11th Grade Mathematics - By
Transcript
00:07 | Good morning . Very . Does anybody know who this | |
00:11 | gentleman is up here ? I knew you'd know Donnie | |
00:14 | , That's Michael Phelps , That is Michael Phelps . | |
00:17 | And what is he famous for ? He is famous | |
00:19 | for winning eight olympic gold medals at Beijing olympics and | |
00:23 | he also has the record for the most olympic medals | |
00:27 | of all time . Awesome . Very good . I | |
00:29 | take it you're a swimmer . Mhm . Little bit | |
00:32 | . Mhm . So if you were going to swim | |
00:35 | in the 2016 Olympics , what would you need to | |
00:38 | know about ? Michael Phelps ? Not need to know | |
00:41 | anything because he's retired . Has he really ? He's | |
00:44 | done swimming . He but his mom is probably going | |
00:47 | to force him to make it . So she's probably | |
00:48 | going to It's been a little bit , but it's | |
00:51 | not like normal . Okay , so if you were | |
00:54 | still going to be in the 2016 Olympics and you | |
00:57 | wanted to win a medal , what would you need | |
00:59 | to know shall be the the average speed he usually | |
01:06 | goes and you want to have to try to beat | |
01:08 | his speed by practicing and trying to get past awesome | |
01:11 | . You would need to know how fast he speeds | |
01:13 | . So you want to maybe predict how fast he's | |
01:15 | gonna go so that you would know how fast you | |
01:17 | need to swim . That's kind of what we're gonna | |
01:19 | do today . What we're going to be looking at | |
01:21 | 100 m dash or the men's 100 m dash . | |
01:24 | Okay . I'm going to pass around some data for | |
01:28 | you and it's got the times the speed that men | |
01:33 | have run the 100 m dash from 1900 to 1996 | |
01:37 | . Okay . Once I give this to you , | |
01:39 | I want you to think for a few minutes all | |
01:41 | by yourself . Some private think time . Okay . | |
01:44 | Think about how you're gonna graph this . Okay . | |
01:47 | Think about your X and Y axis . Think about | |
01:49 | your labels . Think about everything . Okay . And | |
01:52 | then after you have some private think time we're going | |
01:55 | to do this in your groups . Okay ? Yeah | |
02:00 | . Mhm . Welcome . Yeah . Yeah . Yeah | |
02:13 | . Okay . Tina . I'm sorry . Yeah . | |
02:22 | Yeah . Mhm . Okay . Talk a little within | |
02:48 | your group and decide how you want to set up | |
02:50 | your graph , how you want to set up your | |
02:52 | scatter plot . And then on the yellow piece of | |
02:54 | paper that's on your table . I want you to | |
02:57 | graph the scatter plot for me . After you've grabbed | |
03:01 | your scatter plot , I want your group to come | |
03:03 | up with the best correlation coefficient . You can get | |
03:07 | estimate what you think the correlation coefficient is going to | |
03:10 | be okay ? And let's go ahead and round that | |
03:14 | to the let's do the thousands place because we want | |
03:18 | to have a winning group because you might get a | |
03:20 | little surprised if you're the winning group . Okay . | |
03:24 | Right . All right . I'm gonna put the year | |
03:29 | of the olympic games as X . And then since | |
03:32 | the independent variable when Now why is uh But why | |
03:36 | is the long time then ? Yes . Way . | |
03:43 | We're going to go by the 1900s . Wait here | |
03:47 | we go . By 1900 instead of doing what did | |
03:50 | yesterday way For this one should easily go by 12 | |
04:07 | 900 . This one uh probably have my .2s or | |
04:12 | something . Very point for us . Can we do | |
04:18 | exactly the near like that ? Sure . Mhm . | |
04:21 | If that's what your group wants , just make sure | |
04:25 | you label . Yes . Um And one of you | |
04:29 | , I want one of you to do it on | |
04:30 | the yellow . Okay , Perfect . What's that called | |
04:38 | ? The break . That's a good It's a good | |
04:41 | one for technical . The brakes quickly thing . I | |
04:43 | knew what you meant . Right , good job . | |
04:52 | Let's go . Did you all decide on 10 years | |
04:55 | at zero ? Awesome . You're going to do tense | |
04:58 | . Okay . We're going to do a break and | |
05:00 | started perfect . Mhm . Sounds good . Christian . | |
05:07 | We're gonna do the calculator later . Okay , help | |
05:10 | them with that group . Y'all think about this crap | |
05:11 | they're all doing . Yeah , I mhm . When | |
05:19 | you get up , it's so hard . Mhm . | |
05:26 | 30 years . Like , do we go from tens | |
05:34 | because we do that or do you want us to | |
05:35 | literally right now ? You can do whatever you want | |
05:38 | . Just remember you're going to type it in the | |
05:40 | calculator eventually . But no , you can , you | |
05:43 | can come by anything you want . Thank us . | |
05:47 | Up to 11 . So is that okay ? Yeah | |
05:51 | , I would actually see how it puts point . | |
05:54 | So when it says 10 and 11 , I mean | |
05:57 | it's the same thing . Yeah . Just to make | |
05:59 | anyone . And then maybe Did you decide on a | |
06:14 | scale ? Yeah , we're going to go about 16 | |
06:22 | units to do that . So , okay , so | |
06:24 | where do you want to start ? Maybe you started | |
06:28 | the exact maybe ? Can you do it on the | |
06:31 | line for the X axis ? You can do you | |
06:33 | need to though , Do you need to do a | |
06:36 | squiggle ? What's that called ? Squiggle a break ? | |
06:39 | Mhm . Do you need a squiggle on the X | |
06:43 | or do you need a squiggle on the why ? | |
06:44 | Why ? Maybe the why not the X . Hmm | |
06:47 | . Why ? What are you gonna start with on | |
06:49 | the X 9.80 or something ? You know , in | |
06:52 | the xx xX 1900 ? So there's really no break | |
06:56 | there . Okay . But you do have a break | |
06:58 | on the wax is good . Good , good , | |
07:01 | good . And you've got a good label . I'm | |
07:05 | going to pass around some questions that you can use | |
07:08 | to help make sure you're on the right track . | |
07:11 | Okay . Just a few little questions to think about | |
07:14 | as you're doing this . Mhm . You're right . | |
07:24 | Yeah , absolutely . Okay . You can write on | |
07:27 | these questions if you want to . Okay . Just | |
07:30 | making sure you're doing that . We're going to do | |
07:32 | that in a minute . Okay . Okay . Okay | |
07:48 | . Tell me tell me a starting point . Where | |
07:50 | could you start ? Do you have to start at | |
07:52 | 9.84 ? Okay . You can start at 9.8 and | |
07:57 | you've got to go to what , 11 point soon | |
08:00 | ? 11.2 or 11 . Let's go . Let's go | |
08:06 | by .2 . Okay , perfect . As long as | |
08:09 | you're consistent , as long as you label there's not | |
08:12 | really a right or wrong . Yeah . 9.8 I | |
08:17 | guess . Right . And then think about these . | |
08:20 | Okay , okay , wherever it goes it goes , | |
08:25 | it doesn't have to do a specific thing . Okay | |
08:28 | . How do you know it's going to make a | |
08:29 | line and not a quadratic ? What do you mean | |
08:35 | ? Like how do you know that's going to be | |
08:36 | a line that you're drawn through it ? David , | |
08:39 | can you tell that ? Because it's they're not all | |
08:42 | spread out . There , not all spread out and | |
08:44 | there's no curve . It looks straight . Right ? | |
08:46 | So that's how you know , it's linear . Okay | |
08:49 | . Good job . Good morning . Time would be | |
08:51 | t okay . Waiting times and then years we thought | |
09:02 | we were just going by the access . Yeah . | |
09:04 | So we could just put like a , like a | |
09:06 | spear , all these questions . You know , if | |
09:12 | you can all answer together based on your yellow . | |
09:15 | So just to have you all done all of these | |
09:17 | , we are going and when you decide on your | |
09:21 | correlation coefficient , I want it on the whiteboard , | |
09:23 | but don't let anybody see it . All right . | |
09:26 | That's going to be on paper . You know , | |
09:28 | you can just sit right there . This is just | |
09:30 | making sure you've done everything . You don't actually have | |
09:32 | to ride out . Okay . It's just help make | |
09:34 | sure you've completed everything . Nice . Nice . Okay | |
09:40 | . Tell me how you knew this was a straight | |
09:41 | line . There's no what ? Uh huh . There's | |
09:46 | no curve to it . Perfect . No curves . | |
09:48 | So , you knew it was linear . Right . | |
09:50 | Alright . Have you estimated your correlation coefficient ? Like | |
09:54 | would this be part of it that we even look | |
09:56 | at this part that helps you decide remember what's a | |
09:59 | perfect Correlation coefficient one or -1 . So , the | |
10:05 | more points away from it or the farther away , | |
10:08 | the closer to zero . So you're going to kind | |
10:10 | of get estimate yes . Yes . Just get Mhm | |
10:19 | . Mhm . Hey guys , how are you all | |
10:23 | doing to go through your questions ? Yeah . Okay | |
10:29 | . I'm gonna change in her prediction because she okay | |
10:36 | , but still I'm agreeing with you . All right | |
10:44 | . When you're , when you're set , put it | |
10:46 | on your white board . Thank you . All are | |
10:49 | good . You're a perfectionist at this table , aren't | |
10:56 | you ? Yes , I like it . Nice . | |
11:00 | Okay , let's talk about what type of function this | |
11:04 | is . Does it have any kind of curve to | |
11:07 | it ? Uhh I can't say that it's a door | |
11:11 | because you've got to decide what kind of function linear | |
11:15 | . I think it makes a line . I would | |
11:18 | probably agree with you . It doesn't really curve enough | |
11:20 | to make make it anything different . Mm . Yeah | |
11:26 | . So draw the line you think has the best | |
11:28 | fit to that job . Nice . Nice . It's | |
11:36 | a correlation . What is that 1 ? What's that | |
11:40 | called ? That one . Lonely point out there . | |
11:43 | It's like , oh , good , good , good | |
11:47 | , good , good Marine . All right . We're | |
11:51 | all going to come up with your correlation prohibitions . | |
11:54 | You want the press , don't you ? Yeah . | |
11:57 | Yeah . Mhm . Do you go through all your | |
12:01 | questions ? Yeah . Did you come up with your | |
12:04 | correlation coefficient yet ? Yeah , we got and Yeah | |
12:08 | . Okay . We put it on your white work | |
12:09 | for me . Okay ? We're going to hold them | |
12:11 | up in just a second . You're not bad . | |
12:24 | Let me be really off . Okay . Mhm . | |
12:28 | Okay . You have about 10 seconds , 10 seconds | |
12:33 | and I'm going to ask for them . Mhm , | |
12:36 | yep . I want it to the thousands . I | |
12:42 | want you . I want it to the thousands every | |
12:46 | year . Okay , That's the past plus this . | |
12:52 | Yeah , you're back . Okay . Can I have | |
13:00 | everybody's attention up here ? Let me see those white | |
13:05 | boards . Let's see what we've got . Negative 0.987 | |
13:10 | negative 0.974 negative 0.85 957965 . These are very very | |
13:18 | good predictions . Who can tell me why everybody has | |
13:22 | a negative raise your hand ? Alright , other line | |
13:26 | is going down the lines going down to if you're | |
13:29 | slopes negative , your correlation coefficient is gonna be negative | |
13:33 | as well . Okay . So somebody tell me who | |
13:36 | wants to show the graph rally , will you bring | |
13:39 | it up here for me ? Just let me move | |
13:44 | this for just a second . Okay send it right | |
13:50 | there for me . Let's see it . If it's | |
13:54 | gonna show we'll get there we'll get there . Okay | |
14:08 | ? So here's their group . That's pretty good . | |
14:11 | So you let your X axis be years . Okay | |
14:15 | . Why did you choose that ? Because it was | |
14:18 | an independent variable And like how I had to explain | |
14:21 | to my group the time is dependent on the years | |
14:24 | , not the years , depending on the time . | |
14:26 | Nice , very nice . Very good graph . I | |
14:28 | like it , Katie , you want to show yours | |
14:31 | ? Thank you . Riley . Take that back . | |
14:38 | Is that Oh I say you did years But they | |
14:43 | didn't do the exact year . They did their years | |
14:46 | by 10s . Is that okay ? Yeah . Nothing | |
14:49 | wrong with it . Right . As long as it's | |
14:51 | labeled , you're good , anybody have something different ? | |
14:55 | Parker . Thank you . Nice . Why did you | |
15:05 | choose to use two digits for your years ? Um | |
15:08 | it was just easier and crying out 1900 and it | |
15:12 | just kind of simplified it for you . Okay , | |
15:15 | awesome . Thank you . Okay how can we check | |
15:18 | our graphs using technology ? What can we do Amanda | |
15:22 | ? You could use your calculator and deuce . That's | |
15:25 | awesome . Okay let's do it . Let's use your | |
15:28 | calculators , enter your data and let's draw our stat | |
15:33 | plots . Yeah , mm . The same thing . | |
15:52 | They're clear . Inner . Okay thank you . You're | |
15:55 | welcome . Yeah . Where do we go after we | |
16:04 | put in our lists ? You wanna first we want | |
16:07 | to see the scatter plot . So where do you | |
16:09 | go ? Okay . Remember zoom ? What ? Mhm | |
16:14 | . Was that A . X . Not yet . | |
16:17 | That's your regression zoom stat because all your data is | |
16:21 | in your status . Good good good good . I | |
16:28 | see some of you started at zero . Some of | |
16:30 | you are using the full year so it's good options | |
16:36 | . Good options . Yes . Mhm . This stuff | |
16:41 | . Okay . Yeah we want to graft first . | |
16:47 | Okay . Hey I'll look up here for two seconds | |
16:51 | . We've got some questions on graphing what you enter | |
16:54 | your data into your calculator . Where do I go | |
16:58 | to actually see it on my graph if I want | |
17:00 | to see the picture ? Well uh let's zoom and | |
17:04 | then push nine zoom and nine . And what is | |
17:07 | number nine ? That would be zoom stat . Zoom | |
17:12 | stat . Because we went to start to enter our | |
17:14 | data so zoom stats gonna show our graph . Why | |
17:19 | could it look a little different on the calculator than | |
17:22 | on your graph ? Yes the scale is different . | |
17:27 | The calculator is a lot smaller than your P . | |
17:28 | C . L . A . Paper would have been | |
17:30 | in on the size that you drew . Okay . | |
17:35 | So how are we going to test our correlation coefficient | |
17:39 | ? Where can we go to determine what it really | |
17:42 | is ? You click stat and you era over the | |
17:47 | couch and then go to the line . We know | |
17:51 | this is a linear function . So we're gonna do | |
17:54 | our linear regression . Okay so do your linear regression | |
17:57 | . And let's see who got the closest to their | |
18:01 | correlation coefficient . Who thinks they got the closest who | |
18:08 | got the closest ? Yeah I think you are close | |
18:12 | . Let's see what it really is . Did you | |
18:14 | get it ? We did a stat calculate linear regression | |
18:23 | negative 0.974 Who thinks you're the closest you've got the | |
18:29 | exact one . Awesome . Guess what you win . | |
18:33 | Mhm . How about a gold medal ? You've already | |
18:38 | won your gold ? Awesome . I apologize , but | |
18:45 | I can't sing the national anthem and you probably don't | |
18:48 | want me to sing the national anthem . Um Okay | |
18:52 | . Who can tell me what else ? We can | |
18:54 | use this linear regression for ricardo to make predictions . | |
18:59 | Okay . To make traditions . What what data do | |
19:02 | we have now that we didn't have before ? From | |
19:06 | your calculator . A prediction . Mhm . I'm not | |
19:10 | sure . Cohesion parker . The prediction equation . Perfect | |
19:16 | . Absolutely prediction equation . So we can now predict | |
19:19 | future events . Now . Do you think we're going | |
19:22 | to get the exact time ? Probably not . Probably | |
19:26 | not . But we can get close using the data | |
19:29 | that we've already collected . Right . Okay . I | |
19:31 | want you now to predict . Let me ask one | |
19:38 | more question . Does it matter If I used 0 | |
19:46 | , 12 , 24 36 , or 1900 1912 1924 | |
19:51 | . Does it matter with my will change ? My | |
19:53 | prediction will not change your prediction . But what will | |
19:56 | be different ? Your equation will be different . Your | |
20:01 | prediction equation will be different . But that's okay . | |
20:05 | If you use 19 hundreds , what kind of year | |
20:08 | are you going to enter for your ex the exact | |
20:11 | year that you give us ? Perfect . Okay , | |
20:15 | if I started at your zero , am I going | |
20:18 | to use the exact year ? No , you're going | |
20:23 | to correlate that . Okay , let's try one . | |
20:32 | I want you to predict the winning time for the | |
20:35 | 100 m dash in 2020 . Hey , predict the | |
20:40 | time for the winning time for the gold medal in | |
20:43 | 2020 . Mhm . That's why you didn't have that | |
20:48 | . You're welcome . Are you rounding ? She gave | |
20:53 | us 2020 2020 so you do Y equals eight . | |
20:59 | So what are you going to use Phase 32 A | |
21:02 | plus B times X one ? You have to have | |
21:05 | that exact well nothing can be exact around around it | |
21:14 | . Alright , write your answers on your white boards | |
21:16 | when you're ready . Yes . Okay . Can you | |
21:24 | around ? Okay . And did you , what did | |
21:31 | you enter your own one ? Okay , let me | |
21:34 | see those white boards . What's your prediction in 2020 | |
21:39 | ? Yeah . 9.54 seconds . Everybody got it awesome | |
21:43 | . Okay , did anybody watch the 100 m dash | |
21:46 | in the summer olympics this summer ? You did Don't | |
21:49 | give it away . Do you know the time he | |
21:51 | ran it in ? No idea . Okay , good | |
21:54 | . We're going to do the exact same thing , | |
21:56 | but we're gonna do 2012 this time . Okay . | |
21:59 | Does anybody know who the winner was ? Yes bolt | |
22:04 | both . The one that ran it . I want | |
22:05 | you to predict what he won gold as this time | |
22:09 | . Do your prediction for what bolt ran the 100 | |
22:12 | m dash in at the olympics this summer ? Not | |
22:16 | yet . Let everybody do it when you get to | |
22:17 | put it on your white board around to the hundreds | |
22:23 | . Yeah , Yeah , 60 . Hold up your | |
22:32 | boards . Can anybody do a drum roll ? Because | |
22:36 | I can't awesome . Ready ? Whoa , exact exact | |
22:49 | . Isn't that cool . Handmade . Okay . I | |
22:52 | want to talk about our data and the future . | |
22:57 | Okay . Now your original data . If we go | |
23:02 | back and look at that , your original problem , | |
23:05 | Right . What's the trend starting at 1900 and 1996 | |
23:11 | and even going to 2012 ? What's happening to your | |
23:14 | winning time ? It's decreasing , right ? So it's | |
23:18 | going down . So I want you to think for | |
23:20 | a second how long that trend could continue ? Could | |
23:24 | it keep decreasing and decreasing and decreasing thomas ? It | |
23:29 | might keep going down , but eventually there might be | |
23:31 | such a good time . That's really hard to be | |
23:34 | exactly . Could anybody ever run the 100 m dash | |
23:37 | in zero seconds ? No . So eventually , what's | |
23:41 | going to happen to your graph ? It's going to | |
23:45 | level out , It's going to go horizontal with that | |
23:48 | ? Change your correlation coefficient ? Yes , it would | |
23:51 | . Okay , let's think for a second about who | |
23:54 | could use this data ? Who could use information like | |
23:57 | that ? What kind of career Amanda , people who | |
24:00 | are running against him ? People who are running against | |
24:03 | him . If you're going to prepare for the olympics | |
24:05 | , you need to know how fast he's running . | |
24:07 | You need to know the trend of how fast people | |
24:09 | are running . Somebody else . Think of think of | |
24:13 | other careers , other people who might be involved . | |
24:17 | Donnie , Vegas gambling . Say that again , Vegas | |
24:22 | gambling , Vegas gambling . You need to know the | |
24:25 | odds , You gotta know the odds . What about | |
24:28 | um , think of a shoe company , Could they | |
24:31 | use it like Nike , what could they do with | |
24:34 | it ? Bless you . They could name a shoe | |
24:38 | brand after the time . Think about maybe shall be | |
24:42 | , they could try to create different types of shoes | |
24:46 | that are fit for that kind of speed . Perfect | |
24:48 | . They could come up with a brand new shoot | |
24:50 | Kelsey people writing an article for the newspaper about it | |
24:54 | . Perfect . Absolutely . What about , what about | |
24:58 | if you're a commentator for the olympics and the race | |
25:01 | hasn't happened yet , would it be nice to know | |
25:04 | what he might run it in ? You could use | |
25:06 | that to protect it right Bridget um , people who | |
25:09 | are investing in him . We want to know if | |
25:11 | he's going to do as good as he is projected | |
25:13 | to or if he's going off of his game . | |
25:15 | Excellent answer . Very , very good . What about | |
25:19 | the health field ? Hey , did anybody by any | |
25:23 | chance think performance enhancing drugs or anything like that ? | |
25:27 | Yeah , a little bit . But even for the | |
25:29 | better for health . Okay . You could even in | |
25:32 | the health field maybe they could use this data . | |
25:34 | Okay . All right . We're going to do one | |
25:35 | more thing . This is your exit ticket to leave | |
25:39 | the class today . Okay . And this is by | |
25:41 | yourself , not in your group . I want you | |
25:44 | to predict what you would have to run the 100 | |
25:48 | m dash in and girls just pretend like you're running | |
25:50 | in the men's Final . Okay . What ? You | |
25:54 | would have to run in 2016 to win gold . | |
25:59 | Okay . And explain your answer to me what time | |
26:05 | you would have to run it in and then explain | |
26:08 | while you chose your answer . Mhm . In order | |
26:13 | to win gold in order to win gold , we're | |
26:17 | not going for the silver . Are we writing ? | |
26:20 | You're gonna ride on the exit ticket , you're gonna | |
26:22 | write on the yellow ? Yeah . Mhm . Mhm | |
26:30 | . Yeah . Mhm . Mhm . Okay , explain | |
26:55 | why you're picking what you're picking . I like it | |
27:02 | . Mhm . Class . Did anybody write ? There's | |
27:13 | no chance I could ever win gold because that's what | |
27:15 | I would have written . I can't even fathom running | |
27:19 | it like three times the amount he ran into . | |
27:26 | Nice record of . Okay , if you will collect | |
27:32 | your predictions in your group and I'll come grab them | |
27:35 | for you before you leave . |
Summarizer
DESCRIPTION:
11th grade math lesson in which students interpret linear models and the correlation coefficient, and make predictions based on data.
OVERVIEW:
11th Grade Mathematics is a free educational video by .
This page not only allows students and teachers view 11th Grade Mathematics videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.