In this video, I want to provide the proofs for Fermat's little theorem and Euler's theorem. These are pretty important theorems from number theory, elementary number theory. They talk about reduction one can do with modular exponents. But in the context of group theory, these two theorems are just trivial corollaries of Lagrange's theorem. Remember that Lagrange's theorem says that if you have a subgroup of a group, then the order of H must divide the order of G. As a consequence, if you take any element inside of your group, if you take that element raised to the G power, the order of G power, you always get the identity. That's really the consequence we have right there. Lagrange's theorem tells us that you raised an element to the order of the group, you get back the identity. Euler's theorem and Fermat's little theorem are two things that are going to use that fact right there. While oftentimes in a number theory course, we would first prove Fermat's little theorem for primes, and then you generalize it to Euler's theorem for composite numbers, we're going to work backwards because Lagrange's theorem could shink right here, already gives it to us from that direction. We have to first introduce Euler's totient function. This is often denoted as a phi. The totient function is going to be a function from the positive integers to the real numbers, which admittedly you're not going to get anything other than a whole number, but I'm defining it broadly because, I'm introducing that the totient function here is an example of what's called an arithmetic function. Arithmetic functions are essentially these functions of this form, you take positive integers to the real numbers. But more importantly, this is what we're going to call a multiplicative function. A multiplicative function will define just in a second, but the totient function does the following. If you take phi of one, we're going to define that to be one, and for any other positive integer, phi of n is going to be the number of positive integers that are co-prime to n when you go from zero to n, like so. Let me give you some quick examples of that. Phi of one by definition is equal to one. Phi of two is equal to one because one's the only thing co-prime up to two. Phi of three, you're going to get two, because you have the numbers one and two, which are co-prime to three. Phi of four, you're going to get likewise two because you get the numbers one and three. The issue is that two and zero, they're not co-prime to four, so you get just one and three. If we do say phi of five, you're going to get four numbers because you get zero, one, two, three, and four. Zero is never going to be co-prime, but you get four other ones, one, two, three, four. If you get phi of six, there's going to be two numbers there. So you get zero, one, two, three, four, five. You take away zero, two, three, and four. You're just left with one and five. And we can keep on going with these things here. You're going to get phi of seven is equal to six. Phi of eight, let's see, that's equal to four, I believe. And you can keep on going. Now there's a couple of tricks for computing this totion function quickly. If you ever take phi of a prime number, this is always going to equal p minus one because other than zero, all the numbers less than p will be co-prime to the prime. And one can generalize this principle by taking phi to the pk. If you have a power of prime, this will always equal p to the k minus p to the k minus one. And the idea is because you have a power of a prime, the only thing that would be not co-prime to p to the k will be multiples of p. And so if you count from zero up to pk there, pk should say one less than pk. If you count all the multiples, there's gonna be p to the k minus one many multiples of a prime. And so you take that difference right there. So this allows us to compute prime powers. And then another thing that I was mentioning earlier is that the phi function is multiplicative. A multiplicative function has the following properties that first of all, phi of one is always defined to be one. And then phi of a times b equals phi of a times, and I'll move this a little bit down, I got crowded there. So if the GCD of a comma b is equal to one, then this tells us that phi of a times b will equal phi of a times phi of b. So, and I'm not gonna prove this fact, that that's a very appropriate thing to do like in a number theory course. But what we're just saying is that if two numbers are co-prime, we can compute the phi by factoring amongst co-prime factorizations. So for example, how do I do six? Which is phi of, that's gonna be phi of two times phi of three. Two is a prime number. So it's gonna be two minus one, which is a one. And then three is also prime numbers just three minus one, which is a two. One times two is equal to two. How did we do eight? Well, eight as a power of a prime, you're gonna get eight minus four, which is the previous power of two. So you end up with just a four right there. If we wanted to do something a little bit more complicated, like say, phi of 12, it's not too complicated, but phi of 12 would look like the following. You get phi of four times phi of three. Four is a power of prime, so it's gonna look like four minus two. And then phi is a prime itself, so you're gonna get three minus one. So you end up with two times two, which is equal to four. There's gonna be four numbers co-prime to 12, and this is gonna be one, five, seven, and 11. Those are the four numbers co-prime to 12. So calculating the totion can be very useful. Why is it so useful from a group theory perspective? Well, if you take the multiplicative group, mod n, we've seen that this group will, the number of elements that are in this group will be those elements co-prime to n. Well, if phi counts the number of elements co-prime to n, the order of this group will always be phi of n. All right, so let's now talk about Euler's theorem. Euler's theorem from number theory says the following. Let a and b be integers, so that n is positive, and the GCD of a and n is equal to one. Then if you take phi raised, sorry, if you take a raised to the totions of the modulus power, that is always congruent to one mod n. And how do we see this? Why is this true? Well, this comes from the following fact. If the GCD of a and n is equal to one, that means that a belongs to the multiplicative group Zn star, which the order of Zn star, as we've already mentioned, is equal to phi of n. And by Lagrange's theorem, if you take an element and you raise it to the order of the group, you always get the identity. Therefore, if you take a, which belongs to the multiplicative group Zn star, and you raise it to the order of Zn star, you're gonna get back the identity. So this is a complete immediate consequences of Lagrange's theorem. If you look at it in the perspective of group theory, if you wanna prove this using just divisibility and number theoretic things, it's a lot harder proof. Group theory's already done all the heavy lifting right here. And then a special case of Euler's theorem is what's referred to as Fermat's little theorem, not to be confused with Fermat's last theorem or even Fermat's Christmas theorem, which are other related theorems in number theory. Fermat has a knack of stating theorems in number theory, but not actually proving any of them. I'm not sure if he proved this one either. But anyways, we'll prove it. So if P is a prime number, and if P does not divide A, then A to the P minus one is congruent to one, mod P. Or more specifically, it's often written, I should say more specifically, it's often written in the alternative form that B to the P is congruent to B mod P. So if you raise a number to the Pth power, it's used to get back to the original number when you work mod P. Which I want to admit that this equation right here implies the second one very quickly, because if you have A to the P minus one, this is congruent to one. If you times both sides by A, you'll get A to the P is congruent to A, great. So this version right here is the immediate consequence of this version. So let's prove the first version. This is again an immediate consequences of Lagrange's theorem. We're actually using Euler's theorem right here, because Euler's theorem tells us the following. P of a prime is equal to P minus one. We saw that already. And if P does not divide A, that actually tells us that the GCD of A and P is equal to one. So then by Euler's theorem, this identity holds, which we already approved the second identity. And so that gives us the proof of Fermat's little theorem. Now, why are such theorems actually useful whatsoever? Well, I want to mention that Fermat's little theorem provides one of the first basic primality tests that we have, primality tests. These are actually very important things from number theory. They have some important consequences in computer science, which we'll see actually in the next chapter. A primality test is a test to determine whether a number is a prime number or not. And the most naive of any primality test is just a factor. And if you can factor a number, then you can determine whether it's a prime or not because of the factors that it's not prime. But the problem is when the numbers get big, right?  That would take a long time to do it. Is there some other way of determining whether the number's prime or not, even if we don't factor it? Well, if we are uncertain if n is a prime number, what we can do is we can compute. So basically, this primality test that we're gonna run right now is, we have a number n and we're asking, is it a prime? We don't know. So what we can do is we can then compute b to the n mod n. So we're gonna compute this. And because what we're gonna see is the following is that by Fermat's little theorem, if b to the n is not congruent to b mod n, then that implies that n is not a prime number. So we can prove that a number is composite without factoring it, which is a very impressive thing. Now, in order to compute b to the n mod n, that could be, n could be a very big number. And if we're running this primality test, n is probably very big. So how do we deal with something with really big exponents? Oh, well, we could use the repeated squares algorithm that we presented earlier in this lecture series. We could run this primality test by using repeated squares. So we could very quickly, I mean, because the complexity of repeated squares is essentially just log base two of n right here. It's a very fast algorithm. So we could compute these powers very quickly. And so then we could determine if b of n is congruent to b or not. Now we have to be careful. Fermat's little theorem only goes one direction. If b to the n is not congruent to b, then that will tell us it's not a prime. But if b to the n was congruent to b, that doesn't tell us anything. It doesn't tell us it's prime. It doesn't tell us that it's not prime. We don't know. Now the thing is, in terms of the grand scheme of things, prime numbers are fairly rare. Basically the prime number theorem tells us that the density of the prime numbers amongst the natural numbers is zero. So we chose an arbitrarily large number. Most likely it's not prime. And so if we were to check, like, oh, b to the n, if it's not equal to b, we're done. We know it's not prime. But if it works, if b to the n does equal, or if it is congruent to b, then we just try a different number. Like try a to the n. If that's not equal to a, then we know it's not prime. But if it did equal a, then we try a different one. c to the n, is that congruent to c? If not, then we know it's not prime. If it is, then we kind of keep on going, right? We can often find a number eventually. But of course, if it's a prime number, you'll never find one. And so what this primality test can do is the following. We can determine with confidence that a number is not prime, or we can determine that it's probably prime, right? I mean, it's not an actual proof because this is not a necessary, all right, this condition right here is sufficient to show that a number is composite, but it's not a necessary condition. And so the fact that we can't find a number could just be that, oh, it's hard to find. So this primality test is not the best of any primality test because it can never prove that something's a prime. It can only prove that it's probably a prime. But the issue is, the reason why we can't use this to prove exactly primes is because we have something called Carmichael numbers. Carmichael numbers are exactly those numbers which trick this primality test. Carmichael numbers are numbers which b to the n is congruent to b for any choice of b, but they themselves are, they're their composite numbers. Now the good news is prime numbers, our Carmichael numbers are extremely rare. I think they're even rarer than primes, I believe. I believe they're infinite, but they're very, very sparse. So if you have this primality test and it says this thing is probably prime, it's more likely prime than a Carmichael number. And in fact, you can kind of compare it. So again, this is not the most sophisticated primality test. There are much more sophisticated ones that do come from number theory. But I wanna present to you just to start to think, how does one do these type of algorithms? How does one check whether a number is prime or not? Turns out Lagrange is there and provides us a very naive way of checking whether something's a prime number or not. And I would encourage you to try to practice some of these things yourself. So you could try testing some of these things like with the computer software program, Magma. A link to Magma can be found on this video right here. If you use the command mod exp of a comma n comma, excuse me, a to the m comma n, this will compute, put a semicolon at the end. This will compute a to the m mod n. And so for example, with this primality test, you would put the n right here as the same number over and over again. And so you can check, you could run a for loop. Let me scroll up a little bit. You could run a for loop that basically did the following. So it's like, how do I test? How do I test if n is prime? You could run basically the following test.  And then we're gonna do the following. What we're gonna do is we're gonna compute mod. And we'll have a number to represent this. So let's say that the exponent is equal to E is equal to mod exp of a comma n comma n, semicolon. And then you're gonna run basically, you're gonna kind of return the following, just return these values right here. And so we could, I'll just kind of stick it the following way. So we're gonna say A comma this, we're gonna return the number. And so if these numbers are in agreement, that means that you move on to the next one. And if it's not in agreement, right? We wanna probably do some type of test. So like, are these things equal? If these things are equal, if these things are equal, then we can return if A is equal to that, then, well, basically we just keep on going. So if they're not equal, basically we're gonna do the following. We're going to break, we're gonna break the for loop. And so maybe you could do like a while loop or something if you wanted to. This is just pseudo code, so don't take it too seriously. We wanna break the loop and then we're gonna basically return false in that situation, something like that. But then if the for loop ends without terminating, then instead we return true, which of course that's only probably true. But this is a very simple primality test that one could implement either in magma or gap or basically any computer software program that can support large powers of exponents mod end. And so this is just a simple test that you just have to be able to do. So on the other hand, you can justStar benefits and then wrap up this into pre-signed and then you can do all sorts of things, and then just repeat it and then start working. So that's a simple test. We're gonna do it like this, I'll show you what it's like. So let's say we're running a thing


Then I'd like to call the meeting to order at 5.03, subcommittee meeting to discuss a portrait of a graduate and ownership linkage of the board. Heather, are you taking minutes or is that something you'd like someone else to do? I can. That would be wonderful, Lisa, thank you. Thank you, Lisa, wonderful. Lisa will take the minutes. Great. So, Katya, since you're the subcommittee leader of this subcommittee, would you like to take over the leadership of the mayor? Oh, great. Yeah, I'll go for it. So I think with this committee, we discussed coming up with that portrait of a graduate and really working on the ownership linkage part with this as well. So getting input from the community and working on kind of this joint effort to come up with that vision of what our student looks like once they've reached graduation point and build off from there. So I think for us for this first meeting, it's basically like meeting for the first time, coming up with kind of a game plan for what that looks like, some ideas for what some of those community events could be. This is basically in our minds just that planning stage, and most of this work will be done in a very public setting with a lot of input from our community members and that really kind of comprehensive and collaborative situation. So, yeah, I mean, I think it would be just interesting to hear from other board members what the vision is for the end goal and then trying to work it back from there and the steps that we're gonna take to get it to that point and really focusing on the fact that this is gonna be a community endeavor and not a board endeavor. Yes, wonderful. Anne has joined us. Welcome, Anne. We just called the meeting to order at 503. And Katja has introduced the purpose of the meeting. Hi, I'm in a different space and I was having a little internet issue. I think I'm gonna be able to stay with wifi in here, we'll see. I may try and move rooms if I have to, but hopefully this will work. Do we have a new public comment at the start of subcommittees or no? We have to do public comment. So, we should have a brief public comment. Will you leave that, Anne, please? Okay, so it does look like we have a couple of folks here. So, there is a, I have to get my little preamble that we're just trying to say at the beginning of every meeting, just so that folks are clear about public comment, how it needs to be done and sort of what the parameters are for it. So, the board welcomes comments but is not able to take any action on them other than to direct the public to the appropriate staff member or to the complaint procedure. Comments are limited to three minutes per speaker. Time may not be seated to another speaker. Comments are to be addressed to, I'm gonna say Katja is sort of our, I don't know if she's gonna be our board chair or our committee chair or if it's gonna be you, Heather, but Katja's the committee chair as she's on the board and I am advising her and so, right. So, we'll say for public comment, you can address them to Katja, although we're in virtual land. So, they'll be to everyone. Let's see, please, there should be a raise hand icon at the bottom of your screen. So, if you can click on that to let us indicate that you would like to speak, that would be helpful and Katja, I'm gonna have you recognize whoever would like to speak. Please identify yourself with your first and last name in your town of residence. Please refrain from restating comments that have already been shared. You can express agreement with those comments that were already shared. Order in decorum shall be observed by everyone. Shouting and profanity are prohibited. As the chair of the committee, Katja will maintain order in decorum for the meeting. So, Katja, we are now open for public comment. So, we'll see. Is there anyone who'd like to make public comment? Lucy. John Hellfant. I guess it's, can you hear me first of all? Yep. John Hellfant, Brookfield, Roxbury have kids in the district. I'm wondering what ownership linkage is, what the definition of that is? So, I guess that is a good definition to kind of provide at this meeting, as this committee goes on. So, ownership linkage is really looking at how we are interacting with what are considered our owners. So, defining, first and foremost, who the owners are. That's kind of be one of the steps that we take. And then building that relationship and how we are helping to fulfill kind of our duty to those owners. Okay, so we don't know who the owners will be yet. Is that what I'm gathering? John, I think I can just interject. Like this, this is a new committee, which just is our first meeting tonight. So, yes, there are steps that we are going to take to define things in this committee. So, there may not be answers that we're able to provide yet. Okay. For something like this, I guess I'd make a recommendation that public comment be put to the end, because I can't comment when I don't know what exactly we're gonna talk about. So, just a thought. Appreciate it. Thank you, John. I appreciate that thought. Thank you. Do we have anyone else who'd like to make a comment at the beginning, and then we will likely open up at the end again for some comments, takeaways. All right, so seeing none, I guess we can kind of move into this. And again, as I just mentioned, this is really an initial planning meeting. Just, we are meeting currently for the first time at this new committee that's formed. And so these first initial meetings will be a little bit more on that planning and trying to develop kind of what the vision is for how we move forward with our community. So, saying all that, Heather, I'm gonna throw it over to you as there are some ideas. And we do know that there are other districts that have done this kind of work previously. Thank you, Katja. Good evening, everyone. I'm Heather Waller, assistant superintendent. I am so excited to get started with this board ownership linkage work and launching a community engagement initiative to craft a portrait of a graduate that reflects the community and all stakeholders vision, a combined vision of what we hope for every graduate, the skills that we would like to see our graduates leaving our building with ready for their post-secondary choices, be those to go straight into work entrepreneurship, be that to go to college, straight into a career, to work the family farm, to go to the military. We as a community need to identify, here's a set of skills. We want students to be able to work with technology, we want students to be able to communicate, collaborate, whatever those things are. And so when we talk about owners, I'd like to propose we consider all stakeholders, our parents, our students, our teachers, every community member, every taxpayer, and students and teachers, faculty, parents. And I would like to emphasize student folks. So in beginning this work, I'd like to propose that we plan for an introductory meeting that would start at the community forum recently. Many community members asked for community dinners, gathering of people that would be community building and a comfortable space to talk about things in a non-confrontational way and build bridges between different portions of our community. And so I'd like to propose that we launch this with a community dinner. And at the community dinner, I'd like to propose that we have a considerable presence of students who can either do a celebration of learning or possibly help with the preparation and service of food. I'd like to propose that at that meeting, we explain what a portrait of a graduate is because that's educational lingo that many people may not know what that is. I'd like to share samples of other districts, portrait of a graduate as just models, like ideas, and start to collect initial input. And then I'd like to propose that we plan a series of at least three meetings subsequently, where we can refine and revise the work, also in a celebratory way with students present and a lot of community building. So I think I've said a lot. I welcome some feedback from the board. And if you'd like, I could share some samples tonight, but I don't know if that's necessary tonight. I'll jump in. I think I do really like the idea of this. I mean, I think it's so important for this to be like that collaborative community growth effort. And I don't want it to be something that just this like coming from the board. Actually, I kind of want the board like in a little bit of the background and really allow the community to step forward and say what their vision is, what they see. And also just make sure that, you know, it really is that ability for everyone to come to the table and be a part of it. Cause everyone is, everyone should be represented in that because we do have, like we said, that all the different stakeholders. So I really, I like the idea of that launch of doing these community dinners. You know, informal events like that that just bring people together. We can have small conversation, larger conversation and just hear from a lot of different people. And I love the idea of involving students too. Cause obviously this is, this is where they should be ending up. So yeah, I'd love to hear from other board members on some of the ideas about that. I agree. I think a phrase you use Katya was come to the table. I think a lot of times in board meetings and forums it becomes this kind of here are the speakers and here are the crowd that's gathered. And yeah, we're sharing ideas, but it's this very separated thing. But that last forum that happened in the elementary school cafeteria did not have that feel at all for me, especially once those small conversations started. So I think as much as we can encourage within a dinner like that cross, you know, getting cross genres at each table, a sprinkling of students, a board member. And I agree we should really take a backseat here so that it's very clear that this is to be a community guided effort with us as part of the community, but not speaking to or directing. Awesome. I'll jump in quickly. I agree with both of you. I think that's great. I'm wondering, and maybe this is too early in the process to even think about this type of option, but are there any ideas or plans around, and Heather, this is kind of directed towards you, do you have any ideas about maybe like student ambassadors who would wanna kind of lead the pack, you know, to join this community dinner setup or just a group of students who are interested in being part of this as well, kind of on an ongoing basis with us as we create this. I'd like to invite Principal Lisa Floyd to speak to that as I believe we have a plan to start exactly as you said that your phrase is perfect, student ambassadors. Today what we discussed was perhaps having our middle school and high school student council groups create regular reports to the board and be able hopefully to come to board meetings and present those reports from the middle school and high school perspectives. I think that that could give them a lot of investment in the process and there would be regular membership. Historically, there has been a lot of focus on what happens during the school day or fun events that our student council members plan, but I think this kind of work would really help our students feel like they were a part of a process to improve their school. So that's what we had been talking about, but we certainly are just in the beginning stages of sort of formalizing that work. So if you were thinking of something different, then we absolutely could discuss that. No, I think that sounds like a great plan. Oh, sorry, Heather. The only thing I was gonna throw in there was if you open, I mean, the student council groups are great. I just would like to see that anybody has an opportunity who might be interested only because not everyone is on student council for whatever reason. So just keep that in mind. Megan, you are speaking exactly what I was thinking. So in addition to, yes, in addition to any student who's sort of like nominated as an ambassador, we want to recruit diverse voices, students who may be influencers, but they're not in national honor society, but they want to be involved, they're interested. And also beyond that, a student who just wants, say we run three or four of these meetings, any student who wants to attend and have a voice is going to be welcome. And we also want to bring in student groups such as we have a science teacher who's raising money to take her students on a marine biology trip and have them come in and talk about their vision for their future and serve food and maybe accept donations. So we don't want it to just be, okay, we've identified this student who always says everything exactly in line with what we want to hear and only present that voice. We want many, many voices. So it sounds to me like we're almost talking about two different things. We're talking about sort of an ongoing community dinner type of thing where students are sharing what's going on. And we're also talking about the portrait of a graduate which is gonna be an end result that by June we'll have the OSSD portrait of a graduate. Am I understanding that correctly? That- Yes, the portrait of a graduate will be an aspirational document documenting our end's vision at this time for a graduate who'd be ready to proceed to beyond their secondary education. And that aspirational document will be an outcome of a series of community events. So it will take at least three. I anticipate possibly four before we could say, here's our draft, here it is, this is the thing. And subsequent to that, we can move forward with your ownership linkage efforts to other projects or just a continuation of community events, but yes. So there's an initiative to create more community outreach but with a structured desire for an outcome, an outcome at this time to have a shared community vision on one piece of paper that says, this would be wonderful if we can achieve this for every student. How can we then inform our curriculum, instruction and assessment to get there? How can we inform special education? How can we be equitable for every learner despite poverty or disability or any other complications? So it will be an aspirational document. It won't be like once we have it, we're there. I had another question. So are we bringing in facilitators or how, because a lot of times if you're gonna do community discussion, especially if you really want people to feel comfortable sharing and if there may be people who have differing viewpoints will we have facilitators or are you planning on training some people or how is that part gonna work? And that may be, I don't know how far along you are and kind of thinking yet about like when the different dinners would take place and how they would be organized. But that last forum that happened I think everyone saw that it allowed for better communication to do it in a location where people were face to face. They were in smaller groups. And I think thinking about, again, I like that you're already sort of planning ahead a little bit to be making sure that we're hearing from all student perspectives because just like everyone in the community may not all be on the same page, not all students are on the same page to sort of make sure that we're sampling kids from a variety of different groups with different perspectives. So I have reached out to an organization called Betel for Kids. Betel for Kids specifically leads this work and they've done the work with multiple organizations in the state of Vermont. And they're currently just beginning the work with Essex Westford as well. And so I've reached out to them. I think they, I've actually been led by them previously when they did the portrait of the graduate for the Woodstock Union High School and Middle School. And as you said, their leadership was very helpful in facilitating conversations and making sure all voices were heard. So I'm hopeful that they will lead our work. And if not, I have some other ideas but that would be my first choice given their experience in our state. And I was going to ask the board. I understand there are some funds allocated to the board. We have this small equity grant, which is $5,000. And then I understand you have some funds at your discretion as well to fund a portion of the community dinner. What I'd like to do is offer a base meal like an entree and a dessert and invite community members to also if they're able to bring a potluck offering. But I'd like to pay for at least the base meal with some of those funds and possibly to set aside funds for a consultant to lead some of this work. I realize that may need to go on the consent agenda for the next board meeting on the 14th. So I think what will be beneficial then is to do like, the goal is to have this completed by the end of this school year to this June. We're talking about doing potentially up to four of these community dinners. So that next step of kind of planning when this work would begin, what that would look like. Maybe doing a monthly do it once a month or four months.  I want this done. It would be great to have this done by June. So, but I also want to make sure that we're taking that time to really be thoughtful about that process and making sure that people can join and not just having like one, two, three in rapid succession, but letting people kind of think about it and be able to bring their thoughts to it as well if they're not able to join some of the earlier sessions. We have an opening on December 21st, if that would be agreeable as a possible first community dinner, or if that's too soon, we can book it for the subsequent month. I feel like if we start this in January, I think that trying to plan anything right before the holidays is just a little hard for everyone. Wasn't something- But I think if we kind of- I think it's the 21st. Yes, well, here's what's happening. That's the night that the superintendent is having a community forum. And so we could do the community dinner, starting at five and then do an introduction to the portrait of the graduate and then Lane's event would start at seven. Oh. No, so it was- I didn't realize we could piggyback on something else. Yeah, so it would just be like a gentle introduction. Here's what the portrait of a graduate is. Here's some samples. Next month we wanna get together and hear your ideas. That's a long night for kids with, for people with young kids. Yes. Good point. So it seems that the agreement is we'll start in January. So you were thinking start at five and then go through. So that, yeah, that would be, except that the kids would be fed, Hannah. You still think it would be too much? I think that there would be too much of an expectation of, and validly so, childcare. I'm talking about a very chastity. Oh. So, yeah, I think trying to do two, when we really want people to engage and bring energy to both of these things, right? And I think trying to package it up is asking a lot, especially with my chatty six-year-old in the room. That's really helpful feedback. Thank you. Heather, do you have any idea, you've reached out to Battelle for kids, but they haven't responded yet too. That's right. So that may, I mean, that might be another reason why if we put it off because there may be some initial training that needs to happen. Do you foresee using, I know with some other districts, some board members were trained as part of the group sort of facilitating, or are you gonna have an outside, or does this Battelle group not train facilitators within the district? They just bring their own facilitators in, or do you know at all how that works or not yet? I don't know the answer. The way I experienced it when I was in like the audience, I was a principal in, right? I experienced it as they had provided the superintendent with all of the resources to lead the work. And it was like even though their name was on things, and there was one representative present, like to support and facilitate, it was almost like they had just provided all the tools and the structure and they were just there for support. And I may not have seen everything that happened behind the scenes you see. So I, and I will, as soon as I, if I don't hear back from them tomorrow, I'll get them a phone call and I'll get more details on their process. But I remember, I do remember that it, there was room for every voice. There were a lot of turn and talks. There were a lot of opportunities to write things down. There was a lot of opportunity to vote. There was, it felt very designed to facilitate all voices in multiple ways so that no one felt I was too nervous to speak out loud and I never had a chance to write, right? Like so everybody, it's a well-designed process and they're a nonprofit organization. So I don't anticipate the cost to be highly expensive. Their focus is on helping schools to achieve this vision. I'll get you more information and have it for you possibly. Should I add something on this to the agenda for December 14th or is it too late? I think it's on there. Didn't we put it on there, Ann? Did we put something on there? Yeah, yeah, we said a report out from the ownership linkage committee. So yeah, you can add to that. I think the only thing we might have to change on that agenda is possible vote if we're gonna be voting on using the finances for. Right. Yeah, I think just having that structure will be helpful. And I know for the board, that's been part of always sort of struggling with how to reach out and get community engaged and get stakeholders engaged without sort of having that extra sort of feeling like the structure is there. And just for board members, we don't have the time. So that's where having you as sort of the point person to sort of lead this process will be really helpful. I think it's also will be really important for us to make sure that we're inviting local business owners, especially business owners who are employing our students or doing like internships and whatnot with our students maybe working with our TCC so that we have those voices involved as well. And I know when we created our ends, we also tried to incorporate, I mean, because there's limited access but some professors from the different colleges in the area just because they run into our students as students in higher education. So in addition to our community members, parents, students, families add business owners and college representatives from local colleges and trade schools. And so all we can do is invite people. So that's another thing I did add into the equity grant in my proposal was that the creation and distribution of marketing materials may be an expense on that equity grant. So we will make sure to create marketing materials and distribute them broadly. Yeah, and I think honestly, like the emails, it was good. I mean, I know like with doing events here, if we have an email list for sending things out to or if there's, that's always a nice way to get the word out. I'm thinking of all of your, I know with senior projects, there's people who are leading those individuals, whether they're, again, those would be a great group to have invited as well. So, but I just also wanna stay mindful of our timing with this meeting tonight. So it sounds like we have kind of a nice rough plan of what this will look like as far as these community dinners involving our groups, bringing potentially this group to the table to help facilitate this, a plan to start in January. So we would have January, February, March, April with the potential for those community meetings with our rough draft then landing right in May, which would be great as far as the timeline goes. So is there anything else that we need to, as this is our, again, our first meeting of kind of coming together, is there anything else that we should be looking at or addressing tonight? No, I think you made some good progress in identifying who the stakeholders are, right? Or the owners, as you say. And also in creating a rough plan for the creation of this document. Yeah, and I think it's, you know, again, important that this is like an ongoing effort. I mean, this is the first step in many as far as trying to have that connection with our community. And this Portrait of the Graduate is just one part in defining that ownership linkage and all those other aspects that go into it as far as stakeholders and everything. And I think that this conversation will be good to kind of help us really define some of those things in a more community-minded way too. So, any other comments from the board? I will spend a few minutes opening it up to comments now that we've had some discussion first. So any board members have anything else they'd like to say before we open up to public comment for a few minutes? So I just want to make clarification on, so with our policies, when we talk about owners, owners are the taxpayers in our region. We haven't, and in the students to a certain extent, when we talk about stakeholders, those will be teachers. Sometimes a stakeholder will be both an owner and a stakeholder. And sometimes they will just be a stakeholder. But in this process, our linkage is really, we need them in this portrait of a graduate process, but they may not be owners in the sense of owners of the district or when we look at defining that. Thank you for that important clarification of language. That language is very precise, and I really appreciate that. I will keep those two terms separate. I was just gonna say quickly, this is great, I'm really excited and I'm glad that I was able to kind of step into Scott's role here. So looking forward to how we move forward with this. Other comment for the board before I give us some time for public comment? So I also don't, I wanna make sure that we don't lose sight of the other aspect that I think we're talking about, and that is the student representation or student involvement with the board. Cause I really, the way I'm looking at it, that almost seems like it's a little bit of a, it's a little bit separate from just the project of creating the portrait of a graduate. Having student input and a regular basis on the, within the board is a, I see that as a slightly different process or something that we need to clarify because one of the things from, again, the BSBA meeting in hearing from students who have been involved with boards and other districts, one of the things that they really said that was helpful was to understand their role on the board. So I think we need to think about that and clear, you know, and be clear about that. Again, because we're a board that works on policy level, not on sort of how the, you know, the things that oftentimes students have issues with involve sort of the day-to-day operations within the school. And so we need to make sure that we're clear about, as we present this to students and try and get them involved with the board that we're clear about their role and how their voice will be heard on the board. So they're, because otherwise you set them up and they're like, why would I do this?  So I think we need to just, as we roll that out, I think, but am I the only one who's sort of seeing that as a little bit separate from the development of the portrait of the graduate? I see these as two things that are important to develop, but they're not exactly the same. Yep, I agree. This is specifically our portrait of a graduate committee. So this is all that we're looking at in this committee right now. Is this process that we're getting to in June? And then there can be other conversations as we've had in the past about having student representation on the board, but that's gonna be separate from the conversations that we're having here in this committee meetings. All right, so it's 5.40. I'd like to give some time for public comment as I don't really feel like we need to restate the rules around public comment since they were stated earlier. So everyone knows what those are. So I will open the floor for public comment if there is any on this discussion today and just raise your hand. You have the floor. So I didn't hear a lot of talk about parents as owners. I don't know if it's because it's just a foregone conclusion or not, but parents I think would be significant owners along with students because we are the main guidance for students as they grow. And once they're out of school, we'll continue to be for an extremely long time. So we have a serious vested interest in what a graduate should look like. Other than that, I do have some significant thoughts on what a graduate should look like, but I think it's way too early for that with this current meeting. So thank you. Thank you, John, I appreciate your comments and I look forward to having you join us then for these dinners if you have some great thoughts about that. So I hope that you will be there for those as well. Are there any other comments tonight from public? Seeing none. I think we have a good start to this meeting tonight. I'm gonna give us an extra 15 minutes early. We will report out at our school board meeting at our next one in December. And hopefully we will have some dates at that time that we can start rolling in a January 1st meeting for the public. And with that, I will call the meeting ending at 5.43 against, since this is our first committee meeting I will apologize. I'm assuming that we need to take a motion to adjourn. So I'll hearing one. I would take a motion to adjourn. I move we adjourn at 4.43. Thank you. I second. Thank you. And all those in favor to adjourn, please say aye. Aye. Aye. Aye. All right.


This is stock number 9J160B. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used sports car headquarters. Today we are checking out this super clean, really good-looking 2017 Dodge Challenger RT Shaker. This vehicle has the 5.7 liter V8 Hemi motor. Pumps out 375 horsepower and this one has been fully safety and inspected per our state of Wisconsin Inspection process has a fresh oil and filter change all the fluids have been checked and topped off and this car is 100% ready to go White knuckle is the color. You can see it has the over-the-top stripe and we shoot all of our videos in 1080p 60 frames per second So if you have HD capabilities on your computer tablet or smartphone device turn them on right now because it is like you're right here looking at the car with me and Definitely your best way to check out the vehicle Before seeing it in person if you want to check out more photos in the upper right hand part your screen is a link right to our website Click that and check us out there comes with the 20 inch Granite crystal-painted alloy rims go to your Eagle 245 45R 20 tires with about half the tread left on them Didn't see any dents or dings on that front fender. It does have that shaker hood It's a true cowl induction with the hood scoop there Very cool has the LED running lights projector lamp headlamps projector lamp fog lamps that front bumper and lower valence are in Excellent shape. I didn't see any scuffs or scrapes on that and as you go down this side of the car Very very clean. No dents or dings on that Fender there and the passenger side rim. I didn't see one scuff or scrape on that and As you go down this side of the car, you can see just how clean that body is how reflective and mirror like that paint is We take these HD videos So if you are far away or even if you're close by and just cannot make the trip down But you're still interested in purchasing the vehicle you can see the vehicle hear the vehicle and of confidence in what you're looking at Before you even get here so that when you do get here You're all ready to go Really like that over the top stripe there. I didn't see one dent or ding down this side That's really why we take these videos. In fact, we offer a summit auto fast-pass option in the upper right hand part your screen a link Right to our website where you can apply for financing get pre-approved even see a payment quote off from the comfort of your own home So when you get here, you'll know exactly what you're doing and you'll be all ready to go back tires So just as much tries the front tires that back rim looks great as well Rear bumper no dents. No dings. No scuffs. No scrapes. It does have the backup parking sensors and the dual rear exhaust tips You get the LED tail lamps the deck lids spoiler. I like that they got the button back here that you can open up the trunk without actually Without having to use a key Underneath here you have your tire inflator kit as well as the Extra as the as well as the battery and we have a set of factory formats back here for this car as well trunk shuts nice and solidly trunk lid is nice and cleaned and see any denser dings on that and as you go down this side of the car just as clean as that passenger side has the metal fuel door there and This back rim for full disclosure is an excellent shape as well four-wheel disc brakes, of course And the driver's side door is an excellent condition.  We have weather tech floor mats inside It comes with the Alpine premium sound system power windows power locks power mirrors auto headlamps power tilt and telescopic Steering wheel as long as we're back here the back seats are very clean as well No rips or tears on them. It does come with the latch child safety system Those seats do fold out and we do have the factory floor mats back here as we hop inside the vehicle here You can see that this one has 12,902 miles. You get the digital speedometer outside temp compass display You get the heated leather wrap steering wheel No scuffs or scrapes on that cruise controls on the right with the Paddle shifters on the back. You also have audio controls in the back of the steering wheel Bluetooth and information center controls on the left. This one comes with the 8.4 3c radio and FM and Sirius XM radio capabilities on here. You do get your heated seats Controls heated and cooled seat buttons as well as the heated steering wheel buttons one does come with the Factory navigation system and this is also where your backup camera shows up You also have your performance pages, which are really cool. It takes a second for that to load while we're doing that We got the sport super track pack your backup parking sensors You can turn those off your stability control you can turn the screen off You can mute it and you can do your climate controls down here as well eight speed automatic transmission You can put it into that manual tap shift mode. 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Those are features of the vehicle We'll take a quick look under the hood. We'll check out that shaker hood And I'd really like to thank you for checking out the video today and hopefully from this HD video You will have been able to tell just how clean this car is all the way around Inside and out under the hood. We have the 5.7 liter V8 Hemi motor engine base very clean runs really smooth You can see it as the Mopar cold air intake the shaker hood That's a nice shape and it also has of course the real intake up here Has a nice rubber gasket. That's a nice shape Like I said before this car has been fully safety to inspect by a service shop has a fresh oil and filter change All the fluids have been checked and topped off and this car is 100% ready to go see more pictures of this car One of our other 450 new and used cars trucks SUVs minivans Wranglers half-tons three-quarter tons one tons You name it. We got it go to our website www.summitauto.com full pictures and descriptions of every single vehicle from two locations all at summit auto commy If you'd like to check out more HD videos you can go to youtube.com Slash summit auto remember to like subscribe and share on this video and all the videos that you see there In fact any second you'll see a link to subscribe to our YouTube channel on your left They link to more challenger videos like this one on your right if you've not been to our website on the bottom A link to this vehicle on our website click those check us out and we're super excited to help you with this Extremely clean 2017 Dodge Challenger RT shaker. Thanks again


Creating layouts with CSS can seem quite complicated at times and be a frustrating endeavor, but being confident with it and being able to understand what's going on boils down to one really important thing, which is relationships. Hello, my friend and friends. Thank you so much for coming to join me once again. And if you're new here, my name is Kevin and here at my channel, I help you fall madly, deeply in love with CSS. And I know one thing that people get frustrated with with their CSS is creating layouts because I hear it all the time. So in today's video, I want to look at the most important part of becoming confident in creating layouts with CSS, which is relationships. And it's a little bit like in life, relationships are very important in understanding the dynamics of all the different relationships and everything, the same applies to CSS. And that might seem a little bit strange, but well, let's dive in and take a look at the code to understand what I'm actually talking about. There's a lot of different relationships with CSS. And this is where things are different from other languages, where things are often much more in isolation, whereas a layout, each individual component, as much as we want them to be, has to, they don't live in isolation, they live in relation to other things that are on the page. And so the first relationship I want to look at is the parent-child relationship and it's a two-way relationship, just like in real life. And so in my CSS, we're going to start here with this primary header content and take a look at that. So on this primary header content, what I'm gonna do is set a width and we're gonna set a set width for now just to make sense of things. We're gonna set 750 pixels and you can see that that changes what's happening here. And let's just put a border on there so we can actually see things. Three pixels solid and we'll do lime so it stands out a little bit. And what's happening here is we've set the width of the parent and Kevin, this is obvious. I set the width of the parent and the children don't escape that by default. They don't overflow. Of course, there are overflow issues that can happen in different situations but this is one of those relationships that people take for granted and they don't think about it very often but if I have a width on the parent, the width of the children, which is auto. So my every child in this layout, primary header, content star has a width of auto. That's what's happening right now. And if you'd like to know the difference between the two, there is a card popping up right there or a video where I dive into the difference between them. But yeah, this is what's happening with the children. So the width of the parent is sort of dictating what's happening with the width of the children because the children are adapting to the parent. But what's interesting there is it's the inverse relationship when it comes to the height. So here the width is 750 but you'll notice the height actually got bigger when I did that. And so let's undo that for a second. So here the height is actually smaller and then let's even make this a bit more dramatic. We'll make it 450. And now the height of this has gotten a lot bigger because the area that the children are taking up has to be the same. So they have less width, they need more height to maintain the same area. And this is a very important relationship but one that people don't spend enough time thinking about. And the reason it's important is, you see people all the time setting heights on a parent and then wondering why there's overflow issues or other things going on. We want to, in general anyway, we want to let the children dictate the height that things need to be and just allow that height auto to do what it needs to do. Whereas the width auto on the children is a super useful situation where you can use a parent and often I'm doing it on my primary header content but often what you see is we have like a container or a wrapper div and then everything is inside of that. So let's just grab all of that and throw it in there. And then the same thing here, let's just do another wrapper for my card. So there that's, they're both in the wrappers now. And then this one, let's just change this instead of being on my primary header content, we can change this over to my wrapper and we can throw the margin inline auto on there which is margin left and right auto so it becomes centered on the screen. Very typical type of thing we're doing where we're using the parent to set a width and to hold all of the content in the middle. And again, this is something that you've probably seen and done a lot of times on your own and I'm just gonna switch this over to a max width and we'll make it a bit bigger. Let's do like 45 rem, there we go. So not too bad. And we're gonna get to the relationship between siblings as well, but there's more relationships with the parent and the child that I do wanna look at. So one of those is let's give my primary header content or let's give primary header actually a background because this is a very common design pattern that we see. So let's give this say a background of three, three, three. And actually one relationship I wasn't planning to talk about is inheritance where most of the font are pretty much all the font things other than form elements like inputs and stuff are inherited, right? So we have the relationship where inheritance comes in so I can set a color on my primary header and all the children will inherit that unless we overwrite it specifically for individual elements inside of there. And one of the things that catches people off all the time is the relationship of margins between children and parents where you can see that my primary header isn't actually touching the top of the viewport and throw a margin zero on there because it's frustrating and it's still not touching the top where if I look in my dev tools we have my primary header there and you can see the primary header has no margins on it it's highlighting on the page. I have my wrapper, you can see the auto margin on the left and the right there but nothing on the top and the bottom the content has nothing and then we get all the way down here to the H1 that has a margin on the top and the bottom but because of the way collapsing margins work the margin here on my page title is actually pushing down the primary header and so here let's just choose my H1 really fast H1 margin top of, I don't know, 1000 pixels and it's not putting it on the H1 it's putting that margin on the parent and so understanding collapsing margins is part of understanding relationships and there's also the different times when collapsing margins are actually a thing and whether or not because this part of the relationship goes out the window when we're dealing with a flex or grid formatting context so if the parent is display grid or display flex that collapsing margin goes away and just to show you there on my primary header let's do a display of grid and now that margin is contained on the H1 and that gray background is actually touching the top of the page now that isn't really the solution that I would use in this situation another one we could actually do on here is a flow route if you just wanna keep the display grid flow route just makes a new formatting context so the collapsing margins don't escape out of their parent or merge with their parent I'm not gonna deep dive that too much in this video but I just wanna highlight that collapsing margins are important thing to understand that they happen and that sometimes in different situations when we have new formatting contexts it doesn't happen is the sort of the TLDR of that but there's different ways of dealing with those collapsing margins common way to do that is to add some padding so padding will do padding block so it's top and bottom and I'll do for REM just to add some padding and the reason that the margins are no longer collapsing now is because the top of the H1 and the top of the primary header are no longer touching so if the top of both of them are together in a regular block formatting context where there's regular flow of content those margins will collapse and this is the same when you get multiple paragraphs where the margin between the top and bottom paragraphs are actually merging so you can see here where the collapsing margins on the top and the bottom of those are merging together and that's a good behavior because the default is for them to have the top and the bottom margin and that would just cause headaches if not now of course you might wanna remove the top margin from your H1 here to prevent too much space and other things so once you understand that and you know that there's margins and sort of the interaction between padding and margin and things like that we start to be able to move away and understand okay there's a collapsing margin here these are different strategies I can use to take care of that and not worry about it anymore and so you have a instead of just saying this is frustrating it's not working how I think it should work you're going okay this is happening because and now I have different strategies that I could use to try and circumvent it or get around it so another type of situation like that is when we have something like here I've done a simple card and there's not too much happening with it but we're gonna move a little bit into the world now of dealing with siblings and how siblings interact with each other so here normally siblings and different elements just stack one on top of each other and so in that situation the relationship between the siblings is pretty easy to understand even if I just came here and I did a paragraph with one word in it we're gonna have the word one and then even though we have empty space visually here the rest of the stuff goes underneath cause we know that's a block element that force new lines nothing too complex but when we get into the world of dealing with grid and flex so let's say I come here and I do some even columns because I want to create even columns and we'll wrap all of this the two cards in those even columns then we get into the world of flexing grid and that makes the relationship between things a little bit more complex so even columns and let's just throw a display flex on there and we get two columns and let's just put a gap on there of two REM and so we get two columns and everything looks perfectly fine but where things can actually get a little bit strange with this is let's say the second column over here actually had no image and only a title so we're gonna delete that we're gonna delete all that and now things look completely different and you're going well there were even columns before why aren't they even columns now and you get a little bit frustrated and this is about understanding how flex works and how flex impacts the relationship between siblings and now I mean one way you could do it is to make sure that all the siblings are the same size so even columns star so you're selecting all the siblings and then you can do a width or a flex one and then it does turn them back into even columns because we're now saying that they both have the same size and that's because this is actually setting the width basically to zero and then having a flex grow and they're both growing at the same size because their base size is small anyway we're telling them both to act in the same way and so we basically get even columns by doing it that way and of course we could use grid for this as well in a little bit more of a predictable way by saying grid template columns and in this case we'll do an auto fit repeat auto fit min max say 250 pixels one FR and then I can get my two columns that way as well and then we don't need anything on this side and the nice thing we're taking this approach is just not dealing with flex wraps and other stuff so there's different sometimes things that we might wanna do so if I add a third card you know it wraps underneath the next one because anyway I'm not gonna deep dive it too much because I don't wanna deep dive flex and grid I've talked about them a lot before but it's understanding how using flex and how using grid impacts the relationship of what's actually going on and before I continue going I just wanna mention that a lot of I'm saying formatting context a lot right now with block formatting context and grid and flex formatting contexts and just this idea of relationships is something that I talk a lot about in my course CSS to mystified which is a course that deep dives understanding how CSS works at its core rather than just saying throw these properties at something or follow along with me it's a course that I put together to really teach you to understand how CSS is working and part of that course is deep diving and going deeper into the relationships of different elements and the way different things interact with each other so if you're interested in that the link is down below and with that out of the way I'm actually gonna look at something where we're gonna switch things and talk a little bit like with this relationship of parents because here the parents are especially here the parent is influencing the child or the children but we're gonna go back to having a flex layout on this for a second because I wanna look at something let's turn off that bottom one here and our this whole div here just have these two columns that are identical we don't have to worry about them too much but this is where the relationship between siblings is so the parent controlling the layout is what I like to do and then having the children sort of just behave the way they should behave in there and part of that is understanding also how the relationship of certain things on themselves and how it affects the parents and stuff so let's just select the second card or yeah so we're gonna do even columns and then we'll do nth child two so we're selecting the one on the right here the simple card the second one and we'll let's throw a background on that one background light blue and so we get our card that looks like that but maybe we wanna add some padding on there and padding to REM and you might have noticed when I added that padding it actually influenced the one on the left right we're influencing both of them I'm adding padding to one and the other one's actually getting a little bit smaller which you wouldn't expect because I have my even columns and you go oh it must be that thing with the grid that Kevin you know we need these children to be the same so you do your star and you do your flex one on there but this doesn't actually do anything and this is where you have to be very conscious of how different things like padding and margin are affecting the children or the siblings that are around it in a bigger layout and how things like display flex and how things like display grid work to control the layout and how they figure the layouts out and so what's actually happening here is flex the way the flex algorithm works and this is a good thing it's done on purpose and I deep dive it a lot more in another video which I'll link down below but basically when we use flex box it looks even though I have my box sizing border box here it's not looking at the padding when it's calculating the widths of the different elements to do the flex algorithm with its shrinking and growing on it it's only basing it on the content size and that's because as the shrink or the grow is happening it doesn't want to change the padding that you've put on it because that would be really awkward if your padding sort of got squished in different ways so it's done on purpose but it does mean that if you use display flex and you have two columns once the padding is on one of those or multiple of them but not on all of them they won't be exactly the same size whereas this is a little bit different if we're using grid and then we turn back on my grid template columns because grid is setting cells and the children have to live inside of those cells they're not influencing the cells this is what's creating the grid cells right here and we can even visualize those if we come and take a look at them and so we have these and they're both set and you can see they're both getting calculated to be 344 pixels they're the same size as one another this is doing nothing right now and the children are being forced to live inside of those cells so this is where when using grid the parent has a lot more control on what's happening you're setting up the layout and the children are living within that layout whereas with flex the children have more of an influence on what the parent is doing and what their siblings are doing and as a result also influencing what's happening with their siblings as well in many cases so I know this is sort of a brief overview you might be going well Kevin I don't fully understand everything about these relationships right now I understand that it's about relationships but the best thing to do is to build things but when you run into problems to instead of being like this doesn't make any sense try and find out or figure out what's actually influencing things to result in the way they're you know what's causing the problem that is happening and the way CSS works every tool that we have does have very specific use cases and very specific impacts on how things happen it all makes sense but it's understanding what's actually happening and not just throwing a display flex it's something to get columns and hope that everything's gonna work out there's a lot more going out in the layout algorithms and a lot of complex things going on in the relationship between different elements on the page so even if you're just designing a single component where that component goes and how you're using it and where you're putting it has an influence on other things whether it's the height of the parent that you're putting it inside of whether it is the you know you're creating columns and it's impacting the width of the columns and then that's impacting the siblings and all of that just be very aware of these different impacts when you're creating your layouts now if you'd like to deep dive into the difference between Flexbox and Grid or the way the Flexbox algorithm actually does work in more detail I have those videos right here for your viewing pleasure and with that I would like to thank my enablers of awesome Jan, Johnny, Kyle, Mr. Dave, Patrick, Simon, Steven and Tim as well as all my other patrons for the generous support and of course until next time don't forget to make your part of the internet just a little bit more awesome.


Dmitry Medvedev's official telegram channel posted on July 14 footage of him visiting what said to be his military training ground at Totskoy, in Russia's Orenburg region. Medvedev, who is deputy chairman of Russia's Security Council, in a rare appearance wearing military uniform, is seen being given a tour of the training ground and then talking to officers and other members of the military. The Totskoy training ground, located more than 1,200 km to the southeast of Moscow, has been used by the Russian military for more than a century, including for nuclear drills. Now it is used for building operational coordination between troops due to be sent to Ukraine. The Totskoy training ground, located more than 1,200 km to the southeast of Moscow, has been used by the Russian military for more than a century, including for more than a century.


leaders are increasingly challenged to navigate ambiguous security environments and may become mired in information data. Analysis paralysis and cognitive overload can cripple an individual and a team's decision-making momentum or catapult them prematurely into action. The issue is not just managing the data, but the process of determining its significance. Evaluate if and when data is relevant. How important is this? Before reaching for more, ask what is our intention? Do I need more information for this decision? Avoid stopping short or rushing ahead. Pause, prioritize, begin refining more intentionally your data analysis process. Lead well this week.


Good morning, everybody. I'm Tommy O'Brien, comedy alive from TFNN headquarters in St. Petersburg, Florida, 9 a.m. Eastern time Tuesday morning as we approach that Thanksgiving holiday, short and weak. And right now we got markets again in positive territory. That is after a record close yesterday in the Dow, NASDAQ and S&P. Right now we've got Dow futures of 23 points trading $28,062. S&P futures positive by one trading at $31.33. NASDAQ futures positive by three points, trading at $83.80. Oil right now positive by about $0.30 and $0.5832. Goal contract negative about $2 at $14.54 and the bond tenure yield sitting at 1.736%. We start things off. You see the print overnight on the S&P's, quite a number, $31.45. Looking at the futures contract, we've paired most of those gains back to $31.33 still looking for a relatively positive open near record territory. Jumping over to the VIX, we'll start things off. We got an 11 handle, as you might expect with all-time highs, $11.87 in that volatility index as we await the opening bell about 30 minutes from right now. Start things off. Let's jump over to the indices. We'll start it off with the Dow and you can see the spike in all the indices. Dow made it up to $28,144 currently trading $28,061. There's a NASDAQ 100 reaching a high overnight at about 8.45 PM Eastern time last night of $84.18, pairing most of those gains back down to $83.77. S&P 500, as I mentioned, all the way up last night to $31.44, currently $31.33. Crude oil, $58.34 right now. There's your gold contract trading at $14.55, was up there about $14.58 at 4 AM Eastern time, and the Euro-US dollar trading at $1.1018. Times of what else you have happening across the market, Chairman Powell saying that the Fed is, quote unquote, strongly committed to 2% inflation goal, a sign that rates are likely to hold steady. Best Buy, out with their earnings trading higher this morning, beating expectations and raising forecast ahead of the holidays. Get a little trade optimism, as you have China's top trade negotiator, Lu. He talks to Lighthizer, Mnuchin, about resolving core issues, that adding to some of the strength in the market this morning. And Best Buy, looking to open at about $76.66, closed yesterday at $74.25, with some action as well this morning, up to $6.98. Stay tuned, folks. We've got Steve Rhodes spilling in live for Larry Pezzavento at 9. I'll be back at 10 o'clock with Tom by programming all day. We'll be right back.


What's good y'all Chris from jashescasebreaks.com. We're back with a late-night rally here Got some big names in here to fill out 2022 tops five-star baseball eight-box case break PYT number five with a little uh With a little help from our friends here. We got one more case done of this on our five star new release day So Devin Hoover grabbed the last two spots the D backs in the Cubs, but Jason Grabs a lot of names getting ten names to be exact to get us across the finish line So thanks y'all very much So PYT six on the site. I can probably load up some more if you get PYT six soldiers Got you Jason's the least I can do for you. I can call you out What was Pearl James original name? Are you are you not setting me up for a bit? Are we are you Dennis? Come on At this point in the day, I can't tell you I can't tell you one No problem man. Thank you again. I don't know. I really don't know actually. Oh, yeah, it's up Steven. Happy holidays, man Trivia so I think the trend that I'm seeing is that there's one redemption per case to go like one shadow box one like metallic couple of those silver and golden graphs So let's really see here first auto up Gonna be Fergie Jenkins Hall of Famer for the Chicago Cubs going to go to Devin Hoover Mookie Blaylock Yeah, I think Pearl James a little better Mookie why Mookie Blay? What is going on with these guys? Pacific Northwest man grinds you the dirt kind of shark except we got some gold coming up here Little golden graphs It is a little gold golden graphs For the Atlanta Braves 10 out of 10 Ozzy Albie's kind of hard to see and shut up like this, but There we know 10 of 10 Ozzy Albie's Atlanta Braves going Steve Locke. I do love Ozzy signature This one feels a little light. So either redemption or a shadow box. I'm thinking Oh Excuse me. It's both Five-star base autograph redemption is going to be Jaren Durand Boston Red Sox gonna go to Ed P This one feels a light light Jaren Durand for Ed P in the Red Sox and a nice Dual patch dual two-color patch and auto for the Angels Burt Blaylock 21 out of 25 Los Angeles Angels that's gonna go to Jason K Temple the dog was better and Chris Cornell God The talent just the just off the songwriting Nice Burt Blaylock and Hall of Famer Angel Edition, I don't I don't know if there's a better rock singer ever than Chris Cornell Just a phenomenal talent green one more for the Braves 9 out of 15 Kyle Moore rookie auto Steve Locke one more time for the Braves ATL stand up For the Padres CJ Abrams rookie auto San Diego Padres and Jason K Nice rookie auto there Now a national will have some Padres cards Rookie auto for the Pirates Holy Park Pittsburgh Pirates going to Pat's Pat Wolfe the Rangers one more time 13 out of 50 on the market to share a auto Jason K with the Texas Rangers Four boxes down You know for someone who has who retains as much Not worthwhile information as I have I've never done trivia sports music movies like I've never been to a trivia night Look, I'd be pretty good your 2021 AL rookie of the year Randy arose arena Tampa Bay Rays and Jason K Part of that big 10 spot order It's again man Randy arose arena. Nice Pittsburgh Pirates nice low number there 75 of 75. Oh neocruise Rookie auto going to Pat Wolfe Congrats Pat cruise missile Very nice. There's the wizard Ozzie Smith St. Louis Cardinals Matthew would From one Ozzie on the Braves to the Ozzie on the what the From one Ozzie on the Braves to the Ozzie on the wizard the Cardinals the Wizards a Washington Wizards legend Perhaps a goal. No For the Minnesota Twins Hall of Famer 14 out of 15 Rod Carew. He converted Jason K He's in the Hanukkah song happy holidays. Happy Hanukkah We're in day five Avonica Rod Carew pen ultimate box second to last box here folks. Good luck. Let's get a big one here Been a little quiet Think we're doing something here silver Graphs Marcus Simeon three out of 15 silver signatures Texas Rangers and Jason K very sharp and for the Cincinnati Reds jelly Vada future Hall of Famer Jason K picked up the Reds that they ten spot order very nice And the last box. Thanks again everyone for getting in here case five Up tops five star with case six on the site right now And once you once we get six going whoa, we'll sell out seven We get seven on the sides. I shouldn't say Whether we saw it seven is up to you. But here we go last two odd. It's good luck First up whoo one more for the Rangers golden graphs four out of 30 Adolis Garcia One more Ranger for Jason K and the last auto. Good luck everyone. Thanks again For the Detroit Tigers rookie auto Spencer Torkelson last one of the case Picked up by Jason K, of course Jason. Thanks again. Thanks again everyone Getting in on this break appreciate you. Jasper case breaks.com for five star six And more seven eight nine. Who knows what we may have check back on this one again Thanks again. Jasper's case breaks.com. Bye. Maybe our last break. So happy holidays, y'all. Appreciate you sticking around with us Put in the year with us. Take it easy