8th Grade Math - By
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 answer | |
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 | |
00:33 | can just add that to your previous bell work . | |
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 | |
01:48 | your answer . Is this okay ? And why did | |
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 | |
06:23 | many of you all buy cds ? Sometimes you buy | |
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 | |
07:03 | about on your own . And then after we have | |
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 | |
07:12 | gonna discuss what you've already found on your own and | |
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 | |
07:45 | ahead and put your name and date on this . | |
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 | |
12:56 | something . I'll be happy to help you . Okay | |
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 . |
Summarizer
DESCRIPTION:
8th grade math lesson addressing Common Core Standards (Massachusetts Curriculum Framework Standard 8.EE.6).
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