| 00:06:38 | People who did it with this same method? |
| 00:06:41 | Okay. |
| 00:06:42 | Right. About 10 people. Okay. |
| 00:06:47 | Are there any other methods? |
| 00:06:50 | Oh. One person... Chika. |
| 00:06:54 | Yes. |
| 00:06:55 | Okay. |
| 00:06:56 | Umm, from point B. |
| 00:06:58 | From point B. Okay. |
| 00:06:59 | From point B. |
| 00:07:00 | Okay. |
| 00:07:01 | Is it... L? |
| 00:07:04 | From the top line it would be an L, huh. |
| 00:07:05 | To the top straight line draw a perpendicular line. Then- |
| 00:07:09 | Draw a perpendicular line from point B. |
| 00:07:11 | Then. The B area is 60 degrees. Umm- well not really B, |
| 00:07:16 | but between that perpendicular line and 30 degrees is a right angle. |
| 00:07:22 | So subtract 30 degrees from 90 degrees. |
| 00:07:24 | Yes. |
| 00:07:25 | It becomes 60 degrees. |
| 00:07:26 | Yes. |
| 00:07:27 | The area A is fi- fifty degrees so. |
| 00:07:32 | Umm, the straight line is 180 degrees. |
| 00:07:36 | Right. |
| 00:07:37 | Angle A becomes 130 degrees. |
| 00:07:42 | Since if you add up all of the angles of a quadrilateral it becomes 360 degrees. |
| 00:07:47 | Umm, if you add- |
| 00:07:51 | what is this? It becomes 280 degrees. Eight. |
| 00:07:55 | Subtract 280 degrees from 360 degrees. |
| 00:07:57 | X became 80 degrees. |
| 00:08:00 | Okay. Yes. Here we go. Okay. |
| 00:08:04 | People with the same method as this? |
| 00:08:08 | Oh. Just Doi. Okay. |
| 00:08:11 | Good. Are there any more? |
| 00:08:14 | Think a little more. |
| 00:08:17 | I'm thinking. |
| 00:08:18 | Okay? I am sure there are people who also extended this one. |
| 00:08:23 | Here are methods like that. |
| 00:08:25 | Basically these three are the ones you have thought of. |
| 00:08:29 | Now I will summarize these into main points. |
| 00:08:35 | With just this diagram... |
| 00:08:38 | with just this diagram we can't solve the problem. |
| 00:08:41 | So Sano and others extended the line to make a triangle. |
| 00:08:45 | Bunya and others drew in a parallel line in the middle. |
| 00:08:49 | Chika and others drew in a perpendicular line. |
| 00:08:51 | That means we can't solve it without auxiliary lines. |
| 00:09:12 | The auxiliary lines become important. |
| 00:09:15 | Then by the way we draw the auxiliary lines in all |
| 00:09:20 | we got three types. Sano's, Bunya's, Chika's. |
| 00:09:25 | They were different based on the way the auxiliary lines were drawn. |
| 00:09:28 | That means, one way is to draw a parallel line and |
| 00:09:31 | use the alternate interior angles. |
| 00:09:37 | Another is to extend the line and make... a triangle, |
| 00:09:42 | and use the fact that the sum of the angles of a triangle is 180 degrees. |
| 00:09:49 | And Chika used the method that if we add the four angles of... |
| 00:09:56 | a quadrilateral we get 360 degrees. These are the three we got. |
| 00:10:03 | Now then, any method was okay, |
| 00:10:06 | but the task was to do it using the easiest method. |
| 00:10:10 | And each person seemed to have selected one out of the three we summarized yesterday. |
| 00:10:14 | Today's problems are ones that can't be solved without auxiliary lines. |
| 00:10:17 | We want to do problems of this kind. |
| 00:10:21 | Today. The way this problem is made is that |
| 00:10:25 | it is a problem of an angle bent once between parallel lines. |
| 00:10:32 | The angle is bent once between parallel lines. |
| 00:10:36 | Today by changing this condition, by changing this condition- |
| 00:10:41 | I will have you make your own problems. |
| 00:10:45 | And today we won't change the parallel lines. |
| 00:10:50 | We won't change the parallel lines, but rather the middle. |
| 00:10:52 | Change the middle means- |
| 00:10:54 | Outside. |
| 00:10:55 | Oh. It's okay with the outside. The outside can be good. |
| 00:10:59 | Now it has one bend. |
| 00:11:02 | It is even okay to bend it twice. |
| 00:11:03 | If I say this I know there is going to be someone who is going to bend it like 10 times. |
| 00:11:05 | [ Laughter ] |
| 00:11:08 | Eda (inaudible). |
| 00:11:09 | Eda difficult. |
| 00:11:10 | There are always at least two or three of you thinking about it? |
| 00:11:12 | [ Laughter ] |
| 00:11:15 | I know there will be some. |
| 00:11:18 | But twice or three times. That's the limit. |
| 00:11:21 | After that nobody will understand it. |
| 00:11:23 | You may be creative in between and change the number of bends, or, |
| 00:11:26 | it is also okay to use the outside with one bend, |
| 00:11:29 | or it is also okay to be outside with two bends. |
| 00:11:32 | Please think by yourselves. |
| 00:11:35 | You can't just go and bend it 10 times. Don't draw random squiggly lines. That is not good. |
| 00:11:38 | Okay, umm, I have prepared two on your handout, but one is okay. |
| 00:11:45 | If it's easy please do two. |
| 00:11:48 | It is okay to bend twice or be outside. |
| 00:11:51 | Then put in angles by yourselves and |
| 00:11:55 | write in which angle is X, the one we need to obtain. |
| 00:12:17 | Oh, if 30 students do it, |
| 00:12:22 | even if they made only one problem each we will have 30 problems. |
| 00:12:27 | It's actually pretty hard to put in the degrees. |
| 00:12:30 | You can't just put in any degrees. |
| 00:12:33 | Do we also write the (inaudible). |
| 00:12:43 | When you turn it in you must be able to solve it. |
| 00:12:47 | If somebody says he or she doesn't understand it |
| 00:12:49 | you must be able to say what and why the problem is. |
| 00:12:51 | Please think about how the problem can be understood. |
| 00:13:07 | (inaudible) |
| 00:13:10 | A moment. |
| 00:13:11 | Mmm. |
| 00:13:14 | Wait a minute. |
| 00:13:21 | (inaudible) |
| 00:13:29 | Um? This one, too? |
| 00:13:39 | Which one? |
| 00:13:40 | B:00] |
| 00:13:55 | Huh? |
| 00:13:56 | Um- make one and try it yourself. Make sure you can solve it, okay?. |
| 00:14:28 | These are the same, since there is only one bend between the parallel lines, |
| 00:14:31 | it's the same as this. |
| 00:14:35 | Try to change it. |
| 00:14:40 | Oh, it looks difficult. |
| 00:14:44 | It looks pretty tough. |
| 00:14:52 | This also looks difficult. |
| 00:15:03 | You can put the bends in, but does the number fit in, is the problem. |
| 00:15:16 | Isn't it- |
| 00:15:21 | It has to be a problem you can solve. |
| 00:15:33 | It can be the second one or the outside. |
| 00:15:38 | Bam, bam, and it can be bent on the outside. |
| 00:15:42 | Or you can bend it once, twice. |
| 00:15:47 | (inaudible) Just one? |
| 00:16:01 | Whichever equals. |
| 00:16:02 | If you make it too hard, well it'll be... stressful. |
| 00:16:12 | How many times is this bent? One, two, three, four times it has been bent. |
| 00:16:15 | It's been bent too many times. |
| 00:16:22 | Is this okay for the first one? |
| 00:16:23 | What? |
| 00:16:24 | Is this okay for the first one? |
| 00:16:26 | You can't solve this. |
| 00:16:27 | What? |
| 00:16:28 | Without another angle I don't think it can't be solved. |
| 00:16:30 | What? |
| 00:16:34 | If you try to solve it and you can solve it yourself then it is okay. |
| 00:16:46 | Isn't it difficult? This is difficult. |
| 00:16:55 | If you have finished. |
| 00:16:57 | Where do you solve for this? |
| 00:16:59 | Hum? |
| 00:17:00 | Where do you solve for this problem? |
| 00:17:01 | For this, it is for this. |
| 00:17:02 | Here? |
| 00:17:03 | Then what is this? |
| 00:17:05 | (inaudible) |
| 00:17:07 | There's a reason for this. |
| 00:17:09 | It starts at point A and goes through point B and- |
| 00:17:12 | Ah, I see. |
| 00:17:16 | Ahh, it looks hard. |
| 00:17:18 | This is simple. |
| 00:17:20 | Ahh, it is hard. |
| 00:17:21 | (inaudible) like these. |
| 00:17:25 | Like this. |
| 00:17:28 | This looks hard. |
| 00:17:29 | This is 90 degrees. |
| 00:17:30 | Oh, I made a mistake. This is going to be hard. |
| 00:17:34 | This 65 degrees is last. |
| 00:17:39 | Eventually, if you extend it here is 62. This is 180 degrees. |
| 00:17:43 | Two hundred, 220. |
| 00:17:50 | Ah. |
| 00:17:52 | Is this 62 degrees? |
| 00:17:54 | There. |
| 00:17:56 | Here, lend it to me. |
| 00:18:03 | One hundred twenty. |
| 00:18:07 | (inaudible) |
| 00:18:10 | At 15 you can do it. |
| 00:18:33 | Are you done writing? Are you finished? |
| 00:19:09 | It seems hard. |
| 00:19:12 | Let's try hard to do one problem. Try hard to make one problem. |
| 00:19:31 | Understand. |
| 00:19:36 | Okay? |
| 00:19:56 | Um, if you put it on the inside maybe it'll be easier to solve. |
| 00:20:01 | Wow. This is how you take off from A and bend and reach B. |
| 00:20:08 | What does that mean for A? |
| 00:20:13 | This is fine. |
| 00:20:18 | Is it solvable? |
| 00:20:19 | You can solve this. |
| 00:20:20 | It is solvable. |
| 00:20:21 | Yes. |
| 00:20:22 | It won't be solvable without these angles here. |
| 00:20:24 | What? Add this, like this? |
| 00:20:25 | Where? |
| 00:20:26 | Like this. If you extend it... it's 60 degrees. |
| 00:20:34 | Where? |
| 00:20:38 | This, isn't this 60 degrees, this... like this isn't 60 degrees? |
| 00:20:42 | That doesn't work if this and this are not parallel. |
| 00:20:47 | If you draw a parallel line. |
| 00:20:49 | If you draw a parallel line. |
| 00:20:50 | If this and this are not parallel then this angle is not 60 degrees. |
| 00:20:55 | This angle, too... can't be used under that assumption? |
| 00:20:59 | No. If they're parallel lines then just put in the symbol for parallel lines here. (inaudible) |
| 00:21:16 | Thank you very much. |
| 00:21:19 | I don't know if they'll understand this. |
| 00:21:21 | It looks a little tough. This is too difficult. |
| 00:21:23 | (inaudible) |
| 00:21:25 | And right... I made it a little too difficult. I made it too difficult. |
| 00:21:32 | Here it's hard. |
| 00:22:06 | If there isn't an angle here it can't be understood. Just put something in. |
| 00:22:21 | You guys seemed to have learned that any number just doesn't fit in. |
| 00:22:25 | You guys seemed to have learned that any number just doesn't fit in. |
| 00:22:46 | How many bends are there? One, two, three, four, five bends. |
| 00:22:50 | If you don't make it at most three then it will be impossible. |
| 00:22:53 | I understand. |
| 00:23:10 | (inaudible) |
| 00:23:11 | Let's see. What time? |
| 00:23:12 | Well it seems it was a little hard. I made a mistake. |
| 00:23:16 | There are many of you that are in trouble. |
| 00:23:20 | Well there are not that many people with one, two done, |
| 00:23:22 | but there seems to be a lot of people with one done,so, |
| 00:23:24 | get in your groups and... from the problems you have made... |
| 00:23:33 | pick a problem you and others think is challenging, |
| 00:23:38 | and group leaders please bring them up here. |
| 00:24:01 | Please check if the problem can be really solved and then bring it up. |
| 00:24:21 | One problem is enough. |
| 00:24:23 | There are problems that can't be solved. |
| 00:24:43 | How about this one? This? |
| 00:24:46 | Th- Th- This (inaudible). |
| 00:24:57 | (inaudible) It seems hard. |
| 00:25:03 | Can't it be solved? |
| 00:25:06 | You don't have to make a new problem at this point. |
| 00:25:09 | Just from the currents ones you have. |
| 00:25:19 | This is a good problem. |
| 00:25:20 | Is it good? |
| 00:25:23 | Yes, because it's two bends, and the bends are different. |
| 00:25:27 | And this is also a good problem, whether you can do it or not, |
| 00:25:30 | change that part. Not too much. |
| 00:25:36 | Up to number two? |
| 00:25:56 | (inaudible) a quadrilateral. |
| 00:25:59 | Ha ha. Indeed. |
| 00:26:01 | A quadrilateral. A quadrilateral? (inaudible) |
| 00:26:13 | Who made this? |
| 00:26:14 | Masa- |
| 00:26:15 | Hara. |
| 00:26:19 | Umm. |
| 00:26:20 | You can't solve it. |
| 00:26:23 | Mmm. Can they do it or not? |
| 00:26:45 | Yes. |
| 00:26:54 | Hey, let's bring up one. |
| 00:27:04 | Ha, it looks like a hard one. |
| 00:27:05 | Whose is it? |
| 00:27:06 | (inaudible) |
| 00:27:07 | From which group? |
| 00:27:08 | From group number five. |
| 00:27:09 | This one? |
| 00:27:10 | Right. |
| 00:27:11 | Group five. |
| 00:27:21 | Ah. |
| 00:27:36 | It's a hard one. |
| 00:27:42 | Oh, the diagram was too small. |
| 00:27:45 | You're completely wrong. Do you know what you are doing? |
| 00:27:50 | This part is easy. |
| 00:27:55 | Here. |
| 00:27:56 | Here teacher. |
| 00:27:57 | This- which group? |
| 00:27:58 | This one. |
| 00:27:59 | This can't be used. |
| 00:28:00 | It can't? |
| 00:28:01 | Uh huh. Because this is bent many times. |
| 00:28:02 | Yes. |
| 00:28:03 | Teacher. This one. |
| 00:28:04 | Just a little more- this is too hard. |
| 00:28:06 | He said it was too hard. |
| 00:28:08 | Oh, it looks like a good problem. What group? |
| 00:28:11 | Group one. |
| 00:28:12 | Group one? |
| 00:28:19 | Group one? |
| 00:28:20 | Group one. |
| 00:28:27 | The diagram is a little... |
| 00:28:51 | Here. |
| 00:28:56 | Which number? |
| 00:28:57 | Number four. |
| 00:28:58 | Number four- can you really solve it? |
| 00:29:01 | That can be solved easily. |
| 00:29:02 | We can. |
| 00:29:03 | It seems. |
| 00:29:06 | Is this all? |
| 00:29:07 | Yes. |
| 00:29:34 | Okay, that's good. Yes. |
| 00:29:38 | Next, who's next? |
| 00:29:41 | It's easy. That one. |
| 00:29:44 | Don't say anything yet. Don't say anything. |
| 00:29:47 | Groups that have not yet brought up one, please hurry up. |
| 00:29:54 | Teacher, I solved this. |
| 00:29:57 | I wonder. |
| 00:29:58 | It can- it can be solved teacher. |
| 00:30:01 | Can this be solved? |
| 00:30:02 | I believe it can be solved. |
| 00:30:06 | I think it is impossible. |
| 00:30:07 | Impossible? |
| 00:30:09 | This one, this one. |
| 00:30:10 | Which one? |
| 00:30:11 | This one, this one. (inaudible) |
| 00:30:13 | Mm. It's probably right? |
| 00:30:19 | Which one is that, group three? |
| 00:30:20 | Group three. |
| 00:30:26 | The second time is hard but easy. |
| 00:30:37 | Number one is easy, too. |
| 00:30:50 | Now number four is left. |
| 00:31:01 | Which number? |
| 00:31:02 | Number four. |
| 00:31:03 | Number four? |
| 00:31:04 | Number four. It might be complex. Right, it's different. |
| 00:31:06 | It might be complex, okay? |
| 00:31:08 | I'll do number four just a little. Sorry, okay? |
| 00:31:32 | Can it be solved? |
| 00:31:33 | It can be solved. |
| 00:31:34 | You're able to solve it? Hum |
| 00:31:36 | Hum oh. |
| 00:31:39 | Oh. |
| 00:31:42 | What number? |
| 00:31:45 | Hum. Okay. |
| 00:31:48 | They are problems that we don't know if we can solve or not until we try. |
| 00:31:54 | I'm sorry for taking so much time, |
| 00:31:57 | but there are six problems on the right side. |
| 00:32:06 | (inaudible) if we can solve it or not. |
| 00:32:11 | I wonder. |
| 00:32:20 | It seems impossible to do all of them in this time so. |
| 00:32:23 | So we'll think about them a little next time, too. |
| 00:32:36 | Please hurry up and copy the six problems. |
| 00:32:44 | Imai is X here? |
| 00:32:50 | Hum. (inaudible) |
| 00:32:54 | Oh, I got it. |
| 00:32:57 | Can you solve it? |
| 00:32:58 | I got it. I got it. |
| 00:33:09 | They really seem challenging, huh? |
| 00:33:12 | There seems to be one that is too challenging. |
| 00:33:14 | (inaudible) |
| 00:33:19 | They are really challenging, like eating a dried squid. |
| 00:33:24 | [ Laughter ] |
| 00:33:27 | Umm, this one is not that bad. |
| 00:33:37 | Umm... I'll say it's like a piece of gum. |
| 00:33:44 | Gum. |
| 00:33:45 | Gum. |
| 00:33:46 | Gu-gum. |
| 00:33:47 | Oh, group two's, group two's, the one on the top. |
| 00:33:50 | Umm. Group four. |
| 00:34:01 | This is a rock. |
| 00:34:03 | [ Laughter ] |
| 00:34:05 | Then this is a rock. |
| 00:34:31 | Umm. Um um um. |
| 00:34:52 | Rice cracker. |
| 00:34:53 | Number five. Number five. |
| 00:34:55 | Isn't it easy? |
| 00:34:59 | Rock, it's a rock. |
| 00:35:05 | Then I'm sorry there isn't much time, but there are six problems. |
| 00:35:10 | There may be ones from your own group. There may be ones that are yours. |
| 00:35:12 | Please copy them. |
| 00:35:15 | It can be from number one. It can also be from the hardest one. |
| 00:35:21 | (inaudible) This is gum. |
| 00:35:46 | That means since today's problems can't be solved without auxiliary lines... |
| 00:35:50 | what kind of auxiliary lines. It can't be solved without auxiliary lines. |
| 00:35:56 | Gum. |
| 00:35:57 | If you need the auxiliary lines, |
| 00:35:58 | the problem is what kind of auxiliary lines should you use. |
| 00:36:03 | There were three, but which one is the easiest way to do it. |
| 00:36:29 | For now please finish copying the problems by 35 after the hour. |
| 00:36:35 | I think... the answers will be given next period. |
| 00:36:41 | What shall I do? |
| 00:36:43 | Huh? |
| 00:36:44 | Can you solve this? |
| 00:36:45 | I don't know. |
| 00:36:49 | This is well... this is really hard. |
| 00:37:10 | Genji's symbol is good. It's there nicely working. |
| 00:38:40 | Are there any groups that were able to solve them? |
| 00:38:43 | Plus 15. |
| 00:38:48 | (inaudible) since it's 15 degrees, so 90. Ooh. |
| 00:38:52 | Not so (inaudible). |
| 00:38:54 | Oh- the rice cracker hard problem seems to be solved. |
| 00:38:57 | (inaudible) fifteen. It's 30 degrees. |
| 00:38:59 | Teacher. Fifteen. |
| 00:39:01 | Fifteen, 15, 30, 90, 90. |
| 00:39:02 | It's not 90, 90. Ooh. |
| 00:39:03 | Ninety-nine? |
| 00:39:04 | One hundred. |
| 00:39:05 | Hundred. |
| 00:39:06 | Plus. |
| 00:39:07 | (inaudible) |
| 00:39:11 | It's correct. We got this. We solved this. |
| 00:39:19 | The rock? |
| 00:39:20 | Later. We'll check it later. |
| 00:39:23 | We'll check it later. |
| 00:39:31 | No, at the time- at the time I was solving it I was thinking that I couldn't solve it. |
| 00:40:14 | I didn't write the group names. |
| 00:40:35 | Since all of them are challenging we can't solve it just like that. |
| 00:40:39 | Let's do it step by step. |
| 00:40:43 | People who are done solving the problem from group one? |
| 00:40:47 | Okay good. Group two's? |
| 00:40:50 | A little more. Straight. Raise your hands straight. Ahh, about the same. |
| 00:40:54 | Group three's? |
| 00:40:57 | Oh. Group four's? |
| 00:41:00 | Okay. Group five's? |
| 00:41:03 | Okay. Group six's? |
| 00:41:05 | Really. Group six's. Okay good. |
| 00:41:08 | Number six is easy so- |
| 00:41:10 | (inaudible) |
| 00:41:12 | There is an even harder one. |
| 00:41:14 | This one seems more likely to work out. |
| 00:41:22 | I haven't gotten this one yet, but- |
| 00:41:26 | It's hard? |
| 00:41:27 | I just finally got it. |
| 00:42:04 | Is it group one or group two? |
| 00:42:05 | One hundred eighty degrees? |
| 00:42:06 | Umm. |
| 00:42:07 | Is this 40? |
| 00:42:08 | Umm. |
| 00:42:09 | Forty degrees. |
| 00:42:15 | One hundred twenty degrees. |
| 00:42:16 | One hundred twenty degrees. |
| 00:42:18 | Why is that? (inaudible) Isn't this 47? Right here. |
| 00:42:36 | This is easier. Umm. This one symbol. If you miss that one symbol... |
| 00:42:43 | you can't solve the problem. This is parallel. |
| 00:42:46 | This and this are parallel. Without that you can't solve it. |
| 00:42:54 | That's right. That's right. That's right. If you do that. It's about done. |
| 00:43:23 | Group one's is hard. I think group one's is really hard. |
| 00:43:48 | How you draw the auxiliary lines makes the difference. Something... |
| 00:43:57 | One hundred ninety. This is 190. |
| 00:44:07 | Number eight. Number two. Number eight. Number eight. (inaudible) |
| 00:44:19 | Okay, do you want to try it again? |
| 00:44:28 | I'll give you a hint. Try extending this further. |
| 00:44:32 | Try extending the auxiliary line further. |
| 00:44:45 | Teacher. |
| 00:44:53 | Try this one. This one is easier. |
| 00:44:59 | There is a symbol included here. This parallel symbol. |
| 00:45:05 | Extend the auxiliary line all the way to here. Try extending it. |
| 00:45:15 | Yes, yes. |
| 00:45:18 | This and this are parallel. If you use (inaudible) angles this angle becomes the (inaudible). |
| 00:45:25 | This is a straight line so you know it. So you somehow get this angle. |
| 00:45:56 | You know this angle and this angle (inaudible). |
| 00:46:00 | If you write in as much as you know...it'll work. |
| 00:46:18 | Oh that's good. They're the right auxiliary lines. |
| 00:46:24 | Umm. Ahh, this is (inaudible). This is hard. |
| 00:46:27 | You can't solve it without auxiliary lines. |
| 00:46:30 | That's good. |
| 00:46:33 | Umm, 120 degrees and then the straight line. |
| 00:46:40 | Like this line and like this, use auxiliary lines and try drawing it. |
| 00:46:44 | It's good to draw auxiliary lines. |
| 00:46:48 | Man. This one is amazing. |
| 00:46:58 | Umm, I see. |
| 00:47:24 | Do it one more time. |
| 00:47:25 | I did it once. |
| 00:47:26 | A mistake. |
| 00:47:27 | Uh I thought it was wrong. (inaudible) |
| 00:47:29 | Umm um. That it. That's it. That's it. |
| 00:48:07 | (inaudible)? (inaudible) |
| 00:48:12 | Umm, that one. |
| 00:48:18 | Umm, um, um. Divide it around here. It's the auxiliary lines. |
| 00:48:23 | Auxilary lines. It's a lot different with another auxiliary line. |
| 00:48:29 | But even if you didn't get the last one, you got this one, right? |
| 00:48:33 | This and this are parallel, |
| 00:48:37 | and here and here are corresponding angles, and you get here. |
| 00:48:40 | You got there and with that... |
| 00:49:10 | This is going to be a little bothersome but, well, I want to know the present situation. |
| 00:49:14 | People who are done with group one's? |
| 00:49:18 | You solved it? |
| 00:49:22 | Umm. Group two's? |
| 00:49:27 | Oh, okay. Group three's? |
| 00:49:32 | Um, okay. Group four's? |
| 00:49:35 | Up to where did you get to? Um. Group five's? |
| 00:49:40 | Hum. Two people. This was a hard one. |
| 00:49:42 | Umm. So that's it. Group six's? |
| 00:49:45 | Group six's was simple. |
| 00:49:46 | It was very troublesome. |
| 00:49:48 | Okay. |
| 00:49:49 | Did you do it? |
| 00:49:50 | (inaudible) Okay then there are a lot of people who are using triangles. |
| 00:50:00 | [ Bell ] |
| 00:50:01 | That's okay, but- There were three types of auxiliary lines. |
| 00:50:06 | There are other easier methods of solving... using other types of auxiliary lines. |
| 00:50:11 | We will check these in the next period. |
| 00:50:16 | Return your desks. |
| 00:50:32 | Never. |
| 00:50:33 | You can never do this one. |
| 00:50:38 | Who got group four's? Who said he or she got group four's? |
| 00:50:41 | Fujita Today. Okay. |
| 00:50:46 | Please end the class. |
| 00:50:48 | There's no math class tomorrow so let's check them the day after tomorrow. Okay. |
| 00:50:50 | Do we have math the day after tomorrow? |
| 00:50:53 | We have math class the day after tomorrow right? |
| 00:50:58 | The day after tomorrow is Thursday. |
| 00:51:01 | Thursday. |
| 00:51:02 | Did it change? |
| 00:51:03 | Thursday? |
| 00:51:04 | The day after tomorrow is Friday. |
| 00:51:06 | Huh? |
| 00:51:07 | Today is what day of the week? |
| 00:51:09 | Tuesday? |
| 00:51:10 | Today is Tuesday. |
| 00:51:11 | Tomorrow? |
| 00:51:12 | Wednesday. |
| 00:51:13 | Day after tomorrow? |
| 00:51:14 | Thursday. |
| 00:51:15 | That's right. I got it. Okay. |
| 00:51:17 | Go ahead. |
| 00:51:19 | Stand up. Bow. |