# JP3 SOLVING INEQUALITIES

This eighth grade mathematics lesson focuses on two-dimensional geometry - in particular, the areas of triangles between parallel lines. The lesson is 50 minutes in duration. There are 35 students in the class.

Time | Caption |
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00:00:02 | Leave them upside down. |

00:00:15 | I can't believe it. |

00:00:16 | Well. |

00:00:17 | Huh? |

00:00:18 | Well. Don't say that. |

00:00:19 | It starts with the bell and ends with the bell. |

00:00:21 | Hmm. |

00:00:22 | That's the- |

00:00:22 | I'll also try to aim that as best as I can. |

00:00:23 | What about a ruler? |

00:00:25 | Oh. It's okay even if you don't have it. |

00:00:35 | Pass it back as it is, upside down, okay? |

00:00:37 | What is upside down? |

00:00:38 | Here. |

00:01:00 | [Bell] |

00:01:01 | Okay. Now, let's start class. |

00:01:02 | Stand up. |

00:01:08 | Bow. |

00:01:09 | Onegaishimasu. |

00:01:09 | Onegaishimasu. |

00:01:10 | Onegaishimasu. |

00:01:14 | Okay, then please look at your handouts. |

00:01:21 | Okay, then these are the problems we're going to do today. |

00:01:24 | Okay. Um. It has been one month since Ichiro's mother has entered the hospital. |

00:01:29 | Um. He has decided say a prayer with his smaller brother at a local temple every morning so that she will be well soon. |

00:01:35 | Um. There are 18 10-yen coins in Ichiro's wallet and just 22 five-yen coins in his smaller brother's wallet. |

00:01:44 | They have decided every time to take one coin from each of them, |

00:01:48 | and put them in the offertory box, and continue their prayers until either wallet becomes empty. |

00:01:54 | One day after they were done with their prayers, when they looked into each other's wallets, |

00:01:59 | the smaller brother's amount of money was greater than Ichiro's. |

00:02:02 | How many days has it been since they started praying? That's the problem. |

00:02:07 | Now, I think there are points that are a little too hard to understand with just these sentences, so- |

00:02:11 | Well, I think I would like to look at a figure and check it. |

00:02:14 | Now, pay attention to the blackboard. |

00:02:18 | What the? |

00:02:21 | Okay. This is Ichiro's wallet, okay? |

00:02:24 | Um, then... okay, over here is the smaller brother's wallet. And, also there is an offertory box there, right? |

00:02:38 | Okay? |

00:02:40 | Okay. |

00:02:40 | Now, first we'll start looking at Ichiro's, okay? Okay? If we look at the wallet there are only 10-yen coins in there, right? |

00:02:47 | How much is in this in the beginning? |

00:02:50 | All together. How much is in it? |

00:02:50 | One hundred eighty yen. |

00:02:51 | One hundred eighty yen. |

00:02:53 | Yes. |

00:02:54 | Okay. The amount of money, well, in the beginning. |

00:03:03 | Okay. Compared to the smaller brother's. There are only five-yen coins in it, but how much is in it? |

00:03:08 | One hundred and ten yen. |

00:03:09 | One hundred and ten yen. |

00:03:09 | Yes. One hundred and ten yen. |

00:03:14 | This means in the beginning stages, um, Ichiro has more, okay? In terms of the amount of money, he has more, right? |

00:03:24 | Then, um, after this. Okay? Every morning from each wallet they take out one coin from each, okay? |

00:03:32 | They put them in this offertory box, right? |

00:03:36 | Now, first day one. Okay. Ten yen from Ichiro's wal- let- um, wallet and five yen from over here. |

00:03:44 | Okay? Now, it goes in from here and in this offertory box. |

00:03:49 | Wow. That's great. |

00:03:50 | That's amazing. |

00:03:52 | Okay. It's gets stowed away in here, okay? Is it okay? |

00:03:55 | They're in there. |

00:03:56 | Yes. |

00:03:57 | Okay, then how about it at this stage? Comparing Ichiro's and his smaller brother's wallet. |

00:04:02 | The contents of the wallet. Which one has more in terms of the amount of money? |

00:04:04 | The older brother. |

00:04:05 | Hmm. |

00:04:06 | Ichiro. |

00:04:06 | Ichiro. |

00:04:06 | Yes. Ichiro has more, right? Okay, then second day. |

00:04:10 | Okay. Of course right? They put in the coins in here. |

00:04:16 | How about it in this stage? |

00:04:17 | Ichiro. |

00:04:18 | Ichiro. |

00:04:19 | Hmm. Ichiro still has more, huh? Okay? Now, the fact is they continued things like this every day, okay? |

00:04:25 | But, in the morning of some day, okay? |

00:04:27 | Um. They looked inside of each other's wallets, right? Then the smaller brother had more in the amount of money. |

00:04:33 | Now, that one day was how many days, um, since they started their praying? |

00:04:39 | Now I would like for everybody to think about that. Then, um, in the open space. |

00:04:45 | Well this part we'll be writing in later on, so writing anywhere other than here is fine so, um, okay? |

00:04:52 | You may want to take notes or anything else you want to do is fine, so please try doing it. |

00:04:55 | Where are we going to write it? |

00:04:57 | Hm. Next to it is okay. Okay? |

00:05:34 | Masa. You did it up to the second day, right? Then, on the third day who has more? |

00:05:40 | This one has more? Then, how about the fourth day? |

00:05:44 | If you keep on doing it like that? Okay? |

00:05:52 | That's good. |

00:05:59 | Now, just now see? You did it up to the second day, right? |

00:06:03 | Then, how about the third day? |

00:06:05 | How about it? |

00:06:07 | In the same manner try thinking, like how about the fourth day? |

00:06:11 | Do it the same way over here, okay? |

00:06:58 | Well see? Up to the second day this one has mor- had more, right? Then, on the third day who had more? |

00:07:12 | Okay? |

00:07:13 | How much will it be? Well, if it's the third day, where is how much? |

00:07:19 | Okay? Do it like that then decide the answer, okay? |

00:07:25 | Oh. Is this 180 yen? Right? |

00:07:52 | Oh. Have you already solved at least one? |

00:07:57 | Okay. |

00:08:53 | Up to wh- where have you thought about it? |

00:08:55 | Uh, somewhat. |

00:08:59 | Hm. What do you mean? Did you erase this? |

00:09:00 | Yes. I erased that. |

00:09:00 | Hm. You erased the first day okay. Then, how about the second day? |

00:09:02 | I did this like this and- |

00:09:04 | Hm. |

00:09:04 | The tens. |

00:09:05 | Then, try putting in the dates there. |

00:09:06 | Okay. Okay. |

00:09:07 | Okay? |

00:09:17 | How did you obtain this? |

00:09:17 | I counted all the way. |

00:09:18 | Oh. You counted it all the way? Hm.. |

00:09:21 | Now, well... is there any method to find it that's simpler? Can you please find that. |

00:09:32 | Have you found it? Then, now it was quite tedious to write these out, right? |

00:09:36 | Is there any method to find it faster? |

00:09:39 | Okay? Can you please find that? |

00:09:42 | Now, this is also one of the methods, right? Then, it's tedious to count these, right? |

00:09:47 | Is there any method to find the answer faster? Please think about it. |

00:09:59 | Now, if you have found the answer using one method, okay, aren't there any other methods? |

00:10:05 | Okay? |

00:10:09 | Oh, now it's okay. You can leave that. Oh. |

00:10:15 | Then... without using this Y... it seems you can do it just with this and this, right? |

00:10:26 | Yes. Then, quickly, okay? Put the symbols down on this, okay? On these, okay? |

00:10:45 | Huh? Can you stop for a moment? |

00:10:48 | What is this Y? This? |

00:10:53 | This 180 minus 10 X is... whose money is this? |

00:11:00 | That is? |

00:11:00 | Ichiro. |

00:11:01 | Yes. It's Ichiro's... right? Then how about the smaller brother? |

00:11:10 | See? How much is in that, hum? |

00:11:29 | Hm. Oh. If you do that then? |

00:11:31 | Um? |

00:11:38 | Now, well, you can find it like that also, but can you try thinking about whether there are any methods that you can use to find it faster? |

00:11:46 | This person, this is... Ichiro's, right? Oh. This is the smaller brother's, right? |

00:11:51 | Then it seems you can do it by using this, okay? |

00:12:04 | Oh. You got it up to here? Okay. |

00:12:17 | This. It was obtained as how many days? |

00:12:22 | Oh. It was on the twelfth day, right? Then, can you do it a little more? Okay? |

00:12:35 | Then if you try combining this and this then you can make a mathematical expression. Okay? |

00:12:55 | Was it something like a mathematical expression? |

00:12:57 | Hmm. |

00:12:59 | Then, this okay? Can you do it without using the Y? |

00:13:02 | Okay? |

00:13:19 | Oh. You combined them, right? |

00:13:32 | Whose amount of money is this? |

00:13:34 | Are you talking about this? |

00:13:35 | Yes. |

00:13:36 | Hm. |

00:13:38 | Hm. This is- |

00:13:38 | Hm. |

00:13:39 | Well, 140 yen. |

00:13:40 | Hm... |

00:13:42 | Then, how about over here? |

00:13:43 | Over here is also 90 yen. |

00:13:45 | And, how did you obtain this? This value? |

00:13:49 | Uh well. |

00:13:50 | Hm. |

00:13:50 | You minus 10 yen every single day and- |

00:13:52 | Yes. |

00:13:53 | Over here every single day- |

00:13:54 | Yes. |

00:13:54 | You minus five yen. |

00:13:55 | Oh. That's right, huh? |

00:13:57 | And you obtained this from the table, right? |

00:13:59 | Yes. |

00:14:00 | Then, can't this be found by calculation? |

00:14:09 | Hmm. |

00:14:11 | Oh. You formed a simultaneous equation, right? Okay. |

00:14:46 | Well then. This okay? Can you try thinking if it will be found by formulating a mathematical expression? |

00:14:50 | Okay? |

00:14:55 | Then, this one also, can you try thinking if it can be found by formulating a mathematical expression? Okay? |

00:15:06 | Oh. You made a mathematical expression like this, huh? Okay. |

00:15:31 | Oh. The fact is you've counted all the way, right? Okay. |

00:15:37 | Then, okay? Also, okay? After this I'll have you come up again and present, okay? Okay? This problem. |

00:15:42 | Since we can't write it in and erase it also, so that means would you fill it in here one by one? Okay? |

00:15:46 | No. |

00:15:46 | Don't say that. I'm counting on you. Okay? |

00:16:08 | You went on solving this? Okay. Then you did this by making x equal one. Okay. |

00:16:18 | Then, okay? Well, later on I'm going to have you present this part. Okay? Hm. |

00:16:55 | Hm. |

00:17:07 | Then, okay? Ando, okay? This part, okay? Would you come up to present it later on? |

00:17:12 | Here and also one more. Up to here. Would you write just this part and also this part? |

00:17:18 | The rest is okay with dot, dot, dot. Since it's troublesome to write all of this. |

00:17:21 | Okay? |

00:17:33 | And also. |

00:17:38 | Now, okay? I want Bunmei to. Umm, is it over here? Would you present this part? |

00:17:45 | Am I going to write it? |

00:17:46 | Yes. Please write it. Okay? That you thought of it like this, okay? |

00:18:06 | Then, okay? I want Choshi to present okay? Um, this expression, okay? I'm going to have you present it later on. So- |

00:18:11 | This- this what do you call this? |

00:18:14 | Hm. This is smaller than. |

00:18:15 | What? |

00:18:15 | Smaller than. |

00:18:16 | Smaller than. |

00:18:17 | Hm. |

00:18:20 | Then, please think beforehand why you formulated a mathematical expression like this. |

00:18:31 | Okay. Then, um, would you look up please. |

00:18:34 | Now. When I looked around a little just now, well there were people who did it with different solving techniques. Okay? |

00:18:42 | Umm. Well it seems there were even people who found two or three techniques by themselves, huh? |

00:18:46 | Now, the fact is to show there are methods like these, um, I think I would like some people- |

00:18:50 | Okay? To present them, okay? |

00:18:52 | Then, Daishi. Well, please come up. Okay. |

00:18:55 | (inaudible) |

00:18:56 | Yes. You were saying how you would do it for yourself, right? |

00:18:59 | Will you do it? |

00:19:00 | Ha ha. |

00:19:02 | I guess I'll do it. |

00:19:03 | Please. |

00:19:04 | Ha ha. |

00:19:04 | Ha ha. |

00:19:05 | What am I supposed to do? |

00:19:06 | How would you do it? |

00:19:06 | So before. See? |

00:19:07 | I put them in, right? |

00:19:08 | Yes. |

00:19:09 | And you keep on putting them in. |

00:19:13 | Okay. That's good. Okay. |

00:19:13 | It's a lot faster if we put in many at a time. |

00:19:19 | (inaudible) |

00:19:19 | (inaudible) is more cool. |

00:19:22 | Hmm. |

00:19:29 | There's a lot of 10-yen coins, huh? |

00:19:31 | Then, last the five-yen coins go in. |

00:19:33 | They're sticking out. |

00:19:40 | (inaudible) huh? |

00:19:41 | One, two, [in English] three, four, five, six [in Japanese]. |

00:19:46 | Five, eight, two. |

00:19:48 | Well- |

00:19:49 | Huh? |

00:19:50 | About this much. |

00:19:51 | Hum. |

00:19:51 | About this much? |

00:19:52 | Hmm. |

00:19:52 | About this much- this time it fell. |

00:19:55 | Hmm. Teacher. |

00:19:56 | And, please say it, okay? |

00:19:59 | No. |

00:19:59 | By the way, what day is this? |

00:20:01 | Umm. The fifteenth day. |

00:20:03 | Okay. How is it? |

00:20:05 | It's okay. |

00:20:05 | It's okay. |

00:20:05 | Now. Just now. |

00:20:10 | Umm, for Daishi's method, okay? |

00:20:14 | Okay. While actually putting these in, okay? |

00:20:17 | There were other people that kept drawing lines like this, and solved the problem that way. |

00:20:22 | Doing it like that well the answer is the fifteenth day... they obtained it like that, okay? |

00:20:30 | Then, people who also did it with this method themselves or who also tried doing this method. |

00:20:36 | Then, well would you raise your hands? |

00:20:38 | Okay, then you can lower them. |

00:20:40 | Then, continuing. Um. Is it Etsumi? |

00:20:44 | Then, would you write it around here? In the top part. |

00:20:54 | Okay. Then. Okay. |

00:20:56 | Over here. Around here. Around this side, okay? Around here. |

00:23:34 | Okay. Then can you say your method of thought and also, um, how many days was it since they started. Okay. |

00:23:40 | Umm. |

00:23:42 | Since the fact is they put in the offertory box... one coin each of money in one day so... |

00:23:49 | if we do it in an orderly fashion... the number of days and also the money left over, one by one... |

00:24:00 | on the fifteenth day the smaller brother has more. |

00:24:05 | Okay. That means the answer is? |

00:24:07 | The fifteenth day. |

00:24:07 | Yes. The fifteenth day. Okay. That's good. |

00:24:16 | Okay, then in this case, uh, he did it for us by using a graph, right? |

00:24:17 | B:00] |

00:24:23 | Then, it doesn't matter if you drew lines or not, but people who wrote it this way raise your hands. |

00:24:29 | Okay. Then, you can lower your hands. Okay? Okay. Then, continuing, um, Bunmei. |

00:24:35 | Okay? Then, would you write it around here? That part I asked you to, okay? |

00:24:44 | Yes. Go ahead. |

00:24:45 | My handwriting is not neat. |

00:25:24 | Okay. Then please explain it. |

00:25:26 | Well, in the beginning. Well, Ichiro had 180 yen, and the smaller brother had 110 yen. |

00:25:31 | And since there is a difference of 70 yen, |

00:25:33 | and since the difference between them becomes smaller by five yen each day, so it's 70 divided by 10 minus five. |

00:25:39 | And since by the fourteenth day it becomes exactly the same amount of money, |

00:25:43 | so since on the day after that there will be a difference, so 14 plus one is 15 and it's the fifteenth day. |

00:25:49 | Okay. Okay? Um. In the beginning. He just now said it. There is a difference of 70 yen, right? |

00:25:55 | In this expression that becomes 65 yen. Then 60 yen. Right? Since it becomes smaller |

00:26:03 | B:00] |

00:26:05 | by five yen okay? So he obtained it by noticing this, okay? Are there people who also tried it using this method? |

00:26:11 | Huh? One person. Two people. Just two people? Okay. That's good. |

00:26:15 | Okay, then continuing, um, Fujita. Okay. Then, would you write it around here? Okay? |

00:26:54 | It's okay to not write all the lines of the mathematical expression. |

00:26:55 | Oh. |

00:26:55 | That. Okay. |

00:26:56 | Is it okay with this? |

00:26:57 | Yes. |

00:26:57 | Yes. |

00:26:57 | And, if you can write the amount for X. |

00:27:00 | Oh. Yes. |

00:27:00 | And, the answer. Okay. |

00:27:02 | And, after I've written the answer of X and Y? |

00:27:04 | That's right, huh? Okay. |

00:27:22 | Okay. Okay. Please say- |

00:27:25 | Now. |

00:27:26 | One hundred. |

00:27:29 | In the beginning, Ichiro had 180 yen, and since he takes out 10 yen every day- |

00:27:35 | And we have X as the num- number of days and if we make the amount of money left Y- |

00:27:42 | Then it becomes- the mathematical expression Y equals 180 minus 10 X. |

00:27:45 | And the smaller brother has 110 yen every day. Oh. He has 110 yen. |

00:27:50 | And since he takes out five yen every day it becomes the mathematical expression Y equals 110 minus five X. |

00:27:55 | And when they become of the same amount of money and- |

00:27:59 | And X and Y becomes 14 and 40. And on the fourteenth day they become the same amount of money. |

00:28:07 | And the fourteenth day is the same amount of money. |

00:28:10 | And the next day since Ichiro puts in 10 yen and the smaller brother puts in five yen, so there's a difference. |

00:28:14 | The amount of money put in is smaller for Ic- Ichiro. Oh. It's bigger so... |

00:28:21 | the next day Ichiro... Ichiro's amount of money left is less so it becomes the fifteenth day. |

00:28:32 | Okay. Okay, it's good. Okay? |

00:28:40 | Okay. She did it using letters, and this one we call X, okay? Um, the day it becomes equal, okay? The same amount of money. She thought about this fact, okay? |

00:28:41 | B:00] |

00:28:46 | Well, she put in Y as the amount inside of the wallet for that day, right? |

00:28:49 | Or some people did it without using the Y, okay? It seems there were people who wrote this equals this like this. Okay? |

00:28:58 | Then, well, simultaneous equations like this or an equation with just X, okay? |

00:29:03 | People who have tried doing it using things like these? Can you raise your hands a little? |

00:29:07 | Okay. That's fine. Okay. That's good. |

00:29:09 | And, also of course they are using letters, but there were some people who formed mathematical expressions a little differently. |

00:29:15 | Then, the fact about that mathematical expression. Choshi. |

00:29:20 | Then, in the beginning, well, would you present just the mathematical expression right there? Ah. Ah. Right there is fine. Go ahead. |

00:29:25 | Smaller. Smaller. What came after that? |

00:29:26 | It's okay. Okay. Now, how to say it is a little difficult. |

00:29:31 | Okay? |

00:29:31 | Smaller than. |

00:29:31 | B:00] |

00:29:32 | One hundred eighty minus- |

00:29:35 | Yes. |

00:29:37 | Ten X... smaller than- |

00:29:40 | Yes. |

00:29:40 | One hundred ten minus five X. |

00:29:43 | Yes. |

00:29:45 | Then, well, can you say why you got a mathematical expression like this? |

00:29:48 | Um. The one labeled X is that one day after they finished their prayers and- |

00:29:51 | Yes. |

00:29:52 | And on that day since the smaller brother's amount of money is bigg- oh was bigger than his big brother, |

00:29:56 | well Ichiro's so in short, well, Ich- Ic- who had 180 yen. Huh? |

00:30:07 | Ichiro is one second- in short... in short the difference in the amounts of money on that one day- |

00:30:24 | Yes. |

00:30:28 | The fact is the smaller brother's amount of money is more than Ichiro's and- |

00:30:28 | Yes. |

00:30:28 | And the person who had 110 yen is the amount of money the smaller brother had in the beginning. |

00:30:32 | So the smaller brother's is bigger, and Kazu- oh- Ichiro's is smaller. |

00:30:38 | Okay. Okay. That's okay. Okay? |

00:30:41 | Okay, then just before, okay? There were some people who formed equations or simultaneous equations. |

00:30:41 | So just now there were some people who just wrote some equations. |

00:30:47 | But how this X is placed is a little different, right? |

00:30:47 | Okay. Then, is there anybody who says they also formed equations like this? |

00:30:50 | Um, in the last situation you placed X as the day when it becomes the same amount of money. Okay. |

00:30:53 | Compared to what he just said now, okay? Um... the day the smaller brother's is bigger is X days later. |

00:31:05 | Okay. Then, is there anybody who says they also formed equations like this? |

00:31:11 | Okay, so two people, right? So these kinds of expressions... |

00:31:15 | The fact is these are the ones we're going to use from now on, okay? Equations that use symbols like this... umm, we'll call them inequalities. |

00:31:22 | B:00] |

00:31:28 | Then, um, right around here on the handout, okay? In the box- |

00:31:33 | Um, this part. The part around here, okay? Then, the mathematical expression where the wavy lines are drawn. |

00:31:39 | Then, um, please try writing these in. |

00:33:08 | Okay. You don't have to write the others. Just here is fine. Okay? |

00:33:18 | Okay. Then, would you look up again? |

00:33:21 | If there are parts you haven't written you will have time to fill it in later, okay. Pay attention this way. |

00:33:26 | Is it okay with people who are looking down? Is it okay? Then- |

00:33:30 | Um, actually in Choshi's situation he has already obtained things after this by calculating, |

00:33:34 | but I think there are lot of people who saw this today for the first time, okay? |

00:33:36 | So today I think we would like to find the value for X that holds true for this mathematical expression while actually putting in numbers. |

00:33:45 | Okay? Um. For this. Please write this later. Okay? Um. The value of X. Then, um, the value of left side. |

00:33:53 | Then, um, the value of right side. |

00:33:57 | And, when we put in a number for X, which is bigger the left side or the right side? |

00:34:01 | B:00] |

00:34:03 | Okay? I think we would like to investigate that. |

00:34:05 | Now even if we're to actually put in numbers, well, we don't know starting from what number we should put i- |

00:34:11 | start at right? It's okay if we put in continuously starting from one. |

00:34:14 | But since we'd have to write a lot of calculations that's troublesome. |

00:34:18 | Um, so well, if we look at the solution method from before, it seems we're getting 15. |

00:34:25 | So I think we would like to see a little with numbers in the vicinity of 15. |

00:34:29 | Then, since we are using the vicinity of 15, so ones before that are 14, 13. |

00:34:37 | Then, ones after that are 16, 17, okay? Then, I think we would like to investigate up to around 18. |

00:34:45 | Then... okay? The left side, okay? |

00:34:49 | When we substituted 13 into this X... okay? One hundred eighty minus 10 times 13. |

00:34:58 | Okay. Everybody. How much will this be? |

00:35:00 | Fifty. |

00:35:00 | Fifty |

00:35:01 | Yes. |

00:35:02 | Okay. Compared to that the right side is 110 minus five times. |

00:35:09 | In this X if we still put in 13... how much is this? |

00:35:16 | Forty-five. |

00:35:17 | Yes. Forty-five. |

00:35:20 | That means in this situation, the values of the left side and the right side, which is greater? |

00:35:25 | The left side. |

00:35:27 | Yes. The left side is greater, right? That means since this side is greater, if we ask about the size relationship, okay? |

00:35:32 | The greater than symbol goes in, right? |

00:35:35 | That means, can we say that putting in 13 for X holds true for this inequality? |

00:35:42 | We can't say it. |

00:35:42 | We can't say it. |

00:35:43 | Yes. Well, the direction is different, right? That means, since we can't say it when it's this, it's wrong. |

00:35:48 | Because of the fact that we can't say it, okay? I think I would like to put marks. |

00:35:51 | Then, doing it in the same way if we put in 14... if we put in 14 over here also how much will they be? |

00:35:57 | And, how would the size relationship be? |

00:36:00 | How about it when it's 15? Now, with that, okay? I think I would like for you to do up to here. |

00:36:05 | And, if you find a situation when you can say it is true please try putting circle marks. |

00:36:10 | Then, would you do it up to there? |

00:37:37 | What goes in? |

00:37:40 | When they're the same? |

00:37:42 | That's right, huh? |

00:37:43 | Then, how about over here? See? |

00:37:45 | You put a mark here, right? |

00:37:46 | If you couldn't say, it's the wrong mark X. |

00:37:50 | Are they the same? Since they're not the same, do you understand? |

00:37:54 | That's right, huh? You put a wrong mark, right? Yes. |

00:38:34 | Please put marks also over here, okay? |

00:38:37 | Then, please put marks here, okay? |

00:38:40 | When you can say it is true, put the right mark. When you can't say it is true, put the wrong mark, okay? |

00:38:56 | You're already done writing? Then, now I'm sorry but would you go up front and write this? |

00:39:03 | Okay? This place. You can bring up this handout. Okay? |

00:39:11 | Okay then. |

00:39:29 | How about you, did you finish them all? Are you still in the middle? |

00:39:34 | How about this? Which is it? Is it the wrong mark or the right mark? |

00:39:39 | How about it? It's greater if over here is greater, okay? It holds true, okay? |

00:39:46 | How about it? |

00:39:47 | When you com- compare them. |

00:39:49 | It's greater. |

00:39:49 | That means, what is this? |

00:40:34 | People who are done writing, okay? Look at Goda's and would you compare it with yours to see if it's the same or not, okay? |

00:40:41 | Oh. Th- |

00:40:42 | Here, okay? The right mark or the wrong mark, okay? |

00:40:45 | Have it written, okay? |

00:41:09 | Okay, then up to here is okay. Okay? Try putting marks here. Okay? Doing it like that, okay? |

00:41:36 | Then. Okay. It's good. Okay. |

00:41:44 | Okay. Thank you. |

00:41:46 | Okay, then please look in the direction of the blackboard. Okay? How about it? |

00:41:50 | Well, would the people who had theirs the same as this raise your hands? |

00:41:55 | Okay. Then, please lower your hands. |

00:41:57 | That means, well if we look at the symbols over here, an X that holds true for this mathematical expression is |

00:42:03 | these four: 15, 16, 17, 18, right? |

00:42:08 | If we look exactly at the relationship of the size, the first one was greater than, but the next one is equals. The next ones are all smaller than, right? |

00:42:15 | That means it changed here, right? |

00:42:19 | That means what can we say about the kind of numbers for X that will make this mathematical expression work. |

00:42:23 | Based on 14. Numbers that are what than 14? |

00:42:29 | Greater. |

00:42:30 | Uh huh. Numbers greater than. Okay? |

00:42:32 | Huh? |

00:42:42 | Okay. The values of X that hold true for this mathematical expression, um, like this. Okay? |

00:42:50 | We call this value... um, I think it came up before but, um, we call it... the solution, um, of the inequality. |

00:43:06 | When we were doing equations, we said to solve for X that will make expressions like these work, right? |

00:43:13 | Um. We will think about inequalities in the same way. |

00:43:15 | Well would you not write it yet? Okay? |

00:43:17 | Then... it's about the answer to this problem, but... |

00:43:25 | Um, if we look at the things written before, all of them are on the fifteenth day. But the answer, that one day, is it just the fifteenth day? |

00:43:39 | From 15. |

00:43:39 | Then, will somebody say it for me? Is it like this? Then, just now, well, Higashi said it for me, but well would you say it for me? |

00:43:47 | Hm. |

00:43:49 | It's from the fifteenth day up to the eightee- eighteenth day. |

00:43:53 | Hm. It includes up to. How about the nineteenth day? |

00:43:56 | It's not included. |

00:43:56 | Why? |

00:43:58 | Since Ichiro's wallet becomes empty and- |

00:44:00 | Yes. |

00:44:01 | at that time they'll end it. |

00:44:01 | Yes. |

00:44:03 | Yes. Since if it's the nineteenth day, there isn't any more, right? |

00:44:08 | Money, right? That means, like it was said just now, it's not just the fifteenth day, |

00:44:12 | but that one we call one day is of course the fifteenth day but it might've been on the sixteenth day, right? |

00:44:18 | The day they looked accidentally was sixteenth day or the seventeenth or the eighteenth day... |

00:44:23 | of these... well it was one of these days, right? |

00:44:32 | Okay. Then please write in this part, okay? At the bottom of the handout. |

00:44:44 | Then, would you pass it to the back? |

00:44:52 | Then, would you pass it back while doing that. |

00:45:01 | Oh. Was there one extra paper? Well, one paper. |

00:45:05 | Oh. It's passed back. Well, will there be one paper extra? One paper will be left. Okay. |

00:45:50 | Okay, then are most of you done? Then, the small handout that was passed out just now. Please look at that. Is it okay? |

00:45:59 | Then, I will try reading it, okay? |

00:46:02 | Umm. The prayer was answered and, um, their mother was able to leave the hospital safely and- |

00:46:07 | Um, that night they gave a toast with juice. |

00:46:09 | Um, currently there are 50 milliliters of juice in Ichiro's cup, and 80 milliliters in the smaller brother's cup. |

00:46:17 | When the mother poured juice into Ichiro's cup it made Ichiro's amount become greater. |

00:46:23 | The question is how many milliliters had she poured? |

00:46:27 | Form an inequality and think about it. It's a problem like this, okay? |

00:46:32 | Okay, then like before, I would like for you to look at the figure. |

00:46:41 | Okay, then okay? Since the fact is the mother, okay? Feels better so, um, that night, um, they gave a toast, right? |

00:46:47 | And, the smaller brother drank a little but Ichiro drank deeply, okay? |

00:46:54 | So it's greatly decreased right? Hm. Now, then the mother, um, after this... okay? |

00:47:02 | Since he had less, she poured some for him, okay? The juice, okay? |

00:47:06 | Now, then since it would be poured rapidly, the amount of juice increases like this, right? |

00:47:09 | Wow. |

00:47:10 | Okay. If she did it like that... when they looked, the fact is that Ichiro's amount become more than the smaller brother's. |

00:47:17 | Then, the problem is about how much did she pour in, okay? |

00:47:21 | Take this. An inequality, okay? Form an inequality like this, then we want to think it from there. |

00:47:27 | Then, for that, okay? In this situation what should we place as X? |

00:47:33 | Somebody? |

00:47:35 | What should we place as X? |

00:47:40 | Well, is it hard to say it in words? Or it's also okay with you saying it's here. |

00:47:46 | Okay. Then, Choshi. Okay. |

00:47:48 | Yes. |

00:47:50 | For Ichiro- |

00:47:51 | Yes. |

00:47:51 | to pour more than the smaller brother's, |

00:47:53 | the amount needed for that. |

00:47:53 | Yes. |

00:47:54 | The amount needed. Then, did you understand that one just now? |

00:47:57 | I don't understand. |

00:47:57 | Then, would you point with your finger? [Laughter] |

00:47:59 | Huh? |

00:48:00 | Come up front and- Okay. |

00:48:02 | Where is it? |

00:48:05 | In short, here is 50 milliliters so- |

00:48:05 | Yes. |

00:48:07 | Yes. |

00:48:08 | Let's have it so we need up to 80 milliliters and up to here. |

00:48:10 | Yes. |

00:48:11 | Up to here. |

00:48:13 | Yes. |

00:48:13 | That amount I think we should make X. |

00:48:15 | Yes. Okay, if we do that, it's when they become the same, right? Yes. What else? |

00:48:22 | Then if we think like that, did it became more? |

00:48:31 | When we're asked how about when it's equal, okay? We could think things like this, but we can get a viewpoint of it becoming more, right? |

00:48:35 | When it's an inequality, okay? When it's that- |

00:48:41 | When we exactly... go from this situation... what part is it? |

00:48:50 | What do we want to obtain? In this situation. |

00:48:53 | The increased amount. |

00:48:53 | Yes. The increased amount, right? So, um, about the inequality, if you thi- if it's an equation we can also do it exactly here, okay? |

00:49:02 | Or if you thought about forming an inequality just like that, it may be okay if you place this as X. Okay. |

00:49:07 | Then, write in X milliliters in the figure and this relationship, okay? |

00:49:15 | Using symbols like this, please try expressing it. |

00:49:34 | Well, just the mathematical expression is okay. Well, among some of you there are people who made tables and are about to put in numbers. |

00:49:43 | Okay. Please try writing X here. That X is milliliters, okay? |

00:49:52 | Okay. |

00:49:53 | Hm, so all you have to do is make a mathematical expression that says this here is greater than this. |

00:50:05 | Since all you have to do is make a mathematical expression that says this here is great than this. How much was the total here? |

00:50:13 | Huh? It's 50 plus X, right? How about over here? |

00:50:18 | Eighty. |

00:50:18 | Eighty. And, which is more? |

00:50:20 | Over here. |

00:50:21 | Over here? So for that... all you have to do is use that symbol, right? |

00:50:25 | Ah. Okay. |

00:50:28 | Okay. Now. We don't have much time so, well I'm sorry, but okay then. |

00:50:33 | Let's have somebody say the mathematical expression. Okay. Anybody who wants to say it becomes a mathematical expression like this. |

00:50:38 | Huh? How to say it is this. All you have to do is use this. |

00:50:42 | Okay? Mostly, everybody seemed to be able to do it. |

00:50:44 | Okay, then. Izumi. Would you try saying it? |

00:50:45 | Yes. |

00:50:49 | Fifty plus X- |

00:50:49 | Yes. |

00:50:53 | bigger than- |

00:50:54 | Hm? Which? |

00:50:55 | bigger than- |

00:50:56 | Bigger than. Okay. Greater than. Okay. |

00:50:57 | eighty. |

00:50:58 | Okay. |

00:50:59 | [Bell] |

00:51:00 | Okay. People who can say they also got equations like this? |

00:51:04 | Okay. Now, you may lower your hands. |

00:51:05 | Then... this mathematical expression's... um, the solution. Meaning the values of X that hold true for this mathematical expression. |

00:51:19 | If we say that, what kind of numbers can we say they are? |

00:51:25 | Somebody? How about it? If we talk about values of X that hold true for this mathematical expression. Okay. Then, Fujita. Go ahead. |

00:51:38 | More than- |

00:51:39 | Yes. |

00:51:39 | Thirty. |

00:51:40 | Yes. More than 30. |

00:51:48 | Well, if we have it in numbers, numbers more than, okay? Thirty. |

00:51:53 | Now, since the fact is if we ask what kind of numbers are more than 30, well I think I would draw a number line. |

00:51:58 | Now, we will write it later, so would you look this way. |

00:52:03 | Okay. Then, have zero around here and, okay? We'll have 30 around here, okay? |

00:52:08 | Then just now, um, she said numbers more than 30 for us, but then, for example, what number should we think about it? |

00:52:14 | If we ask about numbers more than 30. Concretely. |

00:52:16 | (inaudible) |

00:52:17 | Fifty. |

00:52:17 | Fifty. Yes. There is one like 50, right? |

00:52:20 | Then, if we say one between these? |

00:52:22 | Thirty point one. |

00:52:22 | Forty. |

00:52:23 | Oh. It's thirty point one? |

00:52:25 | Ahh. |

00:52:27 | After that? |

00:52:29 | Anything else? |

00:52:29 | Thirty. |

00:52:29 | Thirty point one. |

00:52:31 | Thirty point? |

00:52:32 | One one. |

00:52:33 | [Laughter] |

00:52:33 | One one. Oh. Thirty point one one. Anything else? |

00:52:37 | Forty. |

00:52:38 | Thirty point one one one. |

00:52:40 | Forty. Okay? Now, incidentally, um, just now we got one, two, three, four- four numbers that are more than thirty. |

00:52:46 | But about how many are there? |

00:52:51 | Infinite. |

00:52:52 | Infinite. |

00:52:52 | Yes. There is an infinite amount. Okay? Meaning thirty. Is thirty included or not included? |

00:52:57 | It's included. |

00:52:57 | It's not included. |

00:52:58 | Yes. It's not included, but if it comes over here even a little like thirty point one, the fact is it becomes more than 30, right? |

00:53:06 | That means all the drawn parts here are included. |

00:53:11 | If we say that, if we ask what the answer is... okay? If we use this compared to 30 milliliters, right? Amounts more than that. |

00:53:28 | Okay? It becomes like this, right? |

00:53:33 | Then, um, time has run out, okay? After the ending bow is finished, well, I think I would like you to write it. Then, for now we'll end. |

00:53:42 | Stand up. |

00:53:50 | Bow. |

00:53:51 | Thank you very much. |

00:53:52 | Okay. |

00:54:06 | Teacher. Do we copy everything from here? |

00:54:09 | Oh. You don't have to copy it. Well, just this part is fine. I want you to know that there are ways of thinking like this, okay? |