11th Grade Mathematics - Free Educational videos for Students in K-12 | Lumos Learning

11th Grade Mathematics - Free Educational videos for Students in k-12


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 .
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11th grade math lesson in which students interpret linear models and the correlation coefficient, and make predictions based on data.

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