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
00:36 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
01:49 ? 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
06:26 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
07:05 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
07:47 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 ,
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
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).

#### OVERVIEW:

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

This page not only allows students and teachers view 8th Grade Math videos but also find engaging Sample Questions, Apps, Pins, Worksheets, Books related to the following topics.

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