NL2 PYTHAGOREAN THEOREM

This eighth grade mathematics lesson is an introduction to the Pythagorean theorem. It is the first in a sequence of five lessons focused on Pythagorean theorem. The lesson is 49 minutes in duration. There are 25 students in the class.

TimeCaption
00:00:03A lot.
00:00:08Yes?
00:00:08I really don't understand it.
00:00:10Teacher, aren't we allowed to (inaudible)?
00:00:11Yes.
00:00:16Yes, yes, yes, yes.
00:00:17I said just leave it.
00:00:22Okay, ladies and gentlemen. Ravi, your punishment lines?
00:00:24Oh, yes.
00:00:26As first thing, before I forget again.
00:00:27(inaudible) that too?
00:00:29I have already shown that one. He already had that neatly signed off. The rest of you also grab your things.
00:00:37Where are you coming- oh, you already went. Okay.
00:00:46Wasn't that twice then?
00:00:47Once.
00:00:48Twice we were supposed to, didn't we? Oh.
00:00:57Yup! Very good. Very good.
00:01:05Okay. Um, like I said yesterday, today we will begin with Pythagoras. Which one of you ever heard of Pyth- Pythagoras?
00:01:18Uh...
00:01:19Uncle Pete.
00:01:20Pete, Pete, Pete.
00:01:21Tell us, what do you know about it?
00:01:23It's a gentleman.
00:01:24A squared plus B squared, equals C squared.
00:01:25You know the equation A squared plus B squared equals C squared. Who else can say more about it?
00:01:29Uh, I think this guy was a Greek.
00:01:32The, uh, this gentleman was Greek.
00:01:33Yup.
00:01:34Or at least during that time period, somewhere in that region.
00:01:37Okay. Does anyone know when you would use the Pythagoras' theorem and what you would use it for?
00:01:43Yes, in a diagram.
00:01:44In a diagram. You obviously have a diagram. I am crazy about diagrams.
00:01:48(inaudible)
00:01:49Something about triangles, indeed. Well, let's take another look.
00:01:55What well-known triangles do we know? We have different types of triangles.
00:01:59Right-angled.
00:02:00We have a right-angled triangle.
00:02:01Isosceles.
00:02:07What is a characteristic of a right-angled triangle?
00:02:10It has, it has one-
00:02:13Ruben?
00:02:14It has a right angle.
00:02:15In any case, it has a right angle.
00:02:20You can see that by the little symbol. What other kinds of triangles do we have?
00:02:24An isosceles triangle.
00:02:25An isosceles triangle.
00:02:31What is characteristic of an isosceles triangle?
00:02:34Two equal sides.
00:02:35Two equal sides. Like this, for instance. I will just name the sides that are equal, for example A, the other one B. Meaning:
00:02:47if I fill in a number for A, then I have to use the same number for every A I come across.
00:02:52What else do I know about an isosceles triangle?
00:02:57If I look at angles, for example? Maarten.
00:02:58That A and B are equal.
00:03:00A and B are equal in size. Very good. And I have another special triangle. Which one?
00:03:07Equally shaped.
00:03:08An equilateral triangle.
00:03:09Oh.
00:03:15What is characteristic of an equilateral triangle? Julie.
00:03:18All sides are equal.
00:03:19All the sides are equal, all three sides.
00:03:29So one could say: all the sides are A. Would there be anything else I can mention about an equilateral triangle?
00:03:35Um, all angles are equal.
00:03:38All angles are equal. And can we tell how wide they are?
00:03:41Yes, 180 divided by three.
00:03:42One hundred eighty divided by three and that is?
00:03:45Sixty.
00:03:46Sixty.
00:03:51Okay. So as we noticed before, we use Pythagoras in a triangle. But I have three types of triangles.
00:03:59And we only use Pythagoras in a right-angled triangle. So we are going to continue with a right-angled triangle.
00:04:06And the other triangles you will come across at some point later in the chapter.
00:04:09Because you will be making right-angled triangles from these- or in these. Which enables you to cal- calculate things.
00:04:19Another thing we noticed yesterday-
00:04:23No, let me first pick up something else. I'll go- I'll return to the right-angled triangle.
00:04:30Except I placed it on its side.
00:04:33We know that the edges of a triangle- or any figure- are called "sides".
00:04:38In a right-angled triangle, this side is attached to a right angle. So what should we call this side? A right-angled side.
00:04:47Yes? Because this side is attached to a right angle so you call that a right-angled side.
00:05:00Do we have any other right-angled side in there?
00:05:02Yes.
00:05:03Yes, all the way on the other side. That one is attached to the right angle as well, therefore you call that a right-angled side as well.
00:05:19Then I still have one side left. It isn't so obvious because it is laying flat. But if you see this triangle, what can we call that side?
00:05:28The long side.
00:05:29The long side. That is correct. Or in a different way?
00:05:33The right side?
00:05:34It is actually at an angle. If you see it in such an- like a diagonal- so you call this the sloped side or the hypotenuse, is what you call this one.
00:05:45These are just names, you know, you may also keep calling this "the long side", no problem.
00:05:50Okay, with Pythagoras, soon, once we have gotten to know Pythagoras, we will use Pythagoras to calculate the sides.
00:05:58Because all we know now about a triangle and the size of its side, is when we measure it.
00:06:03However, those triangular protractors, how exact are they really?
00:06:07We know from, uh, the drawing of your number line, from, for example, of the square root of five-
00:06:14Well, you can't really measure that exactly.
00:06:16Because the square root of five had such an odd number behind the point. And still we can calculate things in the end with Pythagoras.
00:06:26Yesterday we saw, when I have a square, with a surface of, say, 37,
00:06:35we could calculate, or at least determine how large the side was of such a square.
00:06:40And we were actually able to do that quite precisely. Namely, Maarten?
00:06:44The square root of 37.
00:06:45The square root of 37. Okay, so that's "when I know the surface area of a square, how do I determine the sides again?" Okay, very well.
00:06:59That is already kind of what's explained in assignment one.
00:07:03This has to do with assignment two. That diagram is shown at assignment two.
00:07:12We have here- I am just going to skip several parts of exercise two because we will not do all that.
00:07:18We have a large square here: O E F G. As well as a square that is tilted at a corner: square A B C D.
00:07:29I would like to know what the size the lengths are of the square A B C D,
00:07:34for example what's the length of A B. We can't measure it and yet we are able to calculate it right now.
00:07:41Because we have seen that once I knew the surface area of a square, I was able to determine the sides.
00:07:46So I would like to calculate what the surface area is of the square A B C D. How can we do that? By which method? Rene?
00:07:55Well, I think you have to up on top of the large square- oh, no, that's something you don't know-
00:08:01Yes, though.
00:08:02Yes, then you have to, uh, remove those angles- or, uh, yes, well, that's how you get the small square.
00:08:07Very good. You have to calculate the surface area of the large square: O E F G.
00:08:12And then you take the surface areas of the triangles, you subtract that. Very well.
00:08:17What is the surface area of the large square, of the O E F G?
00:08:28How much?
00:08:30Uh, nine centimeters squared.
00:08:31Nine- well, what the unit is I don't know, I didn't specify that. But if it were shown in centimeters, then you're right.
00:08:37Right now I don't have a unit. Therefore the total surface area is indeed nine.
00:08:40Namely three by three, or you can just count the squares- that gives us nine.
00:08:45So we're told that we have to remove the surface areas of the triangles. What is the surface area of one of those triangles?
00:08:50How do we calculate that again?
00:08:54Willem?
00:08:55I don't know how you calculate it but I can just see it.
00:08:57You can just see it. What is the outcome according to you if you are just able to see it?
00:09:01Um, four in total comes off because one of those, uh...
00:09:06One of these triangles?
00:09:07That is one.
00:09:08That is one. Okay.
00:09:09And there are four of those.
00:09:10Correct, but how are you able to calculate that again? Leni?
00:09:14You make it into a rectangle?
00:09:16I- I am just going to pull it aside. So these are then the three surface areas of the triangle that we want to calculate.
00:09:24We will make it into a rectangle. And then?
00:09:29We calculate the surface area.
00:09:31We calculate the surface area. That was one by two, so the whole surface area together of the rectangle is then two.
00:09:37And I just need to take half of that, which brings us to one, very good.
00:09:46So the surface areas of the triangles-
00:09:54So the surface areas of the triangles together here is four. So what is left is five.
00:10:05So the surface of the square in the center, A B C D, is five.
00:10:12And now we can finally, after all that calculating, determine one of those sides. Namely, that is?
00:10:18The square root of five.
00:10:19The square root of five. Very good.
00:10:24So we've got no problem figuring this out. We may not even need Pythagoras at all.
00:10:28No.
00:10:29But it is kind of a hassle if you constantly have to draw on like this.
00:10:32Because, suppose you wanted to know the length of this little line.
00:10:38If you want to calculate that you first have to, you first have to draw a square again, like this one and another square around it.
00:10:44And then calculating it again. So it's a real hassle. So we're going to do that differently.
00:10:50The example given in the book is that assignment four and five. I will just do that one with the overhead projector.
00:11:00:00]
00:11:14Okay, we see, we see at assignment four, they have given two plates. Well, I drew those too, I have two plates.
00:11:24They should be equal in size.
00:11:26Well, if I place them on top of one another, they are indeed- if I place them very neatly on top of each other, equal in size.
00:11:33Yes. Yes.
00:11:35Well...
00:11:36Approximately.
00:11:37They are really equal in size but they stick a bit.
00:11:40Yes.
00:11:41There. Yes? Convinced?
00:11:43Yes.
00:11:44Very good. Yes, of course there are some who will never be convinced.
00:11:48I said yes.
00:11:49Yes, but I also heard a no.
00:11:56Then we also see- here they made eight right-angled triangles.
00:11:59Namely, four right-angled triangles in the one board and four right-angled triangles in the other board.
00:12:05I cut those as well. Those are also equal in size. When I stack them on top of each other they're all equal in size.
00:12:10So it's truly a stack of eight and I will take them off from there.
00:12:14We will lay it down just like it is shown in the diagram in the book.
00:12:17Which question?
00:12:18Question four is what we are working on.
00:12:24:00]
00:12:32Very well, we are now able to, in the same way as exercise- what? Is one lying incorrectly?
00:12:37No.
00:12:38Oh? Yes, it's crooked- I mean it is loose.
00:12:42(inaudible)
00:12:45Now, should we know the size of everything, we could calculate what the area is of the square in the middle here.
00:12:51Namely, in the same way that we did over there.
00:12:54The surface of the whole board and then the surface area of those three- of those four triangles taken off. We won't do that.
00:13:01Now I will, with the other four triangles I have, I will make the other one.
00:13:11It lies in this corner over here, and it lies in that corner over there.
00:13:22Those triangles- those four triangles that are lying over here, are equal in size as the triangles that are lying over there.
00:13:27Yes.
00:13:28I knew that the board is equal in size. What am I able to say about the surface of this square and that square?
00:13:34They are equally big as the other ones.
00:13:36Together they are- if I add these two surface areas together- are equal in size as that one. Yes?
00:13:41Because the boards are equal in size. And the triangles are equal in size. Okay...
00:13:47What they indicate in the book, then, is that they are going to put those boards on top of each other. Yes?
00:13:52Well, you can't see through the board but you can through the overhead sheets.
00:13:55So I will just remove that then because in the book it is shown underneath it. And I will try to place it on top of it.
00:14:03Approximately. I may not move anything. There.
00:14:08We are still aware that the surface area of this square is equal in size as the surface of this square plus that square together.
00:14:15Because they are still the same boards and they are still the same triangle.
00:14:21What are we going to say now? What are we going to look at? Imagine that this side- that that is 12,
00:14:23then what is the surface area of the square that is attached to it?
00:14:30Twelve times 12.
00:14:31Twelve times 12. And that is?
00:14:32One hundred forty-four.
00:14:33One hundred forty-four.
00:14:34Without a calculator.
00:14:35Oh yes.
00:14:37The short side, that is five.
00:14:40Twenty-five.
00:14:41So it becomes 25 indeed. What do I know about the large square, then?
00:14:47One hundred forty-four plus 25.
00:14:48That 144 plus 25 and that is?
00:14:53(inaudible)
00:14:54One hundred sixty-nine.
00:14:57If I know that the surface area of the large square is 169, can I say something about how long this sloped side is?
00:15:04Which angle?
00:15:05Of this- of this side of the square. It is also the side of the triangle. Namely?
00:15:10Half of 12.
00:15:11Twelve.
00:15:12The square root of 169.
00:15:13The square root of 169. Why should you take half of 12?
00:15:20On this side, I have this triangle lying over here. The one side is 12, the other side is five. I want to know the hypotenuse.
00:15:27I knew that the surface areas of the squares that are lying here- that have exactly the same sides as the sides of the triangle-
00:15:35if it'd be so kind as to stay on it's spot-
00:15:39is equal in size as the surface area of the large square. Yes?
00:15:42We have seen that the surface area of the large square is 169.
00:15:46Now I would like to know one side, that is the side of the square, which is at the same time also the side of this, of this triangle,
00:15:54which is indeed the square root of 169, which is 13.
00:16:01Yes? And that is actually sort of- of what Pythagoras was talking about.
00:16:06Pythagoras says that if I place a square on the one right-angled side,
00:16:11so the surface area of the square I will calculate. I will place another square on the other- the shorter side.
00:16:19I will take the surface area of that too, of that square. If I add these two surface areas together,
00:16:24apparently- he discovered all this- they are exactly the same as the surface area...
00:16:32of the square that is placed on the hypotenuse. Yes?
00:16:36I'll show that one to you in a second. As I will write the general rule on the board.
00:17:26We have seen- ladies and gentlemen, we are going to continue. Ravi. Rick!
00:17:36Okay. This is the same as what was just on the screen. Suppose that this is the triangle of which this side is 12.
00:17:46Then we would know that the surface area of this square was 144.
00:17:50If this surface area is five, then this one is 25.
00:17:55This one was 144 plus 25, is then 169.
00:18:00So the length is 13.
00:18:02So this one is 13. That was also what we just had on the screen. But now we are going to construct very generally-
00:18:06Now I get it!
00:18:10It is also actually in the book, except I am writing it down a bit more detailed.
00:18:13So perhaps it would be smart if you copied it. Then you can always retrieve it.
00:18:34Yak!
00:18:43The Pythagorean theorem. What have we done? We had a right-angled triangle. It only applies to right-angled triangles.
00:18:52One of those right-angled sides, let's take 12 as the first right-angled side. What did we do with this right-angled side?
00:18:57We took the square of this right-angled side. In fact we glued a square over it and calculated its surface.
00:19:04So you took one right-angled side, squared. So we will write that down: one right-angled side, squared.
00:19:11Are you supposed to-
00:19:13Yup.
00:19:14You are supposed to copy that thing, right?
00:19:16What I am writing down you have to copy.
00:19:18Oh. Ah.
00:19:26So we had: one right-angled side squared, that is, in other words, the surface area of the square. What did we do with that?
00:19:37We added the surface area of the square that was on the other right-angled side to it.
00:19:41How did we determine the surface area of the other square again?
00:19:44So that is plus- taking the other right-angled side squared.
00:20:08So we had the one right-angled side squared, which is in fact the surface area of the square that you attached to it.
00:20:13Plus the other right-angled side squared: the surface area of the other square that you attached to it.
00:20:19What is it equal to? To the surface area of the large square that is on the hypotenuse.
00:20:24So actually, surface area is the same as that side squared.
00:20:31This is: the hypotenuse.
00:20:39:00]
00:20:50So that is the hypotenuse squared. Does that thing bother you? Sorry. Since I won't be needing this one anymore.
00:21:05There.
00:21:10The table is slanted.
00:21:14So this is the general theorem. Let's see if it will work if we apply it.
00:21:32Gentlemen! Come on.
00:21:39By now you guys must know that I am crazy about diagrams and tables and things like that.
00:21:44Yes, we knew that because you already told us yesterday.
00:21:46There we go. There we go. Good thing the book utilizes that too. Otherwise I would have to explain it all by myself once again.
00:21:52But the book utilizes it too. So we are going to- to calculate those sides, we will also use the diagram.
00:21:59Well, if you copy this, Ravi, it'll speed up your homework for you will have done this assignment already.
00:22:03(inaudible) fast hey (inaudible).
00:22:24Okay. Here I have a right-angled triangle of which I already know two of the right-angled sides. The hypotenuse I don't know yet.
00:22:32That's what I want to calculate. We will make a small table. I named it "side" on one side.
00:22:39As in: how long is the side going to be that I am about to fill in- Rick?
00:22:41You know you can also proceed in the hallway if you're so sure you understand it.
00:22:48And the squared value actually represents the surface area of the square that you placed on the sides.
00:22:55Yes.
00:22:56What?
00:22:57So here I have- what were we supposed to do? The one right-angled side. "The right-angled side" I will abbreviate.
00:23:03Because otherwise you will keep writing. I need the one right-angled side; I need the other right-angled side.
00:23:15Yes?
00:23:16Ladies, would you please just be a little more quiet as well?
00:23:19They are filming in this chicken coop.
00:23:22That doesn't matter. I just want it quiet for myself.
00:23:26And we have a hypotenuse. Yes?
00:23:31So what did we see? We were going to take the one side and square it because that was in fact the one with the square attached to it.
00:23:36And you were going to determine the surface area of that. That one side is in this case, for example, three.
00:23:41What is- is that squared? Or in other words, what is the surface area of the square that you attach to it, Julie?
00:23:44Nine.
00:23:45That is nine.
00:23:46Julie?
00:23:47Julie? Am I-
00:23:49She is sick!
00:23:50Oh, she is sick, yes, well then people shouldn't move around like that. Sorry, Myrte.
00:23:54The other right-angled side is four, so that is squared.
00:24:01Now you should listen very carefully because this is a mistake that is often made.
00:24:05We had said, the one right-angled side squared plus the other right-angled side squared. Those are the only ones you may add together.
00:24:10So only the squared sides. So not your regular sides.
00:24:16So you are allowed to only add this side. And that gives you?
00:24:22Twenty-five.
00:24:24Oh, that is four times four and three times three and then subtract-
00:24:26Then the other one is five.
00:24:28And then I would indeed want to know: how long is the hypotenuse.
00:24:32You know that the 25 represents the surface area of this square up here.
00:24:36Or, in other words, you are going to take the square root, this way. And that leaves me with five.
00:24:43Yeah. I already knew that.
00:24:47Yes, but it is- no.
00:24:49No, no questions? Regardless that you say: "yes, but".
00:24:54Oh, like that, yes, yes I got it.
00:24:56Yes, do you? Myrte?
00:24:58But it says, uh, "the other right-angled side equals the hypotenuse squared", but do we have to take the square root of it instead of, uh, squaring it?
00:25:07Yes. The general equation therefore is- uh, Rick, could you please go into the hallway now?
00:25:13Bye!
00:25:23What it says here is "one right-angled side squared plus the other right-angled side squared equals the hypotenuse squared".
00:25:31Therefore, if you want to know what the hypotenuse is, then you have to take the root of the number representing the hypotenuse squared.
00:25:38Is it squared and then you have to- yes, okay.
00:25:40This whole table over here shows these numbers squared.
00:25:42Yes.
00:25:43Yes? Very well.
00:25:44You figured it out.
00:25:45Well, in this way you can also reconstruct...
00:25:52In this way you can also reconstruct how the A squared plus B squared equals C squared is found- gentlemen,
00:26:00I wasn't quite finished yet. You can start shortly.
00:26:06If I have a right-angled side of which I call the one side A, the other side I call B and the hypotenuse I call C,
00:26:13and you apply the equation, then indeed you will get my first right-angled side squared.
00:26:19For example my first right-angled side is A, and you take that one squared. Plus my other right-angled side, take that one squared as well.
00:26:28Equals your hypotenuse squared. And that is how most of your parents learned this.
00:26:33Oh!
00:26:34They never had it explained to them with squares. They just learned it kind of like "this is how it is so you better get to work with it".
00:26:42A squared plus B squared equals-
00:26:46Oh, right.
00:26:49Okay.
00:26:50(inaudible) shows the thing squared there?
00:26:52Because that notion squared is the surface area that you want to calculate. The surface area of the square.
00:27:01Like that would help!
00:27:08Okay, ladies and gentlemen. As far as the homework is concerned. Suzanne?
00:27:14Jeffrey, Maarten?
00:27:19So far, by way of what I showed you on the board- and I am hoping that you guys did copy it-
00:27:26we have already completed quite a lot of the exercises.
00:27:28We did exercise one and we did exercise two. We haven't done exercise three yet. That's homework...
00:27:41Hey! You are being filmed!
00:27:53They will just edit that out.
00:27:54That's right. Each time Ravi's head will be cut out. Yes.
00:28:07You guys still have 20 minutes left.
00:28:08Twenty. Yes. Yes.
00:28:10That means that you have to- of these exercises, be able to get as far as exercise 11. Presumably even further.
00:28:17These we haven't all done yet, those are new. The only advice I'll give you on exercise 11, a lot is written down about triangles there-
00:28:25Sorry, Willem-
00:28:26The only thing (inaudible).
00:28:27Yes, it is fine like that.
00:28:28Yes? So with exercise 11 you will only get data on what angles are 90 degrees and what the lengths are of certain sides.
00:28:37Half of you are now missing this instruction.
00:28:38Oh, oh, sorry, you have it right here.
00:28:40Annelies and Myselle? You girls are missing the instruction.
00:28:44Shh.
00:28:50Exercise 11 only states what angle is 90 degrees and what the sizes are of particular sides.
00:28:57If you want to know exactly how things are put together, make a diagram, which explains the comment at the bottom;
00:29:02make diagrams of those triangles at exercise 11 so that you know what data you've got.
00:29:07Either both of the right-angled sides will be given, or perhaps only the right-angled side and the hypotenuse will be given.
00:29:15So that you can complete your calculation. Yes?
00:29:18Yes, understood.
00:29:20For those of you who want to check, I have answer booklets over here. You can grab those and get started now.
00:29:38From now on I really want it to be quiet when I am instructing.
00:29:39Yes.
00:29:40Yes?
00:29:41Yes.
00:29:42You are one of the few- or one of the few, together with a few more- but there are several who want nothing but to pay attention.
00:29:46Yes.
00:29:47If you keep on disrupting, then you are disrupting everyone.
00:29:48Yes.
00:29:49And certainly me.
00:29:50Yes.
00:29:51Just quietly get to work, the homework is on the blackboard.
00:29:56:00]
00:30:12Just put it on, uh...
00:30:13It doesn't make any sense, you don't feel (inaudible).
00:30:18Yes, no, don't close it completely, just put it on- I do want some oxygen to come in.
00:30:21Oxygen?
00:30:22The heater is still on.
00:30:23Well, I can't turn it off, it is central heating. Otherwise I would be the first one to turn it off.
00:30:27Here: two plus four plus six.
00:30:39Uh, ladies, ladies and gentlemen, when you are working I would like it to be more quiet. Discussions are fine but please do it in a whispering voice.
00:30:52:00]
00:30:57He has the best-looking notebook in the whole class, of course.
00:31:00Beautiful notebook.
00:31:11How can you determine how much of it is tiled?
00:31:14What does it look like, the example, the diagram? How does the whole diagram look, the whole garden?
00:31:20As a square.
00:31:21It's an exact square.
00:31:23Yes?
00:31:25Yes? And what is the shape of that tiled part?
00:31:28A triangle.
00:31:29A triangle. How could we calculate again the surface area of such a triangle?
00:31:35We just did that on the board on the other side.
00:31:37Yes, I already have it!
00:31:39Ladies and gentlemen, the fact that I have my back turned towards you doesn't mean you are allowed to turn things upside down.
00:31:45I agree.
00:31:51How did we do that? What can you make of this, of that one triangle?
00:31:54A, uh, rectangle.
00:31:56A rectangle. Yes? You can make a rectangle of this. What is the surface area then of that rectangle?
00:32:04Eight times six is 48.
00:32:05Forty-eight. And what part of the triangle is it?
00:32:09I don't know.
00:32:11Considering you know that the whole rectangle- because you said it's six times eight-
00:32:13This one is 24. Twenty-four squares (inaudible).
00:32:15Correct, is half of it. Yes?
00:32:18Yes.
00:32:19Okay.
00:32:22Shh! Whisper, Maarten. Maarten, whisper!
00:32:25I don't know it anymore.
00:32:27Ladies should be whispering as well.
00:32:29I still don't understand G eight.
00:32:32No, right. Okay, oh. Come over here for a second.
00:32:39:00]
00:32:47G eight.
00:32:50What does G eight say? We have a tiler, who uses white as well as blue tiles.
00:32:55Yes.
00:32:56Yes? The surface area of every tile is one square decimeter. The white ones as well as the blue ones.
00:33:03Yes.
00:33:04Okay. Five tiles together make the square A B C D. A, B, C, D. What is the surface area of that square?
00:33:14Um, (inaudible).
00:33:17Sorry?
00:33:18Twenty-five.
00:33:19Why 25? We are only looking at this one.
00:33:30You know that every tile, the white one as well as the blue one, is one square decimeter.
00:33:33Yes.
00:33:34Yes?
00:33:35Five.
00:33:36So it's five, because there are five tiles in there. Yes? The surface area of this is five.
00:33:41What is the length then of A B, given the surface area of that square is five?
00:33:49The square root of five.
00:33:50The square root of five. Yes? Maybe later you should add for yourself an ex- a written explanation on how you got that square root of five, okay?
00:33:57Because if later on you- you read it again you won't know how you get that square root of five.
00:34:00Yes.
00:34:01Yes? Now we have to fill in the length of A E, A E goes from here to there.
00:34:07Is two times AB .
00:34:08Yes, is two times A B. Because that section is just as long as this. And that is, then, twice?
00:34:14(inaudible)
00:34:15Yes, very good, two times the square root of five.
00:34:20Very good. No, no, no, no sorry, no. We've seen that yesterday. How can we write the two differently?
00:34:25But you don't have to do that here yet, that will come later on.
00:34:28(inaudible) to write the two differently?
00:34:31How can I write the two into a square root? What is two equal to again?
00:34:36Yesterday we had that whole list on the board.
00:34:39You knew that the square root of 16 was equal to four?
00:34:42Yes.
00:34:43Yes?
00:34:44Oh, uh, it is equal to, uh, the square root of four.
00:34:45Correct, equal to the square root of four, very good. So you have the square root of four times the square root of five here.
00:34:52Look, the two was correct, but-
00:34:53Oh, yes.
00:34:54It says the same. What is the outcome of this then?
00:34:58Yes! Yes, perfect. Very good. Try to do the rest of them now, too.
00:35:03Yes.
00:35:04Yes?
00:35:06Look, I have a question, since yesterday I had something from chapter one-
00:35:09Oh, yes.
00:35:10And, um, look, this is, for example, um, the regular square-
00:35:13Yes?
00:35:14And that one is 40 square centimeters.
00:35:18So the reduction goes to 10 square centimeters. Then the factor isn't four, is it?
00:35:22No.
00:35:23It is two, isn't it?
00:35:24Correct, because the surface area becomes four times smaller-
00:35:26Yes.
00:35:27But your magnifying factor will be the square root of that.
00:35:31So if you have, for example, a really large number, for instance, uh- well, yes, I don't know, uh, for example with five numbers-
00:35:35Yes?
00:35:36And, uh, it becomes a lot smaller, you have to divide it by four?
00:35:40So, uh, the magnifying factor with reduction has to be divided by four, whereas if you make it from small to large it is times four? Okay.
00:35:47Yes, correct. You were first.
00:35:50I just have a question.
00:35:51Yes?
00:35:52Uh, could it also be that you only get this number?
00:35:55Yup. Well, not only that, you need two sides at least, otherwise you cannot calculate anything. Yes?
00:35:59So this one, and that one, and then all you have to do is calculate this one here?
00:36:02Yes. Very good.
00:36:03Okay.
00:36:04Great.
00:36:05Where is this key on my pocket calculator?
00:36:07Oh, it is fine, right?
00:36:09Here. Only yours doesn't have an X below. And this is your root.
00:36:11So it's the same thing.
00:36:12Yes. This is your root.
00:36:13Okay. Yes.
00:36:37Was it clear for you guys?
00:36:38Yes.
00:36:39Yes? Very good.
00:36:44You keep track of this a little too, I hope?
00:36:45Yes, yes, I just wrote it down.
00:36:46No, okay. Oh, okay.
00:36:47That's just the nature of the assignment.
00:36:58Is this one clear to you guys?
00:36:59Yeah, sure.
00:37:00Really?
00:37:01Yes with the explanation earlier it made it, in any case, clearer.
00:37:02But in the beginning it seemed a bit weird, but now I understand it.
00:37:03Yes, very good. So it is very important that it is written down properly here. Yes?
00:37:09I mean you copied it here very nicely but try to retain some of that for yourself too.
00:37:13Technically this doesn't get explained until here. So if afterwards you try to calculate the numbers, make sure you use it.
00:37:19So don't try to be stubborn or anything like that. So really try to stick to the rules, those steps. Yes?
00:37:24Yes.
00:37:25Yes?
00:37:26Yes, okay.
00:37:29The same problem.
00:37:32Three you can still do, in principle, in the old method. Because this one, the one I explained won't be explained until the next paragraph.
00:37:40But it is allowed, you'll still work through it.
00:37:41And, uh, the square root of (inaudible).
00:37:45The square root of six.
00:37:46Yes.
00:37:47Yes, very good.
00:37:48Yes? But if you want to calculate that one, what do you need then?
00:37:52Then I can- just this one- like that? And, uh-
00:37:55Yes, you can that way, very good. Yes, of course, only it hasn't been explained over here yet.
00:38:00But since I have already explained it and as you understand it, then, as far as I am concerned, you can go ahead and use it.
00:38:03Yes.
00:38:08Yes?
00:38:09If you want to measure this side-
00:38:12Yes?
00:38:13Then you have to- this is 225.
00:38:15Yes.
00:38:16And this is 64.
00:38:17Yes.
00:38:18Then aren't you supposed to take two- 225 plus 64-
00:38:21Yes.
00:38:22Is 289.
00:38:23Yes, indeed, that square-
00:38:24That you have to make into a square root?
00:38:26Yes, very good.
00:38:27So that becomes 17, then.
00:38:28And that is 17.
00:38:29Yes, perfect. Are you writing down what you are doing, though? Not only, uh, writing down the answers?
00:38:33Oh.
00:38:39Ehm, look here.
00:38:44Can you see it?
00:38:45Yes, I can see it.
00:38:46One hundred ninety-six square meters.
00:38:48What is this? What exercise are you working on?
00:38:51Oh, with, um, three.
00:38:52Yes? And what is this 196?
00:38:55That is the whole garden.
00:38:56Okay, the whole garden. Yes?
00:38:58Then I have to do minus-
00:38:59Yes.
00:39:00Twenty-four square meters.
00:39:01Yes.
00:39:02But doesn't that just become- can you just take this off then, like, like in the same way if there wasn't a square meter on here?
00:39:10Yes, because- the whole garden is in square meters-
00:39:13I must be confusing it with something else then.
00:39:14Very small sections of square meters.
00:39:15So you can easily subtract square meters from square meters.
00:39:17Now I don't understand any of this anymore.
00:39:19Here I have the table, yes? There are square, well- let's just say meters. If I chop a piece off here, then this piece is also in square meters.
00:39:29Then this piece will remain, in square meters. That is the same thing you will do with the garden.
00:39:34Yes, fine.
00:39:35Yes?
00:39:42Everything is clear for you guys?
00:39:43(inaudible)
00:39:45Okay.
00:39:46This is how it should be done? Like this?
00:39:49Yes, perfect. Perfect, very nice.
00:39:51Of course not, are you crazy or something?
00:39:54But you were too warm weren't you?
00:39:56Yes, right, I will just go and sit here without my T-shirt, in my bare chest.
00:40:03Well, if the wind is gone, if the rain is gone then it can be opened again. I mean, uh...
00:40:08Then it'll get even colder.
00:40:10Are you cold?
00:40:12(inaudible) only wearing this really thin thing.
00:40:21Yes. You aren't going to infect your sister, are you?
00:40:24No, she is, she is already sick.
00:40:26Yes? She is at home, though?
00:40:28Yes.
00:40:32And have you changed her yet, or are you going to leave that to...
00:40:37Because I did that by myself-
00:40:39Yes?
00:40:40I am allowed to carry her into the church for the baptism.
00:40:41Oh, how neat. Oh, you don't like that?
00:40:44Well, I do think it is kind of neat and all-
00:40:45Yes!
00:40:47Wow!
00:40:52Well, wonderful...
00:40:53Really, uh, great. No, I think it is kind of neat.
00:40:56Yes.
00:40:57Do you have the answer booklets?
00:40:58Yes.
00:41:06Shirley isn't here and uh...
00:41:07Sixty.
00:41:10A B.
00:41:11No, she was sitting on Shirley's seat and that's confusing me again. I thought I finally knew all the names. Okay, thank you.
00:41:21And who normally sits next to?
00:41:24Sander.
00:41:25Oh, yes.
00:41:26Four times the square root of 20 is eh-
00:41:28De Boer? Thank you. Easy? They were, weren't they?
00:41:35One, two, three, four, five, six, seven... eight, nine, 10- 20. One, two, three, four, 25, 26, 27-
00:41:41No? Yes though, it's 28, 29, it is correct.
00:41:44Are you going to proceed with the work?
00:41:49Can it be a little more quiet, uh, Jeffrey? And Maarten?
00:41:53We just have to calculate this one, so we have to take half.
00:41:58And then?
00:42:00Well, then-
00:42:01Will you indicate how you got the numbers?
00:42:02Oh, yes, I will-
00:42:03Yes? Because once again with the test I had a lot of- actually, I haven't seen yours yet, but from the other classes-
00:42:08I had to mark a lot incorrect because they only had put answers down.
00:42:14:00]
00:42:34Very well. My handkerchief will go into the laundry tonight. I'll need it again in a minute.
00:42:41Sixty-four. And then this you have to add together-
00:42:45No.
00:42:46Which makes 89.
00:42:47No, they have been here on Tuesday and now.
00:42:51What class was that then?
00:42:53On Tuesday it was A 2 C.
00:42:56With Dennis.
00:42:57Yes.
00:43:05Teacher?
00:43:06Yes?
00:43:07Can you check exercise three for a moment?
00:43:09Of course.
00:43:10Because if I have that one correct then-
00:43:11Then you understand it, you mean.
00:43:12Yes, because I am not sure if I understand it.
00:43:13Yes. Except you have already used the new method which is explained to you in the next paragraph.
00:43:18But if you understand it, then it doesn't matter at all.
00:43:19No, I took the old method, I think. Oh, no! That is the new one.
00:43:22Yes, that one won't be explained until the next paragraph.
00:43:24Oh, so according to the book, I am actually working ahead.
00:43:27Yes, but that doesn't matter because the answer should be the same. All right?
00:43:30Here it says: how big is the (inaudible) and here I've got five, but do you just have to (inaudible)?
00:43:37Yes, that is correct. Because the surface area of the square is five.
00:43:39Yes.
00:43:40So the side, that is just one side-
00:43:42Yes.
00:43:43Is the root of this.
00:43:44Oh, yes.
00:43:45Yes? That is what we saw several times yesterday.
00:43:47(inaudible)
00:43:49Sorry?
00:43:50This square over here has four points-
00:43:52You may draw it-
00:43:53(inaudible) draw it?
00:43:54No, you're not obliged to, no, you're not obliged. But if it clarifies things for yourself, then you may, of course.
00:43:58But you don't have to.
00:44:02I got it right.
00:44:03Yes, very good.
00:44:06You can check it this way.
00:44:08(inaudible)
00:44:13It should, I believe. But what, why?
00:44:15How does one calculate this?
00:44:17Surface area is square A E F G. How does A E F G go?
00:44:22Okay, well, what is the surface area of that?
00:44:26How much is, what, what is the surface area again of one of these angles?
00:44:28Twenty.
00:44:30No, the surface area.
00:44:31Five.
00:44:32Five. And how many of those little squares do I have in here?
00:44:35Four.
00:44:36Yes, so?
00:44:37Twenty?
00:44:38Twenty.
00:44:39Yes, but I thought (inaudible).
00:44:41Yes, that is correct. Because they are determining how you can write things in a different way.
00:44:45Okay.
00:44:46What I explained yesterday on how you can write out those roots in different ways. Yes?
00:44:50Yes, okay.
00:44:52Heinjan and I are going to BEVO shortly.
00:44:54Yes, fine.
00:44:55We have a test to take.
00:44:56Yup.
00:44:58Yes?
00:45:03Hey, hey, Ravi you still have to, uh, take the test as well.
00:45:05May I come along with you?
00:45:09Then you have to come right now.
00:45:20Never mind, I'll go, I also have to go to BEVO.
00:45:23Well, then why don't you go instead? That makes a lot more sense, doesn't it?
00:45:40Well, go ahead then.
00:45:47Where is (inaudible)?
00:45:48Just to the restroom.
00:45:49In the rectangle one diagonal.
00:46:01It is explained over here?
00:46:03Well, that is explained with the surfaces-
00:46:05Yes.
00:46:06How that works.
00:46:07Oh, that is right here-
00:46:08So you can go right ahead- and now you just have to calculate this again. Yes.
00:46:10Oh, with the surface area?
00:46:11Yes, because as far as the (inaudible) diagram is concerned that doesn't get explained till over here in exercise seven.
00:46:15That's why you don't have to do that one.
00:46:16And then over here it is explained again and then you can continue on working.
00:46:20Plus five is 17- no,
00:46:23It is 14.
00:46:27:00]
00:46:36Myrte? It was, uh, chapter one, wasn't it?
00:46:38Yes.
00:46:39Sorry, that one is wrong.
00:46:43This is also wrong.
00:46:45No it's not.
00:46:46Yes it is.
00:46:50Don't make me cry.
00:46:52Is it that bad?
00:46:58:00]
00:47:27The numbers on your triangle have completely faded.
00:47:43Yes?
00:47:44(inaudible) do wrong?
00:47:45Excuse me?
00:47:46I don't see why this is wrong here.
00:47:49What is done wrong here?
00:47:50Look it (inaudible) is wrong but how are you supposed to know?
00:47:56What does that triangle look like? What kind of triangle is this? Why don't you make a diagram of that triangle.
00:48:01One like that.
00:48:03Yes, but with the sides and all, so do it with the correct- oh, you have it already. Oh, no, that is not it.
00:48:08Although? Yes that's the one though. What does it say? Angle K is 90 degrees. Correct. K L is 15.
00:48:15That is also correct. And then it says: L M is 25. And where did you put it? Yes?
00:48:21Oh, here-
00:48:22You see? And that is what has gone wrong here too. Do you see that?
00:48:26Because first you had to take a right-angled side and then another right-angled side.
00:48:31That is why it is so important that you really make the right diagram with the letters in the correct place. So that you know exactly what belongs with what.
00:48:39Yes?
00:48:44Ladies and gentlemen, it is almost time, so you can start to pack.
00:48:49Yes?
00:48:52Is it- if you, uh, write it down like this because you have to measure the other right-angled side-
00:49:00Yes?
00:49:01Then is this, uh, correct then, because, uh-
00:49:03The calculation is correct but you still have to answer it.
00:49:06Because now we have to search, no, you don't have to explain anything.
00:49:10Because now I have to search for your answer. Like do I need 41 or do I need 40, or do I need nine?
00:49:15Yes?
00:49:16I need to know what you calculated. Then you can just say the other side is- well, what did you calculate? Forty.
00:49:21Yup.
00:49:22Yes? So you still have to give an answer because otherwise I will have to search in such a diagram.
00:49:25Yup.
00:49:26And you know that I will always find the wrong one.