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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