# CZ3 EXPONENTS

This eighth grade mathematics lesson focuses on raising numbers and algebraic expressions to certain powers, and adding and subtracting numbers raised to certain powers. It is the second lesson in a unit of work focused on raising numbers to powers. The lesson is 45 minutes in duration. There are 22 students in the class.

TimeCaption
00:00:16Good day everyone. Finish up drinking your sodas and eating your lunch. You may stay seated.
00:00:28Today we're not going to have tournaments, but since I will walk around the room,
00:00:32I would like you to zip up your backpacks and place it under your desks.
00:00:36Zip up your backpack please. Good. In our last class, we talked about the concept of powered numbers.
00:01:00We worked with terms like the value of a numerical expression and the sequence of the mathematical operations.
00:01:04Which one of you can describe- which one of you can describe, what is a squared number. What kind of product or creation is it?
00:01:11Give us an example of a powered number.
00:01:13Five squared.
00:01:14Not everyone at the same time because we can't understand it. Marcela?
00:01:17Five squared.
00:01:18Five squared. At what power.
00:01:19To the second power.
00:01:20To the second power, good. What is the number five, what do we call the number five, if five...
00:01:24Exponent.
00:01:27Number five is an exponent?
00:01:29No. (inaudible)
00:01:30Number two is an exponent?
00:01:31No. (inaudible)
00:01:33Jana, come up here and write it up on the left side of the board. Here is a piece of chalk.
00:01:41(inaudible)
00:01:42Yes, good. What Jana wrote up there is the second power.
00:01:47So, number five is the foundation of a power and the number two is, you've already mentioned it here?
00:01:51Exponent.
00:01:52Exponent, or we may use a foreign word exponent, that's correct as well. Fine.
00:01:56May we use, or can you give us an example of one other than the second power? To the third power.
00:02:01The third power.
00:02:02Go ahead. And once again, we raise our hands.
00:02:04Five to the third power.
00:02:05Five to the third power. What power is that?
00:02:07The third power.
00:02:08To the third power. Any other power. Lubo?
00:02:11Eight to the tenth power.
00:02:12Excellent, eight to the tenth power. What power is it?
00:02:14The tenth power.
00:02:15The tenth power, fine. We have here... we have already... we'll do it again, calculating some of these problems.
00:02:23The value of a numerical expression, so why don't we... before I give you some work, think about it for a minute.
00:02:29And if you know it, raise your hand.
00:02:32Two to the second power minus three times five, two to the second power minus three times five. Martin?
00:02:43Minus 11.
00:02:44Minus 11. And how did you calculate it?
00:02:46Two to the second power minus three times five equals 15.
00:02:49Minus 15. And why didn't you calculate, two squared which is four, minus three equals one, times five?
00:02:55Because first I figured out the power and then I multiplied it.
00:02:59So as a rule, we use multiplication first, we figure out the power by multiplying it first, then dividing, and last is adding.
00:03:04You'll all receive the same work, but each person will be calculating something different.
00:03:10So, first take a look at it, don't calculate anything yet, don't sign it. Paul, can you pass these around? Here and Marcela as well?
00:03:23You'll give it a try, okay? Okay, two more? You will get the rest of it.
00:03:38(inaudible)
00:03:45All of you have one?
00:03:46No, we're missing one.
00:03:47Okay I... Do you boys each have one?
00:03:50No.
00:03:51Each person must have one. Good. I would like you to mark which one you're going to do in order to be quick.
00:04:05Lucka will do letter A, you will do B, you will do C, D, you E, you F, G, H. You will do A, B, C, D, E, F, H, G.
00:04:33G and H, you don't have one yet? You'll do B and you will do C.
00:04:40I have the letter A.
00:04:41Fine, you'll have the letter A. Do you have one? You do. Good. Calculate it, and when you're done raise your hand, so we can...
00:04:50(inaudible)
00:04:51Very good. Come up here Paul, take your work with you.
00:05:16I'm not sure if I have it correct.
00:05:18Then we'll correct it. That's why we're in school, to learn.
00:05:36May I go up to write the next one?
00:05:39You may and do you have the same one as Paul is doing?
00:05:41I'm doing (inaudible).
00:05:42Go up there and do it on the board. Your own assignment and if you have it completed and it's not already on the board, go up there and do it.
00:05:57If it's not on the board, go up there and do the problem. Be careful so...
00:06:02Teacher, may I do the letter H?
00:06:05You want to do the letter A?
00:06:06The letter H.
00:06:07Letter H, yes you may. Of course. You can't go up anymore but you may check the work.
00:06:17Teacher, so I can go up?
00:06:20Which assignment do you have?
00:06:21Letter B.
00:06:22You may go up and do the assignment. You as well. Just check your work to see if you have it correct. Chalk is over there, yes.
00:06:42If you've checked your own work, you have the entire text in front of you so you can check the other assignments as well.
00:06:51So, who has done the letter A?
00:06:54Me!
00:06:56No one else has the letter A? I guess so. Lucka is not finished yet.
00:07:04I will do letter A.
00:07:06Excuse me?
00:07:07I just have the last two assignments remaining.
00:07:08The last two assignments. I would like to have someone do the letter A. Who has the letter C?
00:07:15Who has an A?
00:07:16It's not possible yet? How about the letter C, if any of you has it done. We still don't have the letter F completed.
00:07:22I did not assign the letter F to anyone?
00:07:25I have that one.
00:07:26Excuse me?
00:07:26I'm doing that one.
00:07:27Nikola, okay. I know that she's concentrating on the other assignment. Which problem do you have?
00:07:35Letter A.
00:07:36The letter A. Go up, to do the problem. Write it up on the board.
00:07:37I'm done.
00:07:38Write it on the board.
00:07:39I'm done.
00:07:40Lucka is done, so she can check her work. Now Denisa will go up to the board.
00:07:55I have the letter C.
00:07:57Okay!
00:07:58I have done the letter C as well.
00:08:03You will do C and what else.
00:08:08Teacher!
00:08:09Yes? We'll check all the work. Just wait for a moment. Good job. Good.
00:08:37I would like all of you to pay attention. You have the assignments in front of you. Let's all check the work together.
00:08:45Which one... rather letter 1A, tell me which calculating performance is it or what is the last calculation, we must do in this problem.
00:08:53We'll know what kind of problem it is based on that information.
00:08:56Additions, correct. From which two numbers did she come up with 16?
00:09:01Four plus 12.
00:09:02Four plus 12, correct. In number two, what is the last calculating performance?
00:09:08Product. Correct, from what two numbers did she get the result.
00:09:11Number four and... number seven.
00:09:14Seven and four. Good. Number three. What is the last calculating performance.
00:09:21Subtraction.
00:09:22Subtraction, no addition, and from what two numbers?
00:09:25From 12 and four.
00:09:26From four and minus 12. Excellent. What does it say? I can't see it.
00:09:32It's incorrect.
00:09:33Minus eight.
00:09:34Minus eight. Go up there to correct it. Okay and number four, what is the last calculating performance?
00:09:43Multiplication.
00:09:44Good. Excuse me? I can't hear you.
00:09:47Multiplication.
00:09:48Multiplication, good, and what two numerators?
00:09:51Four (inaudible).
00:09:54Okay, I heard the number four somewhere. That means we'll have to take a look at what's in the parenthesis.
00:09:59Calculate what's in the parenthesis. Veronika.
00:10:03Two squared is four and four minus three is one.
00:10:06So, it will not be negative one, but a positive one. Denisa has four up there, which is fine. Let's go to letter B and let's try quickly.
00:10:13What last two numbers will be calculated. Go ahead. Jarko?
00:10:19It's seven. Nine minus two.
00:10:20Nine minus two equals two. Good. Next, number two. Lukas?
00:10:25Nine minus four.
00:10:26Excuse me?
00:10:27Nine minus four.
00:10:28And the answer is five. Good. Next, number three. Paul.
00:10:31Three minus four minus one.
00:10:33Excellent. And we do have minus one there. Number four.
00:10:37One.
00:10:38Dennis!
00:10:39One (inaudible).
00:10:40Excellent. Let's do letter C, the first problem. Once again, I want to know which two numbers are calculated... Go ahead Jana.
00:10:51Nine plus ten.
00:10:52The answer is 19. Number two? What is that?
00:10:56Fourteen times two.
00:10:57And what is it? A product, correct Jarko. It's 14 times two. Fine. Number three is?
00:11:05Nine minus 10.
00:11:07Difference? The answer is, minus one. Number four is?
00:11:11Four times two.
00:11:13Yes, it's correct. Make sure to check the products, which are up there as a hint. Letter D?
00:11:20Sixteen minus five.
00:11:21Dennis?
00:11:22Sixteen minus five.
00:11:25Sixteen minus 25.
00:11:26Good, Paul and the answer is?
00:11:28Minus nine.
00:11:29Minus nine, fine. Number three, Paul?
00:11:31Four minus 25 equals minus 21.
00:11:33Minus 21? Number four.
00:11:36Me?
00:11:37You may.
00:11:38Four minus five equals one squared.
00:11:40Be careful here.
00:11:40(inaudible)
00:11:41Okay, but four minus five does not equal one.
00:11:43Minus one.
00:11:44Minus one. Minus one squared. Is it in fact one? Isn't it negative one?
00:11:50It's (inaudible).
00:11:51It's one squared.
00:11:58Now, let's do letter E. Excuse me?
00:12:01(inaudible)
00:12:04Can you repeat it, Martin?
00:12:05(inaudible)
00:12:07Where. The problem in letter D?
00:12:09Yes.
00:12:10We'll take a look at it. Eleven minus nine minus 21 and one. Eleven minus nine equals. Excuse me?
00:12:19Two.
00:12:20Two. Two minus 21 equals negative...
00:12:23Negative 19.
00:12:24Negative 19 plus one equals negative 18. Martin is correct, we should check the work for mistakes. Next is letter E.
00:12:33Fifteen minus 36.
00:12:35Fifteen minus 36 equals...
00:12:37Negative 21.
00:12:38I see something else up there. I would like someone to put negative up by the number. Who did that problem! Good.
00:12:46Number two.
00:12:47Fifteen minus 18.
00:12:48Fifteen minus 18 should be. Excuse me?
00:12:51Negative three.
00:12:52Negative three, it's already up on the board, good. Number three is?
00:12:56Fifteen minus 12.
00:12:57Correct, 15 minus 12. Fine, and number four?
00:13:00Fifteen minus six.
00:13:01Fifteen minus?
00:13:02Six.
00:13:03Six, because the root of four times nine. Fine. Letter F. Go ahead Nicole.
00:13:09In this problem we're not going to have only a sum of the number nor a product of the number.
00:13:12The assignments in F are composed of? Problem, number one?
00:13:17One plus four... minus 25.
00:13:21Minus 25 equals?
00:13:24Negative 20.
00:13:25Negative 20, correct. Number two?
00:13:28One plus four minus five equals zero.
00:13:31Excellent. Number three?
00:13:33Negative one minus four minus five equals negative 10.
00:13:37Correct.
00:13:38And one minus four plus five equals...
00:13:43Plus two.
00:13:44Plus two. One minus four equals minus three plus five is positive two. Fine. How about the problems in letter G.
00:13:53Ten minus 12.
00:13:56Ten minus 12 equals negative two.
00:13:57Correct and do number two as well Jana?
00:14:00Seven times four equals 28.
00:14:02Yes and Paul will try number three.
00:14:06Number three?
00:14:07Yes.
00:14:08Sixty-five minus three is...
00:14:14Martin is helping him out so why don't you tell us since you know it.
00:14:18Okay, so first we calculate the power of a number...
00:14:21The root of the number, yes.
00:14:22The root of the number, (inaudible).
00:14:27Excellent, Martin. How about number four.
00:14:30Ten minus 36.
00:14:31Ten minus... you're already doing the next one, in that case go ahead Denisa, give it a try.
00:14:36The square root of 100 is 10 minus three times two is six squared equals 36. So the answer is negative 36.
00:14:44The answer is negative 36, which is up on the board. Now we'll get to the last one, which is letter H.
00:14:50Why don't you try the first one Paul.
00:14:52Me?
00:14:53Yes.
00:14:54So the square root of 25 is so it's five, two squared is four, five minus four is one.
00:15:00Be careful you have multiplication there. Multiplication.
00:15:06Five times four is 20 and 30 minus 20 is 10.
00:15:10Fine. Jarka will try the next one?
00:15:13Parenthesis, 30 minus the square root of 25 is five, so 30 minus five is 25, times four equals 100.
00:15:22Excellent. Lubo will try number three.
00:15:26Thirty minus 20 equals 10 squared which is 20. Twenty times two is 40.
00:15:37I would say it's going to be a bit different. You've calculated the parenthesis correctly.
00:15:41Thirty minus 20 equals 10 and 10 squared is 100.
00:15:46One hundred times two equals 200. It's on the board. Mike, please read number four.
00:15:54I meant Mike Papez. Mike Brizek has not been here in class for a while so he's just reviewing the work.
00:16:00(inaudible), 10 squared is 100, 30 minus 100 is minus 70, times two equals negative 140.
00:16:14Negative 140. Martin did a good job, I suppose... I see.
00:16:20Negative 145. Negative...
00:16:22Why does it say 100... it does say negative 100 but why does it say 145 on the board?
00:16:27Because someone wrote it up there.
00:16:29Someone must have made a mistake. We should correct it on the board. Go over there and write negative 140.
00:16:34I'm very pleased to see you checking the work.
00:16:36And once again I want to give high marks to Martin who was keeping an eye on all the work to make sure the calculations are correct.
00:16:43Even if it did not come out right, he kept a good eye on it. Good.
00:16:47Now I would like you to put these papers away and take out your books. Last Friday we started to discuss the power of a number.
00:17:00Which is in the variable form. Open your books to page 24. Honza will open his book as well.
00:17:24And as a review, we'll go over some of these problems on page 24. Let's review, start with 1A. Jana?
00:17:32(inaudible)
00:17:35(inaudible)
00:17:36Excuse me?
00:17:37A raised to the fifth power.
00:17:38That was letter C and B.
00:17:41Negative four to the third power.
00:17:42Negative four to the third power. Go ahead Jana.
00:17:45Parenthesis.
00:17:46What are we going to call it.
00:17:48Negative four to the third power as a whole number.
00:17:49Negative four, Nicole.
00:17:50Negative four to the third power.
00:17:51The whole number to the third power. Good. We'll know that it includes the negative number. Great. How about D?
00:17:57(inaudible)
00:17:59You've said it already, so it's X to the fourth power. Fine. We'll try to calculate number two in our heads.
00:18:05Six.
00:18:06Nine.
00:18:08Nine. Excuse me? Eight, excellent.
00:18:14One.
00:18:15One.
00:18:16One thousand.
00:18:17Yes.
00:18:18Zero.
00:18:19Yes.
00:18:20(inaudible)
00:18:21Very good.
00:18:22Thirty-six.
00:18:24Good and now we must be careful because we have decimal numbers. The first one is?
00:18:29(inaudible)
00:18:30One hundredth.
00:18:31One hundredth.
00:18:32Hundredth.
00:18:34Zero point.
00:18:36Eight.
00:18:37To the thousandths.
00:18:39Correct.
00:18:43Zero point... thousandths.
00:18:48Speak up. Everyone else should be quiet, Lukas will tell us...
00:18:51One ten thousandths.
00:18:52Ten thousandths. And the second to last problem?
00:18:56To the nearest thousandths.
00:18:59And the last one is?
00:19:00Zero point four to the ten thousandths.
00:19:02Jarka.
00:19:03Zero point, four to the ten thousandths.
00:19:04Excellent. Now we'll discuss the letter C, which is a bit more difficult.
00:19:08Just to make sure you realize when the power is positive and when it's negative.
00:19:12So the first one is, Paul? Fine. Number two. Raise your hand and speak up so I can hear you. Paul?
00:19:18Negative 25.
00:19:21Rosta?
00:19:22Negative 125?
00:19:23Good, I'm glad you've gotten it right. Next calculation? Veronika.
00:19:30Sixteen.
00:19:31Excellent. Next problem?
00:19:34Negative one.
00:19:35Negative one because it's what power? The fifth power.
00:19:38The fifth power.
00:19:39The fifth power and the last one Paul?
00:19:41Positive one.
00:19:42Positive one because it's...
00:19:44Sixth power.
00:19:45Sixth power. Fine. That should be enough reviewing. We'll eventually get back to that because we'll have a test on this.
00:19:52You will need more practice.
00:19:53If you can recall, on Friday in our math class, you've worked with numbers, which in principal had the powered numbers.
00:20:03And in one way or the other we did some calculations. What do we call... look it up on page 25.
00:20:11When we add up, two A cubed plus three A cubed, what did we call it on Friday? I also drew out a picture for you? What is A cubed?
00:20:19Cubed.
00:20:20What is A cubed? How do I imagine it?
00:20:22Cubed.
00:20:23Volume of a cube. Fine, and Paul has already said that it will be...
00:20:25Two A cubed.
00:20:26Two A cubed because two A cubed is like two squares, A cubed plus A cubed. Good. So, what can we sum up-
00:20:38Based on the picture which we have there or based on the notes.
00:20:42We have X cubed which is once again a volume of a cube but we also have Y squared which is not a volume of a cube but it's what?
00:20:50Square.
00:20:51The area of the square. Fine. So, Jana what can we sum up?
00:20:56What page are we on?
00:20:57We're on page 25 on top of the page. Someone else may try it as well.
00:21:04The cubed numbers may be added.
00:21:06The cubed numbers may be added up.
00:21:09And the squared numbers.
00:21:10The squared numbers separate.
00:21:11We have a paragraph in the book that talks about which powered numbers we can add up and which powered numbers we can't.
00:21:17We can only add and subtract powers with the same base and exponent.
00:21:22Good and now you have an expression which can't be added together. I would like someone to explain why.
00:21:27Which ones can't be calculated and explain why. Denisa?
00:21:32Two A plus three A to the second power.
00:21:34And what is it, or why is it that we can't add them together. Jarko?
00:21:37Because A is a side, and A squared is the area of the cube face.
00:21:43Very good. A segment of a squared number as I've shown you by drawing it out, cannot be added together.
00:21:55Yes, five X minus four Y, can't be calculated.
00:21:59Why can't we calculate it?
00:22:02(inaudible)
00:22:03Because it's two different things. I must admit that I can't think of a better example than X and Y.
00:22:10I can't put these two together because I would not have anything out of it.
00:22:16In your books you have some examples such as number one. Since it's difficult to write in your notebooks, I'll distribute these strips of paper.
00:22:27Apply it to your work and write your work. Paul, please pass these behind you, count how many of you are on this side.
00:22:35This should be enough. Place the remaining sheets on my desk. I don't think you'll have enough on this side. I'll get more from Paul.
00:22:44So, use it to answer the questions and just write the answers, okay? Was there enough for you guys back there?
00:22:53No.
00:22:54I knew there was not enough on your side. Yes, I'll give you a bigger one. Give me back the smaller sheet and you may start calculating.
00:23:08Assignment number one.
00:24:06I'm done.
00:24:07You're done? Great. Why don't you just take a look at this problem, don't do it yet. Good.
00:24:30I can't figure it out.
00:24:32This is five cubed plus three cubed equals...
00:24:40Eight.
00:24:42Eight cubed, so it's eight...
00:24:45Cubed.
00:24:46X cubed, correct. This is three squared, write it on the sheet of paper.
00:24:56Those of you that are finished, please raise your hand so I know when to check the results. Good, is it working out for you Paul?
00:25:06Yes, I'm done.
00:25:07Good, we can start reviewing the answers. Why don't you start Lubo?
00:25:13Three X cubed.
00:25:16Eight X cubed.
00:25:18Yes, you just made a verbal mistake, fine. Paul?
00:25:21Three X squared.
00:25:23Four X squared.
00:25:26Okay? The problem is three squared and one squared, which is four. Marcela?
00:25:34Ten X to the fifth power.
00:25:38Good, that's a bit more difficult for us at this time because we've said that we'll go up to the fourth power for now, but the answer is 10 X to the fifth power.
00:25:48Paul?
00:25:49Four A to the fourth power.
00:25:50Good. Marcela?
00:25:53Six A to the fourth power.
00:25:54Good. Lubo?
00:25:57Negative one A to the fourth power.
00:25:59Yes. Jana?
00:26:02Negative Y squared.
00:26:03Great. Teresa?
00:26:06Negative one Y to the fourth power.
00:26:08No, no. One.
00:26:10Positive, number correct? Two Y minus one equals two. Lukas?
00:26:14That one can't be solved.
00:26:15Very good. Why is that?
00:26:17There are two different exponents.
00:26:19Okay, two different exponents. One is squared and the other one is cubed, of course.
00:26:26Okay, Martin was the first person to be done, so he had the time to take a look at number two.
00:26:31Now he'll try to explain what exactly are we going to do with this problem.
00:26:35We'll use either subtraction or addition depending on the circle.
00:26:40Very good, so give it a try so we know how to do it.
00:26:43Well, plus three X squared, we'll subtract it from negative two...
00:26:54X squared which is in the middle.
00:26:56The middle which is X squared. Calculate three X squared.
00:27:00Four.
00:27:01Four X squared. Now we keep on going.
00:27:03(inaudible)
00:27:05Yes, that's two X squared and what else?
00:27:07Six X squared.
00:27:08Good six X squared, minus...
00:27:10Is one X squared.
00:27:11Is one X squared and as you can see we got into the circle. Let's try another one.
00:27:17Two A cubed.
00:27:19Yes!
00:27:20Three A cubed.
00:27:21Yes!
00:27:22Eight A cubed, one A cubed.
00:27:24And once again we got back into the circle. Great.
00:27:26I guess we know these assignments and now I'll give you some assignments and you'll try to calculate them.
00:27:34Once again, please write the calculations on the sheet of paper. Here you go? Paul is getting a little something different.
00:27:43One for you Martin, here is one for the other Martin. Please clean up your desk so you can have plenty of... yes you may start calculating.
00:27:56Okay, you may do this one, you were very good with that one last time. You can try this one, you this one, Peter and Bara gets one.
00:28:11I can give you this one as well. Martin, this one and this as well. Start calculating the assignments. Yes, it's not too much work.
00:28:32I have enough for you two. Great. Very good Martin. Yes, yes. You're a clever girl. Sit up or you'll have crookback.
00:29:04Really?
00:29:05Yes.
00:29:08We have to do the entire page?
00:29:10Yes, the entire page. Do you need anything?
00:29:24No, nothing at this time.
00:29:25Fine.
00:29:32(inaudible)
00:29:35(inaudible)
00:29:36Can this be for an example, three plus one.
00:29:38Well and what is it going to be, zero A to the fifth power. It's zero times A to the fifth power, which is?
00:29:45Zero.
00:29:46Zero, okay? Because when you take this formula and minus it with the same formula, you get zero, so write equals zero.
00:29:58Teacher!
00:29:58Yes?
00:29:59Should I continue here?
00:30:01This is already calculated, you just have to review it to see if it's correct. Done, very good.
00:30:08The entire page?
00:30:09Excuse me!
00:30:13We have to figure out... C and D?
00:30:16Are we doing the entire page?
00:30:17You need an advice? Yes, you're doing the entire page.
00:30:20The results... (inaudible).
00:30:24Yes, you may.
00:30:45What are you saying?
00:30:48(inaudible)... five to the fourth power.
00:30:54Okay.
00:30:57Five C to the fourth power. And it is five C to the fourth power isn't it?
00:31:00Well yes.
00:31:02You have negative here so you're going to find five C to the fourth power over here.
00:31:06Fine.
00:31:11(inaudible)
00:31:20Well, A squared minus two A squared. Find out whether it's true or not. You're supposed to change over the expression, okay?
00:31:28That means this is minus A to the second power. This over here, whether it's negative A...
00:31:33(inaudible)
00:31:36Okay and down here you have the answers so why don't you check your work.
00:31:49You've scratched this out because it's not correct, yes?
00:31:52That was already crossed out, fine. You must change over the numbers here as well. Very good, are you checking your work?
00:32:03Unfortunately, you will not be able to see the incorrect answer. Just cross out the incorrect answer next time. Martin is finished?
00:32:12Try this down here, this formula and change over the expression. Okay? Yes!
00:32:22Three. (inaudible)
00:32:30Yes?
00:32:34Is that correct?
00:32:37Very good, you're so smart. Did you check this one to see if it's correct? Verify it to make sure it's correct.
00:32:42Why?
00:32:44This may not be correct.
00:32:46I'm satisfied with it.
00:32:47Are you sure?
00:32:48Teacher! If I have a problem for example zero A to the fifth power, is that zero?
00:32:50Yes.
00:32:51But I can write zero A to the fifth power.
00:32:54Well yes, but that equals zero. The previous formula is a partial answer.
00:32:58Would it be wrong if it said...
00:33:00Do we have to do these along the sides as well?
00:33:02A squared... zero A squared. Is that incorrect?
00:33:03Yes, yes.
00:33:09(inaudible)
00:33:11Correct. Yes?
00:33:14If it says, zero A squared, is that zero?
00:33:18Yes, because zero times A squared is?
00:33:21Zero.
00:33:22Zero, very good. Yes?
00:33:29Teacher, what am I supposed to do here?
00:33:31Here you have a formula and your assignment is to do the same here which is to change over the numbers where it's correct.
00:33:36And where you see the numbers incorrect, you just cross it out.
00:33:38So, I should do it like...
00:33:42I'm done with my work.
00:33:43Excellent and did you finish this part as well?
00:33:46No!
00:33:47Why don't you take a look at it than.
00:33:48These were assigned to us as well?
00:33:50Yes.
00:33:51(inaudible)
00:33:53First of all I would... It's calculated already, very good... It's not calculated here.
00:33:57How do you calculate this... do I just write out the results?
00:34:04(inaudible)
00:34:10No. Here you have negative four A squared, so you'll find it here and cross it out.
00:34:14(inaudible)
00:34:20Yes and you crossed it out, correct? Of course you may.
00:34:30Okay, great. Now I would like everyone to stop. Please place your pencils down for a minute.
00:34:53Lubos is finished,
00:34:55So he'll take a seat in the back of the room and I will send him those students that have the same assignments and they will discuss and check their work.
00:35:03Once again, please raise your hand those of you that have A and B assignments.
00:35:07Fine, so Denisa is the second one to be finished, so she'll sit in the middle desk.
00:35:14Okay raise your hands so I can send you to your proper desk. Which of you had A and B assignments?
00:35:20Denisa is back there already so let's see...
00:35:21Where am I going.
00:35:23You're going to Denisa's team, Petra goes to her as well, Bara... quietly please. Wait until I'm done.
00:35:30Bara goes to Lubos' team, Paul goes to Denisa, Teresa is with Lubos, Lukas is with Lubos as well.
00:35:39Is there anyone I did not call up?
00:35:40Me!
00:35:41Rosta, you will go with them, good. Quietly please. Paul, let him pass you by. Which students had C and D assignments?
00:35:51You have what?
00:35:52A and B.
00:35:53Okay, so you'll go with Lubos, yes? Which of you have C and D?
00:36:00The only people that will stay up here are Martin joined by Lukas, Marcy, Veronika... you will get Honza, Jana and Paul.
00:36:23And you two remained. Okay, one of you will go with the girls and the other one will go here, okay?
00:36:31I should go with Verka?
00:36:32You will go with them. Actually, why don't you come back here, bring up a chair, stay here with this group to make it simple.
00:36:43You're supposed to compare the answers and if your results come out different, discuss it, okay?
00:37:03This over here is incorrect. That should be zero. (inaudible)
00:37:14Honza will explain it to you. Which one did you work on?
00:37:19I'm done. I had only one incorrect problem.
00:37:21What team were you part of?
00:37:23Well...
00:37:24Come back here so I can take a look at how you went over your work. Come back here.
00:37:26(inaudible)
00:37:27Come back here so I can talk to you about it. Petra, Paul, come here.
00:37:33I have everything correct.
00:37:34That's very good. Come, come. Petra as well, and Paul. Come on Paul so I can take a look at it and share information.
00:37:55Petra's work is here, fine and Paul is here, good. Once again, going over these math problems is important so all of you can learn.
00:38:03Okay, I would like to know how did you come up with number five.
00:38:07Because we substituted X with one and one minus one equals zero. So X A cubed equals zero.
00:38:12I see, you've substituted X with one for example, and one cubed minus one cubed equals zero. Okay, now we know.
00:38:17Some students asked me, if they can use zero times X cubed. Would that answer work or is zero a more accurate answer?
00:38:26It can be used as well.
00:38:27What is the result when you multiply zero times X cubed. If you calculate zero times X cubed the answer is zero.
00:38:34Zero.
00:38:35So this is a complete answer. The previous example would have been an incomplete answer. Okay?
00:38:39Paul, which one were you having a hard time with so we can discuss it.
00:38:42Well, I was having some difficulty with the last one.
00:38:43The last one.
00:38:44And why did you have problems with this one. You did not read it accurately.
00:38:47Okay, I see.
00:38:48Okay, so you didn't read it. Basically this part is similarly calculated, yes?
00:38:54Fine. Lucko, how many problems did you calculate on your own?
00:38:57All of them.
00:38:58All the problems and you're satisfied with the results.
00:38:59Yes.
00:39:00Yes? So you had some problems in the beginning...
00:39:01When I figured out the formula, it got easy after that.
00:39:02It got easy for you, great. You may quietly return to your seats. How are you doing over here?
00:39:12We've discussed all the problems.
00:39:16No.
00:39:17Fine.
00:39:21Negative C to the fourth power.
00:39:23Negative C to the fourth power.
00:39:24You're making up the assignments.
00:39:25Well, fine. You did check the rest of your work, yes?
00:39:28Yes.
00:39:35May I go to the restroom?
00:39:38Five X cubed plus X minus X. Is that possible to calculate it?
00:39:42Yes, you can calculate it. The only thing remaining is? Positive X minus X equals to?
00:39:45X, X, zero X.
00:39:47Zero, and the only thing remaining will be the grand total of...
00:39:50Five X cubed.
00:39:51Five X cubed.
00:39:52I was right, do you see?
00:40:20Good, I would like everyone to put everything down. We'll get back to... Lubos!
00:40:26We'll get back to the assignment which was given to you on Thursday.
00:40:31The story is... or the text is as follows. I'll read it again since you don't have it in front of you.
00:40:37Mr. Blacksmith forged Ritirov's horses. How do you want to trade?
00:40:41Horseshoes are for free Mr., but you must pay me for the 16 nails. Pay me for the nails which I used.
00:40:52For the first nail, give me two pennies, for the second nail give me four pennies.
00:40:55And for each additional nail pay me twice as much as the previous nail. This low amount will not even equal to one dollar.
00:41:02There is an error in the text. Evaluate if Mr. Ritirov is correct, when one dollar equals 100 pennies.
00:41:08Then you calculate how many pennies is Mr. Blacksmith going to get, and if it comes out to more than one dollar, tell us how much is it in dollars.
00:41:14I took a look at some of the students' work and I congratulate some of you on a good job.
00:41:19I looked at Martin's work which was completed here in class.
00:41:22And I'll ask him to come up here and write the result on the right side of the board. Write it vertically, okay? I'm listening?
00:41:33I have it calculated (inaudible) two plus two is four, plus four is eight, eight plus eight is 16,
00:41:44and from 16, I got 66,176.
00:41:48And did you calculate it in dollars?
00:41:53No, I didn't because I did not want to add it up.
00:41:54Fine. I would like Martin to...
00:41:58Yes, you've all done your calculations but Martin will write on the board what he has done here on his paper.
00:42:03He wrote number two... okay fine and underneath that... now he'll write number one next to it. Next to it, write number one.
00:42:17Later on you'll understand where he's going with this. Then he wrote number four slash two, eight slash three,
00:42:26sixteen slash four, 32 slash five, 64 slash six, don't worry you will not have to write all the numbers.
00:42:39One hundred and twenty-eight slash seven, good. That should be enough. Can you figure out reasoning behind all of this?
00:42:50Is there some kind of correlation, or is it just a coincidence that it's number one, two, three times two, etc. Yes?
00:43:01Power numbers.
00:43:02Power of what number.
00:43:03The power of one and two.
00:43:05To the second power.
00:43:06To the second power, very good. So number two is to the first power, four is...
00:43:15Two squared.
00:43:16Excellent. Number three is... I mean number eight is...
00:43:20Two cubed.
00:43:21Two cubed. So, these numbers are exponents...
00:43:25Exponents.
00:43:27And the main number is always two and this is a powered number.
00:43:31[ Intercom ] Excuse me for the interruption.
00:43:35Due to our current situation, students will not be allowed to go out during the break.
00:43:41Great!
00:43:42I'm handing over the microphone to the class representative of 8A.
00:43:46Today at 2:00 p.m. we have tournaments of between 8A and 8B.
00:43:518B (inaudible) and now it's our turn.
00:43:55Today at 2:00 p.m. there is a tournament called "Who wants to be a millionaire" which will decide who moves up to the next level.
00:44:02Those of you that are interested in this tournament should go to room 8A at 1:55 p.m. to take an exam in mathematics.
00:44:11We look forward to your participation.
00:44:17Okay, since we don't have any time left, finalize... I'm very pleased that you recognized this as a squared number.
00:44:24Let's outline your homework. Number one to six may look overwhelming but it's just simplifying the expressions.
00:44:32Which you just did in class, okay?
00:44:40Why didn't you assign number seven?
00:44:43Because I would like to go over number seven in class. But you may try it on your own.
00:44:55Did you write down your homework assignments?
00:44:58Yes, I did.