# NL4 EQUATIONS

This eighth grade mathematics lesson focuses on factoring. The lesson is 45 minutes in duration. There are 22 students in the class.

TimeCaption
00:01:35What kind of guy is that?
00:01:49I will tell you that now, I will tell you that now.
00:02:01Lis- listen for a second.
00:02:12If you listen for a second, then I will tell you exactly. You guys see Ruud Gort, that is the name of this gentleman.
00:02:20He will be taping a complete lesson on video, as part of a study that is held in various countries. Yes, that is what those videotapes are used for.
00:02:40It is a study about math education in the Netherlands, compared to Australia and etc., etc.
00:02:48He thinks it is best, and the recording works best if you pretend he is not here, okay? So we are going to act normal, as usual. What?
00:03:00(inaudible)
00:03:03(inaudible)
00:03:04Aren't you? Or still just in time, just in time.
00:03:05You guys are so late!
00:03:10(inaudible) for the camera.
00:03:19Oh I see. You wanted to step into the picture very explicitly.
00:03:30Sir?
00:03:31I was just saying... I will briefly repeat it once more.
00:03:35That gentleman will be taping a complete lesson on video as part of an international study. That's why.
00:03:46If you guys could already take your homework out in front of you.
00:03:50And homework, according to the study calendar, was the last- the last part of the basic materials.
00:03:54[ Bell ]
00:04:02Sir!
00:04:03The very last part. Bram?
00:04:07I, uh, brought the wrong notebook with me.
00:04:10That, that is very clever. I wanted you to demonstrate later how you do those types of exercises.
00:04:18No! But I do have (inaudible).
00:04:25Then, what have you just been doing during Dalton hour?
00:04:31But that wasn't the homework assignment, was it?
00:04:35Marian, what is it?
00:04:36I don't understand 31.
00:04:37Yes, well first you are going to... let's have a quick look...
00:04:44Will you guys calm down a bit! Can you guys calm down a bit here?
00:04:49Yes, but (inaudible) isn't here yet.
00:04:51But you can still calm down a bit, right? That has nothing to do with it? I am sure he will arrive shortly. Keep that bunch quiet over there.
00:04:52Okay, I'll keep those little ones quiet.
00:04:56Very good.
00:05:06As usual you can first ask questions yourself about the homework, what didn't go well. I will have, uh, one of your fellow students explain it.
00:05:17And after that I will have a couple of questions myself about the calculations that you have learned in your homework. Marian?
00:05:27Which assignment?
00:05:28Thirty-seven.
00:05:29The very last one.
00:05:30Yes. (inaudible)
00:05:31The very last one, I'll keep that in mind.
00:05:34Twenty-eight C?
00:05:37Twenty-eight C. Oh that was last time's homework, that's the previous homework. You are very late with that, aren't you?
00:05:49Yes.
00:05:50Why don't you take care of that during a Dalton hour.
00:05:56Thirty-six.
00:06:00Do I understand it correctly that this is only about the last two assignments?
00:06:07:00]
00:06:26The last two assignments, Sam help me out here.
00:06:31Thirty-six?
00:06:32Thirty-six, we will start with that one. Copy the table and fill it in. I'll start off with that and then you can tell me what else I need to write down.
00:06:52What is it?
00:06:53Didn't I have to stay behind now?
00:06:55Can you guys just sit here and work? You can't just interrupt a class, can you?
00:07:12The intention is that this equation gets resolved.
00:07:21Right? So you have to put the right parts of this equation in the right place of this table.
00:07:27Sander! And as a suggestion- as a suggestion the factor X is put up front already. How can you get this equa- multiplication to resolve?
00:07:40The four X, uh, squared two divided by X (inaudible) four (inaudible).
00:07:49Write down what you think is the correct answer and check it right away. X times four X, is that four X squared, or not?
00:07:58Yes.
00:07:59Yes, then it is correct. Here you do the same. X times what?
00:08:06Twelve.
00:08:07Twelve. And then you can write the equations with brackets. Hans?
00:08:16Y equals X and between brackets four X plus twelve.
00:08:23Exactly right. We are going to do that again in question C. This was question B, right? We are going to do it one more time. Daan?
00:08:42We can fill in the terms of the equation in the correct places of the table. Daan? He wanted to put four X up front.
00:09:01Resolve the equation, complete it.
00:09:05Four X times- What makes four X squared?
00:09:10Four X times X.
00:09:12X. And four X times what makes 12 X?
00:09:19Plus three.
00:09:20Plus three. If you apply that, then you can write down-
00:09:27Four X and between brackets X plus three.
00:09:36You have to remember this carefully because this was a good exercise.
00:09:40Remember carefully, if you have to resolve this equation, you can make it into this equation or this one.
00:09:50They basically come down to the same thing, but the last one is better. And use that as a guideline.
00:09:58You have to keep as much as possible in front of- in front of those brackets.
00:10:06As much as possible. If you have to do this for a test, writing this equation between brackets,
00:10:15then I won't consider this completely wrong of course, because in essence it is a correct equation. But this one is better.
00:10:22So, this one will get you more points, than this one. Try to get as much out of it as possible.
00:10:30You can also say, if I resolved- because this is called "to resolve", if you write the equation with brackets as a multiplication-
00:10:42if I resolved then I always check if those two terms, that are written between brackets, still have a common divisor, a common factor.
00:10:55And then you come to the conclusion that there is still a common factor four in there, we have to take it out as well.
00:11:05That's the idea. Make sure you remember this.
00:11:09We are not going to do every assignment of question 37, because that one was also requested. Not all of them, but a couple of examples.
00:11:28I think that question B is actually a- a good example.
00:11:48Tim?
00:11:50Yes.
00:11:54Where do I have to fill in these two parts?
00:12:02Below the, uh...
00:12:04Why don't you- just point it out in your notebook, then I know- What, no tables? Wait a minute.
00:12:08No, I tried without any.
00:12:09What have you got?
00:12:14You have only the final results. Right?
00:12:19Yes.
00:12:21Did you do it yourself, without using a table?
00:12:24I did it with the help of (inaudible).
00:12:27Not with the help of the answer book, I hope?
00:12:29Some of them I did.
00:12:30Well, that's no use. That's the- the wrong attitude, Tim.
00:12:34If you say, I can't do it without a table that's not a disgrace. Most of us can't and that's fine with me. But then make the table!
00:12:49What do you learn if you copy it from the answer book?
00:12:52Not much.
00:12:53Well, you might as well say nothing at all. And your goal, I would hope, is that you learn something new.
00:13:01Table, participate, right now, in your notebook. Right away, do the table.
00:13:16Lisa, where do I fill this in?
00:13:20You didn't finish it you said, but that doesn't matter. We're making it right here and now. Where does it belong?
00:13:34Um, below the, below the multiplication, um, sign?
00:13:37Did you draw the table?
00:13:38Yes.
00:13:39Point it out to me where- no, no, no, no, no.
00:13:42Because that is part of a multiplication, in the equation it doesn't say that you have to multiply two X squared by something.
00:13:53Oh, no you need to write it here.
00:13:54There, yes. So the equation without brackets comes from these places in the table. Filled out.
00:14:06Furthermore the book suggests that you fill in minus two X over here.
00:14:16That was already printed, suggested. You only have to figure out this part. Lisa, please complete the multiplication correctly.
00:14:27Minus two X times what is minus two X squared?
00:14:33Um, I don't know.
00:14:38Where did the little squared come from, Lisa?
00:14:40Oh, times X.
00:14:42Times?
00:14:43X.
00:14:44X, that's correct. Minus two X times what? Makes minus 54 X?
00:14:57Twenty-seven? 27.
00:15:05Exactly right, minus two X times 27 is minus 54 X. No flaw in that argument. Correct? So what equation do you get with brackets?
00:15:17Minus two X, um, times X plus 27.
00:15:27This is how you score an A for your test. And all those- since naturally I can't guarantee anything,
00:15:37all those who looked at the answer book too often during homework won't be able to do this during a test.
00:15:48And they won't just score a C or C+, but a D or even an F.
00:15:56Because this is a subject in which you either perfectly understand what is going on, you kind of know what you are supposed to do,
00:16:03regardless a little calculation error or a sloppy error,
00:16:08or you don't understand the intention at all and then you can't do one single exercise.
00:16:19I want to do one more of 37. And then we are going to have a short quiz on this lesson. Well let us do the very last one.
00:16:36:00]
00:16:59This is printed in full. That is what we are trying to work towards.
00:17:04Well, it is in fact kind of a stupid remark, "that's what we are trying to work towards" because there is actually nothing printed.
00:17:10The only thing that is printed is that you have to make something with brackets. Pleun, tell me, tell me, tell me...
00:17:20Where does the minus three S squared come from in the table?
00:17:21Um. Um, in front it says three S...
00:17:29No, that is not my question, Pleun. This, where do I have to fill this in?
00:17:33Uh, underneath.
00:17:34Where?
00:17:35Uh, underneath.
00:17:37Yes there, that's right. And the plus nine S?
00:17:42Well, next to it.
00:17:43It goes next to it. You can leave out the "plus" or you can write it down there as well.
00:17:50Yes, now you have to solve the puzzle. I do want to end up with a "plus" here.
00:17:58Yes? Let's take a look. Suggest something.
00:18:03Um... in front three S.
00:18:05In front three S.
00:18:08And then an S at the top.
00:18:10And S over here. Correct, or not? Three S times S makes?
00:18:13Um... no, I mean negative S.
00:18:19Negative S. So, always check right away. As soon as you write something down, check it. And here?
00:18:28Um, three.
00:18:30Three?
00:18:31Yes, three.
00:18:32That's all?
00:18:36Yes, you can add the "plus", but it is not necessary. Okay, equation?
00:18:42That becomes three S and in between brackets minus S plus three.
00:18:54Perfect, completely correct, right. Marian?
00:18:59Where did you come up with three S and that minus?
00:19:06What you can do, what you can do is for yourself, on a scratch note, or on top, resolve this completely to a multiplication.
00:19:24Minus three S squared, what exactly does that mean? Minus three times...
00:19:31S.
00:19:32S, times-
00:19:34Squared.
00:19:35Yes, squared, but I want to resolve it completely to a multiplication.
00:19:39S times S.
00:19:44And nine S, completely resolve to a multiplication. Nine S is in fact...
00:19:53Nine times S.
00:19:54Nine times S. And the nine you can resolve even further. Write further as a multiplication.
00:20:02Three times (inaudible).
00:20:04Three times?
00:20:05Three times S.
00:20:06Three times S. And what do those two have in common?
00:20:23(inaudible) last times S (inaudible). (inaudible) last times S (inaudible).
00:20:30They both have a factor S in common. And what else?
00:20:38A factor...
00:20:41Three.
00:20:42Three. This has a three in it and this has a three in it. And that is the common part, which you can write down in front.
00:20:51Sir?
00:20:52You also see now what is left over.
00:20:58And that is written above here. Because here you only have a three left over. Right, so you can try to do this by heart.
00:21:09But if you can't do it, then take a piece of scratch paper and write it all out on it.
00:21:15I put, uh, the minus in front of the three S instead of the S.
00:21:19Yeah, there's no space for that.
00:21:21Okay, we will just do it, will just do it. That's this equation.
00:21:39This is how we started. You wanted to do this. What will the upper part look like, Freek?
00:21:53The S on top.
00:21:55This is correct, yes.
00:21:57And on the left, uh, the minus three.
00:22:00Here?
00:22:01Yes, (inaudible).
00:22:03What equation would you write down next?
00:22:06H is minus three S and then in brackets S minus three.
00:22:17Uh huh. Freek, let me tell you something, son. If you do this on a test, that is fine with me.
00:22:29The only reason why you actually shouldn't have done that in this particular exercise, is because that little "plus" sign is the only thing that was given in print.
00:22:40And this way you will not get this.
00:22:44I think personally, but that is my personal opinion, I think that this resolution is even- even better. But I would-
00:22:51But is it correct then?
00:22:52But I would, on a test, consider them both correct. I would not pre-print that information on the test.
00:23:02You see? So I think that is a good solution and this one too. Peter?
00:23:06But you have to end up with the highest number up front, in front, eh?
00:23:09As many as possible.
00:23:12Oh, as many numbers as possible or, letters and such?
00:23:15Yes. As many as possible. As long as you can still see a common factor here then you haven't taken out enough yet.
00:23:26Oh, I see.
00:23:42Um, I am going to ask you to do an assignment that none of you have done yet. Just do that one. Page 145. Assignment E.
00:24:00And just start, uh, first on E 12, start on E 12. Maximum five short minutes.
00:24:11(inaudible)?
00:24:12E 12. E 12, E 12 A, B, C. Maximum five short minutes.
00:24:22Then I will ask a couple of calculations, that way we can check if you can apply the trick.
00:24:34(inaudible)
00:24:35If you need a table, then you'll have to make one.
00:24:40If you are so good at this that you don't need a table, you may do that as well. But not with the answer book.
00:24:59Then I will just have a look at who is missing. Five, 13, 14, 16, 18, 20, 22. I am missing- what, four people? (inaudible) Seventeen, 18, 20.
00:25:19:00]
00:25:40What happened to Patty?
00:25:42Over here.
00:25:43You went and sat over there? Okay.
00:25:48:00]
00:26:37Were is Christianne? Is she ill?
00:26:43:00]
00:27:25Let me see, let me see. That is correct, very well.
00:27:37Sir? Sir? Is this a little plus sign? For if we put minus eight H over here this one over here is 24-
00:27:44Uh huh.
00:27:45Then again minus 24 H (inaudible) and then simply plus three?
00:27:51This is right this way, isn't it?
00:27:57Is it not working out? Let me see. Oh, that's going well, that's fine.
00:28:04Though you didn't copy exactly what was shown in the equation, right? There is a little sloppiness there.
00:28:14You had written down in the equation 18 X and?
00:28:17Yes. Oh, minus.
00:28:20Minus, you're missing the minus.
00:28:28This one you can already put in the right place.
00:28:32(inaudible)? Here?
00:28:35No, just in front.
00:28:38Here?
00:28:39Yes there. You have to- to- to remove that. Yes, like that. Now that 18 isn't correct any more, is it?
00:28:48No.
00:29:02What? What? Because this you don't know yet. What times three gives you this?
00:29:15That's right, like that.
00:29:24Without a table. Let's have a look. Yes, that's going fine, that's going fine.
00:29:38You should try to write an S differently than a five, don't you think?
00:29:43Is this, is this an S then?
00:29:44Yes, because I almost don't see a difference here. I am inclined to say it is 55.
00:29:49Okay.
00:29:50Try to differentiate them a bit. Yes?
00:29:55Sir, I just don't feel well.
00:29:59The second one.
00:30:00But I, I just don't feel well.
00:30:01What's the matter?
00:30:03I just don't feel well.
00:30:05Too sick to stay inside? Do you want to go home, is that what you mean?
00:30:09No, because this is the last hour.
00:30:14What do you want to do?
00:30:16Outside the classroom, I don't really know.
00:30:19Em...
00:30:20I am just very nauseous.
00:30:22All right. Just go together, to the bathroom, there you can drink a little water. The two of you go. Who should come along? Yes?
00:30:38Yes?
00:30:39With the other ones you could always fill in- there you could already do one-
00:30:45The last one you can fill in something else, right? You placed this correctly. This one, where can you put it as well?
00:30:54Here?
00:30:55Uh huh. And now you can start. Resolve this multiplication. Yes? And now you can start with the second part.
00:31:09Resolve that multiplication as well. That's incorrect, isn't it? Because then you get five.
00:31:21(inaudible)
00:31:22Yes, now it's still not right. Five times seven is not minus 37. Yes?
00:31:29And then, in addition to that, S times S squared. That's not S squared. That would be S cubed.
00:31:40That has to be S.
00:31:41Yes, look at that, three mistakes in one cell.
00:31:46But, fine, now it's complete and now you can write the correct equation down. Five minutes have been up for a long time.
00:31:52Shoot, I'm only at three.
00:31:53Well, you didn't have to finish it completely. The idea is that you know how this works.
00:32:02Take your answer book in front of you then we can check if you did it right. Just whatever you, whatever you finished, you check.
00:32:17Give me a signal if you came up with something different.
00:32:23:00]
00:32:44Bram.
00:32:45Look at this one, it says minus, no, so that becomes three T. Minus three T, minus two squared.
00:32:52Yes, yes?
00:32:53B-6-
00:32:54And then...
00:32:58B-6. And then here I have, since minus three T- you've got to have a T here, in any case, and over there as well.
00:33:07Yes, well, your resolution is correct; your resolution is also a good example of what I wrote on the center board. I just told you: you could have gotten more out of it.
00:33:18Because those two- do those two still have anything in common?
00:33:22Oh, I could have made this three T.
00:33:25Yes. Yes, you are better off making a new table because you are crossing out so much now.
00:33:47So, here just a minus?
00:33:49Yes, but you also need to add a number, right? You will never multiply with just signs, will you? Yes, like that. Yes, that's correct.
00:34:05There.
00:34:06Yes, which resolution are you doing in that case?
00:34:10And now here- here you took out minus T. Where is-
00:34:14It is now over here.
00:34:15It is now over here. While in the assignment it is suggested that you end up with a plus. You could have made sure of that by taking out the minus.
00:34:27Yes, then you have to remove it there.
00:34:33Over here nothing.
00:34:34And remove that one as well-
00:34:35So then this becomes-
00:34:36And now you can make the correct equation.
00:34:43Gives minus three T, one T.
00:34:46Yes. Yes?
00:34:50So, your equation wasn't wrong but you could have done it a little bit better.
00:35:04Which one didn't work?
00:35:07Well, that's a good example of what I wrote on the center board. Your resolution is correct, but you could have done it better.
00:35:14The seven P and the 21, do they have anything in common?
00:35:19Um. Yes.
00:35:20What is it?
00:35:21Um, let me see. Ah, the seven itself.
00:35:26So the seven you could have also taken it to the front. Yes? And it has an effect on the top and that way it'll be all right.
00:35:33So your equation isn't wrong but not exactly correct either.
00:35:40Let me put it this way, Lisa, if I would give, for example, four points for this assignment on a test, then you would still have gotten three.
00:35:41Oh, right.
00:35:48Because the resolution is fine, but it could have been a bit better. Someone who takes out the seven just deserves that extra little point.
00:35:56Yes. Can I take your eraser?
00:36:03Minus three T and then why is this here-
00:36:06Wait a second, wait a second. Um, for those of you who did it right and finished the checking by now, you can continue working.
00:36:18Homework for next time is given in your study calendar.
00:36:22G and P.
00:36:23The G and the P, but you will never be able to finish it all, because that would be four pages.
00:36:27The agreement is always at least two pages of homework. You can choose a few of the G assignments and a few of the P assignments,
00:36:37because you guys have to know the P section as well. Okay?
00:36:42Here it says minus three T. Do you have to fill that in over here?
00:36:46Wait a second, wait a second. Assignment D. Let me see... you can fill this in the right place, which is not the problem.
00:36:53Yes. And then-
00:36:54And now you have to solve the puzzle.
00:36:55Yes.
00:36:56And you solved the puzzle. This is completely correct. This is a good example of what I did earlier on the middle of the board. Your equation is correct.
00:37:06But you could have done-
00:37:07Oh-
00:37:08You could have done it better. Because do those two still have anything in common?
00:37:10Oh, yes. Well, yes.
00:37:12Yes.
00:37:13The factor.
00:37:14Which one?
00:37:15Three.
00:37:16You could have taken three out as well.
00:37:17Oh, right.
00:37:18Furthermore, it says here, not that that's a very big deal, here it said a plus and you wrote a minus.
00:37:25Oh yeah, that's right.
00:37:26So, if you also put the minus in front, you better make a new table-
00:37:30Oh right.
00:37:31That way you won't take out a T but?
00:37:36Here you don't write a T but?
00:37:38Oh, but minus three T?
00:37:39Yes, and if you complete it, then it will work itself out. Just make a new table, okay?
00:37:45This one, wait a minute over here. I had, this one is here, and then I had this one-
00:37:54Yes, that is the same story, actually. You have two H and a six. Do these two still have anything in common?
00:38:03Yes.
00:38:04What?
00:38:05Yes, you can divide them again by- oh no-
00:38:08Yes, though.
00:38:09Yes that, by three uh...
00:38:11No, two H and six you can both be divide by?
00:38:14Two.
00:38:15Two. And this two you could have taken out as well.
00:38:16Oh.
00:38:19You are better off in making a new table, otherwise you may not understand it anymore.
00:38:22And you don't need to write the one down, do you, at uh...
00:38:23No, you don't have to write it down, but you do have to write the first part of the equation down.
00:38:29Oh.
00:38:30That's part of it.
00:38:31Okay.
00:38:32It is a small thing, but you have to do it. Okay? Just make a new table,
00:38:35but then don't write four H but eight, minus eight H, that will make it correct.
00:38:48Sir, I don't get- do I need to finish C?
00:38:49Yes.
00:38:50Huh?
00:38:51I understand the equation, but I don't know how to explain it.
00:38:52Why?
00:38:53I do understand that I have to end up with six plus nine and one, (inaudible).
00:39:00Just look carefully. Um, do you still remember that Australian gentleman?
00:39:01Try to find the patterns, patterns. How can you determine the little blocks from the first figure? That can be done in many ways,
00:39:15One could say I do three times four. Or uh, sorry three times three. Three times four, three times five. Etcetera.
00:39:22But you have to make a combination with that number.
00:39:27The other thing you can do is, let's say, I am going to take six cells plus one times three. Here, I will take the same six cells plus two times three.
00:39:43Oh, right.
00:39:46And over here six cells plus three times three. Etc. Then you can use this equation.
00:39:52Okay.
00:39:53It depends upon what pattern you see, because you may see a slightly different pattern there then Daan does.
00:39:58Which would mean that if you have to make your own equation, then you could find the equation in a slightly different form than Daan.
00:40:05But they can both still be correct.
00:40:07Okay.
00:40:08But you have to find the connection with the number that is given with it. That's your aim.
00:40:14If you succeed with that then you can immediately calculate the amount for every given number.
00:40:22But if all you see is this pattern: 9, 12, 15, 18, etc., can you tell immediately? Uh, what is in number 30?
00:40:32Ninety-six.
00:40:33Without writing down the whole list. Right, so-
00:40:37Ninety-six (inaudible) should be correct.
00:40:39Yes, maybe, but how do you explain that?
00:40:41Well, I did it like this, I thought three of these little blocks make one row, that left me with two rows, that means six.
00:40:48And then I had 30 left; 30 times three plus six.
00:40:52So you are actually working with the equation that is shown there. Did you cheat a little? Or did you find it yourself?
00:41:00Yes, I thought it sounded logical, actually.
00:41:02Yes, well, that is in fact the trick of these types of exercises. Can you recognize a pattern and then try to involve that number in it as well. Right?
00:41:13Look, if all you say is three are added each time.
00:41:17So you have to keep adding until you're there?
00:41:18That will get you there as well. Sure, that will get you there as well. That way you can say three are added each time.
00:41:23I just asked for number 30. This is number one.
00:41:28But you do have to indicate the step. After number 30 there are another 29 left. And if you argue from there on you will figure it out as well.
00:41:37Sir!
00:41:38Yes? Try to keep making a connection with the numbers up above.
00:41:45You will be known all over the whole world, right, that this is your math notebook. They are going to be looking at it in Hong Kong.
00:41:54Then they will know right away that they may take a piece of paper of mine.
00:42:01Tell me, what did you want to ask?
00:42:04The T. Why is the T R?
00:42:07Yes?
00:42:09I just see- how, how, how do you have to do that?
00:42:12Can you do T one, T two, T three, T four, T five, T 20. Here, you had to, to demonstrate two of them-
00:42:20Yes I've got those.
00:42:21Oh, you've got those? So at T five you calculate 10 plus four, times three.
00:42:27Yes.
00:42:28What has that got to do with this five?
00:42:33What is the relationship between the number of the term and your equation?
00:42:37It is one less each time. This one is...
00:42:40Is that correct here?
00:42:41Yes.
00:42:42At T 20?
00:42:43Nineteen.
00:42:44Why don't you go ahead and apply that.
00:42:45Oh right then that makes N minus one.
00:42:47If you write nothing in between there then you mean times, right? You do have to write something in between there. Yes, like that. Well, perfect isn't it?
00:42:55But how does it work here? In the row five, seven, nine, 11, 13 is T one five. Then this must be T two, T three, T four, T five-
00:43:02Yes.
00:43:03The difference between two terms is the same each time. We call a series like that an arithmetical series.
00:43:08Yes.
00:43:09Each number in this series is T one plus N, minus one.
00:43:15Times two.
00:43:16Yes.
00:43:17It is almost the same as the one you got here, right?
00:43:22But then you explain why the equation for the arithmetical series can be written as T N... T and...
00:43:33I don't understand that one.
00:43:34Do you recognize the part that is on the board.
00:43:38Yes.
00:43:39In this, in this equation?
00:43:40Yes. Those brackets.
00:43:46This is a multiplication. Can't you write that one without brackets?
00:43:55Go ahead and try, let's say try to get rid of those brackets entirely.
00:44:04X- But may I now write this one here as well?
00:44:09Yes, since the sequence is irrelevant in a multiplication. Sure, go ahead.
00:44:17Don't write two to the power of N, Pleun. You haven't gotten there yet, have you?
00:44:23It wasn't N squared either, was it? What is two times N?
00:44:29Two N.
00:44:30Not two to the power of N, but just two N. That's right.
00:44:47Where did you get this three?
00:44:48Yes, well just copy the equation again. What, what equation do you end up with?
00:44:53It, it is this one, right? T N- yes, write it down, T N equals... equals?
00:45:04T one-
00:45:06One plus whatever is in your table.
00:45:07Two N minus two. No without "times two" then.
00:45:12No, no, no this is correct. Now you can figure out what T one was. What was T one? In this- this row?
00:45:27Five.
00:45:29Okay, fill it in. Write the equation down again.
00:45:38And try to shorten it, Bram.
00:45:46I don't get B three. What are you supposed to do here, do you have to simply-
00:45:49Yes, fill in the equation.
00:45:50Do you simply have to do one plus three?
00:45:51Yes, this means that you fill in one for N and that means that you have to fill in twenty for N.
00:45:59So you have to do twenty plus three?
00:46:02Yes, so you only have to fill it in into the equation.
00:46:04Twenty times 20, equals 20 squared.
00:46:05Huh?
00:46:06And so here you put 20 squared.
00:46:08Yes, and then you have to calculate it further. Yes?
00:46:15Isn't it better here to calculate minus four T plus three?
00:46:17Yes, yes, yes, your table is not completely correct. The table is not really correct because minus four T times two-
00:46:26Oh, no that's not possible, is it?
00:46:27You will never get eight T squared out of that.
00:46:29Minus two, right?
00:46:31That for sure. Wait a second, it still doesn't make sense. Minus four T times minus two, if you don't look at this.
00:46:41If you calculate this multiplication what do you get then?
00:46:45Um, eight T.
00:46:47And here, you have eight T squared. That's correct. Just-
00:46:52Yes, now it should work.
00:46:53Just continue changing the rest.
00:46:55What?
00:46:56Just change the rest of your equation. Yes, perfect. Just a minor error, with big consequences.
00:47:09:00]
00:47:28Well, it is almost time. You guys know- I didn't say that, Freek! You know what you have to do for tomorrow.
00:47:37At least two pages, more is optional, more is optional.
00:47:44G and P.
00:47:57Can I reserve the fifth for tomorrow?
00:48:07Tomorrow the fif- Yes, I think that will work out. You just have to write it down in the small folder, this, uh, that little red folder.
00:48:24Hey, Tim, that doesn't lead to anything, right? Copying the answer book.
00:48:34You will flunk the test that way, really. But I am actually happy that you admit it now.
00:48:47Yes, but (inaudible).
00:48:52Well, it is quite simple, if you only use equations- and you may do it without a table, then of course you can copy it from the answer book.
00:48:54[ Bell ]