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

8th Grade Math - By

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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 .
00:12	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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