record_id: 2c0f8b3e-f83d-8169-af4a-def319a42f0b
created_time: 2025-12-05T04:40:00.000Z
title: 12-04 Lecture: Algebra Modeling, Equation Balance, and Practical Math Applications
source_url: /

[TRANSCRIPTION]
Speaker 1 00:00:24
So, just so you know, Ben needs to see it, so if you don't write it out, follow you as well. It takes him a lot harder. It takes him a lot to understand it if you don't write it out.
Speaker 2 00:00:45
I can't write it out without giving him the answer to it.
Speaker 1 00:00:58
Go get that. I can't write it out without giving him the answer to it. You're locked into the way that you want to do it, and I'm not going to fight you on it. Math is something that's a process. You can easily write it out, right? You just don't want to go backwards.
Speaker 1 00:01:32
Yes or no? Can you write this out or not? Okay, so I asked you to write it out. You said, I can't figure out how to do that. I don't have time for that. So, you decided... You know, to protect Eric.
Speaker 1 00:02:06
So, you want to show him, but you want to show him your way. And that's the problem with the teachers that you hate. Because they want to teach, and they want to teach their way. They don't go to you and ask you if you're understanding. They just go, I told it to you, and you need to figure it out. And that's not what teaching is. So, I asked you to do it a certain way, and you didn't.
Speaker 1 00:02:37
So, you know, they don't know where it is. That's probably a match. So, let's do it here. Let's do it here. Okay, Mitch went to a fancy chocolate store to buy his sister and brother each a box of cookies.
Speaker 1 00:03:09
Give me, I need to focus on this, okay? Hey, hey, hey. Can I put it in my cup? That's one thing I need to do. How much chores have you done? I need a lot more chores done today. I was looking at what you did earlier and you haven't done that much. I know you've done some, but I've got seven minutes, ten minutes so far done.
Speaker 3 00:03:29
Oh, because Mom asked me to do some of them, but I didn't, but I got to do two, put the one thing on.
Speaker 1 00:03:38
Okay, so I've got to take out trash cans, but you didn't take out trash cans today, right. 
Speaker 3 00:03:45
I know, but they were on, some of them, no one, no one needed them.
Speaker 1 00:03:49
Okay, how about bringing in trash cans? Can we go do that. 
Speaker 3 00:03:51
The trash cans haven't been taken. They weren't done.
Speaker 1 00:03:56
Can you see my point here? I say, can you go do this? And I get told, no, you didn't see the trash cans, yesterday and today out front.
Speaker 3 00:04:09
Yeah. Can you go bring the trash cans here? I just didn't use a lot for that one.
Speaker 1 00:04:16
Oh, they didn't get emptied? Is that what you're saying. 
Speaker 3 00:04:24
I didn't look it off just in case. Can I use that in my shirt. 
Speaker 1 00:04:29
Do me a favor. Go outside and check if other people's cans are empty. Okay. All right, let's focus on this. So Mitch went to a fancy chocolate store to buy his sister and brother each a box of Chumbles. He bought X Chumbles to put in each box. And the store charges $1.75 per Truffle. Right?
Speaker 1 00:04:60
So, do we have a formula so far. 
Speaker 3 00:05:02
No.
Speaker 1 00:05:03
I think we do.
Speaker 3 00:05:09
Everyone, one person, that had their trash cans back, but...
Speaker 1 00:05:13
No, no. Are the ones that are still out there full? Or are they empty. 
Speaker 3 00:05:19
Ours? Everyone, other people's.
Speaker 1 00:05:21
Is Patty's full or empty? Okay, how about Ed. 
Speaker 3 00:05:27
Mr. Parker's house next to Ed, to the side. Ed didn't have his trash cans out.
Speaker 1 00:05:36
So, ours are pretty much the only ones out? Okay, bring them in. So, if he bought X truffles, right, and the store charges $1.75 per truffle, we know... how much you bought, right? At least we know the formula for how much you bought.
Speaker 3 00:05:58
Yeah. What is that? It's a formula. You should know this.
Speaker 1 00:06:12
What is that? Right. And then he got both boxes gift wrapped for $3 each, right? So is that correct? Why not? Now, now we have ourselves a formula, right?
Speaker 1 00:06:55
What is that equal? What is that equal? We don't know. So, we can say, oh, they don't have equals there either, right? So, now what it's saying is, take all the expressions that represent how much Mitch spent at the store, right? So, essentially,
Speaker 1 00:07:38
So, basically, they're saying, it's possible that all four of these solve this problem. Yeah. So, which ones of those solve that problem? Let me ask you this, when you do your double check, when you do your double check, what's a double check. 
Speaker 3 00:08:14
Checking twice.
Speaker 1 00:08:16
Checking twice for what? The answer. When you do your double check for your correct answer, what's that going to look like. 
Speaker 4 00:08:28
Are you going to guess. 
Speaker 1 00:08:36
Okay, it's all going to be x equals something, right? So the double check is really solving for x, isn't it. 
Speaker 4 00:08:48
Yeah.
Speaker 1 00:08:48
So let's solve for x on this for what we know the equation is, and then we can see how we can extract the rest of it.
Speaker 3 00:09:06
Why don't you solve for x if you only have two numbers. 
Speaker 1 00:09:14
If you only have two numbers? Because it can equal... You can make it equal to zero. Now solve for x.
Speaker 3 00:09:33
Hmm. 
Speaker 1 00:09:47
Okay, so we need to isolate the x, don't we? Okay, so how can we do that? how do i get it so it says x equals something you do know we've done this i don't know hey.
Speaker 1 00:10:22
we've done this so what does that tell you because i forgot it okay move to the six to the other side you need to get it so it's x equals something right so first we gotta.
Speaker 4 00:10:36
take care of that six don't we how do we do that so we are trying to make it.
Speaker 1 00:11:18
this is going to be the end x equals something okay so look how do we get we i need this i need this to be on this side and i need this one one seven five to be on this side how do we do that.
Speaker 1 00:11:54
you've done this with me how do i get the x how do i get the six to be on this side. Just move. Would that be correct? You just move the 6 from one side to the other?
Speaker 1 00:12:25
Are you allowed to do that in math? Okay. So, can't I subtract 6 from both sides? So, negative 6 equals negative 6. Is that a correct statement? You sure?
Speaker 1 00:12:57
Why not? Okay, let's try this. Is that a correct statement? Is this a correct statement?
Speaker 1 00:13:31
Is that a correct statement? Why did you say yes now? Okay. Why is that a correct statement. 
Speaker 3 00:13:44
Because if there's nothing else to do, it will finish in just a second.
Speaker 1 00:13:51
Well, is negative six equal to negative six? Yeah. Hey, this is... Here's the problem. Algebra is logical. Just got to understand the rule, okay? But it's super logical, okay?
Speaker 1 00:14:21
So, if negative 6 equals negative 6, can't we do this? We take 6 from both sides? Because really, what are we doing. 
Speaker 3 00:14:50
Right.
Speaker 1 00:14:51
It's just 0 that we're doing. There's no difference between negative 6 equals negative 6 and 0 equals 0. So we're not changing this equation at all, right? So, I'm going to take the 6 away from here, and I'm going to add it to here. Sorry, I'm subtracting 6 from this side, because it's positive there, so I want to take it to 0.
Speaker 1 00:15:24
And if I take it from here, I have to add it to here. Okay? So in order to take it from here, or if I take it from here, then I have to add it to here. So whatever I do here, it has to balance out the 0 over here. Does that make sense? So, meaning...
Speaker 4 00:16:03
Yeah, you can.
Speaker 1 00:16:26
Whatever I do to one side, I've got to make up for on the other side. Does that make sense. 
Speaker 2 00:16:31
Mm-hmm.
Speaker 1 00:16:32
So if I take six away here...
Speaker 4 00:16:40
What? Which one do I want? The yellow. 
Speaker 3 00:17:05
It's harder to see.
Speaker 1 00:17:12
What do you mean? Length is harder to see, right? Mm-hmm. Okay. So if I go negative six here, right? That's right. Then I have to add 6 here, okay? So now I have 1.75x. So 6 minus 6 is 0, right? That make sense? Equals the negative. So when we, so that negative 6 goes to here, okay? That's what.
Speaker 1 00:18:05
we did, right? That make sense? Yeah. Okay, so now what do we do? Make x go to 0. Okay, how do we do that? You can't subtract it because it's multiplied, right? So, when it's added, you can subtract. When it's multiplied, you can divide. When it's divided, you can...
Speaker 1 00:18:45
Okay, if we divide 1.75 by both sides, you get your number. So, this cancels out, right? You get x equals 1.75. Does that make sense? Now, look at this, okay? So, right in there, x equals 1.75.
Speaker 1 00:19:44
So look, when you multiply this in, what's it going to be. 
Speaker 3 00:19:49
What. 
Speaker 1 00:19:50
When you multiply this in, right, if you solve for x on this one, then you divide it by 2, right, on both sides, and you divide it by 4.75. Is that going to be 1.75. 
Speaker 4 00:20:10
No.
Speaker 1 00:20:12
What will it be, more or less? Take a guess.
Speaker 3 00:20:22
By 2? Do you want a quick one? Do you want to count 3. 
Speaker 1 00:20:32
Yeah. right so it's not going to equal 1.75 so one's not our answer right so 3.5 x plus six what do you think, all right why not is this how you would have solved it eric.
Speaker 1 00:21:06
or you just did it all in your head is this how you would have solved it or you're just doing it.
Speaker 2 00:21:20
wait what's actually oh i just didn't do it right.
Speaker 1 00:21:34
Huh? X equals negative 6 over 1.75.
Speaker 2 00:21:39
How do you know what X equals. 
Speaker 1 00:21:41
You just fall for it. Hmm? Two boxes, three dollar gift wrap charge.
Speaker 5 00:21:53
Oh, you guys want a dinner portion? No.
Speaker 2 00:22:03
Oh. 
Speaker 1 00:22:18
It's his fault. Huh? I was being distracted. See that? Not my fault. Hmm? You just ate dinner. You don't need dinner. Huh? Whose burrito is that? Mine. Okay. Hmm? I'm making a ham sandwich with that. Hmm? Let's focus on this, okay?
Speaker 1 00:22:56
What is correct? The second one is... I'm not asking you if it's correct. I'm asking you if it's the same as your original formula. Is that the right... Are you saying that's an expression that would be accurate. 
Speaker 2 00:23:16
Have you guys concluded that. 
Speaker 1 00:23:20
No. We haven't gotten there. So what tells you that it's correct, kiddo. 
Speaker 3 00:23:31
It's three points. Three points.
Speaker 2 00:24:32
I don't think you need to solve for the equation.
Speaker 6 00:24:38
so how are you going to teach him how to do this you just need someone to place it so no you're.
Speaker 1 00:24:58
going to show him how to do it but you're going to do it in your head and then he's not going to know how to do it i'm already here dude so look so write the formula here tell me what tell me how.
Speaker 1 00:25:38
It's not out of me.
Speaker 4 00:25:54
It's just a little dried out.
Speaker 1 00:26:05
Give it some moisture. Do I have a blue mark on my tongue? Nope.
Speaker 4 00:26:17
It's a little tricky. It's a little dry.
Speaker 1 00:26:37
Solve it? No, I didn't say write it out. I said solve it.
Speaker 1 00:27:35
I don't know either. But you didn't do what I asked you to. What did I do there? Mom, I solved it out because I'm telling you, right. 
Speaker 5 00:27:60
So then solve it.
Speaker 1 00:28:08
The problem is you have the same issue that I did there. And you're going, I don't know how to do that. Right? And you're stopping.
Speaker 3 00:28:18
No, but it's something. I don't know. What does it turn into. 
Speaker 1 00:28:27
Show me.
Speaker 3 00:28:29
You do what I do.
Speaker 1 00:28:37
No, show me if you want to do it, you can prove it to me, or you can do what I did.
Speaker 6 00:30:32
That doesn't tell me I'm correct, or you're correct, what's 6 divided by 1.75? 6 divided by 1.75 is 3.42.
Speaker 4 00:31:17
Hope for that one.
Speaker 5 00:31:23
That's hard because we don't have a lot of time.
Speaker 1 00:31:29
When you get to something like... First, I want to see it on paper before I just scout through it. Hey, you're wasting my time, kiddo.
Speaker 4 00:32:20
Thank you.
Speaker 1 00:33:45
Okay, so you can already see x equals negative 6 divided by 3.5, x equals negative 6 divided by 1.75, right? Is it going to be the same? We can move on. Alright, what's the next one. 
Speaker 3 00:34:22
Okay.
Speaker 3 00:34:57
It's just negative .50 over six.
Speaker 4 00:35:05
What is that? Here's what I can tell you. Nothing.
Speaker 1 00:35:22
It's less than one, right? No. It's less than one, right. 
Speaker 3 00:35:29
Yeah.
Speaker 1 00:35:30
It's like just over a half. You sure? Okay, so not that one, right? Okay? How about the last one. 
Speaker 3 00:35:45
This has to be the last one. It does, but do you know how to solve that? Yeah.
Speaker 5 00:35:59
Alright. Eric, here's the issue. Next thing, go ahead. Go to the next one. I'll tell you why I'm going to get rid of it.
Speaker 3 00:36:09
Do it. 
Speaker 1 00:36:30
Store charges. 1.75. Well, yeah.
Speaker 2 00:36:39
2 times 1.75, plus 3 is the same. You're just extracting the 2 from it.
Speaker 4 00:36:60
Yeah, I just didn't, I think it was poorly written.
Speaker 1 00:37:21
Oh, here's where it is. He bought X truffles to put in each box. That's what got him. Hey, why are you over there while we're on your homework? Here we are trying to figure out what we did wrong. And this is, this is the thing, dude. It's exactly what I was telling you in there. Here we are trying to figure out what we did wrong so we can, we go, oh shoot, I'm better than this. I could have gotten this right.
Speaker 1 00:37:53
Where did that go wrong? Oh, here's where I went wrong. Right? Hey, I'm not trying to yell at you here. This is key to being the best version of Ben. Okay? So, read the explanation here.
Speaker 3 00:38:15
The explanation.
Speaker 1 00:38:21
And then do the next problem.
Speaker 3 00:38:25
Where it says learn, I finish the one I want to work on.
Speaker 5 00:38:29
Pull in.
Speaker 1 00:38:32
I want you to figure out exactly how the problem works. Me? No. I'm talking to him. I know, but... So, use... They're explaining exactly how to take apart this problem.
Speaker 5 00:38:59
use it. Here's a question. There's other kids in your class that get this, right? There's other kids in your class that get this, right. 
Speaker 3 00:39:11
Yeah.
Speaker 5 00:39:12
Are they smarter than you? No. What do you mean? No, they're not.
Speaker 2 00:39:19
You're not allowed to watch what I'm watching. You can't watch that. So... No, you're not. You're literally not allowed to. If you're allowed to watch what I'm watching, then you don't need to.
Speaker 1 00:39:30
So, use this to figure it out. Believe in yourself.
Speaker 2 00:39:35
Last time I showed you guys something I was watching, I was sitting in my drawers. What's going on with that. 
Speaker 1 00:40:12
Okay. Do you think you'll want to eat it later? Will you want to eat it later when you get back? You don't want to eat it. 
Speaker 2 00:40:34
It's too much. I'm sorry, I'm not going to play.
Speaker 1 00:41:04
What do you have going on with school? Can you open up the canvas. 
Speaker 2 00:41:35
I have this done. It's Tuesday next week. You said it's done. 
Speaker 1 00:41:46
Yeah. Well, let's submit that. You get it? Hey, forget about the Legos. No disrespect, I haven't been able to do any of that because I'm sitting here with you, and you want to play like this. I don't want to disturb my man.
Speaker 1 00:42:18
So if I'm going to take out time to do this with you, I need you to give me 100%, okay? I think that's fair, don't you? All right. I need to do it.
Speaker 3 00:42:33
I need...
Speaker 1 00:42:33
Do you understand what happened here, right? So, they basically created the formula. So there's... Can you explain it to me, actually. 
Speaker 3 00:42:50
So, which one. 
Speaker 1 00:42:54
Hmm? Whatever one you want.
Speaker 3 00:42:57
Go for this one? Since you bought truffle boxes, and there's X truffles, and you multiple the box, since you put that two, like, aside, and then...
Speaker 1 00:43:19
Sure, so where's that two. 
Speaker 3 00:43:22
So, what you're going to do is, it's supposed to be a different box, you do the same thing with the two, so it's still two, and put it in, and then, and then you times it by two, both of them.
Speaker 1 00:43:48
What, why do you multiply it by two. 
Speaker 3 00:43:50
One, two, and... or and it's three dollars for what for gift wrapping you need to times it or i mean you should.
Speaker 1 00:44:08
reply six times two okay what about the other formula um just tell me why it works so for the.
Speaker 3 00:44:30
so for this one it's and they added both of them so he bought two chocolate boxes so he added the.
Speaker 1 00:44:41
two and okay you have when you're dealing with math you gotta be really careful with your words so when you say he added the two when you're talking about math it's not combining it's, actually adding right yeah, So, when you say he added the two, you don't actually mean added, right. 
Speaker 3 00:45:05
Mm-hmm.
Speaker 1 00:45:06
I'm not, I'm teaching you here. I'm not trying to...
Speaker 3 00:45:11
I mean add, not to.
Speaker 1 00:45:16
But not add, right? Hmm? But not add.
Speaker 3 00:45:19
What do you mean. 
Speaker 1 00:45:22
When you say he added the two, is there any point in time where two is added to something else. 
Speaker 7 00:45:28
No.
Speaker 1 00:45:31
So, when you're talking math, you can't use math words differently than, you know, as you would in normal language.
Speaker 3 00:45:39
Okay.
Speaker 1 00:45:40
That make sense. 
Speaker 3 00:45:41
Yeah. So, he added both of the chocolate boxes together to get 3.50. And since it says, since there's two chocolate boxes, and he needs to get both of them out, he added both of them. And since you need to have those truffles, you put in each box and multiply 3.50 times.
Speaker 3 00:46:12
x.
Speaker 1 00:46:16
So look, if I was to ask you, did I drop that. 
Speaker 4 00:46:22
Yeah.
Speaker 1 00:46:25
Um, if I was to ask you to solve this equation, what would be the first thing you did? By what. 
Speaker 3 00:46:46
By this.
Speaker 1 00:46:49
And that's how this is the same. So. What you're saying is this, this is a factored version of this, right? So look, I'm trying to get you to see it. So when we go on to the next problem, you know how to do it.
Speaker 1 00:47:32
Oh, you know what, dude? They're saying that it's going to be cold tonight. So you might want to, I don't know if you want to put an undershirt on or something. We got to leave in 10. So if you can do it now and then come back. Thank you.
Speaker 2 00:47:55
So this one is like really easy, and then you get class time tomorrow to do it. This one and this one.
Speaker 1 00:48:04
Wait, wait, wait. Do it tomorrow at? 11 p.m. Alright, okay. Keep going.
Speaker 2 00:48:11
Um, this one and this one I wasn't in class.
Speaker 1 00:48:14
And you just clicked on one or two times.
Speaker 2 00:48:16
Alright, interviewing a refugee and coming up with an age response, I wasn't in class for, so I'm going to talk to her about that tomorrow. Because I have the chess tournament. Okay. And the quiz is like, it is like ten questions in Spanish, and it's like super easy.
Speaker 1 00:48:34
So you'll get 100% on it, you're sure. 
Speaker 2 00:48:40
I mean, I think I can.
Speaker 1 00:48:50
What else do you have for next week? What do you have coming up? Projects? Tests. 
Speaker 2 00:49:01
I don't have any projects.
Speaker 1 00:49:04
Zero? At all? Then? Okay.
Speaker 2 00:49:07
Yeah. Um... History, Mr. Baviar said that we're not going to have any tests until next year. Okay. He might have signed a quiz, but he doesn't know yet.
Speaker 1 00:49:18
Okay. But there's nothing on the books, right. 
Speaker 2 00:49:20
Yeah. Nothing on the books.
Speaker 1 00:49:21
Okay. Alright. Um, how will you remember to talk to ELA. 
Speaker 2 00:49:29
Um, I have a class first thing in the morning.
Speaker 1 00:49:32
So, you won't forget. 
Speaker 2 00:49:34
I could do that myself. I'll let you do that.
Speaker 1 00:49:40
Alright, Ben. But, I'm good. Happy Gmail. Come on, we got five minutes.
Speaker 3 00:49:52
So... So, there's three friends, and they all want their, they all want S-shaped bracelets, so they're gonna, there's gonna be three S-shaped, so it's S plus S plus S, that's one, then S cubed is just S times three, or S times itself, three times, so.
Speaker 1 00:50:38
How many star-shaped pieces of friends should buy? So, what's the answer? So let's do a quick test. Let's say that s is 2. Okay, s equals 2.
Speaker 1 00:51:21
Okay, so the first one is s plus s plus s? Yup. That's number one? Yup. Okay, number two is s cubed and three. 
Speaker 3 00:51:38
Three times s. Three s.
Speaker 1 00:51:41
Three. So this one is 2 plus 2 plus, right? This one is 2 cubed, and this one is 3 times 2, right. 
Speaker 3 00:52:04
Yep.
Speaker 1 00:52:05
So what is this? What is this. 
Speaker 3 00:52:11
What. 
Speaker 1 00:52:12
8. Hmm? That one is correct. You see a quick little way you can test your theory? Okay. 
Speaker 4 00:52:30
Yes, please do.
Speaker 1 00:52:52
You got your clue, kiddo. 
Speaker 3 00:54:31
I think it's the second one.
Speaker 1 00:54:37
I think it's number two. I don't know because I have to.
Speaker 4 00:55:26
Did you get it. 
Speaker 3 00:55:54
Is that correct. 
Speaker 4 00:55:58
I'm correct.
Speaker 1 00:56:35
Are you willing to risk that? Oh, I'm really willing to risk that. Okay. Are you willing to risk that? Because you have no way of verifying that because you haven't done any actual work.
Speaker 3 00:56:53
I've done work. Okay.
Speaker 1 00:57:06
So, now read what happened. Okay, let me tell you, let me, I'll give you your little tips. Okay? Number one, why didn't I save you from that. 
Speaker 3 00:57:22
Because you wanted to.
Speaker 1 00:57:24
Nope. Well, yes, but why didn't I save you from that? because i told you what to do and you didn't do it so if you want to do it your own way you've got to pay the cost of that okay so what did i tell you to do write it out what did i tell you the last time you were struggling what did i tell you to do write it out okay last time before.
Speaker 1 00:57:59
that too same thing right hey i know it's extra work but it keeps you from making mistakes and, even though it's a it's extra work it ends up being less work in the long run and guess what as you're writing it out look at me as you're writing it out your brain goes to town on it and starts like looking at all the different ways.
Speaker 1 00:58:32
So you become smarter when you write it out. I know it doesn't feel like you do. But Maddie, when I was getting ready for the interview yesterday, what did I start doing. 
Speaker 3 00:58:46
You started writing all this stuff.
Speaker 1 00:58:50
So I started writing down all the things that they said, all the questions I had. That made more questions. And my brain just starts, I have to do the same thing. I have to write this stuff out. Or else I can't see it. It's only the stuff that you're super, super familiar with that you don't have to see. But this is new because you're learning it, right?
Speaker 1 00:59:24
Write it out, okay? Let's go, kid. I'm going to go pee and then we're going to walk out the door.
Speaker 1 01:00:51
Okay, 0.75 is a number, so that's less than one. Is that what it's saying? Minus 0.75? Or it's saying 75% off of what? How is that reflected in here?
Speaker 1 01:01:30
So this is just 0.75. This is 0.75 of what. 
Speaker 3 01:01:38
Of the original, right. 
Speaker 1 01:01:39
Where is that here. 
Speaker 3 01:01:41
With B.
Speaker 1 01:01:43
Huh? B. So, again, give me a guess. Hmm? Give me a price of something.
Speaker 3 01:02:10
Ten.
Speaker 1 01:02:11
Ten? Let's go with something not so round. How about 150. 
Speaker 3 01:02:17
Alright.
Speaker 1 01:02:17
Okay? So B equals 150, right? So let's take your thing. Right? B minus .75. Right. 
Speaker 3 01:02:31
Equals 25. Okay.
Speaker 1 01:02:36
So, look it, equals 25. What do you mean? I don't know. Okay, so let's, just pay attention to this. So, 150 minus 0.75 equals 149.25.
Speaker 3 01:02:57
Yep.
Speaker 1 01:02:58
So, is that the price. 
Speaker 3 01:03:02
Nope.
Speaker 1 01:03:03
So, it's 75% of B, right? So, wouldn't it be 0.75 B? Remember, of is a connection point. No, I just was walking out the door and Ben stopped me. If you're up for it, then right now. Seven minutes.
Speaker 1 01:03:35
So, look. I found a deal on chewing back scoop backpack originally cost B dollars but it was on sale for 75% off so 0.75 B right so pick all of the expressions that represent the sale price of the backpack so if it's 75% off this is the discount.
Speaker 4 01:04:22
right that's the discount.
Speaker 3 01:04:37
So even if it's a real price?
Speaker 3 01:05:22
I don't know how to solve that.
Speaker 1 01:05:37
the best way to handle math is to handle what you know okay so what do we know we're just going to plug in a number 150 bucks the price and the discount so the price is 150 150 bucks right price and our discount we don't know our discount yet do we we know the numbers we know the percentage right so what is that huh 75 no 75 right so what is what is the discount.
Speaker 1 01:06:21
i need you to try for me how do we figure that out.
Speaker 3 01:06:40
Dividing.
Speaker 1 01:06:41
Are you guessing? So every time you get a variable, you can separate it. Point, seven, five. What's a variable. 
Speaker 3 01:06:54
D. Right.
Speaker 1 01:06:55
We put some parentheses there, and we put our number in. Okay? Mm-hmm. Now what do you have to do. 
Speaker 3 01:07:13
Multiply.
Speaker 1 01:07:16
Okay.
Speaker 4 01:07:19
So, I'll play. And this is discount.
Speaker 4 01:07:53
And that.
Speaker 1 01:07:55
Write it in there.
Speaker 3 01:07:60
Where. 
Speaker 1 01:08:04
We're just writing stuff down here. We're writing down what we know. So look, we defined discount here, we made the formula here, where do you think the answer should go. 
Speaker 4 01:08:15
Under.
Speaker 3 01:08:28
Okay.
Speaker 1 01:08:29
Okay? So if that's the discount, and that's the price, how do we figure out... What she bought it for. 
Speaker 3 01:09:28
$150 minus $112.5.
Speaker 1 01:09:52
So, pay is 37.5. So, now let's talk about what we get here, right? You've got B equals original, right? D equals discount.
Speaker 1 01:10:24
And then, what do you want this letter to be? P? P equals paid or price. So, what do we do here? We said, first we did this with 0.75B equals D, right. 
Speaker 3 01:11:09
Yeah, but how do we know if it's times. 
Speaker 1 01:11:14
What do you mean. 
Speaker 3 01:11:16
Your times in 0.75.
Speaker 1 01:11:19
So, this is what we did. See, so you kind of learned the percentages stuff, and then you forgot about it. So we learned this with percentages. So when you take the percent of something, you multiply it against it. Remember? Okay, so here's another trick.
Speaker 1 01:11:56
Okay, look, I'm just drawing this box so I can focus you in here so you don't lose yourself, okay? 100% equals what in numbers? One. Right. 75% equals what in numbers? I'll give you a hint.
Speaker 1 01:12:36
75. 75.75, right. Okay, 25% equals... Okay, so 0.75B equals D, right. 
Speaker 3 01:13:07
Yep.
Speaker 1 01:13:07
And then we also said, we also said that, where is it? B minus D equals P, right. 
Speaker 3 01:13:37
Mm-hmm.
Speaker 1 01:13:38
So look at this. Now what is B? B is, well, B stays what it is, right? B.
Speaker 3 01:13:45
150.
Speaker 1 01:13:46
So look, B minus. What is discount? It's actually .75B. Would you agree with that. 
Speaker 3 01:14:10
Yup.
Speaker 1 01:14:12
Why? Remember, 150 is just a made up number. So that's what we did.
Speaker 3 01:14:18
Wait, why is it B minus. 
Speaker 1 01:14:22
Didn't we just say we took 150 minus the discount of 112 and got 37.5. 
Speaker 3 01:14:32
Yeah.
Speaker 1 01:14:33
Right? So doesn't B minus D equal P? Right? So B, remember D is all of this. D is all of this, right. 
Speaker 3 01:14:52
Mm-hmm. Wait, B? D.
Speaker 1 01:14:57
Oh, yeah, and B is the price that we don't know, right? We just plugged in a number to figure things out, right? So so B minus point seven five B equals what P right? And what is P? Well, not written not anymore because remember it's not really B. P was disc. It was B minus D. Wasn't it. 
Speaker 4 01:15:33
Mm-hmm. B minus D. That's right. Yeah.
Speaker 1 01:15:56
So that's your formula right there, b minus .75b. So it's this one. Right. 
Speaker 3 01:16:04
Yeah.
Speaker 1 01:16:05
Good. Why did you pick that one. 
Speaker 3 01:16:10
Because b has to have something, like one number.
Speaker 1 01:16:19
Oh, actually that's not right.
Speaker 3 01:16:20
What. 
Speaker 1 01:16:20
You're on the right track, though. Keep on going.
Speaker 3 01:16:23
b has to have something, like one number, just like the price. So it has to have like a one, or...
Speaker 1 01:16:38
I'll see. Just guess. All right. No.
Speaker 3 01:16:40
Well, my teacher says, like, if none hides a one, that's like her saying, and then she says... Since if, like, the variable is by itself, then it has a 1.
Speaker 1 01:16:59
It's true, right? So, we'll do it up here. So, b equals 1b, right? Because it's 1 times b is equal to b, right. 
Speaker 3 01:17:19
So, it's not right.
Speaker 1 01:17:21
So, that's not right. But, here's the other part, right? What did we do over here? We said, isn't it really, look, I set you up. I thought you caught it. But, you didn't. 100%. Let me do it a different way. b, d.
Speaker 1 01:17:55
100% minus 75% is, right, the y. So let's look at that same thing, right? 150, we've got our 75%, that gives 112, right? So it gives 37.5, which is right here. So 150 times .75 is 112, right?
Speaker 1 01:18:28
So if we do the same thing, but the other way, before we do the calculation, we say, okay, well, if you've got 75% off,
Speaker 1 01:19:03
of these four squares how many is four is a hundred percent hmm how many of these four squares is a is a hundred percent how many of them let me remember each square is how many percent 25 25, right so all together they're what 100. if i take away three squares what am i left with.
Speaker 1 01:19:34
if i take away three squares 25 i'm left with 25 right so if the sale is 75 i'm left with. 25 25 right so sale is how much the discount is how much you took off of the price right so if.
Speaker 1 01:20:08
this is the backpack right you take off this this is our discount this is our price that make sense yeah so the other way we could look at this is 150 times.
Speaker 1 01:20:40
0.25 this percentage right yeah 37.5 which is the same as. Right. Does that make sense? Does it. 
Speaker 3 01:21:04
Yeah.
Speaker 1 01:21:05
Sure. 
Speaker 3 01:21:07
Yeah.
Speaker 1 01:21:10
Okay.
Speaker 3 01:21:34
It's these two.
Speaker 1 01:21:36
You're not sure, huh. 
Speaker 3 01:21:37
I think it is, because if you just do 75, it's not .75, so, and if you did it, like, you would only get . . . You wouldn't have the full answer. You'd still have to do that number by...
Speaker 1 01:22:02
Well, if you did 75b, right, you'd end up with a really, really big number, wouldn't you? 75 times the number.
Speaker 4 01:22:11
Yeah.
Speaker 1 01:22:12
We don't want that. And if you did 1 minus .75b, you'd have a really, really small number, right. 
Speaker 4 01:22:22
Yeah.
Speaker 1 01:22:23
So that's probably not it, right? Right, so let's just say for a second that b was $100 for the backpack.
Speaker 3 01:22:30
Okay.
Speaker 1 01:22:31
That would mean that 1 minus .75 times 100 is what. 
Speaker 3 01:22:36
.75 times 100. 
Speaker 1 01:22:39
Mm-hmm.
Speaker 3 01:22:39
75.
Speaker 1 01:22:40
Right, so 1 minus 75 is what. 
Speaker 3 01:22:42
74.
Speaker 1 01:22:45
1 minus 75 is what. 
Speaker 3 01:22:48
Negative 74.
Speaker 1 01:22:50
Do you think the backpack was negative $74? No. You see what I mean about a really, really small number. 
Speaker 3 01:22:55
Yeah.
Speaker 1 01:22:56
Okay? So, that's a quick way to say, yeah, those other two aren't correct.
Speaker 3 01:23:08
I'm going to do this after practice today. Great.
Speaker 1 01:23:10
Hit the button. Fantastic. Look, I've taken you through this, and I'm trying to equip you and get you to understand it. Because if you look at how to solve the problem, you're going to get to the next problem, and you won't understand how to solve it. But if you understand how we solved the problem and why it worked, then you can take that to all of the problems. What you're going to notice is all the problems are going to be solved the same way.
Speaker 1 01:23:43
But this is trying to get you to look at it, pull back, and come up with a formula. This. There's probably, look at me, this is probably the most applicable math you will ever use. How do I solve this problem? What is the formula? Okay. Meaning like I use it at my work all the time. This kind of stuff. Okay. All right. Depends on whether or not you work with me or you don't.
Speaker 1 01:24:26
When you're ready to work, dude, you are the smartest kid around. And when you're not. 
Speaker 4 01:24:30
you're not ready to go.
Speaker 1 01:24:52
You good with wearing that? If Alexis is the coach tonight? I'm gonna stay in my truck, but if Alexis is the coach tonight, text me. Maybe. That might come out sooner than later.
Speaker 4 01:25:36
What. 
Speaker 1 01:25:47
I'm wearing some dirty ones. We gotta go. Eric, do you have extra black socks? Do you have extra black socks, practice socks that Ben can use?
Speaker 1 01:26:47
Where your shin guards are? Did you find some or no? Okay. Here, here.
Speaker 1 01:27:31
Yeah. Okay. Keep these going. Sorry.
Speaker 7 01:32:23
um i think it's like a little are you leaving right now i can heat you up some cacao i made.
Speaker 1 01:32:34
it myself but i'm the same thing so i'm okay are you interested in how not at the moment i think.
Speaker 7 01:32:43
you interested afterwards like probably that sounds great. maddie hasn't do you need it with do you want it can i do it with one of these i'm not making.
Speaker 7 01:33:14
it myself so i just need to go pick up maddie. Yeah.
Speaker 1 01:33:31
Did you guys both not do your stretches? Yeah, I'm done in ten minutes. Eric, what about your stretches? What about your stretches? The trackers. 
Speaker 7 01:33:49
The stretches.
Speaker 1 01:33:54
It's very minimal. You need to get this hamster.
Speaker 7 01:33:57
It's cold. You guys are going to be tight.
Speaker 1 01:33:59
I've been cramping a lot. You guys are going to be tight.
Speaker 1 01:34:37
I hope you're not going to try to sit on that ball on the couch. You were going to though, weren't you? Even this is, I don't like this.
Speaker 3 01:34:48
It actually gets it pretty good.
Speaker 1 01:34:50
Yeah, it's just not as good as something before. See what I'm talking about? You're fighting for no reason.
Speaker 7 01:35:11
Now you have 6.15 or 7.30? 7.30, but I don't remember reading anything.
Speaker 1 01:35:23
Practice started at 6.15.
Speaker 7 01:37:21
I know. You only want dodgeballs? You just want me to get you dodgeballs? Everybody get you dodgeballs. 
Speaker 4 01:37:34
I'm crazy at this point.
Speaker 2 01:37:53
I like stood up and like I just started walking around and then right here, whenever I like bend my foot upwards, it just like hurts a lot.
Speaker 3 01:38:02
Mom, did you ever give the shin guards to Jameson. 
Speaker 7 01:38:06
You're fine. I'll give you my own new shin guards. I got him some. What? I bought him some. I didn't.
Speaker 3 01:38:19
I'm fine.
Speaker 7 01:38:33
You guys, don't buy her worship stuff. If it really bothers you, that means you should take some info.
Speaker 3 01:38:55
Can I just get my boots and shingles on right now? Do the other stretches later, then I'll do my goats right now. You guys need to open a video. Did you practice what I said. 
Speaker 7 01:39:40
i don't hate the new ios i don't love it i don't hate it sorry i think it's just you have to get used to it like designing like having it um and like connect it to like your tesla it's like.
Speaker 7 01:40:30
different because you used to go like you know and now it's like oh okay right here you know.
Speaker 5 01:40:58
Are they fighting again. 
Speaker 7 01:41:00
They're just fighting. Ben is telling Eric how he's doing it wrong. And then Eric is defending himself by saying that Ben does it wrong too.
Speaker 2 01:41:08
Eric, I was telling you...
Speaker 4 01:41:26
12-4 is today.
Speaker 1 01:41:34
What? 12-4 is today.
Speaker 4 01:41:49
Okay. Why is that so? Thank you.
Speaker 1 01:43:03
Let's go guys.
Speaker 3 01:44:05
Are we doing a video tomorrow? Are we doing it once a week? When does our subscription end? And when are our subscriptions? Are we gonna show the stretches? Like, the ones that they want us to do. 
Speaker 1 01:44:36
I think the stretches are designed to be something that you guys need to do. Will I make you do them? You know, do you need to do them every day? But should you probably do them more often than not? Yeah, you know... Honestly, I'd get a lot out of doing that.
Speaker 4 01:48:42
What's up? I'm out.
Speaker 4 01:49:32
$6.55 That's $4.50. It's not a yes.
Speaker 3 01:49:59
You guys need to make a cheese.
Speaker 4 01:50:15
Where'd you at. 
Speaker 2 01:50:16
I didn't eat yet.
Speaker 4 01:50:18
What will you eat. 
Speaker 2 01:50:20
Um, I don't know.
Speaker 4 01:51:11
How late. 
Speaker 3 01:51:11
9.30.
Speaker 1 01:51:23
I think it's somewhere around there.
Speaker 3 01:51:33
Come out about like 10 to 20.
Speaker 1 01:51:35
He wanted to eat and he tried to watch his iPad.
Speaker 4 01:51:43
He just can't wake up.
Speaker 1 01:52:53
You're playing jokes with him and you pulled the watch off from behind your back.
Speaker 2 01:53:11
I'm just holding it down on my side. Um, you told me that dad was going to come up and wake us up. No, I don't. I said, are you going to watch it, you? He said, dad said he's going to wake me up. He said, no, he's not.
Speaker 1 01:53:37
It's all good. We don't, this is not worth arguing about. When you guys get into a, you know, just a back and forth, yes, no, yes, no. Conversation's over.
Speaker 1 01:54:44
What are you trying to prove here. 
Speaker 2 01:54:46
He doesn't remember everything.
Speaker 1 01:54:49
How is this helping the situation? It's helping me. But it's not helping the situation. It's hurting the relationship, which is not helping you.
Speaker 4 01:56:04
Victor doesn't beat you on anything when are you going to be big enough to be able to not be.
Speaker 1 01:56:46
if you're really bigger than him then you don't care what he does and you definitely know how to define me which is what you did well i think the real question is why is it so important not this second but that's what you need sure as heck well it doesn't help you.
Speaker 2 01:57:53
Once you're interviewed, you said they're going to call me. Is there like a stages part. 
Speaker 1 01:58:22
I'll likely meet with the guy I'm replacing. So the guy I would be replacing got promoted. So now they're having him meet with whoever they bring on. If he got promoted, he could have been in a plan. That's kind of silly. Huh?
Speaker 1 01:58:54
So, but, so he's only coming back once a month for a week, but since the end of the year, Christopher Lou Janney has been always having a conversation with somebody else today.
Speaker 1 01:59:33
She's somebody that's familiar with the industry that I came from, which is reinsert. She offered me and asked me if I'd be interested in one of the positions that she oversaw. She said, you're probably going to turn it down once you hear the pay. She told me the pay, and I said, no. It's like, it's 90 grand plus bonuses, and da-da, and I said, that's, you know.
Speaker 1 02:00:14
She goes, okay. I had to ask, because honestly, I think you should be one of the directors. You'd be a good fit as one of the directors. I'll send you over to the chief human resource officer.
Speaker 4 02:01:16
The Lord has it. The Morton sidesteps.
Speaker 1 02:01:36
The thing about it is that it starts.
Speaker 2 02:02:03
Wouldn't it just be like, because you, like, you'd have like. Get out of here.
Speaker 1 02:02:26
i don't think that i have actually there the way i see it is.
Speaker 1 02:03:02
you know any move i make is going to be better than what i.
Speaker 1 02:04:56
I think there was one or two times where we didn't practice, but it was like, let's go play some indoor, and then we'll hit a restaurant, and then we'll watch some film back at Coachella.
Speaker 4 02:05:60
Hell yeah.
Speaker 1 02:06:08
High school coach. So my high school coach, it was like three brothers. The youngest brother was the JV coach.
Speaker 1 02:06:59
He ended up... Everybody liked him, so he ended up, like, my sophomore year, he ended up hanging out with us all the time. He was trying to get with Erika.
Speaker 2 02:07:14
Is he your age. 
Speaker 4 02:07:19
He was older than her. He was three years older than her. Something like that. I think they were all, like, too old by then.
Speaker 1 02:07:44
So there was one guy that they used to play with. There was, like, a squad. You know, when I played with him in the alumni game, nobody was like, it wasn't like, like the pros weren't.
Speaker 1 02:08:31
That's why I never, you know, was like the MLS. Because it's like, one of the guys I played with, his name's Jack, you know, made it to the MLS. A year younger than me, you know. He's good, but he wasn't, you know. It was just, it's like one of those things where it's like, oh yeah, but look how good I am.
Speaker 1 02:09:07
You could never hold the ball against me, you know. My biggest issue is that when I played, I wasn't really good, which is why I pushed you guys so hard before. Nobody wanted me in a position, so I never learned.
Speaker 1 02:09:40
And now what's funny is everybody wants to hold the ball in my position, you know. But I do think that could have been if I would have held on to the ball.
Speaker 1 02:10:17
One thing I was known for is my ability to defend. There was nobody better than me in high school and whatnot defending, but the problem was I didn't always create plays because I didn't hope them all, you know. A lot of times I'd block it, and then I'd just send a quick pass, but I didn't, like, creatively, or if I had to punt it, I would, you know.
Speaker 1 02:10:52
I didn't, you know, back then, and that's the point. Back then, it was like, don't pass back to the goalie. You know, don't hold the ball. You're the last man. You can't afford to make a mistake, so just get the ball and send it, right? And in fact, you know, the way that you did offense, too, back then. It wasn't like build out of the back. It was send the ball over the head of defense, and let your strikers.
Speaker 1 02:11:33
And we used to have a striker that was so fast. That's what he'd do. He'd just push the ball past and he'd run. You know? And then I literally, like, he came around the goalie one time and he like slid to stop and then kicked him. His name was Jamie, which is Sue.
Speaker 1 02:12:26
Here's what I know. I could keep up with. My top speed was, it took, my acceleration was slower. My first three, four steps were slower. But by step five, I was at the top speed. I didn't have a problem catching just about anything, especially if they were dribbling.
Speaker 1 02:13:05
Jamie, I couldn't. But a guy like that, unfortunately, he was really skinny. what's that small you know it's not just stepping your way bye-bye that's why i was like you.
Speaker 1 02:14:03
remember like if you're up against him like this right the ball has to go this way so that you can, because if you send it this way right there's no i mean you have to cut like that but he can just go like that right you got to get the inside turn on him now you're going to the goal does that make sense if you're going to go down the side like that then once he starts coming in you fake like.
Speaker 1 02:14:43
you're going to go in and it's supposed to show you this if you look at if you're running down the sideline like that and he's going like that you can fake like you're going to go in so that way he goes remember how he went and just he just nailed you you know with his shoulder you let that happen except before that you cut in like you normally do and then and here's the trick right you cut in, like you normally do so he pulls back and then you and then again you get in between him and.
Speaker 1 02:15:17
the goal right so you block him out again if you can learn how to do that you know you really will i mean because your issue is you when you create a foot race and that you can't win while you're dribbling you're really fast um but you're not really fast when you're dribbling but you don't need to be if the guy's behind you making sense so just get it behind you by stepping and then.
Speaker 1 02:16:05
if he starts coming up alongside of you you do the holland, You step towards him, and then you take the ball. You make him run. If you want this ball, you have to run over him.
Speaker 1 02:17:34
I gave myself 30 minutes to get there. I think we're going to take 20, 27 out of 4. 721.
Speaker 1 02:18:49
You don't want, you don't want the people on the bikes on the sidewalk, and enough people are getting hit on bikes by cars, that you want them to have their own lane, protect them, so, the bikes.
Speaker 4 02:19:52
I don't even know what it's called.
Speaker 1 02:19:60
It doesn't affect us, though. It doesn't affect us. We'd go in this one anyway, so. This is the entrance that we want. I mean, we can use the other entrance.
Speaker 2 02:20:47
You think I'll be a good driver? Yeah. What about Ben? Daddy? Hmm. 
Speaker 1 02:21:10
There's no good answer to that. Oh. Because you guys don't actually care about the other ones. So, text me if it's Alexis. Hey, own it.
Speaker 1 02:21:44
Hey, you want me there? Okay, so if you ever want me to be there you say it, okay? All right. Yeah.
Speaker 1 02:22:56
it's just what is in the back of this car it's just a stand and two pieces of wood it's all good that um my lock bar came loose so that's it so you don't worry about anything i like bridge kind.
Speaker 7 02:23:13
of hard and then all of a sudden i hear a slide and then a boom yeah don't worry about.
Speaker 1 02:23:18
it it's just it's just a metal stand all right sounds good i was are you by yourself yeah i was just thinking about it's like i'm gonna call her up and i'm just gonna go talk dirty to me it's, sexy night talk dirty to me so it was like knowing my luck i'm gonna call her and somebody's gonna be.
Speaker 7 02:23:44
in the car so i'm not gonna do that and then you called um what's in your back of your truck.
Speaker 1 02:23:53
Oh, I could have answered completely differently at that point, huh. 
Speaker 7 02:23:57
I know. Especially if that was... I'm not going to lie, if you had called me and said that to me, I would have been like, what are you asking me to do? I probably would have been caught off guard and confused.
Speaker 1 02:24:14
That's alright. I would have been doing it just to mess with you anyway, so. Is everything okay. 
Speaker 7 02:24:25
Yeah, it's good. Tonight, these late night practices are like, it's like, good, because then we're not like racing around like after five, but also like, it kind of means that we're not doing anything, you know, like, especially if like Maddie's practice is earlier, it's kind of nice that Maddie's practice was kind of later, because at least we were together, kind of, even though I had a meeting. Which I have another one on Monday of next week, but whatever.
Speaker 1 02:24:56
The meetings don't bother me. It was just difficult because, like, Ben is only halfway done with his math homework. So, you know, he's going to need help when he gets home. And, yeah.
Speaker 7 02:25:16
Yeah. No, it's fine. I'm glad that I finished. Like, education committee one is always, like, better. It goes by faster. So, yeah. I was happy to take that. I don't mean to put, like, our whole evening as much as possible on you, you know.
Speaker 1 02:25:35
No, I don't think of it that way. But, like, you know, I don't mind running them to practices. And I feel like when I do that, I'm able. to um just kind of like free you up a bit and like let you have i feel like it gives you a.
Speaker 7 02:26:00
an easier evening yeah i mean it does like absolutely it just kind of gives me time to like work on like i dropped what is it you guys left i finished eating and i sat on the couch for a minute like really only 20 minutes after i finished eating and then i like kind of looked at christmas gifts you know like i'm on my phone a lot right now i'm just trying to find christmas gifts you know so anyways but no i you know but it's like that stuff is like kind.
Speaker 7 02:26:34
of consuming me like i have a bunch of clerical stuff i just have to get done you know right.
Speaker 1 02:26:42
no i anyways i i get all that so um.
Speaker 7 02:26:51
But this is Elijah's dad. Let me call you back. Bye.

[AI_SUMMARY]
The lecture focuses on teaching math through visible processes, emphasizing algebra modeling, equation balancing, and practical applications. Key takeaways include the importance of showing work, using inverse operations, and validating expressions. It covers constructing cost expressions for a truffle purchase scenario, precision in mathematical language, and problem-solving strategies. Additional topics include conflict de-escalation, urban safety, and effective communication in instruction.