High School Math Story Problems - By
Transcript
| 00:05 | so we're gonna start off today with the task . | |
| 00:07 | This is Related to around page 2 71 . And | |
| 00:11 | your binder . If you want to do that , | |
| 00:13 | want to take a look at that . So once | |
| 00:19 | you get this you can go ahead and get started | |
| 00:21 | and I'll pass out calculators also . Okay so put | |
| 00:24 | your name on the purple paper and go ahead and | |
| 00:26 | get started . Yeah well come around and help you | |
| 00:31 | if you need it . Yeah . Okay . I | |
| 00:37 | did 14 . Cool . You like do you need | |
| 00:42 | another function ? So you can do the r . | |
| 00:44 | Yeah we're like elimination or something . Could could you | |
| 00:48 | do either of those methods with just one equation ? | |
| 00:50 | No , that's why I put two . Okay . | |
| 00:53 | Could you grab another one if you needed it ? | |
| 00:55 | Like you guys to see you plus like the next | |
| 00:58 | just another day . Yeah you could do that . | |
| 01:02 | It seems like if you could do the first day | |
| 01:04 | you could also do the second day . So you | |
| 01:06 | could do like three of them into the are what | |
| 01:09 | can sure try it out or try it out , | |
| 01:12 | You could try out that are found the calculator with | |
| 01:16 | one . You can try it out with two . | |
| 01:17 | Can you do everyone try it ? See if it | |
| 01:20 | gives you enough information that you need . Because think | |
| 01:22 | about what you're trying to find . How many things | |
| 01:25 | are you trying to find ? Did you prices the | |
| 01:28 | child and adult ? So if you tried with just | |
| 01:31 | one equation , see if you get all the information | |
| 01:34 | that you need that you're looking for . Okay . | |
| 01:37 | How would you get , why would you have negative | |
| 01:40 | five adult tickets ? That's actually gonna be something that | |
| 01:43 | I asked you to write a little story . How | |
| 01:47 | could how could that possibly happen ? They got lost | |
| 01:50 | in the sink . The tickets got lost in the | |
| 01:54 | sink . Yeah well or they got thrown away so | |
| 01:56 | you don't have five last two years . Okay that's | |
| 02:00 | fine . You're gonna write that down so you're doing | |
| 02:03 | a matrix equation . Do you guys have the same | |
| 02:05 | two equations though ? Yeah . Okay . Doesn't matter | |
| 02:08 | which to you chose . We start to start with | |
| 02:10 | the first one . Okay . And how did you | |
| 02:13 | solve that one ? Okay . Okay . Cool . | |
| 02:19 | Cool . Cool . Cool . How are you doing | |
| 02:21 | your totals ? I'm curious adding all the sales up | |
| 02:24 | for the first seven days . Okay . And then | |
| 02:26 | adding all the adult tickets on the first seven days | |
| 02:29 | and so on . And then you can do the | |
| 02:30 | same thing can appear . So you're gonna make an | |
| 02:33 | equation again with the C . And the A . | |
| 02:35 | And then how you saw that ? If there's only | |
| 02:37 | one equation , well you plug in because we already | |
| 02:41 | have the answer so you're just gonna plug them in | |
| 02:43 | and check . Cool . I'll probably have you guys | |
| 02:48 | do a poster for question two and just sort of | |
| 02:51 | be able to talk through what you did on that | |
| 02:52 | one . Okay . Like it . Cool . What | |
| 02:56 | ? Okay so for this problem are we adding these | |
| 02:59 | up or we put them in each one ? And | |
| 03:02 | um I would say you want to add them up | |
| 03:05 | because it's saying the totals for the first seven days | |
| 03:08 | so we eat uh each one individually and then see | |
| 03:10 | if they match up . Yeah . Yeah . Would | |
| 03:13 | that work ? Yeah . Okay . Yeah sure you're | |
| 03:16 | good , yep . Okay . Right . Why don't | |
| 03:19 | you tell us what you're doing ? Just adding and | |
| 03:24 | and then how are you getting dollars out of that | |
| 03:27 | ? Because I'm multiplying like the mountain Children ticket was | |
| 03:32 | to like them out . They bought it . Okay | |
| 03:36 | . After you total it or before you totally like | |
| 03:41 | what is that ? 56 Try that for a total | |
| 03:46 | . Oh it's four times 14 . So you're doing | |
| 03:49 | each day . Okay . Okay , so mchale is | |
| 03:53 | gonna total and then multiplied by four . So if | |
| 03:55 | you want to you can multiply by four for each | |
| 03:57 | day and then add those up . That'd be fine | |
| 04:00 | . You'll get the same thing . Cool , how | |
| 04:02 | are you doing up here ? Which part of it | |
| 04:08 | ? Okay . And you get feeling and what it | |
| 04:11 | might be asking Times numbers ? Okay . Yeah , | |
| 04:22 | two and three . But really you don't see that | |
| 04:24 | word respectively . So the first thing that's listed like | |
| 04:27 | april 1st , you'll double the second thing that's listed | |
| 04:31 | in april 2nd . You'll triple all of those results | |
| 04:33 | . Okay , So do you see how might that | |
| 04:36 | might lead to two more equations ? Okay . Why | |
| 04:44 | don't you make a list then , of all the | |
| 04:46 | information doubled for April one and all the information tripled | |
| 04:50 | for april 2nd . So if you want us just | |
| 04:56 | to figure out if the prices are so the same | |
| 04:59 | one you want us plugging in the prices equals this | |
| 05:02 | . Can one of you do plugging in the prices | |
| 05:06 | and one of you solve and see if it turns | |
| 05:08 | out to be the same . That'd be good . | |
| 05:10 | Cool . So on this problem right here what it | |
| 05:14 | says they're returning with man triple and then it says | |
| 05:17 | this respectively . So that means whatever is listed first | |
| 05:21 | year , it's doubled and whatever listed second . Triple | |
| 05:24 | . So then do we do a different equation or | |
| 05:27 | just plug it in and see how much so double | |
| 05:30 | everything from april 1st and see what happens and then | |
| 05:34 | triple everything from april 2nd . Okay and then what | |
| 05:36 | do we do after that ? Well it looks like | |
| 05:39 | josh is writing some equations . Is that for the | |
| 05:41 | first one , josh ? Okay . Can you make | |
| 05:43 | another one for day two ? And what Mikhail , | |
| 05:46 | what do you think you could do with those uh | |
| 05:52 | a ticket price ? You're just verifying the ticket prices | |
| 05:57 | again ? Yeah so there will be bigger numbers for | |
| 06:01 | sure . Yeah that looks good . How are you | |
| 06:04 | doing ? I'm just curious . I'm actually doing this | |
| 06:07 | one right , Tell us what you're doing . Well | |
| 06:09 | I'm decided doubling doubling the numbers which means doubling the | |
| 06:13 | people uh tickets . Okay good for these to cool | |
| 06:17 | the information . I'm doing the same thing . Okay | |
| 06:20 | . And how's it working out so far ? It's | |
| 06:22 | working out pretty well but we don't know if we're | |
| 06:24 | going to a direction . It sounds okay . So | |
| 06:27 | you doubled everything in the chart . Okay . And | |
| 06:30 | are the numbers pretty big ? Uh Well the number | |
| 06:35 | that's okay , you can still work with them . | |
| 06:37 | Okay . You do have a calculator . Remember that | |
| 06:40 | calculator can do more than just multiply . Cool . | |
| 06:44 | What's your story ? I was just gonna say a | |
| 06:47 | family with five adults and four Children went into the | |
| 06:49 | parking five adults got hurt . So they sued the | |
| 06:53 | company . I don't know . Okay so is the | |
| 06:57 | negative five negative money or what is the negative five | |
| 07:03 | ? I think it's negative negative thanks money . Well | |
| 07:10 | what is the title of that column of data ? | |
| 07:14 | Okay so I like that story . See if you | |
| 07:21 | can tie that into the number of tickets and why | |
| 07:23 | that would why negative money might imply that that's gonna | |
| 07:28 | be negative number of tickets . Okay . Any story | |
| 07:31 | coming to you ? Okay . Wonderful . When I | |
| 07:34 | wonder like how would it work if I start that | |
| 07:37 | they got a refund ? But that makes sense . | |
| 07:40 | Right . They went there and then they wanted their | |
| 07:44 | money . Okay There's a lack of popcorn . Okay | |
| 07:51 | . I know . So think about this If they | |
| 07:55 | if they bought the ticket , what day does it | |
| 07:57 | have ? The negative april 6th ? Of course this | |
| 08:00 | is very thank you . So april six if they | |
| 08:04 | bought the tickets on that day we go back to | |
| 08:08 | zero . So could could you tweak that story a | |
| 08:12 | little bit so that it's not a zero , it | |
| 08:14 | actually ends up actually lost the tickets or it could | |
| 08:17 | be that you get a refund . But could it | |
| 08:19 | be think about that part where if they bought it | |
| 08:22 | on the same day that might be a little bit | |
| 08:25 | of an issue like culture Stewart and like I mean | |
| 08:31 | that's a different story , it's a lovely story . | |
| 08:34 | Carly . But what do you have here ? So | |
| 08:38 | recent the theater gave the tickets away to students so | |
| 08:43 | it's like a prize . Yeah because they didn't pay | |
| 08:45 | for . Okay cool . I like that . That'll | |
| 08:49 | work . Okay one more minute . If you got | |
| 08:52 | a poster going , let's finish that baby up . | |
| 08:58 | So they had to pay , but okay . Okay | |
| 09:07 | , so the movie kind of lost the money . | |
| 09:09 | Okay , that sounds good . Another group was talking | |
| 09:13 | about a prize like that too . That's good . | |
| 09:16 | Okay , see if you can attack number five and | |
| 09:18 | then we'll be ready to roll . Okay , we're | |
| 09:20 | gonna come together here , folks eyeballs this way yo | |
| 09:25 | um well do if you made a poster for question | |
| 09:28 | one , will have you come up and if they | |
| 09:31 | have something on your post , on their poster that | |
| 09:33 | you don't have on your purple paper , put it | |
| 09:35 | on there . Okay , So we want to be | |
| 09:38 | good listeners and we also want to take notes on | |
| 09:40 | on the good techniques that they are using . Okay | |
| 09:42 | , so if you have your poster for question one | |
| 09:45 | , if you could slap it up on the board | |
| 09:46 | and tell us what's going on . Okay . Mm | |
| 09:53 | . Yeah , that'd be awesome . Okay , so | |
| 09:57 | for the first people that was 14 Children and four | |
| 10:01 | adults and a total of $96 . two Children . | |
| 10:05 | 22 adults , two and 28 . Same for that | |
| 10:09 | . And hold on just one second . So um | |
| 10:12 | did it matter which two days or three days that | |
| 10:15 | you chose ? No . So you just pick the | |
| 10:17 | first three days ? Yes . Okay . Did anybody | |
| 10:20 | pick different days to make their equations ? Okay . | |
| 10:25 | Sorry to interrupt . Go ahead . Okay . So | |
| 10:27 | then we do the R . R . E . | |
| 10:28 | F . Thing in the matrix and we got um | |
| 10:33 | the inverse staying with the prices for the Children and | |
| 10:38 | adults . But but then we got this extra on | |
| 10:40 | the bottom because we had three sort of two , | |
| 10:45 | we only need to find two things . Okay , | |
| 10:47 | Hold on one second there . So the other I | |
| 10:50 | . Worthy identity is what you found . Um Can | |
| 10:53 | you guys raise your hand if you use three equations | |
| 10:57 | to help you find the ticket prices in question one | |
| 11:02 | ? Why not ? You only need to . Okay | |
| 11:07 | so Lauren's going to kind of talk us through how | |
| 11:10 | her group kind of came to that decision . So | |
| 11:12 | did you work with the three equations first ? I | |
| 11:15 | don't remember somebody . Somebody in your group did the | |
| 11:18 | three equations and they tried it out on the calculator | |
| 11:20 | . They did the reduced row echelon form there . | |
| 11:23 | And and if you guys noticed she pointed out that | |
| 11:26 | there's just an extra row of information in that answer | |
| 11:28 | that was given to him . Kind of like what | |
| 11:31 | you're saying ? You don't need that third equation . | |
| 11:33 | You really have some extra information . Okay keep going | |
| 11:35 | sorry . And then we did it was just two | |
| 11:40 | things we didn't get an extra And we got the | |
| 11:43 | same 4 10 With the identity . So the child | |
| 11:48 | is $4 and there is $10 . Cool And mandy | |
| 11:53 | . Do you want to talk to us about how | |
| 11:54 | you started off with one equation ? Yeah I tried | |
| 11:58 | it with just the first day and I got just | |
| 12:02 | two answers and they were all decimal numbers . And | |
| 12:05 | what did you try with ? The first day ? | |
| 12:07 | I tried 14 4 96 . In the matrix . | |
| 12:11 | Okay so what size matrix did you work with ? | |
| 12:14 | I did a one by three . Okay and you | |
| 12:18 | said 14 4 and 96 . So that first row | |
| 12:22 | of information she made a tiny little augmented . And | |
| 12:26 | do you remember what it said ? Um It said | |
| 12:29 | one point something and then six point something . So | |
| 12:33 | weird stuff . Yeah . Okay could we figure out | |
| 12:37 | the ticket prices with just one equation ? Mhm . | |
| 12:42 | Fisher says yes you can do it with just one | |
| 12:46 | but it's easier if you have to . Okay or | |
| 12:48 | even three . Okay and Ashlyn you first circled something | |
| 12:53 | on your paper . Um The one the which april | |
| 12:57 | day had the one on it april Okay . And | |
| 13:01 | what were you what did you tell me about if | |
| 13:03 | there was just the one there ? How did you | |
| 13:05 | think you could proceed ? Remember ? No . Okay | |
| 13:10 | . Can anybody think why that day might be an | |
| 13:13 | important day to work with ? If that was just | |
| 13:15 | the one thing that you had , if you just | |
| 13:18 | had one day's worth of information could you figure it | |
| 13:20 | out ? Okay . That's cool . That will move | |
| 13:31 | on . Did anybody get different ticket prices than four | |
| 13:34 | and 10 ? Okay poster for number two . Who's | |
| 13:38 | got a poster for number two ? Right Thank you | |
| 13:45 | , poster number one mm right up next to it | |
| 13:52 | would be great . Okay , so for problem , | |
| 13:57 | number two , you had to add up all the | |
| 14:00 | totals for everything . So if you added up all | |
| 14:02 | the number of the Children's tickets , it was 43 | |
| 14:05 | . If you added all of them for the adult | |
| 14:06 | tickets , it was 60 . And then we just | |
| 14:09 | plugged in to see if it'll work um $10 for | |
| 14:13 | the adult tickets , like right There and then the | |
| 14:16 | $4 for the children's tickets And it worked as 172 | |
| 14:21 | 600 . Cool , cool . Thank you . Um | |
| 14:25 | I saw some other groups do something different for that | |
| 14:27 | second problem . Um Did anybody try to solve a | |
| 14:32 | new system of equations on problem too ? You have | |
| 14:35 | one equation . Everybody just plugged it in , substituted | |
| 14:40 | in to test it out . Yeah , go ahead | |
| 14:45 | long . And what do you do ? I just | |
| 14:47 | took the like , I don't know . I guess | |
| 14:50 | I did a long equation where I did 14 and | |
| 14:53 | then like so in parentheses like 14 times for parentheses | |
| 14:57 | plus parentheses to and then like continued on . So | |
| 15:01 | it was like at all of them up and then | |
| 15:04 | added each one individually instead of doing the total first | |
| 15:07 | and then multiplying by four . Cool . Got it | |
| 15:10 | . Thanks . Thank you for sure . Any questions | |
| 15:12 | on two ? Okay , poster for three . Do | |
| 15:15 | we have a poster for three ? Come on up | |
| 15:19 | . You can put it over that matrix in the | |
| 15:22 | middle . All right . So what we did was | |
| 15:27 | we doubled the first day . So like the first | |
| 15:30 | day was 14 C plus four equals 96 . And | |
| 15:34 | then we saw that would give us 28 c plus | |
| 15:36 | a goes 192 . And then we tripled the second | |
| 15:41 | day and it gives us 60 and 66 A . | |
| 15:44 | And then the total 6 84 . And then we | |
| 15:47 | put that into a augmented matrix and then did the | |
| 15:51 | R . R . E . F . And then | |
| 15:52 | got 10401 10 . So what did that tell you | |
| 15:58 | that the ticket prices would still be the same ? | |
| 16:02 | Cool . Cool . Thanks . And and matty . | |
| 16:07 | You doubled both didn't you ? Double both days . | |
| 16:09 | And how did it work out ? Um It didn't | |
| 16:12 | work , it didn't work okay so this is what | |
| 16:15 | I would like you guys to do and and I | |
| 16:17 | want to double check Maddie's work here . So i | |
| 16:20 | if we take these first two days worth april 1st | |
| 16:23 | and april 2nd and double the first day and double | |
| 16:26 | the second day . Could you take two minutes right | |
| 16:28 | now and double both and then check the system and | |
| 16:32 | see how that turns out . And it worked out | |
| 16:35 | . Okay . What method did you use ? Did | |
| 16:37 | you use elimination ? So she didn't do it on | |
| 16:40 | the calculator matty . So maybe that could be our | |
| 16:43 | discrepancy . Okay , how about we take two minutes | |
| 16:46 | , everybody check doubling both . Okay , take two | |
| 16:48 | minutes . And if we get something kind of kind | |
| 16:51 | of wacky that we don't expect , raise your hand | |
| 16:53 | and let me know . Are you done ? Did | |
| 16:56 | you double up where you doubled one and tripled this | |
| 17:03 | one ? So right now you're supposed to be doubling | |
| 17:06 | both and checking , Doesn't it not work ? Just | |
| 17:09 | because this one says triple for this day . Right | |
| 17:13 | . And so that is what the wording is saying | |
| 17:15 | ? But Maddie started doubling . And I thought that | |
| 17:17 | that was interesting to take a look at . So | |
| 17:19 | it is a little bit different than the instructions . | |
| 17:21 | So we're just checking that out . Yes , sir | |
| 17:24 | . You got it . So it works . Okay | |
| 17:27 | . What method did you use ? Elimination or the | |
| 17:29 | matrix ? OK . And it still came out four | |
| 17:32 | in 10 . Okay . Okay . Matty . Are | |
| 17:36 | you trying it again ? Uh a in verse . | |
| 17:43 | Okay . And it worked weird . Maybe it was | |
| 17:47 | just something that was entered in a little bit of | |
| 17:49 | funny way Anybody getting something strange other than four and | |
| 17:52 | 10 , it's working . Okay . Okay , so | |
| 17:57 | let's have our creative story team coming up actually before | |
| 18:01 | that . Sorry , I forgot . Um so when | |
| 18:03 | I was talking to Michaela before about this question number | |
| 18:06 | three that we're on , um you wanted to share | |
| 18:09 | what you said ? Like why would it not matter | |
| 18:12 | what we did to the equations ? Um It doesn't | |
| 18:14 | matter as long as you do it on both sides | |
| 18:17 | of the equal sides , because if you only do | |
| 18:18 | it to one , then your problem will be off | |
| 18:21 | . Okay . What do we call that ? When | |
| 18:22 | we do something to both sides of the equal sign | |
| 18:26 | , anybody ? Remember property of equality , Property of | |
| 18:29 | equality . We got it . So that's exactly right | |
| 18:32 | . We could be doing anything like adding up the | |
| 18:34 | first seven days of the week and we're still going | |
| 18:37 | to get those same ticket prices because we're adding the | |
| 18:40 | same thing to both sides of an equation or if | |
| 18:43 | we're doubling both sides of an equation or tripling both | |
| 18:45 | sides of an equation , we're not really changing the | |
| 18:48 | solution to that system . So Very cool , awesome | |
| 18:50 | . Alright story , come on up here please . | |
| 18:53 | And then if some of you have some exciting story | |
| 18:55 | you'd like to share also , that'd be great . | |
| 18:58 | So we had some weird information from April April six | |
| 19:03 | had a negative number . Okay . And some of | |
| 19:05 | you noticed that right away and said how could that | |
| 19:07 | be possible ? So let's hear a couple of possible | |
| 19:09 | explanations . Okay What do you got Carly . So | |
| 19:12 | we thought maybe that somebody somebody reserved five tickets but | |
| 19:18 | never picked them up so and then the movie theater | |
| 19:21 | was never able to sell them . So they were | |
| 19:23 | out five tickets . Very nice . Thank you . | |
| 19:25 | Any other explanations . There were a couple of good | |
| 19:27 | stories . What's the story ? Didn't you have one | |
| 19:30 | about a prize ? Yeah . What was it ? | |
| 19:33 | Nice ? The school would give away five tickets to | |
| 19:36 | students as a prize prize . Okay and so that | |
| 19:39 | would be why would it be negative then ? It's | |
| 19:42 | like not gaining any free ? They're free , they're | |
| 19:45 | not getting anything , nobody's paid for it . Cool | |
| 19:48 | . And that back group you had a similar story | |
| 19:51 | . Okay . What was what was your situation there | |
| 19:53 | ? Sequoia ? You want to tell us on the | |
| 19:55 | sixth of april five adults , 15 movie . Tix | |
| 19:57 | tickets in a raffle . And then on the same | |
| 20:00 | day the four Children went with parents to the movie | |
| 20:04 | and they had to pay for the Children but not | |
| 20:07 | the parents . Okay , so we had a negative | |
| 20:09 | five because they were also free . Cool . Okay | |
| 20:11 | , so to kind of tie this up on that | |
| 20:13 | last question , could you just make up any data | |
| 20:17 | that you wanted ? Yeah , because the ticket prices | |
| 20:26 | stick to the table and what was that ? The | |
| 20:28 | ticket prices never changed , ticket prices never changed . | |
| 20:31 | So this group chose one and one and then two | |
| 20:34 | and to another group chose one and one and two | |
| 20:38 | and two . Which was strange that you chose the | |
| 20:40 | same thing , but you could have chosen anything in | |
| 20:43 | the world as long as you kept those same things | |
| 20:45 | . Okay , so a couple of things that I | |
| 20:47 | want you to write at the bottom of the purple | |
| 20:48 | paper to kind of tie this up um And what | |
| 20:51 | really goes back to all these different things that you | |
| 20:53 | did um As long as we are doing these same | |
| 20:57 | operations to both sides of the equation , using our | |
| 21:01 | properties of equality , we're going to have a system | |
| 21:04 | that has the exact same solution . Okay , so | |
| 21:07 | if we use the properties of equality , I don't | |
| 21:16 | know if you can read this , this solution to | |
| 21:20 | the system will not change . Alright , so take | |
| 21:29 | a minute copy that down and then I want to | |
| 21:33 | show you one more thing on the computer screen . | |
| 21:38 | Okay , so um first of all , it was | |
| 21:41 | totally impressive that you guys right away started writing equations | |
| 21:44 | and no other classes that I've done this um did | |
| 21:47 | everybody immediately start writing equations . That was impressive . | |
| 21:50 | So , um , great job on that . And | |
| 21:52 | I have a question for you about those equations . | |
| 21:54 | What kind of functions are those that you wrote ? | |
| 21:57 | You wrote about 10 of them in the last half | |
| 22:00 | an hour . What kind of functions are they mayor | |
| 22:09 | ? Are they linear ? Yeah . How do you | |
| 22:11 | know that ? Because they're staying the same . What | |
| 22:14 | state if you buy one , it's going to be | |
| 22:16 | $10 to buy two . It's gonna be $20 just | |
| 22:18 | adding that . Okay , so that rate will stay | |
| 22:20 | the same . Okay , so linear functions here , | |
| 22:23 | I think that's also worth noting linear functions or everything | |
| 22:26 | that you wrote down today . So before you came | |
| 22:29 | in , what I did was I took all of | |
| 22:31 | these possible linear functions from April one , all the | |
| 22:34 | way to April eight . And I think I even | |
| 22:36 | put some other information on from possible April nine and | |
| 22:39 | 10 . And I grabbed him . I grabbed all | |
| 22:42 | of those linear functions and I just want to show | |
| 22:44 | you really quickly what that looks like . So I | |
| 22:49 | need to help . Oh my computer take a minute | |
| 22:54 | . Okay . No , that's all right . So | |
| 22:56 | while this is loading at the bottom of your purple | |
| 22:59 | paper , I want you to pretend like you're opening | |
| 23:01 | your next movie theater on your own and you're gonna | |
| 23:04 | choose the prices . So pick a child's price and | |
| 23:08 | pick an adult price because we're going to use that | |
| 23:10 | in just one second . Okay . Pick a child | |
| 23:13 | price and an adult price . If you want it | |
| 23:16 | to be the same as those in your group , | |
| 23:18 | that's fine . Say . Okay , so assuming you | |
| 23:24 | have something written down , Take a look up here | |
| 23:26 | , just for one second . Take a look up | |
| 23:29 | here , eyeballs , eyeballs this way . Um So | |
| 23:33 | this is all of the collection of linear functions from | |
| 23:37 | april 1st to april 8th and maybe a little bit | |
| 23:40 | beyond all of these linear functions . What do you | |
| 23:42 | notice about them ? They are straight , which makes | |
| 23:46 | sense because they're linear . What else looks like they | |
| 23:49 | all like me in this day ? They do all | |
| 23:52 | meet , where do you think this is ? What | |
| 23:55 | do we call that equilibrium point ? And what is | |
| 23:59 | it for this story ? $4.10 dollars . Okay , | |
| 24:07 | so no matter what we do to these equations , | |
| 24:09 | like Michaela said as long as we do something to | |
| 24:12 | the , to both sides of the equation , okay | |
| 24:16 | , it might change the way that this is tilted | |
| 24:18 | a little bit , but that equilibrium point Is not | |
| 24:21 | going to change . Okay , so that's kind of | |
| 24:23 | cool , this is kind of a nice visual . | |
| 24:25 | So if you would take 30 seconds and make a | |
| 24:28 | really rough sketch of this on your purple paper and | |
| 24:32 | maybe make a note what this point is that it's | |
| 24:35 | 4 10 . That's our idea of equilibrium that we've | |
| 24:37 | been talking about . That would be great . And | |
| 24:42 | I have one more question for you about this picture | |
| 24:45 | up here . So and what I have , everything | |
| 24:49 | seems to be kind of tilting this way Except for | |
| 24:53 | this one line right here . What day is that | |
| 24:57 | ? Yeah , The faithful April six . The one | |
| 25:01 | with the negative . Okay , so in some way | |
| 25:03 | that would that would influence the slope of that line | |
| 25:06 | . Okay , cool . Alright . So do you | |
| 25:08 | all have your new chosen movie ticket prices ? Okay | |
| 25:12 | . So what I'm gonna do is give you a | |
| 25:14 | blank table now for april 1st through eighth and you're | |
| 25:18 | going to fill in the numbers of people that came | |
| 25:21 | to the movie theater , preferably not all zero every | |
| 25:24 | day . That's not a really great movie theater . | |
| 25:26 | Um And then fill in the totals . Okay . | |
| 25:28 | So I'm gonna give you about two minutes to do | |
| 25:30 | that . So hopefully you have your ticket prices and | |
| 25:32 | a calculator ready ? I'm gonna give you a new | |
| 25:34 | table . Okay . Okay . two minutes here to | |
| 25:40 | fill in your chart , create some data . You | |
| 25:47 | use your new prices that you selected . Okay . | |
| 25:51 | Hey , and you're on your chart guys don't put | |
| 25:54 | the prices on there . Don't put the prices on | |
| 25:56 | their sorry , sorry , I should have told you | |
| 25:59 | that you're gonna crumple these up if you put them | |
| 26:03 | on there . That's all right . Maybe cross it | |
| 26:04 | out . No , no , no no . The | |
| 26:09 | you're set ticket prices that you wrote on the purple | |
| 26:12 | paper . Okay . Even if you don't have your | |
| 26:15 | table totally filled in , I want you to think | |
| 26:17 | if you have enough information on that table for somebody | |
| 26:21 | to figure out the ticket prices um crumple it up | |
| 26:25 | . So think about how many days worth of information | |
| 26:28 | you need to make this a successful activity . Okay | |
| 26:32 | ? And we'll do a three count , check it | |
| 26:34 | up here to the front board . Okay ? And | |
| 26:37 | then instead of everybody running up here , okay , | |
| 26:40 | let's just send one person from your group and get | |
| 26:42 | as many snowballs as you need for your group . | |
| 26:45 | Okay ? So 123 almost hit rent . Okay ? | |
| 26:54 | Go send one representative up , send one representative and | |
| 26:58 | get enough snowballs for everybody at your group . You | |
| 27:04 | choose your method and I want you to solve their | |
| 27:07 | system . Okay ? Figure out how many days you | |
| 27:10 | need . Even if the answers are on there , | |
| 27:13 | go ahead and take two minutes and solve a system | |
| 27:16 | . Okay . Use whatever method you want to use | |
| 27:20 | , go to it bailey . What do you think | |
| 27:22 | ? How are you going to solve that ? Okay | |
| 27:25 | . So what you gonna do first make the function | |
| 27:29 | ? Okay . Didn't you already do that ? And | |
| 27:32 | now what are you gonna do elimination ? Okay . | |
| 27:36 | Cool . You're gonna use a Matrix . Cool . | |
| 27:39 | Alright let's come back together with our discussion . We | |
| 27:42 | had a couple of interesting cases here . Um Matty's | |
| 27:49 | testing something out where it looked like . What did | |
| 27:52 | it look like ? There was a negative ticket price | |
| 27:54 | , negative 75 negative $75 ticket price . She's going | |
| 27:57 | to test it out and see if that actually works | |
| 28:02 | . And then mason had an interesting set of data | |
| 28:04 | where every day the data doubled , right ? And | |
| 28:09 | and so what did you get when you were trying | |
| 28:10 | to solve it ? Zero . Which method did you | |
| 28:15 | use ? I tried the matrix and I tried elimination | |
| 28:19 | and neither of them were Okay . What did you | |
| 28:21 | get with your matrix ? Um 1.4 . No No | |
| 28:27 | No No one . Yeah like four That 9.4 000 | |
| 28:36 | 000 lets you sneezy . So if we have something | |
| 28:39 | like this okay this is certainly not the identity that | |
| 28:43 | you were looking for and you said you got zero | |
| 28:46 | which is like saying zero equals zero . Will there | |
| 28:49 | be a solution to this system ? Will there be | |
| 28:52 | an equilibrium ? Uh huh . So so what could | |
| 28:56 | the ticket prices even be ? I'm serious . zero | |
| 29:00 | could work . What if you tried $1 dollar one | |
| 29:04 | and 1 or two and 2 ? That's what I'd | |
| 29:07 | like you to try some numbers out in there just | |
| 29:09 | and we'll report back to that on another day . | |
| 29:12 | Anybody else gets something sort of interesting to take a | |
| 29:14 | look at $1 $1.1 . And you were not surprised | |
| 29:19 | where you call ? No . Okay . Cool . | |
| 29:22 | Well we're at about the five minute mark . And | |
| 29:24 | what we're gonna do for your homework is two things | |
| 29:27 | . First of all , I'm gonna give you one | |
| 29:29 | more task , different theater and this time you're going | |
| 29:33 | to consider Children's prices , adult prices and then a | |
| 29:36 | senior price . So think about what you would need | |
| 29:40 | to solve a system in that situation and what method | |
| 29:44 | you would prefer to use that . And then also | |
| 29:47 | if you remember , we're going to have a test | |
| 29:49 | on this stuff next time . So I have another | |
| 29:51 | review paper for you as well . Okay , so | |
| 29:54 | I'm gonna hand out task three which is really related | |
| 29:57 | to this . And if you think right now about | |
| 30:00 | what you're gonna need to solve something for those three | |
| 30:03 | different pieces of information , um you might need something | |
| 30:06 | that's in this classroom to help you do it , | |
| 30:09 | hint , hint , hint calculator , so I'll go | |
| 30:11 | ahead and pass those out . And if I were | |
| 30:13 | you , I'd probably get started on that paper First | |
| 30:15 | . It's green and then I'll pass out the review | |
| 30:18 | paper . Okay ? Yeah . Great job . Please | |
| 30:23 | do the green and follow up with your studying for | |
| 30:25 | friday and bring your triangles back . All right . |
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High school math lesson on problem solving.
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