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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