Educational videos for Students in k-12 | Lumos Learning

Educational videos for Students in k-12

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00:06 Mhm . All right . We're gonna start off ,
00:09 first of all just a little warm up problem .
00:15 . It says which costs more per pound according to
00:20 the graph peas , or cabbage . And don't just
00:23 give me a one more answer . But I also
00:25 want you to explain how you know which one it
00:28 is . So use just a few seconds to do
00:31 that and then we're gonna go over it . You
00:40 Okay . Good . Very good . Right . Mhm
00:55 . Yeah . Mhm . Mhm . Okay . Okay
01:16 . Mhm . Yeah . Yes . Yeah , I'll
01:33 see several different answers , but that's okay because I
01:36 want you to be able to explain why you said
01:38 what you said , how many think it's the cabbage
01:45 that costs more . Program it's okay . Don't change
01:50 you say that parker ? Why did you say that
01:52 you thought the cabbage was more per pound ? Because
01:55 it's sloped more towards the cabbage than the piece on
02:00 uh pounds . So it slipped more towards the pounds
02:04 . That's what you said that . Okay . Someone
02:07 that said that that the peace costs more training .
02:11 Why did you say the piece costs more ? Um
02:14 I said the peace costs more because no matter where
02:16 you're on the r on the graph , the slope
02:19 is higher on the cost range . Okay , what
02:21 do you mean by the slope ? The slope is
02:23 higher how how diagnosed the line is because um if
02:27 you go to the very tip , the peas slope
02:29 is higher than the cabbage is . Okay , it's
02:34 actually it is the piece , it is the pace
02:38 because here what access is this the X axis ?
02:44 So the X axis is talking about pounds as pound
02:48 is increasing what's happening to the cost . It's also
02:53 increasing on both of these . Which means if the
02:57 pounds and the cost for the cabbages here at that
03:00 same poundage , the cost for the pieces what it's
03:05 going to be higher . Okay . Everybody understand that
03:10 . Okay , yesterday we talked about graphing linear equations
03:15 . Should remember . What were some of the ways
03:17 that we can use graphing linear equations ? What did
03:20 we do ? We just started graphing . What did
03:23 we do to graph linear equations ? Ryan , what
03:26 did we do to graph linear equations ? We use
03:28 some tables . Okay , we use tables , function
03:31 tables . What else could we use on that ?
03:34 We used ordered pairs , ordered pairs . What does
03:37 the ordered pairs tell us bailing ? It tells us
03:39 like the number of the X . Like what number
03:42 is going to be on the X and Y axis
03:44 , The X and Y axes . Very good .
03:47 So we use the order pairs from the tables to
03:49 graph that . What else did we talk about ?
03:51 Fractions , fractions . Okay . Um Do we use
03:55 fractions to graph though ? What did we talk about
03:59 with a fraction they were slope like slope is a
04:02 fraction slope can be used as a fraction walk and
04:05 be used as a fraction because slope is a number
04:08 over a number and so it's rise over run .
04:10 Okay . So it's a ratio which is a fraction
04:14 . Okay . Very good . So today we're gonna
04:17 elaborate on that a little bit more and we're actually
04:20 gonna use an a task to investigate rate of change
04:24 in slope . So we're gonna take it just a
04:25 little bit further and we're actually gonna use triangle .
04:28 Similar triangles . What do I mean by similar what
04:31 do I mean ? But similar trying their proportional or
04:34 proportional ? What is proportional me that um That if
04:38 you enlarged it would be the same the same as
04:40 the other triangle . If you shrink it be the
04:42 same as those . Okay very good explanation . So
04:44 we're gonna see why similar triangles is gonna help us
04:48 explain why slope is the same between any two distinct
04:51 points on a non vertical line . Show me with
04:54 your hands . What does vertical look like ? What
04:56 does vertical look like ? Show me with your arms
04:59 . Is it like this or is it like this
05:00 was vertical ? So it's straight up and down .
05:02 So anything that's non vertical which means it's not gonna
05:04 be straight up and down . We can see how
05:07 the distance between any two points on that non vertical
05:10 line is gonna be the same . Then from that
05:12 we're going to derive the equation . Y . Equals
05:14 Mx for a line that goes through the origin .
05:17 You can tell me where the origin is . Where
05:19 is the origin ? Um Taylor . Where's the origin
05:22 ? Right ? Where the eggs and why access meet
05:26 right in the middle . So that order pair is
05:27 gonna be what ? 000 Very good . So at
05:30 the origin is just gonna be why equals Mx .
05:32 And if for a line that's not through the origin
05:37 it's going to be why it was Mx . Plus
05:39 B . How do you like music ? I mean
05:44 like music . I like music . What are some
05:46 ways ? There are places that we use music or
05:49 C . Music or hear music . What are some
05:51 different places that we would have ? Music in your
05:54 car ? In your car ? Just riding around listening
05:56 in your car . What's another place ? And an
05:59 elevator in an elevator ? And we're sitting in the
06:01 elevator here . Due to do to do to do
06:03 uh taylor . What's another ? I don't just at
06:06 home . Okay . What are you gonna say ?
06:09 Out of dance at a dance ? Sometimes we have
06:12 school dances . When you go shopping . A lot
06:15 of stores play music . Very good . Almost at
06:17 stores A lot of times we'll have music . Well
06:20 we're not gonna talk directly about music . But how
06:26 cds ? Okay . So we're gonna look at how
06:28 on a graph how we can relate the price of
06:31 cds and they're not always the same price . But
06:34 we're gonna just give like an average price of a
06:37 cd versus how many cds you may purchase or you
06:40 may have . So we're going to use that to
06:43 do a little investigation . And in our investigation today
06:47 we're gonna have several different segments . First when I
06:49 passed out the task that we're gonna work on ,
06:52 I'm gonna give you a few minutes of private think
06:54 time . That just means that for the first few
06:56 minutes for five minutes I just want you to kind
06:58 of look at the sheet , answer the first few
07:01 questions and just kind of see what you can think
07:06 that private think time , we're going to then get
07:08 in our small groups that you're already in and you're
07:14 then you're gonna further finish that worksheet Then and I
07:18 don't have this on here . But from that small
07:20 group work , we're gonna add 10 more minutes and
07:23 that's what I'm going to give you a chance to
07:25 put your findings on the larger posters that you're going
07:28 to share with the whole group class at the end
07:30 that we'll discuss in the last 10 minutes . Okay
07:33 . Are there any questions right now , as far
07:36 as what we're going to be doing today ? Okay
07:39 . I'm first gonna go ahead and pass these out
07:41 to the groups and I just want you to go
07:49 You go okay ? Just make sure everybody in your
07:58 group gets one . Okay mm . Yeah . Yeah
08:26 . All right . On this test it's called music
08:28 is a must since the data shown in the graph
08:30 below reflects average cost of a music cd . So
08:35 you're gonna take this information that's in the graph just
08:38 whatever you gather from it and you're gonna answer the
08:41 first few questions . All I want you to do
08:43 right now in your private think tom I want you
08:46 to actually just work on our answer letters A through
08:50 D . So right now in this first few minutes
08:52 you're just doing letters A through D . But when
08:55 you finish with a three D . Go ahead and
08:57 just to yourselves , read the other few questions so
09:00 that you already have an idea of what we're gonna
09:02 work on as a group . So but for the
09:05 first five minutes just doing a . Through D .
09:07 Right now . Yeah . Yeah . Yeah . Mhm
09:35 . You know showing . Mhm . I'm just gonna
09:39 be used . What does it mean by what unit
09:43 ? Right and just say that . Yeah if I
09:47 find the rate of something and I want to know
09:50 what the unit costs is . How many am I
09:53 trying to figure out for how many ? Mhm .
09:55 Per pound or per item ? Exactly . So again
09:59 it just means one . Exactly . Okay if you
10:07 think it's that much what makes you from the graph
10:12 figure that because you said you think it's that much
10:15 per city ? What from that gives you what information
10:21 from the graph Makes you think that it's \$15 per
10:24 city ? So explain that . Yes . Uh huh
10:34 . Yes . The cost on the left side that
10:36 is in dollar amounts . So the cost is in
10:39 dollars and that's on your Y . Axis country .
10:45 Oh to the moon . What if we are going
10:51 to be The PIX would be 15 hours because to
10:58 Okay so if you say to is 39 then how
11:03 do you get the unit price ? Like either show
11:09 or explain that you're on the right track , you're
11:11 on the right track . But is it that the
11:13 same way all the way up Because you chose to
11:17 and 30 . But Because you have chosen one of
11:20 five involved I mean seven Or could you have chosen
11:23 1:28 ? You see what I'm saying ? Yes sir
11:35 . How did you find the unit break ? Like
11:39 you know like okay if you do that if you're
11:43 finding unit , if I said that I wanted to
11:45 see I had some apples and I want to know
11:49 how much it was per pound . That means I
11:51 want to know how much for how many pounds for
11:55 one . So unit would be how many one .
11:59 So if But you're saying two and 30 could I
12:02 have chosen 75 and five Or could I have chosen
12:07 1 28 you're saying ? Yes . So how would
12:11 I know that ? What tells me that ? Yes
12:13 I could choose any of those prices or any of
12:16 those amounts . How much ones he called ? Mhm
12:22 . Okay . You know . Right is what you're
12:24 finding ? Mhm . Okay . Yeah . Yeah .
12:36 Okay . I like how you put several ratios on
12:40 there . That's good . That's good . Yeah When
12:49 you have about a minute and 20 seconds just on
12:52 your personal thing you have any questions or stuck on
13:00 let's say that I were buying some apples and I
13:04 wanted to know how much it is per pound .
13:07 Okay lets a unit . Right , so what am
13:09 I trying to find out how much it is for
13:10 how many pounds ? Mhm . Uh £1 for £1
13:16 . So if I'm trying to find the unit rate
13:18 of cds , I'm trying to find out how much
13:20 it is for how many cities , what for one
13:23 exactly ? Um Okay but how can you derive that
13:28 or come up with that based on this table ?
13:31 Yeah , where the points are ? Okay , you're
13:35 on the right track . Uh huh . Mhm .
13:41 Because for instance if I look at this graph ,
13:46 How much is four cities ? Okay , 16 ,
13:49 how much is six cities ? How did you know
13:56 that ? Because there was not a 90 on here
13:58 in in between 1800 . Okay , so you went
14:03 from 60-75 and then 90 . So how did you
14:08 come up with that ? You looked at the chart
14:12 , but what's happening each time ? It's falling out
14:15 fire . Okay . All right . Now , what
14:25 I want you to do , because I'm seeing some
14:26 really good information on there . There are a few
14:28 questions and that's okay . You're on the right track
14:31 , that what I want you to do in your
14:32 small groups . First of all , discuss A 30
14:37 that you just did on your own , just to
14:38 make sure that you are on the right track .
14:40 If someone found it a different way , does that
14:43 mean that they're wrong ? No , not necessarily .
14:45 So just kind of come up or discuss what you're
14:48 different findings were and see if y'all still came up
14:51 with the same solution with the same answers . But
14:54 then I want you to go ahead and take it
14:55 a little further and look at the next several questions
14:59 on that same sheet . Okay .
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