# NL3 SURFACE AREA

This eighth grade mathematics lesson involves students working on a textbook chapter about factoring. The students work either independently or with others in small groups, with occasional public explanations by the teacher. The lesson is 45 minutes in duration. There are 20 students in the class.

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00:00:00[ Bell ]
00:00:15But I looked in the answer booklet and it was wrong.
00:00:18Was the answer booklet wrong or were you wrong?
00:00:20I was wrong.
00:00:21Sir, I don't understand any of this chapter.
00:00:22But you told me it was correct!
00:00:24That's nice.
00:00:25Yes.
00:00:26That gives me something to do.
00:00:29When is little Pete coming?
00:00:31Little Pete? He'll be coming up shortly.
00:00:32I am at 28 but there's a few things I don't understand.
00:00:35That's possible. Um, I think I am still missing a few.
00:00:45I think so.
00:00:46Sir?
00:00:47Good morning! Who isn't coming?
00:00:50Laura.
00:00:51Why not?
00:00:52Well, she's at a funeral.
00:00:53Hm.
00:00:54Sir, what is this? For photo or video?
00:00:56It's called video.
00:00:58Sir, I forgot my folder.
00:01:00Do you have any loose sheets of paper?
00:01:01Yes, I have those in my backpack.
00:01:03That I do have.
00:01:04Yes, okay. Do you still remember where you had difficulties?
00:01:06Uh, no.
00:01:07Well, just have a quick look. Don't worry. Um, as you guys can see, uh, there is a camera here. That should have actually been announced in advance.
00:01:16But it doesn't make any difference otherwise, just pretend it's not here.
00:01:19Why is it here?
00:01:21Uh, I will explain, uh, that to you next time. Okay?
00:01:24What is it for, sir?
00:01:26Uh, to shoot a film.
00:01:27To shoot a film?
00:01:28Yes. Next time I will explain the purpose in more detail.
00:01:32Yes, that as well. So, uh, just grab your book and grab your notebook as I think some people may need this.
00:01:50You're still going to, uh, you're still going to, uh, do Pythagoras?
00:01:52What?
00:01:53Are you still going to do Pythagoras, or chapter five?
00:01:56Oh, I'll do uh...
00:02:05(inaudible)?
00:02:06I would prefer that.
00:02:08Yes, okay.
00:02:09(inaudible)
00:02:15What did you say?
00:02:16Can I fetch my books for a second?
00:02:17Yes, of course. What are you doing here? You guys have class.
00:02:20Yes.
00:02:21Where do you guys have class?
00:02:22Uh, we don't know.
00:02:24Hurry up then.
00:02:29Bye ladies! Those cases from one A, or one D, whatever it is.
00:02:38Sir, you really have to explain this!
00:02:40Yes, I know.
00:02:41How are we supposed to do that?
00:02:43I don't understand a thing. I am at three. I didn't understand it at all!
00:02:49Ha! Excuses!
00:02:51Yes, excuses! There are more of us who don't understand it!
00:02:54This is it, I think.
00:02:57No, I don't understand it.
00:02:58Very well.
00:02:59I (inaudible) understand it. Really.
00:03:00Yes, all right.
00:03:04(inaudible) add it up because I don't really understand it.
00:03:08In a moment I will explain something about calculating variables. Uh, several people are still on assignment three, four or five,
00:03:18uh, while some haven't even reached one yet.
00:03:21Um, at the end of this week, the whole chapter has to be finished. Good morning, Erik!
00:03:28Um, those people who are at assignment one, have not been doing anything last week. That is my conclusion.
00:03:37So Erik, uh, you will have to work hard to catch up.
00:03:42Also if you cry, "I don't understand, don't understand", try to keep working nonetheless so that you will, uh-
00:03:46Because it's quite possible that you do not understand problem three, but suddenly see the light at problem five,
00:03:51and find yourself right back on track. Um, you didn't understand three. You-
00:03:57I didn't bring my notebook.
00:03:59That is not too smart. Can you get some paper?
00:04:01Can I get some paper?
00:04:02Yes, there is some paper in the folder over here. Do you know where you were?
00:04:07Yes, at 16.
00:04:08Then afterwards you just need to copy that into your notebook. Yes?
00:04:11Yes, I don't understand assignment 15.
00:04:13Assignment 15.
00:04:15I don't have my notebook with me either.
00:04:16I have a piece of paper for you.
00:04:17This is going great, you guys!
00:04:18Yes.
00:04:19Will you make sure to put it in your notebook?
00:04:21Yes.
00:04:22Um, very well. We are just going to start. I will come by several people and then I will, uh, for everybody-
00:04:27He's copying it.
00:04:28Yes, but that is his choice.
00:04:31That is his responsibility. You have the answer booklet.
00:04:36(inaudible)
00:04:37You have to get to work now. That's a different thing. And, yes, right now you are calculating variables aren't you?
00:04:38That's right.
00:04:44So, for example, with three, E is three E plus seven E.
00:04:49Yes, if you add that, then the outcome is-
00:04:51How many- how many E's do you have?
00:04:53Ten E altogether. That is ten E squared.
00:04:54No, why squared?
00:04:56Yes, because you have two E's.
00:04:58How much are three E's plus seven E's?
00:05:01Ten E's.
00:05:03Period. Only if you'd multiply it then it'll get an E squared.
00:05:08Oh...
00:05:10So, two E times three E? Two times three is?
00:05:13Two times three is six.
00:05:14And E times E, that is the E squared.
00:05:16Yes, but still, here-
00:05:17Yes, but you don't seem to have any E squared whatsoever.
00:05:19No, but here.
00:05:20Yes?
00:05:21No, but if this here is- you have to take the same ones. I multiplied all of them but I still ended up with the same thing. Just 11 P.
00:05:29Uh-
00:05:30But you are not allowed to multiply those with each other, as stated somewhere over here, look. Two different letters you cannot, uh-
00:05:34No, that is correct.
00:05:35Yes.
00:05:36L equals 11 P and always leads to the same solution. Well, let's see if he is right- by filling in P equals one, P equals six,
00:05:42and, and P equals 10 in both equations.
00:05:46So in this equation you have to fill in P equals one.
00:05:50Yes.
00:05:51Yes? What is the solution to this?
00:05:53Eleven times one. Eleven.
00:05:55Yes. And what is the solution to this?
00:05:57Also 11.
00:05:58Yes. Is it possible that they could be the same?
00:06:00Yes.
00:06:01It is possible, very good. So I will fill in P equals six.
00:06:03Is 66.
00:06:05And over here?
00:06:06Sixty-six.
00:06:07Yes. And now fill it in for real. Three times six is?
00:06:09Three times six is uh, 18. Six times eight is 48- oh, no, that is not correct.
00:06:14Eight plus 18 is? Twenty-six.
00:06:16Yes.
00:06:17Well, that is something completely different.
00:06:18Oh!
00:06:18No.
00:06:19Could this and that be the same then?
00:06:24Because P equals 10.
00:06:26Well, 110 and 80 plus 30, that one does work out fine.
00:06:29Yes?
00:06:30Yes.
00:06:31What is three times 10?
00:06:32I have that one- three times 10? Thirty.
00:06:36And eight plus 30?
00:06:38Eight plus 30 is 38. I need to multiply eight by 10 as well, don't I? Oh, no. Now I'm lost.
00:06:45Well, yes, the last one you did was correct. What's eight times- what is eight plus 30?
00:06:50Eight plus 30? Thirty-eight!
00:06:51That is just 38. And 11 times 10 is 110.
00:06:56Oh, like that.
00:06:57Beware, that's simply 110, right? For P you just fill in 10, not 11 P times 10.
00:07:02Oh.
00:07:04Yes?
00:07:04Yes.
00:07:05You have to fill in something at this spot.
00:07:07Yes.
00:07:08That is what it is about.
00:07:10(inaudible) make over again.
00:07:13Which one?
00:07:15Do I have to make some calculations- or, uh, resolve this I mean? Or do I just have to (inaudible).
00:07:18How much are six A's plus five A's?
00:07:20Eleven A's. (inaudible)
00:07:24And two B plus three C, can you add anything up here?
00:07:27No, it just remains as it is.
00:07:28Exactly. Are you able to proceed now? Where are you at?
00:07:32I am now at H because it is- uh, how are you supposed to- it's not possible because there is no E written at the end.
00:07:41Not over here, but in the other one there is.
00:07:43There is, I see. So this is six.
00:07:46Uh, huh.
00:07:48So what are you supposed to do with that? Do you just have to (inaudible)?
00:07:51How many F's do you have here?
00:07:52Huh?
00:07:53How many F's do you have here?
00:07:55Three.
00:07:56And here?
00:07:57One, uh, three.
00:07:58So what's the total?
00:07:59Nine.
00:08:01No. Here you have three. Three F's plus three F's is?
00:08:05Six. Eleven F's. Oh no, here it says minus.
00:08:09Therefore? You're left with? Six minus five F's equals?
00:08:16You have to see which numbers have F's in front of them. Over here is- I mean behind them- here is an F, here, and there.
00:08:21Yes.
00:08:22Over here we have three and over here we have three as well, so that is six, minus five equals one F.
00:08:24So one F is clear. And then one F minus three.
00:08:29F minus three.
00:08:31Okay.
00:08:32All right?
00:08:33That one is clear? Can you move along?
00:08:36Yes.
00:08:37Okay.
00:08:40Let's have a look. You are succeeding? With that table?
00:08:45This one. If I am correct, it should be correct.
00:08:48Well, yes, if you are correct then it should be correct, that's-
00:08:51Yes, okay, but-
00:08:52But do you understand what you are doing?
00:08:53Yes.
00:08:55At least you are caught up. And you are not caught up, so you better continue working.
00:08:59Yes.
00:09:04Are you just starting now? Or are you at, uh, five?
00:09:07But I don't understand.
00:09:08Which one don't you understand?
00:09:10Problem D. Twelve Y minus Y, is that 12 or is it (inaudible)?
00:09:16How many Y's do you have?
00:09:18It is minus Y, isn't it- 11 Y?
00:09:22Yes, I know that much too. But how did she get it? How many Y's did you get over here?
00:09:27One.
00:09:29No, how many do you have here? The first section?
00:09:34Twelve.
00:09:36Give me a break and keep working, please.
00:09:38Twelve.
00:09:39Twelve. How many do you have here? How many should be subtracted? One Y.
00:09:44Yes, or two.
00:09:45No, because it says minus Y here, so that means minus one Y.
00:09:49Oh.
00:09:51If I say, take X, then that means take one X. And here too, minus Y means minus one Y. So 12 minus one equals 11, so you have 11 Y's.
00:10:04How are you supposed to know that because Y could also be two.
00:10:07No, then you fill in a two for Y. That is something else because then you will fill in a number for Y.
00:10:13Yes.
00:10:16How many Y's do you have here?
00:10:17One.
00:10:18No.
00:10:19Twelve.
00:10:20Twelve. How many do you take away?
00:10:23One.
00:10:24So how many will you have left?
00:10:26Eleven.
00:10:27Eleven. Eleven Y are left. It is not exactly, uh, what number the Y is because it's only afterwards that you'll fill something in for Y.
00:10:38Yes, but if you start filling in something for Y then it doesn't make sense any more.
00:10:41Yes, it does. Just cal- calculate it. Why don't you fill in for, uh, uh-
00:10:46(inaudible)
00:10:46No, because you have 11 Y left over.
00:10:49Suppose for example you fill in three for Y?
00:10:53Thirty-six.
00:10:54Minus?
00:10:55Three, that's-
00:10:57Thirty-three. You are left with 11 Y and that times three is indeed 33. Do you understand it?
00:11:03Yes.
00:11:04Yes? Very well.
00:11:06Teacher?
00:11:07Are the diagrams coming along?
00:11:09This one?
00:11:10Yes.
00:11:16Uh huh.
00:11:18And we're still clueless.
00:11:20Which eight?
00:11:21This one.
00:11:24Did you make a drawing of this?
00:11:25Yes.
00:11:26Can you show me?
00:11:27But I (inaudible) because I copied this.
00:11:30Yes. That's no big deal.
00:11:31Yes, it is.
00:11:32Um, what is the surface area of the top part?
00:11:39Fifty centimeters?
00:11:40Do you have a pencil? If you have a look here. Here you have the 50 and there the 15.
00:11:48Oh, yes. You have to do 50 times 15.
00:11:50So here- this is 750 square centimeters. What is the surface area of this here?
00:12:01How long is this section?
00:12:03Um, 750 centimeters.
00:12:06No, that is the surface area.
00:12:09Well, um-
00:12:11What is the length of this here?
00:12:12Fifty centimeters.
00:12:13This is also 50. What is the height of this?
00:12:17Fifteen.
00:12:18This one you don't know yet, correct? Of this whole area-
00:12:20Oh, yes.
00:12:22You don't know that yet, that is just H. Now how do you determine the surface area? You do 50 times H, length times width.
00:12:30Yes.
00:12:31Which is 50 times the H. Yes?
00:12:34Yes.
00:12:37Just like with those diagrams you're using over here, you actually just calculate a surface area. Fifty times 15 and 50 times H.
00:12:46So the surface area is 50 times H?
00:12:49Plus 750.
00:12:53Okay.
00:12:54Yes? And then over here you have three equations- or, uh, four equations and two out of these four are correct.
00:13:01You need to figure out which ones. Just now you wrote down, A equals C. I know this is correct, but in a minute I would like you to tell me why. Okay?
00:13:15Could you please throw a window open?
00:13:20Are you able to sniff your way through it?
00:13:23Huh?
00:13:24Are you able to sniff your way through it? Or are you doing okay?
00:13:27Oh, oh, yes, it is not too bad.
00:13:29Sir, question 18 B.
00:13:32Yes, I was just entertaining myself.
00:13:36I had time to finish my homework and (inaudible).
00:13:38But what is it?
00:13:39To see if I have too much homework. But that is not what you asked. Look, this is question 18 E. You have to take similar terms together.
00:13:50Yes, what did you get in, uh, the first part?
00:13:53Huh? Here. This one here. First you have to calculate this.
00:13:59Yes.
00:14:00Then this, I already did that. Seventy times 50 equals 3,500. Then 60 times 120 equals 7,200.
00:14:05Yes.
00:14:06And then divide-
00:14:07And then here you have something written here.
00:14:08Yes-
00:14:09Uh.
00:14:10That is something like- uh, then you had to write this one- no, write it without brackets, this one.
00:14:13Right.
00:14:15And then this one is 3,500 plus 120 and then say 20 times 60 and 120 time B, say-
00:14:21Exactly, so, uh-
00:14:23And one 120 times 60 is 7200.
00:14:26Let me check, here you have 60 times this 20 is 7200. That is correct. And you have 120 times minus B.
00:14:36Yes.
00:14:37How much is 120 times minus B?
00:14:40Minus B. Yes- or uh-
00:14:42One hundred twenty- minus 120 B.
00:14:43Yes, and do you have to write that down here as well?
00:14:47Whereas here you write 120.
00:14:49Over here 20? One hundred twenty?
00:14:50No, what is this 120 about?
00:14:53That relates to uh, this 3,500 plus 120.
00:15:01But you have to multiply the 120 with this. So you can- you cannot just add this together.
00:15:06So this 120 over here doesn't make much sense. For here you calculated something. Sixty times 120.
00:15:15Is 500 plus 7200 and then minus 120 B.
00:15:19Exactly. So the B has to be taken away over here.
00:15:21Plus or times?
00:15:22What does it say? Minus.
00:15:24Yes, but-
00:15:26So minus 120 B. Yes?
00:15:28Yes, okay.
00:15:29Fifteen didn't work?
00:15:30Huh? No, it did work. I just didn't come around to it yet. I still had a question about this. I'll make it in a second.
00:15:35Okay, yes.
00:15:36Are you actually wearing a microphone?
00:15:37Yes?
00:15:40Could you step over here, oops, I don't understand half of this. I understand A, though. Yes, I don't know.
00:15:53Take a moment to draw it.
00:15:55This?
00:15:56Yes. Just, uh, the- no, you've got it already, it's already here, the multiplication table.
00:16:02What's stopping you from filling it in? Or how much is three times two D?
00:16:05Six D.
00:16:06Yes, and you can fill in the second one as well.
00:16:09Sir, at 20 you just have to add, uh...?
00:16:11With?
00:16:13At 20, don't you simply have to do, uh, minus 50 minus 1,540?
00:16:21Yes.
00:16:24Kind of a dumb question, really.
00:16:26Yes, but we need those too.
00:16:32Those have to be calculated just as well. Is it coming along?
00:16:38I don't understand 15.
00:16:39Fifteen? More people have a problem with 15. I will circulate for that one shortly. Or actually explain it on the blackboard in a minute.
00:16:46Can you write them down more briefly?
00:16:47Yes.
00:16:48Okay.
00:16:53Where are you uh- oh, here.
00:16:57What? Eight. Not far enough but further than some of the others. Try to catch up. Can you do that?
00:17:06Yes.
00:17:08I am tired.
00:17:09That is possible.
00:17:10Why wouldn't it be possible?
00:17:12Did you succeed with 15?
00:17:13Uh, no.
00:17:14You also don't have a notebook with you?
00:17:15No.
00:17:16Next time please report that beforehand, not afterwards. Just go ahead and do 16 together. Check it out together.
00:17:23And then in a minute you will also- did you succeed with 15?
00:17:26No, we didn't do-
00:17:27Did 15 work out?
00:17:28I didn't do that one.
00:17:30Very well, then we'll do that one on the blackboard in a minute. Okay?
00:17:33I don't understand this at all. Is, uh, yes-
00:17:35Just, uh, yes-
00:17:36the circumference of-
00:17:37One of these sides, this one, is H.
00:17:39Yes.
00:17:41That is the surface area of this small section: length times width is five times that H. Five H. The surface area of this whole square, how long is this section?
00:17:53Five.
00:17:54And this?
00:17:55Five.
00:17:56So what is the surface area?
00:17:58Five squared.
00:17:59Right.
00:18:00Yes, but isn't all of this part of it as well?
00:18:03And you have four times five times the H. Four sections of five multiplied by H.
00:18:08Yes.
00:18:09And you have to take the sum of all that. That is the surface area, and the circumference is H plus H plus five plus H plus H plus five.
00:18:18So do I need to add them all up?
00:18:21Yes. Yes?
00:18:23Yes, but I don't understand the circumference- uh, the surface area, do you have to- this must be, uh, five squared.
00:18:30Yes.
00:18:31And then afterwards you still have to write down five, um, times five, five times H.
00:18:36Plus five times H, plus five times H, plus five times H, plus five times H.
00:18:40Or can I do four times... H as well?
00:18:47Uh, five times H and do that four times. Four multiplied by five times H.
00:18:54Oh, right.
00:18:55This is 25. You know that one. And this is five H.
00:19:01Yes.
00:19:02And then you have these four pieces of five H.
00:19:05Twenty H.
00:19:07Then it becomes four times H. Four times five times H.
00:19:09Four times- yes. Yes?
00:19:13Okay.
00:19:14Twenty H.
00:19:15Sir, I don't understand it.
00:19:17How are you supposed to do this then? For example: Q is two B-
00:19:21Plus three C, can you do anything with that?
00:19:23Yes, I think- I don't know.
00:19:26I can't do anything with it.
00:19:27No?
00:19:28Those are two different letters. So can you do anything with it?
00:19:31No.
00:19:32Exactly.
00:19:33This will remain the same then. Then at C. What are you supposed to do here? Only minus?
00:19:37Yes.
00:19:39So you do eight G minus six G?
00:19:41Yes.
00:19:42Uh, what do you call those things? Is there a two G?
00:19:45Sure.
00:19:46Oh, well that is an easy one.
00:19:47Yes? Very well, um, have a look ahead at assignment 15. Um, almost- not everybody is there yet, I believe. But we'll get there.
00:20:00(inaudible)
00:20:01Which one?
00:20:02(inaudible)
00:20:06For Dalton? Um, yes, I think so, but I have a lot more folks. I will have to look and see how many reservations I have.
00:20:14Yes, we too.
00:20:17Otherwise I will get in an argument with class two B because they all want to reserve as well.
00:20:21Yes, but we are not two B.
00:20:24Yes, but that is my mentor class.
00:20:26Yes, but you cannot play favorites?
00:20:28No, you are not allowed to play favorites, but I'm doing it anyway.
00:20:31Well, that is not allowed.
00:20:32Well, sir, that is your problem, not ours.
00:20:35Uh, that depends. Um, take a look at 15. Um, what are you supposed to do?
00:20:43I don't know.
00:20:44What are you supposed to do at 15? How would you start? Yes?
00:20:48Draw an axis system.
00:20:51Draw an axis system.
00:20:53The ones of A, B and C.
00:20:55And you will use the equations of A, B and C- please look for a moment, exercise 15. Um, drawing an axis system.
00:21:02From how far to how far does that axis system need to run?
00:21:10The X-axis has to go from minus six to eight.
00:21:11From minus six through eight. Well, that's something we can picture. Minus six, huh, huh, huh, minus four, minus two.
00:21:21Over here somewhere a zero, two, four, six and eight. Very well, the Y-axis, do you know anything about that?
00:21:31No.
00:21:34You don't know that yet. Um, what should you do, though? You have to plot those three equations. How do you plot an equation? How do you start?
00:21:49Just imagine something.
00:21:51Um, a line like this and a line like that?
00:21:53Yes, that is the axis system. How are you going to plot the equation itself? Marjolein?
00:22:02The lines in there.
00:22:03Yes, the lines in there. But how will you get those lines? Erik?
00:22:08I don't know.
00:22:09You don't know?
00:22:11By calculating those equations.
00:22:12By calculating those equations. You start by making a table. So the first thing you want to do when you plot an equation, is definitely making a table.
00:22:26The table A, if you fill in the X's and calculate the Y's, which numbers do you need to fill in for that? Erik?
00:22:37The ones that are shown in the graph, uh, uh, the equations.
00:22:41Go ahead and do it. What numbers are you going to fill in for the X?
00:22:46Uh, I don't know. How are you supposed to know that yet?
00:22:53No, there is indeed no way you could know that yet. Therefore you may fill something in at random. Go ahead and pick a number.
00:23:00One.
00:23:03One. Very well, if you fill in one, what is the outcome? I will fill in one for the X.
00:23:10Um, that will be, um, one plus four equals five. And then times three.
00:23:19Exactly.
00:23:20Is 15.
00:23:22So to: "X is one" belongs "Y is 15". If you fill in a one for X, you have to calculate it, one plus four so in between brackets it becomes five.
00:23:41Three times five equals 15. You can obviously do that with more numbers. Which numbers can you do that with? Just name one. Marjolein?
00:23:50Three.
00:23:51Three, for example. What is the outcome then?
00:23:57Seven.
00:24:00Three plus four is indeed seven, and then?
00:24:03Twenty-one.
00:24:04Twenty-one, yes. You can do that with many other numbers. I'll just do it really quickly.
00:24:10You guys may, uh, do a bunch. You can do it all from minus six up till eight. So, what is the outcome at minus six? Also minus six. Why?
00:24:22Minus six plus four is?
00:24:25Minus two.
00:24:26Three times minus two.
00:24:27That is minus six.
00:24:28Minus six. And I will also just fill in eight.
00:24:34Thirty-six.
00:24:35Why would I choose minus six and eight?
00:24:39They are, uh, (inaudible).
00:24:40Minus six is at the beginning and eight at the end.
00:24:43Precisely. So it is not exactly a coincidence. We also need to have a few points in between. What is the outcome at eight?
00:24:50Thirty-six.
00:24:52Because eight plus four is 12, three times the 12 is 36. Very well, now you fill this in.
00:25:00It appears something will show up between minus 10 and 40. We can draw the vertical axis.
00:25:09Um, this goes up to 40. Ten, 20, 30 and 40. And this goes minus 10 and minus 20. Yes?
00:25:22Um, it makes no big difference what you fill in on the vertical axis, as long as you're taking the same steps every time.
00:25:29So if you took steps of two over here, that's fine. If you took steps of five, that's just as fine. What matters is that the steps are equal.
00:25:39Um, then we will draw it. At minus six, we had an outcome of minus six. That is over here. At one, we had an outcome of 15, that is over here.
00:25:50At three we had an outcome of 21. And at eight we had an outcome of 36. Uh, that is over here somewhere. And I am not sure whether we have a nice ruler over here-
00:26:03I don't think we do. So now I will draw a very straight line... Ah, not too bad. Um, you will do the same thing in order to get the second and third line.
00:26:17Well, the second line, four X plus six, let me just- that starts at minus 18. You guys may calculate that one yourselves real neat. At zero it is six.
00:26:30And at eight it is 38. That one will be over here. Well, we can draw that one more or less like this.
00:26:41And the third line, that one I do want everyone to calculate for now. Go ahead and make the same table,
00:26:49and calculate it briefly, just a couple of points.
00:26:56After which you may tell me what caught your eye.
00:27:04Yuck, disgusting!
00:27:08No, no, that one's right as well.
00:27:10What you said is correct.
00:27:22Is that a pencil or a pen?
00:27:24Pencil. And a pen.
00:27:29I don't have a triangular protractor.
00:27:31Yes, but you can borrow one.
00:27:33No.
00:27:36Do you have a triangular protractor or not? You don't have a triangular protractor? You don't either?
00:27:40Yes, I do have one but it is at home-
00:27:41Yes, I don't have, I don't have a, uh, a triangle but I do have a triangular protractor.
00:27:43Yes!
00:27:46No, you have to- look, this one you have to (inaudible).
00:27:50Were you able to follow this, at 15?
00:27:52Well...
00:27:55You continued, okay.
00:28:00I really don't understand how you do it.
00:28:03The things I do? I calculate each time what I get with, uh, with every number. So, for example, if you, uh, fill in one for the X-
00:28:16Uh, do me a favor and keep working.
00:28:19Once I fill in a one for X, then what does it say? Three times one. What is that?
00:28:27No, three.
00:28:28Three. Twelve plus three is?
00:28:33Fifteen.
00:28:34Fifteen. So once you fill in a one for the X- well, just put a one here somewhere, what does that do for the Y?
00:28:43Is that times three?
00:28:44What did we just calculate? Fifteen. So what you write down is 15. Very well, now you are going to fill in a different number for X here.
00:28:52Tell me what number you want to fill in.
00:28:53Three.
00:28:54Three. Go ahead and calculate it. You replace the X by a three, and then what does it say?
00:29:01Three times three is nine.
00:29:03Exactly.
00:29:04Plus 12.
00:29:05Is?
00:29:06Twenty-one.
00:29:07Precisely. Well...
00:29:08That is exactly like the previous one.
00:29:10Yes.
00:29:12But then different.
00:29:14Try to fill in another number.
00:29:19Um, three times eight equals...
00:29:20Twenty-four.
00:29:23So then it's...
00:29:29What do you think the outcome will be?
00:29:31Minus six, I think.
00:29:32Well, check it.
00:29:35(inaudible)
00:29:38Three times minus six equals? Three times six equals 18 so three times minus six equals minus 18.
00:29:45Yes?
00:29:46Yes.
00:29:47Plus 12.
00:29:49Equals minus six.
00:29:50And indeed. They do seem very similar. Have a look at those equations.
00:30:00Is it possible that the A and the C are the same?
00:30:02Yes, because, um-
00:30:04No, because uh-
00:30:07Steffi, is it possible?
00:30:09It has to be.
00:30:10Yes, it has to be, I know that much as well, but...
00:30:14(inaudible)
00:30:16Exactly. Three times this four, that becomes 12.
00:30:20And three.
00:30:22Times...?
00:30:23Times-
00:30:24Uh, no, here you've got three times that X, and, uh-
00:30:27Exactly.
00:30:28Tah-dah!
00:30:29Precisely, those equations are exactly the same.
00:30:32Do we need to draw it once again?
00:30:34Yes, you may draw it again. But actually it is already there. So you can add A plus C. Yes?
00:30:40Yes.
00:30:41Do you understand what is going on? Do you understand why these two are the same?
00:30:47Well, no...
00:30:50If you make a multiplication table,
00:30:54here's an X- or uh, here's a multiplication sign. This is a multiplication sign, not an X. It stays tricky, doesn't it?
00:31:00Those multiplications signs mixing with those X's.
00:31:02Yes, but, uh, weren't X's always written like this and multiplication signs like that?
00:31:06Yes. Yes, exactly. Um, doing that will give you a three over here.
00:31:12The X will be and over here, and the four over here.
00:31:17Three times four is 12. Then you are done with this surface area over here. And three times the X equals that three X.
00:31:26So the equations of A and C are exactly the same.
00:31:30Oh, right.
00:31:31You get the picture? So earlier you calculated the surface area first, then you used the multiplication table. And finally you can see it at one glance.
00:31:41But until you're there you'll utilize the multiplication table.
00:31:43Okay.
00:31:44Yes?
00:31:45So did I also answer B since these are the same?
00:31:48Yes, what particularity do you notice?
00:31:50Well, that the A and the C are the same.
00:31:52Very good.
00:31:53Tah-dah!
00:31:54Tah-dah! Yes?
00:31:59Is it true that A and C are the same?
00:32:02Yes, certainly, it is correct [ in French ].
00:32:07Sir, that's the first sentence of (inaudible).
00:32:09It disappears completely? Why don't you move all of this out of the way. You guys have French class later on?
00:32:15Yes we do.
00:32:16Test or paper?
00:32:17A test.
00:32:18But it's really (inaudible).
00:32:19From whom?
00:32:20(inaudible) There are a lot of sentences.
00:32:21Ooh...
00:32:22An awful lot.
00:32:23It is really difficult, you know.
00:32:25Yes.
00:32:26Are you going to put it away now?
00:32:27He told me to-
00:32:28She snatched it from me.
00:32:35That is not allowed, is it?
00:32:37Sir, can we do Biology then?
00:32:40Sir, today we have a Biology test. May we study a little?
00:32:44Don't say that because then for Math-
00:32:49You guys have a Biology test shortly?
00:32:51No, sir, we have French.
00:32:55Sir, shortly we will have reproduction.
00:33:00We have a lot of labs, you know.
00:33:02La-bor-a-tor-ies.
00:33:04Art!
00:33:05No.
00:33:06(inaudible)
00:33:08Yes, I know.
00:33:10Meanwhile, how far did you get? You made exercise one, 15 and 20 in the meantime.
00:33:19No, I am, I am already beyond that.
00:33:20You are beyond that? You've even gotten as far as 36 by now?
00:33:25I will at some point.
00:33:28Let me see.
00:33:31Just put it away for the time being. Really people, put your French away for now. I mean now.
00:33:40Um, let me see. Steffi? Why don't you just get to work.
00:33:48Laurie, just get to work.
00:33:53:00]
00:34:13Uh, by the end of this week the chapter has to be completely finished.
00:34:18Oh. Yes, sir! [ In English ]
00:34:20Um, so be sure you make that. Because next week we will continue with chapter six.
00:34:26Is the additional subject matter tough?
00:34:28Which makes this week the last opportunity to ask questions about chapter five.
00:34:30Yes.
00:34:32Yes?
00:34:34Also the additional subject matter. Everything on chapter five.
00:34:37The test, when is that?
00:34:39The test isn't until the exam week.
00:34:42Ooh. Oh, yes!
00:34:47Sir, are the additional assignments due tomorrow?
00:34:49What?
00:34:51Sir?
00:34:52Yes?
00:34:53Are the additional assignments due tomorrow as well?
00:34:55Yes. Of course.
00:35:02Tomorrow is essentially the last time that you can ask questions about it.
00:35:09We will still continue anyway, but that's not the intent.
00:35:14Yes. We don't have a test.
00:35:18Sir?
00:35:20Uh, ladies! Do cut the French now.
00:35:24Okay.
00:35:28But sir, (inaudible) last five minutes.
00:35:30Last three minutes.
00:35:32Yes, but...
00:35:33But sir, aren't we off then- sir?
00:35:35Do you really think that you can learn something all of a sudden in the last five minutes?
00:35:39Of course.
00:35:40Then you might as well do it in the last three minutes.
00:35:45Could you be so kind as to check if (inaudible).
00:35:50Oh, uh, for Dalton in a moment.
00:35:55Tomorrow we don't have math and Friday is our last day.
00:35:58No, then it is Friday.
00:35:59"A de" is not possible I think.
00:36:00No, that is not possible.
00:36:01Whatever you want.
00:36:03No, that becomes "au".
00:36:05Uh, who else?
00:36:06Louise and I, sir.
00:36:08Louise?
00:36:09Yes.
00:36:10I have five- I already have five tests from two B and five papers from two F here. Ah, Harley is sick again?
00:36:19Yes. Yes, (inaudible). We have two quizzes coming up.
00:36:23I have four things, dude.
00:36:26So, uh, you can't reserve, you just have to be here in time.
00:36:32All right? Because in a minute I will be all filled up. Or, uh- at least, yeah.
00:36:46Yes, very difficult.
00:36:47German is what we have then.
00:36:48I have a very special one for you, three times more difficult.
00:36:51Can I join the class of Harley in that case?
00:36:54Uh, you may, yes, you just have to hurry- you just have to get here fast.
00:37:00You just have to get here fast. Hey, I want you to finally start doing something now.
00:37:04Huh? I am hurrying, I am busy.
00:37:06Yes. You are very busy.
00:37:10That is three times X, isn't it-?
00:37:11Keep working. Hey, just get to work.
00:37:17Sir, I don't understand 18.
00:37:18I am calculating it the other way around. If I have to calculate a surface area- look, 45 meters is five meters times eight meters.
00:37:25I think that, uh, 40 is five times eight or 45 is five times nine.
00:37:29Oh, right.
00:37:30Oh, right. But it's fine-
00:37:32I'm not very good at doing it by heart.
00:37:35Uh, it is fine that you do it the other way around.
00:37:37Yes, because otherwise I can't calculate it too well.
00:37:39And now you do-
00:37:41Now let's have a look. This is exactly a square, so that is nine times nine.
00:37:46True. Iris?
00:37:48I can't figure out 18 with that, uh, Ruben and the orchard and all that-
00:37:53Yes, you have this orchard. What is the surface area of that?
00:37:58Um, 350- no, 3,500.
00:38:01Yes. What is the surface area of the other area? How do you calculate a surface area to begin with?
00:38:09Um...
00:38:10Just real simple-
00:38:11[ Knocking ]
00:38:12Ruben, Ruben!
00:38:14Ruben, pick it up. Yes, I know but you are the one who is picking it up.
00:38:19Length times width.
00:38:20Yes. What is the length here?
00:38:23Sixty.
00:38:25Sixty?
00:38:27Yes. Oh, no, wait, 120.
00:38:29One hundred twenty. What is the width?
00:38:31Uh, 16.
00:38:33But do you need the whole 60?
00:38:40Do you need to include the B or not?
00:38:42Yes, no.
00:38:43No, because that is away a bit, that doesn't belong there. So you have to take 60- and what are you supposed to subtract from that?
00:38:49Twenty.
00:38:50Minus B.
00:38:51Minus B. Exactly. And what that B is you don't know yet. So the length is 120 times the width and we know, in this case, that is 60 minus B.
00:39:05The last part you have to put in between brackets.
00:39:07Sixty minus B in between brackets.
00:39:08Yes. Write that down and then calculate further from there.
00:39:11(inaudible)
00:39:14Even better: exactly.
00:39:16Yes.
00:39:17Is that possible?
00:39:18Yes, I don't know...
00:39:20Have a look, uh, at the equations.
00:39:23Yes.
00:39:25Could they be identical?
00:39:26Over here, uh, it is, uh, four by minus 12.
00:39:29Yes, but over here it has three times in front of it.
00:39:31Yes, but over here it has three times behind it.
00:39:33How much is three times... what is shown in between brackets? Three times X plus four. Three times the X is?
00:39:41Three X.
00:39:42We have that over here. Three times the four is?
00:39:45Twelve.
00:39:46Twelve. We have that one over there. It could be the same, right?
00:39:49Yes, of course.
00:39:50Yes. So what do you notice and what is the answer for B?
00:39:55That it's identical.
00:39:57Exactly. Yes? You understand that one?
00:40:05Are you going to show me on Friday that you have completed up to paragraph five?
00:40:09I will.
00:40:11Yes? And of whatever you couldn't finish you need to copy the text and the answers.
00:40:20Usually on Fridays I have some happy hours left, since on Fridays I'm sitting here until 11 o'clock in the evening anyway.
00:40:26Oh, yes, then it is party time.
00:40:28Yes, then it is party time. Are you joining us as well?
00:40:31No.
00:40:32Why not?
00:40:33Yes, I don't know?
00:40:34I wish you would.
00:40:35Oh no, I have a match for school, for soccer.
00:40:38Well, just make sure you are there.
00:40:41Yes, well, I, I don't know-
00:40:43I said: make sure you are there.
00:40:46Fine then.
00:40:47Okay.
00:40:48Yes, of course.
00:40:50Me too.
00:40:52Yes, you bet.
00:40:53Five more minutes to go. Sir, may we study a bit?
00:40:55Sir?
00:40:56Yes?
00:40:57Here it says that Robin has a width of 50 centimeters. That is the length, isn't it?
00:41:01Yes, but that depends on how you look at length and width.
00:41:06Yes, but this is the width, isn't it? From the top to the bottom?
00:41:08Does it matter what you take as the width or the length?
00:41:12Yes, sometimes I think it does.
00:41:15Length times width or width times length is the same.
00:41:19Three times four is the same as four times three.
00:41:22Yes?
00:41:23Yes?
00:41:24Okay.
00:41:25So, if they mean something different when they talk about length and width here-
00:41:27No but look over here-
00:41:28Yes?
00:41:29Over here is uh- suppose that this is the width-
00:41:32Yes.
00:41:33Then that is H centimeters- then you need to do 50, but if you'd turn it around would it still stay the same? Oh, I see.
00:41:38H times 50 or 50 times H is the same. Three times four and four times three is the same.
00:41:46Yes but that is not an H.
00:41:47Yes, but- hey, four times three and three times four is the same as well, isn't it?
00:41:50Yes, that's true.
00:41:52Well, there.
00:41:53Okay.
00:41:57Laurie, try to keep working just a wee bit longer.
00:42:00We were allowed to study, weren't we?
00:42:02Have the last three minutes started yet?
00:42:03Yes.
00:42:04Yes.
00:42:06They did for me.
00:42:08Look how fast the French books are appearing on the tables now.
00:42:11Sir, can I ask you one more thing?
00:42:13Yes?
00:42:14This one. What is...?
00:42:16How much is three times 40?
00:42:20And how much is three times four?
00:42:21Oh right, 120.
00:42:22Yes. So that one you can write down.
00:42:27And what is, uh, the outcome of the whole equation? You know that you can just write this down here.
00:42:34Three D plus 120.
00:42:37And the 'aux', the AU and X, that's what you get with A and plural.
00:42:41This is how you use the table.
00:42:43Oh.
00:42:44Yes? Do you understand it?
00:42:47Why don't you try that one again.
00:42:49Uh, let's see which one. At 13 you will get a few more. Yes? You have to keep on making multiplication tables.
00:43:01What is the matter? That you are kind of blushing?
00:43:05Me? I always have that.
00:43:07No but he said something and then I went like that and then he went like- It was kind of funny.
00:43:12Good morning, um...
00:43:16Yes, I have I note.
00:43:17A note?
00:43:18Yes.
00:43:19Do you have it with you?
00:43:21Yes.
00:43:22Yes.
00:43:23Where are you coming from?
00:43:25I went to the doctor.
00:43:26Oh, okay. Um, you just have to drop it off at Mr. Fort. He eventually will remove that.
00:43:34Where did the braids go?
00:43:40Uh, huh. Were you still able to do anything for, uh, later on. Pythagoras. Test.
00:43:47Yes, I completed some problems but I should think I can get at least a seven and a half.
00:43:52Oh yeah? What should we bet for?
00:43:53Well, the fact that I'm doing that test.
00:43:56Oh, yes, we already agreed on that, yes. That is true. But please mention that at least three more times to me otherwise I will forget. Yes?
00:44:07Um, let's have a look, who else is absent?
00:44:13Uh, Laurie, who else is absent over there?
00:44:16Loes.
00:44:17Right, Loes.
00:44:21Uh, j'ai mal a la...
00:44:23Loes and Laura? Why?
00:44:25Laura (inaudible).
00:44:26Yes, but why?
00:44:35Is you memory perhaps also like, uh... Really? Like what?
00:44:45What is the date today, the 11th?
00:44:51Hey, "l'air", isn't that "looks like".
00:44:57As in: you look sporty.
00:45:01Well, good luck with uh, French!
00:45:04Thanks.
00:45:05Um...
00:45:07The third period you have here, uh...
00:45:13[ Bell ]
00:45:17See you soon!
00:45:18Next week.