8th Grade Math - Free Educational videos for Students in K-12 | Lumos Learning

8th Grade Math - Free Educational videos for Students in k-12


8th Grade Math - By Lumos Learning



Transcript
00:06 mhm . All right , we're gonna start off ,
00:09 first of all , just a little warm up problem
00:12 . So I want you to read this question and
00:15 answer . It says which costs more per pound according
00:20 to the graph , peas or cabbage . And don't
00:23 just give me a one more answer . But I
00:25 also want you to explain how you know which one
00:28 it is . So use just a few seconds to
00:30 do that , and then we're gonna go over it
00:33 . You can just add that to your previous bell
00:36 work . Okay , Good . Very good . Right
00:54 ? Mhm . Yeah . Mhm . Mhm . Okay
01:12 . Okay . Mhm . Yeah , Yes . Yeah
01:32 . I'll see several different answers . But that's okay
01:36 . Because I want you to be able to explain
01:38 why you said what you said . How many think
01:43 it's the cabbage that costs more program ? It's okay
01:47 . Don't change . Your answer . Is this okay
01:49 ? And why did you say that , Parker ,
01:51 Why did you say that ? You thought the cabbage
01:53 was more per pound because it's sloped more towards the
01:57 cabbage than the piece on , uh , pounds .
02:01 So it slipped more towards the pounds . That's what
02:04 you said that . Okay , Someone that said that
02:08 that the peace costs more training . Why did you
02:11 say the piece costs more ? Um , I said
02:14 the peace costs more . Because no matter where you're
02:16 on the r on the graph , the slope is
02:19 higher on the cost range . Okay . What do
02:21 you mean by the slope ? The slope is higher
02:24 . How ? How diagnosed ? The line is because
02:26 , um if you go to the very tip ,
02:28 the peas slope is higher than the cabbage is okay
02:34 . It's actually it is the piece . It is
02:37 the pace because here , what access is this ?
02:42 The X axis . So the X axis is talking
02:46 about pounds as pound is increasing . What's happening to
02:50 the cost ? It's also increasing on both of these
02:54 . Which means if the pounds and the cost for
02:58 the cabbages here at that same poundage , the cost
03:03 for the pieces what ? It's going to be higher
03:06 . Okay , everybody understand that . Okay . Yesterday
03:12 we talked about graphing linear equations should remember what were
03:16 some of the ways that we can use graphing linear
03:19 equations . What did we do ? We just started
03:22 graphing . What did we do to graph linear equations
03:25 ? Ryan , what did we do to graph linear
03:27 equations ? We use some tables . Okay ? we
03:30 use tables , function tables . What else could we
03:33 use on that ? We used ordered pairs ordered pairs
03:36 . What does the ordered pairs tell us ? Bailing
03:39 . It tells us like the number of the X
03:42 . Like what number is going to be on the
03:43 X and y axis the X and Y axes .
03:46 Very good . So we use the order pairs from
03:48 the tables to graph that . What else did we
03:51 talk about ? Fractions . Fractions . Okay , Um
03:54 , do we use fractions to graph , though ?
03:58 What did we talk about ? With a fraction they
04:00 were slope like slope is a fraction slope can be
04:04 used as a fraction walk and be used as a
04:05 fraction because Slope is a number over a number .
04:09 And so it's rise over . Run . Okay ,
04:11 so it's a ratio , which is a fraction .
04:14 Okay , Very good . So today we're gonna elaborate
04:18 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 ?
04:31 What do I mean ? But similar trying their proportional
04:34 or proportional . What is Proportional me ? That ,
04:36 um that if you enlarged , it would be the
04:39 same . The same as the other triangle . If
04:41 you shrink it , be the same as those .
04:43 Okay . Very good explanation . So we're gonna see
04:45 why similar triangles is gonna help us explain why Slope
04:49 is the same between any two distinct points on a
04:52 non vertical line . Show me with your hands .
04:54 What does vertical look like ? What does vertical look
04:57 like ? Show me with your arms . Is it
04:59 like this , or is it like this was vertical
05:01 ? So it's straight up and down , so anything
05:02 that's non vertical , which means it's not gonna be
05:05 straight up and down . We can see how the
05:07 distance between any two points on that non vertical line
05:10 is gonna be the same then from that we're going
05:12 to derive the equation . Y equals MX for a
05:15 line that goes through the origin . You can tell
05:18 me where the origin is . Where is the origin
05:20 ? Um , Taylor , where's the origin ? Right
05:22 where the eggs and why ? Access meet right in
05:26 the middle . So that order pair is gonna be
05:28 what , 000 Very good . So at the origin
05:31 is just gonna be Why equals MX ? And if
05:34 for a line that's not through the origin , it's
05:37 going to be why it was MX plus B .
05:42 How do you like music ? I mean , like
05:44 , music . I like music . What are some
05:46 ways there are places that we use music or C
05:49 music or hear music ? What are some different places
05:52 that we would have music in your car ? In
05:55 your car ? Just riding around , listening in your
05:57 car . What's another place and an elevator in an
06:00 elevator and we're sitting in the elevator here due to
06:02 do to do to do , uh , Taylor .
06:04 What's another ? I don't Just at home . Okay
06:09 . What are you gonna say out of dance at
06:11 a dance ? Sometimes We have school dances when you
06:13 go shopping . A lot of stores play music .
06:16 Very good . Almost at stores . A lot of
06:18 times , we'll have music . Well , we're not
06:20 gonna talk directly about music , but how many of
06:23 you all buy CDs ? Sometimes you buy cds .
06:26 Okay , so we're gonna look at how , on
06:29 a graph how we can relate the price of CDs
06:32 , 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 ,
06:49 when I passed out the task that we're gonna work
06:51 on , I'm gonna give you a few minutes of
06:53 private Think time . That just means that for the
06:56 first few minutes for five minutes , I just want
06:58 you to kind of look at the sheet , answer
07:00 the first few questions and just kind of see what
07:03 you can think about on your own . And then
07:05 after we have that private think time we're going to
07:08 then get in our small groups that you're already in
07:11 and you're gonna discuss what you've already found on your
07:14 own , and then you're gonna further finish that worksheet
07:17 then and I don't have this on here , but
07:19 from that small group work , we're gonna add 10
07:22 more minutes . And that's what I'm going to give
07:23 you a chance to put your findings on the larger
07:27 posters that you're going to share with the whole group
07:29 class at the end that we'll discuss in the last
07:32 10 minutes . Okay . Are there any questions right
07:35 now ? As far as what we're going to be
07:36 doing today , Okay , I'm first gonna go ahead
07:40 and pass these out to the groups , and I
07:45 just want you to go ahead and put your name
07:47 and date on this . You go . Okay .
07:56 Just make sure everybody in your group gets one ,
08:00 okay ? Mm . Yeah , yeah . All right
08:26 . On this test , it's called Music is a
08:28 must , since the data shown in the graph below
08:31 reflects average cost of a music CD . So you're
08:35 gonna take this information that's in the graph , Just
08:38 whatever you gather from it , And you're gonna answer
08:40 the first few questions . All I want you to
08:42 do right now in your private think , Tom ,
08:45 I want you to actually just work on our answer
08:48 letters . A through D . So right now ,
08:51 in this first few minutes , you're just doing letters
08:54 a through D . But when you finish with a
08:56 three D , go ahead and just to yourselves ,
08:58 read the other few questions so that you already have
09:01 an idea of what we're gonna work on as a
09:03 group . So But for the first five minutes ,
09:06 just doing a through D right now . Yeah ,
09:19 yeah , yeah . Mhm . You know , showing
09:36 mhm . I'm just gonna be used . What does
09:40 it mean By what unit ? Right . And just
09:44 say that , Yeah , if I find the rate
09:48 of something and I want to know what the unit
09:50 costs is how many am I trying to figure out
09:53 for how many ? Mhm per pound or per item
09:58 ? Exactly . So again , it just means one
10:00 . Exactly . Okay , if you think it's that
10:08 much , what makes you from the graph ? Figure
10:13 that because you said you think it's that much per
10:15 city . What from that gives you what information from
10:21 the graph makes you think that it's $15 per city
10:25 . So explain that . Yes . Uh huh .
10:34 Yes . The cost on the left side that is
10:36 in dollar amounts . So the cost is in dollars
10:40 , and that's on your Y axis country . Oh
10:46 , to the moon . What if we are going
10:51 to be the PCI would be 15 hours , because
10:55 to Okay , so if you say to is 39
11:03 then how do you get the unit price like either
11:09 show or explain that you're on the right track ?
11:11 You're on the right track . But is it that
11:13 the same way ? All the way up ? Because
11:16 you chose to And 30 . But because you have
11:19 chosen one of five involved , I mean seven .
11:22 Or could you have chosen 1 28 ? You see
11:25 what I'm saying ? Yes , sir . How did
11:36 you find the unit ? Break like , you know
11:39 , like , okay , if you do that if
11:43 you're finding unit . If I said that , I
11:45 wanted to see I had some apples and I want
11:48 to know how much it was per pound . That
11:51 means I want to know . How much for how
11:53 many pounds for one . So unit would be .
11:56 How many ? One . So if But you're saying
12:01 two and 30 Could I have chosen 75 5 ?
12:06 Or could I have chosen 1 28 ? You're saying
12:10 yes . So how would I know that ? What
12:12 tells me that ? Yes , I could choose any
12:14 of those prices or any of those amounts . How
12:18 much ones he called mhm . Okay . You know
12:23 , right is what you're finding Mhm . Okay .
12:32 Yeah . Yeah . Okay . I like how you
12:38 put several ratios on there . That's good . That's
12:41 good . Yeah . When you have about a minute
12:50 and 20 seconds just on your personal thing . You
12:55 have any questions or stuck on something ? I'll be
12:57 happy to help you . Okay , let's say that
13:01 I were buying some apples and I wanted to know
13:05 how much it is per pound . Okay , lets
13:08 a unit . Right . So what am I trying
13:09 to find out ? How much it is for how
13:11 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
13:27 you derive that or come up with that based on
13:30 this table ? Yeah , where the points are .
13:34 Okay , you're on the right track . Uh huh
13:37 . Mhm . Because , for instance , if I
13:43 look at this graph , how much is four cities
13:47 ? Okay , 16 . How much is six cities
13:54 ? How did you know that ? Because there was
13:56 not a 90 on here in in between 1800 .
14:01 Okay , so you went from 60 to 75 then
14:07 90 . So how did you come up with that
14:11 ? You looked at the chart . But what's happening
14:13 each time ? It's falling out fire . Okay .
14:24 All right . Now what I want you to do
14:26 because I'm seeing some really good information on there .
14:28 There are a few questions , and that's okay .
14:30 You're on the right track . That what I want
14:31 you to do in your small groups ? First of
14:34 all , discuss a 30 that you just did on
14:38 your own , just to make sure that you are
14:39 on the right track . If someone found it a
14:42 different way , does that mean that they're wrong ?
14:44 No , not necessarily . So just kind of come
14:47 up or discuss what you're different . Findings were and
14:50 see if y'all still came up with the same solution
14:52 with the same answers . But then I want you
14:55 to go ahead and take it a little further and
14:57 look at the next several questions on that same sheet
15:00 , okay ?
Summarizer

DESCRIPTION:

8th grade math lesson addressing Common Core Standards (Massachusetts Curriculum Framework Standard 8.EE.6).

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8th Grade Math is a free educational video by Lumos Learning.

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