# CZ4 EXPONENTS

This eighth grade mathematics lesson focuses on operations with numbers raised to certain powers, and calculating the area of a triangle and a trapezoid. 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 26 students in the class.

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00:00:07 | Please sit down. Do I have all of your grade books up here? |

00:00:19 | We didn't think we needed to bring it today. |

00:00:21 | Absolutely not. Please, those of you that have not turned in the assignment yet, hang on to it. |

00:00:37 | Under unusual circumstances, why don't you take it home, calculate the similar problems on your own. |

00:00:48 | And my offer is... you all have a regular schedule on Friday. |

00:00:54 | The information you read about not attending your music class is not accurate, that was an old schedule. |

00:01:01 | So, you'll have all five classes and my offer or bonus is that those of you that want, I'm willing to help you at the sixth hour. |

00:01:15 | Those of you that are having difficulty or don't understand the work can attend and I'm willing to devote some of my time for you. |

00:01:24 | Considering the fact that in today's third class, you'll have the opportunity to write similar assignments as well. |

00:01:34 | I'm offering you this opportunity, it's optional, okay? This Friday, after the last class. |

00:01:41 | Today in our class, we'll calculate and review work which we discussed in our previous class. Turn to page 50. |

00:02:05 | Before we start to go over this homework, we'll go over some of the rules which we did not discuss. |

00:02:19 | Rules which we studied and calculated. |

00:02:25 | We've dealt with powered numbers, which had concurrent elements and a powered number. |

00:02:36 | If you recall, you had a homework assignment in which a grandchild was taken to a theme park and every... |

00:02:45 | [Intercom] |

00:02:54 | Is that supposed to be a class bell ring? |

00:02:55 | I don't know. Every roller coaster ride cost him eight korun. |

00:02:59 | Grandmother gave him enough for two rides, which is two times eight korun. |

00:03:05 | Plus he received from his grandfather an additional five times eight korun. |

00:03:12 | So he went on the roller coaster and he could have gone on the roller coaster how many times? |

00:03:18 | Seven times. |

00:03:19 | Seven times. Then we simplified it. Instead of letter A we used some other examples, some kind of gifts to your relatives. |

00:03:30 | Do you recall that? |

00:03:31 | No. |

00:03:32 | You were saying or rather I encouraged you that you will pick two of your best friends and invite them to your Christmas dinner. |

00:03:40 | So you'll buy each of them a gift. Two identical gifts, okay? You don't know what kind of gifts, but it will be two. |

00:03:48 | But then you were at some kind of event and you said to yourself, |

00:03:54 | I will expand the list of my close friends who will receive a gift from me. So, you will add five more gifts. |

00:04:04 | See how it matches what's on top, which doesn't necessarily have to happen. So, how many gifts is he going to buy? |

00:04:12 | Seven. |

00:04:13 | Seven times D. Fine. And from that we derived a rule that we use addition and multiplication when the powered numbers are the same. |

00:04:33 | Imagine instead of a gift, you'll give them a holiday card which will include a powered number. |

00:04:42 | Give me a number. |

00:04:46 | Eight cubed, fine. So you'll give them a card eight cubed, nicely wrapped. You'll give it to these two and to your five new friends. |

00:04:59 | And now we can simplify it as... |

00:05:04 | Seven times eight cubed. |

00:05:06 | Seven times eight cubed. You can see that we work with the same powered numbers. |

00:05:14 | The main number is the same as well as the exponent. Correct? Do you remember? Good. |

00:05:24 | Then we had another category in which the only thing that was the same was, the main number or the exponent. |

00:05:35 | If we look at it in the same order as we studied it. Anna? |

00:05:39 | The main number. |

00:05:40 | The main number is the same, fine. We learned how to deal with powered numbers with the same main number and we learned to calculate what? |

00:05:54 | Open up your notebooks, the rules are in there. Open it up! And we're trying to figure out what, Kuba? |

00:06:23 | We worked with powered numbers that had the same main numbers, Vasek? And we studied how to figure out the product and the quotient. |

00:06:36 | And the quotient. |

00:06:36 | Please tell me... we multiply two powered numbers with the same main numbers. |

00:06:46 | Give me a calculation which includes two same main numbers. Ondras. |

00:06:56 | Five to the sixth power. |

00:06:57 | Five to the sixth power. I'll write it differently so you can understand the main concept of this example. |

00:07:07 | It's the same, so five times five, which is the same. You've said to the sixth power and... |

00:07:15 | To the fifth power. |

00:07:16 | And to the fifth power. Please tell me guys, what remains. Jitka? |

00:07:25 | Five to the eleventh power. |

00:07:26 | Five to the eleventh power, fine. We've also studied... powered numbers with the same main number and its... |

00:07:41 | Quotient. |

00:07:42 | Quotient, good. Give me an example of two powered numbers that have the same main numbers. Vojta! |

00:07:52 | Three to the eighth power. |

00:07:54 | So, the two main numbers are three, fine, and we'll divide these two numbers. |

00:08:01 | And in order for these numbers to be powered numbers we must include the exponents. Very good. Vojta! |

00:08:08 | Three to the eighth power. |

00:08:10 | To the eighth power and make sure this one is smaller. |

00:08:12 | To the sixth power. |

00:08:14 | To the sixth power, equals... is the main number going to be the same, Vojta? |

00:08:18 | Yes, three squared. |

00:08:20 | Three squared. Fine, that's another category. Here we worked with powered numbers that have the same main numbers. |

00:08:31 | The next three rules apply to... Radka? |

00:08:43 | Power of a product and power of a quotient? |

00:08:46 | Yes. Tell me the power of a product, Radka? |

00:09:00 | Two times three. |

00:09:01 | Two times three, for example. |

00:09:04 | To the fifth power. |

00:09:06 | And the same exponent will apply to both of the main numbers. Because it will unfold into what... Andrea? |

00:09:20 | Two to the fifth power. |

00:09:21 | Two to the fifth power. |

00:09:23 | Times three to the fifth power. |

00:09:24 | Times three to the fifth power. You can see that the exponents are the same, do you see that? |

00:09:31 | Here you have the same main number and the exponent, here just the main number and here we'll work with the same exponents. |

00:09:41 | Furthermore, we know the power of what, Marketa? |

00:09:47 | Quotient |

00:09:48 | Quotient. Give me a simple example. |

00:09:51 | Eight divided by two to the third power. |

00:09:57 | To the third power, fine. And even here, we'll have the same exponent. Its product. |

00:10:08 | So, it's going to be eight to the third power... |

00:10:12 | Divided by two. |

00:10:15 | I said product, excuse me I meant quotient. Okay, and we also studied what else? Katka? |

00:10:26 | Power of the exponent. |

00:10:27 | Power of the exponent. Here we go. Give me an example. |

00:10:33 | Two cube and the entire thing is to the fifth power. |

00:10:39 | To the fifth power. |

00:10:42 | This equals to? Lucka Maresova? |

00:10:47 | Two and we multiply it by... |

00:10:50 | This number stays the same and the exponent will be... |

00:10:55 | We multiply three times five. |

00:10:57 | We multiply it. That is three times five equals 15. It's two to the fifteenth power. These are rules which you must master. |

00:11:14 | Those of you that are having some difficulties with this, should practice at home with his friends in order to get comfortable with this. |

00:11:26 | Okay, let's look up page 50. |

00:11:31 | Open up your notebooks and write today's date, twenty-eighth of November and we'll do problem three, five letter A. |

00:11:41 | One problem after another, this time we'll do the work together with someone up here by the board. |

00:11:47 | First student to come up to the board is Paul. We must... as I told you yesterday, we must write down the assigned problems. |

00:11:59 | Okay, Paul. Calculate 30 to the third power and describe to us how you're going to figure it out. |

00:12:12 | First I multiply three to the third power. |

00:12:15 | You'll raise the powers. |

00:12:15 | Raise the powers of three cubed. |

00:12:17 | Which totals? |

00:12:19 | Seven is 27. |

00:12:20 | Wait a minute. Don't write three cube, that would confuse all of us. |

00:12:26 | Seven equals to 27. |

00:12:28 | Correct. |

00:12:30 | Plus- |

00:12:31 | No, not plus. Just write the number. It's actually... |

00:12:40 | Twenty-seven and three... three to the tenth power is 1,000 so that is 27,000. |

00:12:47 | Excellent. The answer is 27,000. Call up the next person and read them a problem. |

00:12:52 | Alena! |

00:13:00 | No one is absent today? |

00:13:01 | Martusova is absent. |

00:13:03 | Negative three to the fourth power, you're supposed to compare it. |

00:13:12 | Okay! |

00:13:13 | And negative five to the third power. |

00:13:15 | Leave a blank between the two. |

00:13:16 | Okay! |

00:13:18 | Lucka was absent in the first class as well, correct? |

00:13:25 | What is the exponent? |

00:13:27 | To the third power. |

00:13:29 | So, it will be... negative three to the fourth power is larger because we have an even number, negative coefficiency. |

00:13:41 | Yes, the exponent is an even number but in the other one, the exponent is an odd number so what kind of number will you come up with? |

00:13:47 | Negative. |

00:13:47 | Negative, but in this one the number will be... |

00:13:49 | Positive. |

00:13:50 | Positive, fine. So do you have it correct or not. |

00:13:56 | I have it correct. |

00:13:57 | Incorrect, you need to reverse the numbers. |

00:13:59 | You described it correctly but you wrote it wrong. Good, next person, let's hurry up. |

00:14:15 | Write the main number two, 128. |

00:14:33 | Number two is the main number so write number two and now find out the exponent. |

00:14:38 | If it's two squared then it's four, so try to the third power which is eight and so on. Who's finished with this problem? |

00:15:03 | Continue by multiplying it here on the side. Two, four. Here try this marker. |

00:15:48 | Who can help him out. Michael Onderzak. |

00:15:56 | To the seventh power. |

00:15:59 | Two to the seventh power. |

00:16:02 | (inaudible) |

00:16:03 | That's fine. Two to the sixth power is 64, two to the seventh power is 128. Excellent. |

00:16:09 | You know how you came up with this, yes? Let me have the marker. |

00:16:11 | Two to the first power equals two, squared is four, cubed is eight, times two is 16, which is the fourth power. |

00:16:21 | Thirty-two is to the fifth power, 64 and 128. Call up the next student. |

00:16:30 | (inaudible) |

00:16:37 | We're not done yet. |

00:16:41 | Seven squared times seven cubed. Write the exponent of seven. |

00:16:48 | That equals to seven and I multiply two times three. |

00:16:53 | No, no. |

00:16:54 | Adding it up. |

00:16:55 | I meant adding it up, so the answer is seven to the fifth power. |

00:16:59 | Show us which rule you followed to complete this problem. |

00:17:02 | That one up there. |

00:17:04 | Okay, why don't you pull down the board and point it out to us. Very good. Next person! |

00:17:11 | Anna! Six times three cubed, minus four times three cubed. |

00:17:28 | Six times three cubed, please erase it and Radka, start again. |

00:17:37 | Six times, |

00:17:40 | Don't put it in parenthesis, six times... |

00:17:43 | Three cubed. |

00:17:45 | Times, she said times so it's multiplication. Three cubed. |

00:17:53 | Minus four times three cubed. |

00:18:00 | Before you start calculating it, which rule will you use in this case. |

00:18:08 | It's an assignment which has the same main number as well as the exponent. |

00:18:14 | Power of the exponent. |

00:18:16 | Take a good look at it. Show me the two powered numbers in this example. Show me the first one? Read it out? |

00:18:26 | Three cubed. |

00:18:26 | Read the other one! |

00:18:28 | Three cubed. |

00:18:29 | Which rule applies to this? |

00:18:38 | That one. |

00:18:39 | Correct. These are formulas that have the same main number as well as the exponent. |

00:18:46 | Okay, six times (inaudible) minus four times (inaudible) is the same as six times three cubed. Yes of course. Which equals... |

00:18:57 | Three cubed is 27 times two equals 54. |

00:19:05 | Do you all agree with the answer? |

00:19:06 | Yes! |

00:19:07 | Katka, do you agree? |

00:19:08 | Yes. |

00:19:08 | Correct. Is there a simpler way of doing this? You may sit down now. |

00:19:14 | Isn't there a simpler way? Two times three is six and calculate six cube. Why not. |

00:19:21 | (inaudible) It's not possible. |

00:19:23 | We would not have to go through all these steps. Jitka! |

00:19:28 | (inaudible) |

00:19:29 | Why can't I do two times three is six cube. Ondra? |

00:19:38 | Because, power of a product surpasses everything else. |

00:19:40 | Because, raising powers surpasses multiplication, correct. Anna did it correctly, except she did not call up the next person. |

00:19:49 | Yes, Lukina! |

00:19:50 | Come up here Vasnovsko. Catch Lukina. |

00:19:59 | One point two to the eleventh power divided by one point two to the ninth power. |

00:20:09 | Tell him the instructions on what to do with the problem. |

00:20:12 | And you're supposed to calculate it. |

00:20:14 | So, which rule will you follow? Stand aside and tell us which rule you will follow. |

00:20:21 | This one. |

00:20:24 | We're dealing with power of quotient with the same... |

00:20:29 | Same main number. |

00:20:29 | Very good. Equals! You're supposed to calculate the problem, you just simplified it. |

00:20:40 | Calculating the problem means, you come up with a number. You can calculate it in your head. |

00:20:48 | First, you calculate 12 squared, which is how much? Just ignore the numbers that are to the nearest tenths for now. |

00:21:03 | That's 144, and you separated the two because of the decimal numbers (inaudible). Very good. |

00:21:12 | You just didn't underline the answer twice. Next person. |

00:21:32 | Eight to the X power divide it by eight to the third power equals eight to the eighth power. (inaudible) |

00:21:45 | So write next to it X equals... |

00:21:48 | X equals. |

00:21:50 | Point out the rule you're going to follow! Correct. |

00:22:06 | X equals eight... |

00:22:12 | No, no. Our only concern is this X. |

00:22:14 | X equals... |

00:22:16 | We can't be mixing it up, okay? |

00:22:18 | X equals 11. |

00:22:20 | Correct, how did you figure that out? How did she come up with that answer, that X equals 11! |

00:22:25 | I added up number three and number eight. |

00:22:27 | Fine and in order to verify it, try to insert the number in there. Instead of X, write in number 11. |

00:22:35 | Eight to the eleventh power divided by eight to the third power equals to eight to the eighth power. |

00:22:44 | Excellent. Please underline X equals 11. Underline X equals to 11, that's the answer. Good, next person. |

00:23:04 | Andulka! |

00:23:07 | Write down a number which is greater. Seven squared in parenthesis. (inaudible) |

00:23:10 | May I write it like this. Is it Okay? |

00:23:14 | Here you did not write what X equals. Please write it in. |

00:23:18 | And seven to the third power. |

00:23:22 | That's why we're doing this together in class. |

00:23:29 | First of all I calculate what's in the parenthesis. Seven squared equals 49. |

00:23:36 | Is that important? Which rule will you follow for this problem. Move aside and point it out for us. |

00:23:43 | That one? |

00:23:49 | Correct, so use it! |

00:23:54 | Here we have two X and three times three is nine. |

00:24:01 | Yes, very good. Why don't you come over here to write on this side of the board. |

00:24:23 | Write the answer for 305,026. |

00:24:34 | Equals, good. |

00:24:37 | Three times 10 to the fifth power. |

00:24:42 | He'll figure it out on his own. |

00:24:44 | Plus five times 10 cubed. |

00:24:50 | Very good Michael. |

00:24:52 | Plus two times 10 to the first power, plus six times one. |

00:25:08 | Very good, call up the next person. It's correct. I'll just ask you. Could this have been just two times 10, not 10 to the first power? |

00:25:16 | Yes. |

00:25:16 | Because 10 to the first power is 10. The way he did it is correct as well because that's how we studied it. |

00:25:24 | Why is there so much noise in here? Here he wrote times one. Is that correct? |

00:25:30 | Yes. |

00:25:30 | Absolutely it's correct. He also could have... instead of one, he could have put in times... |

00:25:34 | Six times... |

00:25:37 | Six times... |

00:25:38 | Ten to the N power. |

00:25:39 | Ten to the N power. Both answers are correct. |

00:25:43 | Write A times 10 to the N power. |

00:25:48 | Write the formula, A times 10 to the N power. That's what we can use when we deal with large numbers on a calculator. |

00:26:00 | Go ahead. |

00:26:01 | Seven hundred and thirty-four thousand... |

00:26:20 | No, no. |

00:26:23 | Leave it up there. In order for you to have 10 cubed here and not be a mistake as the final answer. |

00:26:32 | You would have to have over here... |

00:26:34 | Seven hundred and thirty-four. |

00:26:34 | Seven hundred and thirty-four. That's still not a final answer. This will equal... |

00:26:51 | Very good. |

00:26:52 | No, that's not correct. It should be times 10 to the fifth power. |

00:27:05 | Underline the answer twice. Good. Ladies and gentlemen, look on page 51, exercise number one. |

00:27:19 | Please take out a number two pencil, number two pencil and you're supposed to calculate exercise number one. |

00:27:36 | Write it into your notebooks as well. |

00:27:38 | Using the pencil? |

00:27:40 | Excuse me? |

00:27:40 | With the regular pencil? |

00:27:42 | Start with the outline of 51 over one! I will dictate you the following assignment. Negative 50 in parentheses to the fifth power. |

00:28:00 | I thought we were going to complete the assignment in the book but instead we'll copy the assignment into our notebooks. |

00:28:04 | I'll start over again. Negative 50 in parentheses to the fifth power plus negative 30 in parentheses to the third power. |

00:28:14 | Plus negative 20 in parentheses to the second power, plus negative 10 to the first power, plus zero to the tenth power, |

00:28:28 | Plus 10 to the first power, plus 20 squared, plus 30 cubed, plus 50 to the fifth power. |

00:28:42 | And I would like to find out if you can figure out why did I ask you to use a regular pencil. Figure this problem from your memory. |

00:28:58 | How is the pencil going to be useful to you. Marta! |

00:29:04 | So we can reduce a fraction... to the lowest term... |

00:29:08 | Not to reduce a fraction but to calculate... |

00:29:11 | When we have negative 50 to the fifth power plus 50 to the fifth power, it will equal to zero. (inaudible) |

00:29:16 | Yes of course. So you cancel out those numbers that equal to zero. For instance, negative 50 to the fiftieth power and plus 50... |

00:29:32 | Excuse me, I just made a mistake. Negative 50 to the fifth power and plus, Tom? |

00:29:37 | Plus 50 to the fifth power. |

00:29:39 | Fifty to the fifth power, very good. Just cross it out lightly. |

00:29:44 | This does not mean you're eliminating these numbers, it just means you're done with those numbers. |

00:29:54 | Can you find another pair of numbers which can be crossed out? Jitka! |

00:30:00 | Negative 30 to the third power plus 30 to the third power. |

00:30:02 | Very good, those two equal to zero as well. What else? Kuba. |

00:30:10 | Negative 20 squared and 20 squared. I see. |

00:30:14 | Does anyone object to that? Tom objects, who else. |

00:30:18 | Me! |

00:30:19 | Why not... why do you object to that answer. Kuba. |

00:30:24 | Why didn't some of you have a problem with negative 30 cubed but object to negative 20 squared? |

00:30:35 | Negative 30 cubed was fine but you object to negative 20 squared. Do you know, Ondra? Please tell us. |

00:30:54 | There is an even number... it's an even exponent. |

00:30:59 | The negative main number has an even exponent. That's not the same thing, is it! Iveta. |

00:31:07 | Because a positive number will come out of this. |

00:31:09 | Because in this case we get a positive number. Negative 20 squared does not come out to a negative answer but a... Kuba! |

00:31:15 | Positive number. |

00:31:16 | Positive number, so these two numbers can't be crossed out. What else can we cross out... which other pairs equal zero, Vojta? |

00:31:26 | Negative 10 to the first power. |

00:31:30 | Yes and... |

00:31:31 | And negative... and positive 10 to the first power. |

00:31:33 | Good, do we all agree? |

00:31:35 | Yes! |

00:31:37 | Are there any other pairs we can cross out? Vasek. |

00:31:44 | No, maybe zero? |

00:31:48 | Okay, let's try that one, why not. Zero to the tenth power equals... |

00:31:52 | Zero. |

00:31:52 | Zero, so what numbers remained untouched and remain to be calculated. Michael! |

00:32:07 | Negative 20 squared and plus 20 squared. |

00:32:13 | What's the result? |

00:32:15 | Eight hundred. |

00:32:16 | Eight hundred, write in 800. |

00:32:19 | Negative 20 squared equals 400, plus 20 squared is also 400, and that totals 800. |

00:32:27 | Wow, we're moving along just fine. At home you will verify number two, my original idea was to do it in class. |

00:32:41 | You'll do number three and four large A and small A will do. Alenka up here on the board. |

00:32:55 | Number four A and small A. You need to calculate the second root of a number which is in the parentheses. |

00:33:07 | First of all, figure out the estimate, so the second root of six, second root of six. |

00:33:15 | (inaudible) |

00:33:17 | Next math class which is tomorrow. |

00:33:20 | (inaudible) |

00:33:22 | Oh yes, that's correct. So it's for Friday. Quiet. First of all you must figure out the estimate. |

00:33:32 | Estimate. |

00:33:34 | The second root of a problem, we do an estimate based on what? |

00:33:37 | Based on the closest squared number. |

00:33:39 | Correct. |

00:33:40 | The squared number is four and (inaudible). |

00:33:49 | Fine and now do the calculations. You're supposed to do it to the nearest decimal number. What do you need for that? |

00:34:04 | Table chart. |

00:34:04 | Go get it. Exactly to the nearest decimal number. Very good. Can someone calculate it on a calculator? |

00:34:38 | Two point four, four, nine, four, eight, nine, seven. |

00:34:40 | So based on the calculator the number will be rounded to... Alenka, come here. |

00:34:46 | This on the board is correct, she followed the table chart. |

00:34:50 | What is the number again? |

00:34:51 | Two point four, four, nine... |

00:34:58 | We don't need to go that far. That's enough. Equals to approximately... just write it in. It's more accurate with the calculator. |

00:35:16 | Because, the table chart is rounded to the nearest tenth, okay? This nine here was shown in the charts as 545. |

00:35:30 | And you continued to rounded up but there isn't much of a difference. Call up the next person, Alenka! |

00:35:58 | The second root of 60, the second root of 60. |

00:36:05 | Rounded up to the nearest decimal point. First of all, do the estimate. That will be an approximate second root of what nearest squared number? |

00:36:16 | Sixty-four. |

00:36:19 | Wait a minute. Not from 64 but from the root of 64 and that equals? |

00:36:28 | Very good, that's your estimate. Now calculate it. The second root of 60 equals... use the graph chart. |

00:36:57 | And now round it up to the nearest tenth. |

00:37:01 | [Laughter] |

00:37:06 | It's a good thing the gardeners didn't put water in it. Thank goodness for that. To the nearest tenth is eight. It is accurate, fine. |

00:37:27 | Students, please complete A, five large A, six and seven large A... |

00:37:37 | We're not going to do it in class? |

00:37:38 | Well yes but it's taking us too long to complete these problems. And on page 53... I thought we would have time to do this here in class. |

00:37:48 | On your own or in a group of two, please do number 16 right now, okay? |

00:37:56 | Now? |

00:37:57 | Yes, now. |

00:38:02 | The entire page of 51. |

00:38:06 | Please do the problem in your personal notebook, okay? I'll be filling this in. |

00:38:36 | You may work in a group of two, if your group is still having troubles you may turn to another group for assistance. |

00:39:17 | You will work with an area of what kind of geometric configuration? |

00:39:21 | Trapezoid and triangle. |

00:39:22 | Triangle and... |

00:39:24 | Trapezoid. |

00:39:25 | Trapezoid. To calculate the area of a triangle, you need to know what. |

00:39:29 | Height and length. |

00:39:30 | The length and height of one side. To calculate trapezoid, you will need to know... |

00:39:39 | A and C. |

00:39:41 | So, the base and the height, very good. And you'll calculate the height based on your knowledge of the Pythagorean theorem, which are marked in here. |

00:40:04 | Everyone who completes the problems will get an A grade. A very high A grade. We have three minutes remaining in class. |

00:41:32 | Use what's on the board... oh you mean that one, yes you may use a calculator. |

00:42:27 | Don't forget that these problems require that you reserve about 15 percent, okay? |

00:43:27 | Don't spend too much time on this. You have this here... hurry up so you can finish it up. You can just calculate the triangle here. |

00:44:08 | What is this? Height? |

00:44:12 | The height of this triangle. |

00:44:15 | Of this triangle and this is the height of... |

00:44:19 | Trapezoid. |

00:44:20 | Trapezoid, correct. Do you need an additional minute to complete this... do you need it? |

00:44:47 | Yes, yes. |

00:44:48 | Fine, I'll give you one more minute. Actually, you'll get two minutes. |

00:47:02 | Excuse me? |

00:47:03 | How much... |

00:47:03 | The answer is obvious... well it is a verbal answer. Let me see. |

00:47:18 | Two hundred and one point twenty. |

00:47:21 | Why don't you round off the number. |

00:47:22 | So, it will be 200. |

00:47:26 | Lukine, would you be able do describe the entire process? |

00:47:29 | What do you mean. |

00:47:29 | The process... |

00:47:30 | Well, some of it. |

00:47:32 | Well, he helped me on something and I helped him with something else. |

00:47:35 | Okay, both of you can write an A grade in your notebooks. Congratulations. |

00:47:45 | Lukine, you will come back here with Tom later for me to sign your grade. Let me see what you got. No, no, no. |

00:48:04 | Well, where is the answer? |

00:48:06 | Here it is. |

00:48:07 | No, no, no. Okay, students, time is up. |

00:48:17 | No not yet. |

00:48:22 | Twenty more seconds. I'm counting seconds. No, no, no. |

00:48:44 | It's over, we'll get back to it in our next class. No, I don't want to see anybody. |

00:48:53 | Okay students, please stand up. I want to remind you, make sure you clean up this class before you leave. |