# 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.

TimeCaption
00:00:02Leave them upside down.
00:00:15I can't believe it.
00:00:16Well.
00:00:17Huh?
00:00:18Well. Don't say that.
00:00:19It starts with the bell and ends with the bell.
00:00:21Hmm.
00:00:22That's the-
00:00:22I'll also try to aim that as best as I can.
00:00:23What about a ruler?
00:00:25Oh. It's okay even if you don't have it.
00:00:35Pass it back as it is, upside down, okay?
00:00:37What is upside down?
00:00:38Here.
00:01:00[Bell]
00:01:01Okay. Now, let's start class.
00:01:02Stand up.
00:01:08Bow.
00:01:09Onegaishimasu.
00:01:09Onegaishimasu.
00:01:10Onegaishimasu.
00:01:14Okay, then please look at your handouts.
00:01:21Okay, then these are the problems we're going to do today.
00:01:24Okay. Um. It has been one month since Ichiro's mother has entered the hospital.
00:01:29Um. He has decided say a prayer with his smaller brother at a local temple every morning so that she will be well soon.
00:01:35Um. There are 18 10-yen coins in Ichiro's wallet and just 22 five-yen coins in his smaller brother's wallet.
00:01:44They have decided every time to take one coin from each of them,
00:01:48and put them in the offertory box, and continue their prayers until either wallet becomes empty.
00:01:54One day after they were done with their prayers, when they looked into each other's wallets,
00:01:59the smaller brother's amount of money was greater than Ichiro's.
00:02:02How many days has it been since they started praying? That's the problem.
00:02:07Now, I think there are points that are a little too hard to understand with just these sentences, so-
00:02:11Well, I think I would like to look at a figure and check it.
00:02:14Now, pay attention to the blackboard.
00:02:18What the?
00:02:21Okay. This is Ichiro's wallet, okay?
00:02:24Um, then... okay, over here is the smaller brother's wallet. And, also there is an offertory box there, right?
00:02:38Okay?
00:02:40Okay.
00:02:40Now, 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?
00:02:47How much is in this in the beginning?
00:02:50All together. How much is in it?
00:02:50One hundred eighty yen.
00:02:51One hundred eighty yen.
00:02:53Yes.
00:02:54Okay. The amount of money, well, in the beginning.
00:03:03Okay. Compared to the smaller brother's. There are only five-yen coins in it, but how much is in it?
00:03:08One hundred and ten yen.
00:03:09One hundred and ten yen.
00:03:09Yes. One hundred and ten yen.
00:03:14This means in the beginning stages, um, Ichiro has more, okay? In terms of the amount of money, he has more, right?
00:03:24Then, um, after this. Okay? Every morning from each wallet they take out one coin from each, okay?
00:03:32They put them in this offertory box, right?
00:03:36Now, first day one. Okay. Ten yen from Ichiro's wal- let- um, wallet and five yen from over here.
00:03:44Okay? Now, it goes in from here and in this offertory box.
00:03:49Wow. That's great.
00:03:50That's amazing.
00:03:52Okay. It's gets stowed away in here, okay? Is it okay?
00:03:55They're in there.
00:03:56Yes.
00:03:57Okay, then how about it at this stage? Comparing Ichiro's and his smaller brother's wallet.
00:04:02The contents of the wallet. Which one has more in terms of the amount of money?
00:04:04The older brother.
00:04:05Hmm.
00:04:06Ichiro.
00:04:06Ichiro.
00:04:06Yes. Ichiro has more, right? Okay, then second day.
00:04:10Okay. Of course right? They put in the coins in here.
00:04:16How about it in this stage?
00:04:17Ichiro.
00:04:18Ichiro.
00:04:19Hmm. Ichiro still has more, huh? Okay? Now, the fact is they continued things like this every day, okay?
00:04:25But, in the morning of some day, okay?
00:04:27Um. They looked inside of each other's wallets, right? Then the smaller brother had more in the amount of money.
00:04:33Now, that one day was how many days, um, since they started their praying?
00:04:39Now I would like for everybody to think about that. Then, um, in the open space.
00:04:45Well this part we'll be writing in later on, so writing anywhere other than here is fine so, um, okay?
00:04:52You may want to take notes or anything else you want to do is fine, so please try doing it.
00:04:55Where are we going to write it?
00:04:57Hm. Next to it is okay. Okay?
00:05:34Masa. You did it up to the second day, right? Then, on the third day who has more?
00:05:40This one has more? Then, how about the fourth day?
00:05:44If you keep on doing it like that? Okay?
00:05:52That's good.
00:05:59Now, just now see? You did it up to the second day, right?
00:06:03Then, how about the third day?
00:06:05How about it?
00:06:07In the same manner try thinking, like how about the fourth day?
00:06:11Do it the same way over here, okay?
00:06:58Well see? Up to the second day this one has mor- had more, right? Then, on the third day who had more?
00:07:12Okay?
00:07:13How much will it be? Well, if it's the third day, where is how much?
00:07:19Okay? Do it like that then decide the answer, okay?
00:07:25Oh. Is this 180 yen? Right?
00:07:52Oh. Have you already solved at least one?
00:07:57Okay.
00:08:53Up to wh- where have you thought about it?
00:08:55Uh, somewhat.
00:08:59Hm. What do you mean? Did you erase this?
00:09:00Yes. I erased that.
00:09:00Hm. You erased the first day okay. Then, how about the second day?
00:09:02I did this like this and-
00:09:04Hm.
00:09:04The tens.
00:09:05Then, try putting in the dates there.
00:09:06Okay. Okay.
00:09:07Okay?
00:09:17How did you obtain this?
00:09:17I counted all the way.
00:09:18Oh. You counted it all the way? Hm..
00:09:21Now, well... is there any method to find it that's simpler? Can you please find that.
00:09:32Have you found it? Then, now it was quite tedious to write these out, right?
00:09:36Is there any method to find it faster?
00:09:39Okay? Can you please find that?
00:09:42Now, this is also one of the methods, right? Then, it's tedious to count these, right?
00:09:47Is there any method to find the answer faster? Please think about it.
00:09:59Now, if you have found the answer using one method, okay, aren't there any other methods?
00:10:05Okay?
00:10:09Oh, now it's okay. You can leave that. Oh.
00:10:15Then... without using this Y... it seems you can do it just with this and this, right?
00:10:26Yes. Then, quickly, okay? Put the symbols down on this, okay? On these, okay?
00:10:45Huh? Can you stop for a moment?
00:10:48What is this Y? This?
00:10:53This 180 minus 10 X is... whose money is this?
00:11:00That is?
00:11:00Ichiro.
00:11:01Yes. It's Ichiro's... right? Then how about the smaller brother?
00:11:10See? How much is in that, hum?
00:11:29Hm. Oh. If you do that then?
00:11:31Um?
00:11:38Now, 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?
00:11:46This person, this is... Ichiro's, right? Oh. This is the smaller brother's, right?
00:11:51Then it seems you can do it by using this, okay?
00:12:04Oh. You got it up to here? Okay.
00:12:17This. It was obtained as how many days?
00:12:22Oh. It was on the twelfth day, right? Then, can you do it a little more? Okay?
00:12:35Then if you try combining this and this then you can make a mathematical expression. Okay?
00:12:55Was it something like a mathematical expression?
00:12:57Hmm.
00:12:59Then, this okay? Can you do it without using the Y?
00:13:02Okay?
00:13:19Oh. You combined them, right?
00:13:32Whose amount of money is this?
00:13:34Are you talking about this?
00:13:35Yes.
00:13:36Hm.
00:13:38Hm. This is-
00:13:38Hm.
00:13:39Well, 140 yen.
00:13:40Hm...
00:13:42Then, how about over here?
00:13:43Over here is also 90 yen.
00:13:45And, how did you obtain this? This value?
00:13:49Uh well.
00:13:50Hm.
00:13:50You minus 10 yen every single day and-
00:13:52Yes.
00:13:53Over here every single day-
00:13:54Yes.
00:13:54You minus five yen.
00:13:55Oh. That's right, huh?
00:13:57And you obtained this from the table, right?
00:13:59Yes.
00:14:00Then, can't this be found by calculation?
00:14:09Hmm.
00:14:11Oh. You formed a simultaneous equation, right? Okay.
00:14:46Well then. This okay? Can you try thinking if it will be found by formulating a mathematical expression?
00:14:50Okay?
00:14:55Then, this one also, can you try thinking if it can be found by formulating a mathematical expression? Okay?
00:15:06Oh. You made a mathematical expression like this, huh? Okay.
00:15:31Oh. The fact is you've counted all the way, right? Okay.
00:15:37Then, okay? Also, okay? After this I'll have you come up again and present, okay? Okay? This problem.
00:15:42Since we can't write it in and erase it also, so that means would you fill it in here one by one? Okay?
00:15:46No.
00:15:46Don't say that. I'm counting on you. Okay?
00:16:08You went on solving this? Okay. Then you did this by making x equal one. Okay.
00:16:18Then, okay? Well, later on I'm going to have you present this part. Okay? Hm.
00:16:55Hm.
00:17:07Then, okay? Ando, okay? This part, okay? Would you come up to present it later on?
00:17:12Here and also one more. Up to here. Would you write just this part and also this part?
00:17:18The rest is okay with dot, dot, dot. Since it's troublesome to write all of this.
00:17:21Okay?
00:17:33And also.
00:17:38Now, okay? I want Bunmei to. Umm, is it over here? Would you present this part?
00:17:45Am I going to write it?
00:17:46Yes. Please write it. Okay? That you thought of it like this, okay?
00:18:06Then, okay? I want Choshi to present okay? Um, this expression, okay? I'm going to have you present it later on. So-
00:18:11This- this what do you call this?
00:18:14Hm. This is smaller than.
00:18:15What?
00:18:15Smaller than.
00:18:16Smaller than.
00:18:17Hm.
00:18:20Then, please think beforehand why you formulated a mathematical expression like this.
00:18:31Okay. Then, um, would you look up please.
00:18:34Now. When I looked around a little just now, well there were people who did it with different solving techniques. Okay?
00:18:42Umm. Well it seems there were even people who found two or three techniques by themselves, huh?
00:18:46Now, the fact is to show there are methods like these, um, I think I would like some people-
00:18:50Okay? To present them, okay?
00:18:52Then, Daishi. Well, please come up. Okay.
00:18:55(inaudible)
00:18:56Yes. You were saying how you would do it for yourself, right?
00:18:59Will you do it?
00:19:00Ha ha.
00:19:02I guess I'll do it.
00:19:03Please.
00:19:04Ha ha.
00:19:04Ha ha.
00:19:05What am I supposed to do?
00:19:06How would you do it?
00:19:06So before. See?
00:19:07I put them in, right?
00:19:08Yes.
00:19:09And you keep on putting them in.
00:19:13Okay. That's good. Okay.
00:19:13It's a lot faster if we put in many at a time.
00:19:19(inaudible)
00:19:19(inaudible) is more cool.
00:19:22Hmm.
00:19:29There's a lot of 10-yen coins, huh?
00:19:31Then, last the five-yen coins go in.
00:19:33They're sticking out.
00:19:40(inaudible) huh?
00:19:41One, two, [in English] three, four, five, six [in Japanese].
00:19:46Five, eight, two.
00:19:48Well-
00:19:49Huh?
00:19:50About this much.
00:19:51Hum.
00:19:51About this much?
00:19:52Hmm.
00:19:52About this much- this time it fell.
00:19:55Hmm. Teacher.
00:19:56And, please say it, okay?
00:19:59No.
00:19:59By the way, what day is this?
00:20:01Umm. The fifteenth day.
00:20:03Okay. How is it?
00:20:05It's okay.
00:20:05It's okay.
00:20:05Now. Just now.
00:20:10Umm, for Daishi's method, okay?
00:20:14Okay. While actually putting these in, okay?
00:20:17There were other people that kept drawing lines like this, and solved the problem that way.
00:20:22Doing it like that well the answer is the fifteenth day... they obtained it like that, okay?
00:20:30Then, people who also did it with this method themselves or who also tried doing this method.
00:20:36Then, well would you raise your hands?
00:20:38Okay, then you can lower them.
00:20:40Then, continuing. Um. Is it Etsumi?
00:20:44Then, would you write it around here? In the top part.
00:20:54Okay. Then. Okay.
00:20:56Over here. Around here. Around this side, okay? Around here.
00:23:34Okay. Then can you say your method of thought and also, um, how many days was it since they started. Okay.
00:23:40Umm.
00:23:42Since the fact is they put in the offertory box... one coin each of money in one day so...
00:23:49if we do it in an orderly fashion... the number of days and also the money left over, one by one...
00:24:00on the fifteenth day the smaller brother has more.
00:24:05Okay. That means the answer is?
00:24:07The fifteenth day.
00:24:07Yes. The fifteenth day. Okay. That's good.
00:24:16Okay, then in this case, uh, he did it for us by using a graph, right?
00:24:17B:00]
00:24:23Then, it doesn't matter if you drew lines or not, but people who wrote it this way raise your hands.
00:24:29Okay. Then, you can lower your hands. Okay? Okay. Then, continuing, um, Bunmei.
00:24:35Okay? Then, would you write it around here? That part I asked you to, okay?
00:24:44Yes. Go ahead.
00:24:45My handwriting is not neat.
00:25:24Okay. Then please explain it.
00:25:26Well, in the beginning. Well, Ichiro had 180 yen, and the smaller brother had 110 yen.
00:25:31And since there is a difference of 70 yen,
00:25:33and since the difference between them becomes smaller by five yen each day, so it's 70 divided by 10 minus five.
00:25:39And since by the fourteenth day it becomes exactly the same amount of money,
00:25:43so since on the day after that there will be a difference, so 14 plus one is 15 and it's the fifteenth day.
00:25:49Okay. Okay? Um. In the beginning. He just now said it. There is a difference of 70 yen, right?
00:25:55In this expression that becomes 65 yen. Then 60 yen. Right? Since it becomes smaller
00:26:03B:00]
00:26:05by five yen okay? So he obtained it by noticing this, okay? Are there people who also tried it using this method?
00:26:11Huh? One person. Two people. Just two people? Okay. That's good.
00:26:15Okay, then continuing, um, Fujita. Okay. Then, would you write it around here? Okay?
00:26:54It's okay to not write all the lines of the mathematical expression.
00:26:55Oh.
00:26:55That. Okay.
00:26:56Is it okay with this?
00:26:57Yes.
00:26:57Yes.
00:26:57And, if you can write the amount for X.
00:27:00Oh. Yes.
00:27:00And, the answer. Okay.
00:27:02And, after I've written the answer of X and Y?
00:27:04That's right, huh? Okay.
00:27:22Okay. Okay. Please say-
00:27:25Now.
00:27:26One hundred.
00:27:29In the beginning, Ichiro had 180 yen, and since he takes out 10 yen every day-
00:27:35And we have X as the num- number of days and if we make the amount of money left Y-
00:27:42Then it becomes- the mathematical expression Y equals 180 minus 10 X.
00:27:45And the smaller brother has 110 yen every day. Oh. He has 110 yen.
00:27:50And since he takes out five yen every day it becomes the mathematical expression Y equals 110 minus five X.
00:27:55And when they become of the same amount of money and-
00:27:59And X and Y becomes 14 and 40. And on the fourteenth day they become the same amount of money.
00:28:07And the fourteenth day is the same amount of money.
00:28:10And the next day since Ichiro puts in 10 yen and the smaller brother puts in five yen, so there's a difference.
00:28:14The amount of money put in is smaller for Ic- Ichiro. Oh. It's bigger so...
00:28:21the next day Ichiro... Ichiro's amount of money left is less so it becomes the fifteenth day.
00:28:32Okay. Okay, it's good. Okay?
00:28:40Okay. 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?
00:28:41B:00]
00:28:46Well, she put in Y as the amount inside of the wallet for that day, right?
00:28:49Or some people did it without using the Y, okay? It seems there were people who wrote this equals this like this. Okay?
00:28:58Then, well, simultaneous equations like this or an equation with just X, okay?
00:29:03People who have tried doing it using things like these? Can you raise your hands a little?
00:29:07Okay. That's fine. Okay. That's good.
00:29:09And, also of course they are using letters, but there were some people who formed mathematical expressions a little differently.
00:29:15Then, the fact about that mathematical expression. Choshi.
00:29:20Then, in the beginning, well, would you present just the mathematical expression right there? Ah. Ah. Right there is fine. Go ahead.
00:29:25Smaller. Smaller. What came after that?
00:29:26It's okay. Okay. Now, how to say it is a little difficult.
00:29:31Okay?
00:29:31Smaller than.
00:29:31B:00]
00:29:32One hundred eighty minus-
00:29:35Yes.
00:29:37Ten X... smaller than-
00:29:40Yes.
00:29:40One hundred ten minus five X.
00:29:43Yes.
00:29:45Then, well, can you say why you got a mathematical expression like this?
00:29:48Um. The one labeled X is that one day after they finished their prayers and-
00:29:51Yes.
00:29:52And on that day since the smaller brother's amount of money is bigg- oh was bigger than his big brother,
00:29:56well Ichiro's so in short, well, Ich- Ic- who had 180 yen. Huh?
00:30:07Ichiro is one second- in short... in short the difference in the amounts of money on that one day-
00:30:24Yes.
00:30:28The fact is the smaller brother's amount of money is more than Ichiro's and-
00:30:28Yes.
00:30:28And the person who had 110 yen is the amount of money the smaller brother had in the beginning.
00:30:32So the smaller brother's is bigger, and Kazu- oh- Ichiro's is smaller.
00:30:38Okay. Okay. That's okay. Okay?
00:30:41Okay, then just before, okay? There were some people who formed equations or simultaneous equations.
00:30:41So just now there were some people who just wrote some equations.
00:30:47But how this X is placed is a little different, right?
00:30:47Okay. Then, is there anybody who says they also formed equations like this?
00:30:50Um, in the last situation you placed X as the day when it becomes the same amount of money. Okay.
00:30:53Compared to what he just said now, okay? Um... the day the smaller brother's is bigger is X days later.
00:31:05Okay. Then, is there anybody who says they also formed equations like this?
00:31:11Okay, so two people, right? So these kinds of expressions...
00:31:15The 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.
00:31:22B:00]
00:31:28Then, um, right around here on the handout, okay? In the box-
00:31:33Um, this part. The part around here, okay? Then, the mathematical expression where the wavy lines are drawn.
00:31:39Then, um, please try writing these in.
00:33:08Okay. You don't have to write the others. Just here is fine. Okay?
00:33:18Okay. Then, would you look up again?
00:33:21If there are parts you haven't written you will have time to fill it in later, okay. Pay attention this way.
00:33:26Is it okay with people who are looking down? Is it okay? Then-
00:33:30Um, actually in Choshi's situation he has already obtained things after this by calculating,
00:33:34but I think there are lot of people who saw this today for the first time, okay?
00:33:36So today I think we would like to find the value for X that holds true for this mathematical expression while actually putting in numbers.
00:33:45Okay? Um. For this. Please write this later. Okay? Um. The value of X. Then, um, the value of left side.
00:33:53Then, um, the value of right side.
00:33:57And, when we put in a number for X, which is bigger the left side or the right side?
00:34:01B:00]
00:34:03Okay? I think we would like to investigate that.
00:34:05Now even if we're to actually put in numbers, well, we don't know starting from what number we should put i-
00:34:11start at right? It's okay if we put in continuously starting from one.
00:34:14But since we'd have to write a lot of calculations that's troublesome.
00:34:18Um, so well, if we look at the solution method from before, it seems we're getting 15.
00:34:25So I think we would like to see a little with numbers in the vicinity of 15.
00:34:29Then, since we are using the vicinity of 15, so ones before that are 14, 13.
00:34:37Then, ones after that are 16, 17, okay? Then, I think we would like to investigate up to around 18.
00:34:45Then... okay? The left side, okay?
00:34:49When we substituted 13 into this X... okay? One hundred eighty minus 10 times 13.
00:34:58Okay. Everybody. How much will this be?
00:35:00Fifty.
00:35:00Fifty
00:35:01Yes.
00:35:02Okay. Compared to that the right side is 110 minus five times.
00:35:09In this X if we still put in 13... how much is this?
00:35:16Forty-five.
00:35:17Yes. Forty-five.
00:35:20That means in this situation, the values of the left side and the right side, which is greater?
00:35:25The left side.
00:35:27Yes. The left side is greater, right? That means since this side is greater, if we ask about the size relationship, okay?
00:35:32The greater than symbol goes in, right?
00:35:35That means, can we say that putting in 13 for X holds true for this inequality?
00:35:42We can't say it.
00:35:42We can't say it.
00:35:43Yes. Well, the direction is different, right? That means, since we can't say it when it's this, it's wrong.
00:35:48Because of the fact that we can't say it, okay? I think I would like to put marks.
00:35:51Then, doing it in the same way if we put in 14... if we put in 14 over here also how much will they be?
00:35:57And, how would the size relationship be?
00:36:00How about it when it's 15? Now, with that, okay? I think I would like for you to do up to here.
00:36:05And, if you find a situation when you can say it is true please try putting circle marks.
00:36:10Then, would you do it up to there?
00:37:37What goes in?
00:37:40When they're the same?
00:37:42That's right, huh?
00:37:43Then, how about over here? See?
00:37:45You put a mark here, right?
00:37:46If you couldn't say, it's the wrong mark X.
00:37:50Are they the same? Since they're not the same, do you understand?
00:37:54That's right, huh? You put a wrong mark, right? Yes.
00:38:34Please put marks also over here, okay?
00:38:37Then, please put marks here, okay?
00:38:40When you can say it is true, put the right mark. When you can't say it is true, put the wrong mark, okay?
00:38:56You're already done writing? Then, now I'm sorry but would you go up front and write this?
00:39:03Okay? This place. You can bring up this handout. Okay?
00:39:11Okay then.
00:39:29How about you, did you finish them all? Are you still in the middle?
00:39:34How about this? Which is it? Is it the wrong mark or the right mark?
00:39:39How about it? It's greater if over here is greater, okay? It holds true, okay?
00:39:46How about it?
00:39:47When you com- compare them.
00:39:49It's greater.
00:39:49That means, what is this?
00:40:34People 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?
00:40:41Oh. Th-
00:40:42Here, okay? The right mark or the wrong mark, okay?
00:40:45Have it written, okay?
00:41:09Okay, then up to here is okay. Okay? Try putting marks here. Okay? Doing it like that, okay?
00:41:36Then. Okay. It's good. Okay.
00:41:44Okay. Thank you.
00:41:46Okay, then please look in the direction of the blackboard. Okay? How about it?
00:41:50Well, would the people who had theirs the same as this raise your hands?
00:41:55Okay. Then, please lower your hands.
00:41:57That means, well if we look at the symbols over here, an X that holds true for this mathematical expression is
00:42:03these four: 15, 16, 17, 18, right?
00:42:08If 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?
00:42:15That means it changed here, right?
00:42:19That means what can we say about the kind of numbers for X that will make this mathematical expression work.
00:42:23Based on 14. Numbers that are what than 14?
00:42:29Greater.
00:42:30Uh huh. Numbers greater than. Okay?
00:42:32Huh?
00:42:42Okay. The values of X that hold true for this mathematical expression, um, like this. Okay?
00:42:50We call this value... um, I think it came up before but, um, we call it... the solution, um, of the inequality.
00:43:06When we were doing equations, we said to solve for X that will make expressions like these work, right?
00:43:13Um. We will think about inequalities in the same way.
00:43:15Well would you not write it yet? Okay?
00:43:17Then... it's about the answer to this problem, but...
00:43:25Um, 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?
00:43:39From 15.
00:43:39Then, 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?
00:43:47Hm.
00:43:49It's from the fifteenth day up to the eightee- eighteenth day.
00:43:53Hm. It includes up to. How about the nineteenth day?
00:43:56It's not included.
00:43:56Why?
00:43:58Since Ichiro's wallet becomes empty and-
00:44:00Yes.
00:44:01at that time they'll end it.
00:44:01Yes.
00:44:03Yes. Since if it's the nineteenth day, there isn't any more, right?
00:44:08Money, right? That means, like it was said just now, it's not just the fifteenth day,
00:44:12but that one we call one day is of course the fifteenth day but it might've been on the sixteenth day, right?
00:44:18The day they looked accidentally was sixteenth day or the seventeenth or the eighteenth day...
00:44:23of these... well it was one of these days, right?
00:44:32Okay. Then please write in this part, okay? At the bottom of the handout.
00:44:44Then, would you pass it to the back?
00:44:52Then, would you pass it back while doing that.
00:45:01Oh. Was there one extra paper? Well, one paper.
00:45:05Oh. It's passed back. Well, will there be one paper extra? One paper will be left. Okay.
00:45:50Okay, then are most of you done? Then, the small handout that was passed out just now. Please look at that. Is it okay?
00:45:59Then, I will try reading it, okay?
00:46:02Umm. The prayer was answered and, um, their mother was able to leave the hospital safely and-
00:46:07Um, that night they gave a toast with juice.
00:46:09Um, currently there are 50 milliliters of juice in Ichiro's cup, and 80 milliliters in the smaller brother's cup.
00:46:17When the mother poured juice into Ichiro's cup it made Ichiro's amount become greater.
00:46:23The question is how many milliliters had she poured?
00:46:27Form an inequality and think about it. It's a problem like this, okay?
00:46:32Okay, then like before, I would like for you to look at the figure.
00:46:41Okay, then okay? Since the fact is the mother, okay? Feels better so, um, that night, um, they gave a toast, right?
00:46:47And, the smaller brother drank a little but Ichiro drank deeply, okay?
00:46:54So it's greatly decreased right? Hm. Now, then the mother, um, after this... okay?
00:47:02Since he had less, she poured some for him, okay? The juice, okay?
00:47:06Now, then since it would be poured rapidly, the amount of juice increases like this, right?
00:47:09Wow.
00:47:10Okay. If she did it like that... when they looked, the fact is that Ichiro's amount become more than the smaller brother's.
00:47:17Then, the problem is about how much did she pour in, okay?
00:47:21Take this. An inequality, okay? Form an inequality like this, then we want to think it from there.
00:47:27Then, for that, okay? In this situation what should we place as X?
00:47:33Somebody?
00:47:35What should we place as X?
00:47:40Well, is it hard to say it in words? Or it's also okay with you saying it's here.
00:47:46Okay. Then, Choshi. Okay.
00:47:48Yes.
00:47:50For Ichiro-
00:47:51Yes.
00:47:51to pour more than the smaller brother's,
00:47:53the amount needed for that.
00:47:53Yes.
00:47:54The amount needed. Then, did you understand that one just now?
00:47:57I don't understand.
00:47:57Then, would you point with your finger? [Laughter]
00:47:59Huh?
00:48:00Come up front and- Okay.
00:48:02Where is it?
00:48:05In short, here is 50 milliliters so-
00:48:05Yes.
00:48:07Yes.
00:48:08Let's have it so we need up to 80 milliliters and up to here.
00:48:10Yes.
00:48:11Up to here.
00:48:13Yes.
00:48:13That amount I think we should make X.
00:48:15Yes. Okay, if we do that, it's when they become the same, right? Yes. What else?
00:48:22Then if we think like that, did it became more?
00:48:31When 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?
00:48:35When it's an inequality, okay? When it's that-
00:48:41When we exactly... go from this situation... what part is it?
00:48:50What do we want to obtain? In this situation.
00:48:53The increased amount.
00:48:53Yes. 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?
00:49:02Or if you thought about forming an inequality just like that, it may be okay if you place this as X. Okay.
00:49:07Then, write in X milliliters in the figure and this relationship, okay?
00:49:15Using symbols like this, please try expressing it.
00:49:34Well, just the mathematical expression is okay. Well, among some of you there are people who made tables and are about to put in numbers.
00:49:43Okay. Please try writing X here. That X is milliliters, okay?
00:49:52Okay.
00:49:53Hm, so all you have to do is make a mathematical expression that says this here is greater than this.
00:50:05Since all you have to do is make a mathematical expression that says this here is great than this. How much was the total here?
00:50:13Huh? It's 50 plus X, right? How about over here?
00:50:18Eighty.
00:50:18Eighty. And, which is more?
00:50:20Over here.
00:50:21Over here? So for that... all you have to do is use that symbol, right?
00:50:25Ah. Okay.
00:50:28Okay. Now. We don't have much time so, well I'm sorry, but okay then.
00:50:33Let's have somebody say the mathematical expression. Okay. Anybody who wants to say it becomes a mathematical expression like this.
00:50:38Huh? How to say it is this. All you have to do is use this.
00:50:42Okay? Mostly, everybody seemed to be able to do it.
00:50:44Okay, then. Izumi. Would you try saying it?
00:50:45Yes.
00:50:49Fifty plus X-
00:50:49Yes.
00:50:53bigger than-
00:50:54Hm? Which?
00:50:55bigger than-
00:50:56Bigger than. Okay. Greater than. Okay.
00:50:57eighty.
00:50:58Okay.
00:50:59[Bell]
00:51:00Okay. People who can say they also got equations like this?
00:51:04Okay. Now, you may lower your hands.
00:51:05Then... this mathematical expression's... um, the solution. Meaning the values of X that hold true for this mathematical expression.
00:51:19If we say that, what kind of numbers can we say they are?
00:51:25Somebody? How about it? If we talk about values of X that hold true for this mathematical expression. Okay. Then, Fujita. Go ahead.
00:51:38More than-
00:51:39Yes.
00:51:39Thirty.
00:51:40Yes. More than 30.
00:51:48Well, if we have it in numbers, numbers more than, okay? Thirty.
00:51:53Now, since the fact is if we ask what kind of numbers are more than 30, well I think I would draw a number line.
00:51:58Now, we will write it later, so would you look this way.
00:52:03Okay. Then, have zero around here and, okay? We'll have 30 around here, okay?
00:52:08Then just now, um, she said numbers more than 30 for us, but then, for example, what number should we think about it?
00:52:14If we ask about numbers more than 30. Concretely.
00:52:16(inaudible)
00:52:17Fifty.
00:52:17Fifty. Yes. There is one like 50, right?
00:52:20Then, if we say one between these?
00:52:22Thirty point one.
00:52:22Forty.
00:52:23Oh. It's thirty point one?
00:52:25Ahh.
00:52:27After that?
00:52:29Anything else?
00:52:29Thirty.
00:52:29Thirty point one.
00:52:31Thirty point?
00:52:32One one.
00:52:33[Laughter]
00:52:33One one. Oh. Thirty point one one. Anything else?
00:52:37Forty.
00:52:38Thirty point one one one.
00:52:40Forty. Okay? Now, incidentally, um, just now we got one, two, three, four- four numbers that are more than thirty.
00:52:46But about how many are there?
00:52:51Infinite.
00:52:52Infinite.
00:52:52Yes. There is an infinite amount. Okay? Meaning thirty. Is thirty included or not included?
00:52:57It's included.
00:52:57It's not included.
00:52:58Yes. 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?
00:53:06That means all the drawn parts here are included.
00:53:11If we say that, if we ask what the answer is... okay? If we use this compared to 30 milliliters, right? Amounts more than that.
00:53:28Okay? It becomes like this, right?
00:53:33Then, 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.
00:53:42Stand up.
00:53:50Bow.
00:53:51Thank you very much.
00:53:52Okay.
00:54:06Teacher. Do we copy everything from here?
00:54:09Oh. 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?