It's all about the green, about the green, no yellow...
If you think about it, the Flash's powers wouldn't help him catch a cab, although he could beat it to where he wanted to go.
And if Green Arrow shot one with an arrow, he'd need to use another trick arrow to jack up the car while he changed the tire.
Of course, the probability of Batman catching a cab in the rain is 100%, metaphysical certitude, because, you know, he's Batman.
It's all about the pun.
And once I'd decided on going with an allusion to What's It All About, Alfie, I had to lose the examples that didn't go with Algebra. There were a number of variations that I had written down (some better than others) and some I forgot because I wasn't near that piece of paper. Going to happen.
But if you're going to round the bases, make sure you know who's on first. I don't know.
Update: So I discovered that Get Smart used the title What's It All About, Algie decades ago in Season 5, Episode 23, which is very illuminating according to the Law of Fives.
And it's about a month later than I planned it.
"The Law of Fives" was also the name of a (x, why?) comic published 5/23/10.
One of the school's Living Environment teachers has been out sick. (I don't know how many the school has.) I've covered her classes every day this week, so far, and likely will continue to do so. I don't mind, but the kids do. They're objecting to the work posted on the board with no one to teach them. They're frustrated and confused and don't like to be told to read the text book. Some of them do what they have to do and try their best. Some of them, I think they just want a teacher to tell them the answers to the questions. And some don't seem to care at all. And none are happy that there's a math teacher in their science class.
Today, I tried to talk to a few of them. It was a good day for this because many of the freshmen were gone on a trip and some of my classes had fewer than a dozen students present. Unfortunately, they just wanted to complain (which is fine, so far as that goes), but they didn't want to hear any solutions -- not the ones that are possible or likely. They need to step up and take matters into their own hands, but they don't have the maturity for it.
Have you heard me complain lately that today's freshmen are less mature than the junior high school students I needed to get away from a dozen years ago?
I don't have all the facts, just some anecdotals. At my last school, while they were losing teachers to budget cuts, I knew that the Living Environment (aka Biology) teachers were safe. (This is my impression, mind you, not a statement of facts.) They were needed more than any of the other science teachers because they were the freshmen class, and everyone has to pass that class and Regents exam. If I extrapolate this, Living Environment teachers are likely in high demand, meaning that they have options as to what school they teach in. Which means that they'll leave a poor school in a heartbeat if something better becomes available.
Without passing judgment, I tried to explain to the kids that if someone was looking for a position, would they pick a school that's been around for 50 years or one that was reopened in the past five? That's not the perfect measure for adults, but that's something the kids could understand without feeling insulted.
Not all 50-year-old schools are great, but they've "reorganized" the poorer performing ones in recent years. But if you're looking for a position (which I've done too much of in recent years) and you see a school where, say, 80% of the kids graduate in 4 years and 70% go on to college, and a second one where, say, 40% of the kids graduate in four years and who wants to contemplate the low number going to college, which do you think the teacher is going to lean toward? If one school has staff who have been there for more than a decade, and the other is only five years old and no one's been there for more than three of those five years, which do you think the teacher is going to lean toward?
If a teacher were to walk into my classroom while I was subbing and saw what little respect the students had not only for me (the sub), but for the property of their actual teacher and (let's face it) for themselves, would they want to come to this school?
End result: if the school is poorly-performing, then you aren't going to be able to attract a qualified teacher whose future depends on the performance of immature individuals who have been taught to respect themselves above all else to the exclusion of having any respect for others, without actually recognizing that they aren't respecting their own future as they find "disrespect" in everything anyone tells them that is contrary to their own preconceived (and immature) notions of reality.
Is that the school's fault? Is it the kids' fault? The parents' fault? The teacher's fault?
I don't know. I'll play it safe. I'll blame Bloomberg. He didn't create the mess. He just made it worse by trying to remake the schools in his own image. And he's not my boss anymore, so I can get away with that now.
8. I'm doing my work!
7. Why am I failing? I handed in all my homeworks and passed all my testses (sic).
6. I was just about to get started.
5. Hey, why'd you erase it? I was copying that.
4. I said that!
3. I'm finished.
2. Mr. Burke, you the greatest math teacher evah! (week before grades are due and/or parents coming to school)
And the Number One Lie Math Students Love to Tell. . .
1. I did my best. I tried really, really hard.
It started innocently enough, with the $200 answer being: "1 + 2 + 3 + 4 + 5". Quick mental math gave the question, "What is 15?" A simple exercise in triangle numbers, which are formed by summing consecutive numbers. It's one of those things which most kids will see and do even before they hear the phrase "triangle numbers", and long before they know they memorize the formula. Besides, a small sequence like this is quicker to add (if you don't have it already memorized) than computing a formula.
Things got trickier with the $400 answer, "1 - 2 + 3 - 4 + 5". There was some hesitation as the contestants (I almost typed "students") worked that one out before one of them arrived at "What is 3?" (I didn't tape it, so I can't review it to see if someone got it incorrect first. I don't remember.) There are two short cuts for this problem, and both have to do with pairing. If you noticed that each pair "1 - 2" and "3 - 4" yield a result of "-1", you have -1 + -1 + 5, which is 3. If you noticed that "-2 + 3" and "-4 + 5" yield a result of "+1", then you had 1 + 1 + 1, which is still 3. If you just oscillated your numbers, you took more time and you probably didn't buzz in in time.
The kids gave up on the third answer: "1 * 2 * 3 * 4 * 5". Given the ages of the kids, I would have thought that at least one of them had seen factorial before, and this was the definition of 5!, although the numeric equivalent was needed. Perhaps they got stuck on 24 * 5, not thinking to reverse the order (20, 60, 120, 120). Whatever the reason, no one got the answer, and they bailed on the category.
It proved so unpopular that when Trebek cautioned "less than a minute to go" (a.k.a < 1 min), the two Math clues remained, and were the final ones of the game.
The $800 answer: "-1 * 2 * -3 * 4 * -5". This actually bothered me that none of the kids gt it. First, for the reason Alex gave. Second, because I had to listen to Alex give it. The previous clue had a result of 120. The numbers multiplied are the same, only some of the signs have changed. Multiply a negative times a negative times a negative and the product will be negative (times two more positives, which won't affect it). The question should have been "What is -120?", which should have been easy considering the previous question gave them the number, and they only had to add on the sign.
The final reason to be annoyed? Alex took so long to explain what should have been obvious that we didn't get to see the last clue. Would it have had division? Exponentiation? Mathematical minds want to know!
But that clue won't be revealed, and it's likely that they avoid such mathematical categories during future Kids Weeks.
UPDATE: I wrote a little More about that Jeopardy category after the blog The Political Hat referenced this entry.
And Jeopardy had Another Math category, with adults, shortly after this.
But four and four are eight, so whatever the problem, it's not a math problem.
But here's a bonus problem: when was the last time we saw these Eights together?
So, basically, this is the sheet of paper I kept. I'm sharing it with you and, thus, keeping it electronically, so I can throw this scrap away.
SWBAT make a graph comparing numbers of words spoken per second/minute.
Activity: Students will break into groups. Each will have a sports article. Their task is to take turns "auditioning" for a sports announcer job (like "Ron" on "G-Unit Radio")
| Note: Ron was a school aide who did the morning announcements with a little bit of a flair, and he referred to it as "G-Unit Radio", the "G" for the school name and "Unit" for "Family" ... and having nothing at all to do with a similarly-named hip-hop group from Jamaica, Queens.) |
Each article is marked off at 10-word intervals (for easier counting). One group member will be the timer, another the recorder. Students will take turns talking for 10, 15 20 and 30 seconds and then counting the words. After the data is recorded, data will be graphed.
Q: Is there a relationship between time and # of words?
HW: Finish the graph based on the data.
Work on December HW packet.
I remember when making groups, one of the keys decisions in grouping was how many of them had a watch. This was before everyone has a phone as well.
I also remember being told to come up with a Christmas vacation assignment. I hate those, and some of my students would be traveling (some outside the country) and did I really want them to bring books along? So I make a packet of HW for the month of December and told them it was due the day after the day we got back because everyone always forgets it the first day back. (Some of them were doing the entire packet the day we got back, which might explain we I haven't done that since.)
I hope you enjoyed my trip down memory lane. Try the activity yourself, and let me know how it works. FYI: I was in the middle of a free six-week trial subscription of Sports Illustrated, courtesy of whatever store I had started my Christmas shopping in, and I pulled an article from there. The sports pages work, too, especially if your school is listed in them!
Today's events: I brought in doughnuts and put them out in the Teacher Center a dozen at a time during my preps. Some of the folks who hang out there (many stay in their rooms or elsewhere where there are conference tables) knew that today was my last day and that I'm having a birthday next week, when I'll obviously no longer be there. It was a little busy today. Friday's are little crazy because the periods are very short and there's 90 minutes of PD (professional development) at the end of the day for the teaching staff. (This was something that was voted on my the teachers last year.) I was doing double duty making sure that I packed what I wanted and tied up loose ends while creating work for the kids who I'd kept in the dark about the switchover. There can be some troublesome elements in the class, and they didn't need encouragement to misbehave, which they'd do despite the fact that I'm handling the second marking period grades this weekend.
Now, before I forget, when I arrived at work this morning, there was a bag with a bottle in it on my desk. I believe it's essentially an Italian version of Bailey's, which was confusing because it was a gift from a lovely Russian woman. So by the time that PD came around at the end of the day, after a lot of well-wishing (and an incident I'll mention at the end), I hadn't thought more about it. I had to go to the library for yearbook photos and I was going to take the remainder of the doughnuts, and I was supposed to go out for a drink with one or two coworkers.
That's when I ran into Pamela. (I'll call her "Dr. Pamela" this once, just to give her her due on the title, but I'm leaving off the last names right now. I don't know why.) She apologizes that it's Friday and the end of the day, but it's my last day, and could I help her set up that document camera she found in her desk drawer. (True story: I put it in that desk drawer a year and a half ago because it was the only piece of the computer not tied down. No one noticed since. I wasn't in the school all last year.) Well, sure thing. We'd talked about it once, and I hadn't done it, so it was the least I cou---
SURPRISE!
Seriously? The document camera? You lured me into a surprise party with a document camera??? Points for originality. So I celebrated my last day and my landmark birthday with my Math Department colleagues. Unfortunately, my boss couldn't make it, being pulled in "six directions at once". (I'm guessing: each way on the x, y, and z axes.) And others from the Teacher Center were likely corralled with their own departments at the moment, so they missed out.
And the thing is, I knew it was coming. I thought I knew. And yet ... Still a random moment and I expected none of what was there. And just to show you that I'm not the only person who think mathematically all the time, take a look at the equations and expressions on this word wall:
I'm leaving that school in capable hands. And, who knows, I might find myself returning.
As for the unfortunate incident, the less said the better. In literally the last minute of teaching at this school, a fight broke out. I'd hope it was just a flare-up, some hurt feeling that a slap on the arm would resolve and diffuse and not go anywhere else. Sadly, it did go somewhere -- out into the hall. A crowd did form, but I have to give a shout-out to students who tried to separate, restrain(*) and calm the participants. (*: when it comes to "restraining" a student, many are looking to be held back just to save face. However, that was true only for the instigator.) The kids came to each others' aids before it got worse. But like the inevitable car wreck you witness, you know what's about to happen. I wish I could say more, but I've probably said too much already. I was bummed out for the prep period before my PD, which in itself was a bit silly to go to, so I was even happier about the little diversion. Maybe it someone wants to join me for that new job/landmark birthday drink, we can talk!
Short Answer: It's a topic that's worth, at most, two points on the state exams, and that most of you aren't likely to see again. On the other hand, given the number of students I've known who have scored 63 or 64 on that same state exam, ignore this at your own peril.
Another Flippant Short Response: It's actually a very simple topic to grasp if you give your instructor, your facilitator, five minutes to explain and really use that time to understand, not just copy down a few rules in your notebook. Or you can try to figure it out for yourself from the worksheet and then read the textbook when you get home.
Seriously, it's a simple thing.
A couple of days ago, we were talking about Compound Inequalities. Interval notation is another way to express the range of data in the solution to an inequality. Why do we need another way to express this?
This is Algebra. We don't need no steenkin' reasons! However, I like to say that it's shorthand, even if it uses the same number of characters, with the exception of not requiring any underscores. For that matter, as I'm using a simplified form of a mark-up language, the less-than symbol has another meaning, and it actually takes me three keystrokes to ensure that you see this: <.
With Interval notation, there are no < symbols or variables, either. Just the boundaries.
For example, if we needed to represent the compound inequality -3 < x < 5, we could take the two endpoints and stick them in a pair of brackets, like this: [-3, 5].
This means the same thing and seems quicker to write, and doesn't require as much space (or, at least, doesn't seem to, depending on where you're writing it).
Well, that's all fine, but what if you have "less than" instead of "less than or equal to"? Simple, we don't use square brackets; we use parentheses, instead. That means -3 < x < 5 could be written as (-3,5).
Here is where you need to pay attention. I've said in the past that notion is important, and different symbols mean different things. This is one instance where notation can mean two different things. (-3,5) can be a inequality for one variable, such as x, or it can be a point on the co-ordinate plane, using two variables, (x,y). How do you know which? Context!
It's also important to note that you can (and the state will!) mix and match these: -1 < x < 4 would be written as [-1,4).
Finally (for now), what if it isn't a compound inequality. What is you only have, for example, x > 5? In this case, five is the lower boundary, but what is the upper boundary? The graph has an arrow going up to the right, continuing forever until it hits, as Buzz Lightyear might intone, Infinity, and Beyond! ... or infinity, at any rate. This would be written as (5, ∞).
Note that because infinity is not an actual number (that is, x cannot actually equal infinity), it will always have a parenthesis next to it, not a square bracket.
Finally, a proud moment because one of my students put themselves out there and took a chance. I asked where the answer goes to with x < 5. I got blank stares. "Well, think about where it goes off to the right." The student very cautiously hazarded the guess, "negative infinity?".
Absolutely. He had never heard of such a thing before and didn't know it could exist. Then he realized that he didn't know that it couldn't exist. I liked the way he thinks. I hope there's more of that because if you think of it, this isn't any more complicated than the compound inequalities they're representing.
Okay, maybe that's not saying as much as I'd like.
Postscript: For future reference, the infinity symbol (∞) is the ampersand (&), followed by "#8734" (no quotes).
I have been bouncing around the New York City educational system for a few years now, and that's okay. I know that I'm wanted and there will be a soft landing somewhere. I figured that if I didn't get back to where I wanted to be in a reasonable amount of time, I'd find another suitable position. In the meantime, I'd be in the Absentee Teacher Reserve (ATR) pool. The downside to being in the pool is that you never know where you're next assignment will be: good neighborhood or bad, conveniently located or not. The upside? Well, no lesson plans, no mindless nights grading mindless papers writing meaningful comments, which likely wouldn't be read anyway. And I can most likely reset my alarm for a later time. Currently, I have a tendency to get to work an hour early to prep for a first period class because I don't wish to do all that work the night before when I could be sitting in front of the television, watching the insides of my eyelids.
A quick summary of the past few years: my school was shrinking because Bloomberg was trying to close it down despite its high grades on his own report card system. It stayed open but lost staff, including half the Math Department (which was three people, not counting the Support Services teachers). That event inspired this comic: Kiss Today Good-bye. After nearly a decade, I was leaving what felt like home.
That fall, I spent a month in Williamsburg at a small school that really didn't need any substitutes, and I mostly circulated the rooms, trying to help, which was easier to do when the subject was math. That was followed by a week at a school ten minutes from my home. At that point, a teacher at my old school retired, and I was on my way back. Things had changed a little. I had mostly freshmen, unlike the previous year, and the schedule was a little ... challenging. One could theorize that the classes were particularly rough because they wanted to encourage the former teacher to retire sooner. I think he had his plans set from the first day of school. It was a bit of a rough year, but I was promised a better horizons the following year ... and then I was excessed again.
My personal Year from Hell started in August. (I actually asked an A.P., who called to request an interview, if he had time the following day as I would be busy on the day he proposed, attending a funeral.) Professionally, it wasn't a bad year at all. I was called into Bed-Stuy, which sounded worse than it was, and spent a month there, watching them build the sets for The Knick, literally, right outside my window. Note: I am NOT misusing the word "literally". I have pictures. And Clive Owen even retweeted one of them! (Actually, it later turned out it was a FAN account, but I didn't know that at the time.)
This was followed by a few week in Park Slope, at my old zone school, which had been broken up years ago. Park Slope went through Yuppie-ville into Hipster Haven, but many of the kids traveled there from other areas. It wasn't an impressive place, and said to say that the teachers I worked with weren't fully versed in the topic they were teaching. I was able to nonchalantly correct a couple of things as if something was simply misspoken, but one thing in particularly was just so wrong, I kept my mouth shut. I figured that it was a tough topic and I could help individually with the students, but I couldn't undermine the teachers for the rest of the year. They weren't idiots, and I didn't want them to be thought of that way. (And I did explain their mistake later, during a prep period.)
Sometime in October, I got a call from a school in Staten Island. It would be a bit of a hike, and the Verrazano Narrows bridge has an incredibly expensive toll. (Not kidding -- even with a discount, it was costing me more than $10/day to get to work over one bridge.) It was supposed to be temporary, which worked out for me, because I knew that there was going to be an opening for me in Brooklyn at any given (i.e., random) moment. Except that there wasn't. For whatever reason that the teacher was on leave (I wasn't told; I never asked), she didn't come back. I was there until June, and I had settled in and had started to make friends. I attended a graduation dinner for a colleague, a summer barbecue. I even met a parent who I hadn't seen since we were both 13, some
mumblemumble years ago.At the end of the year, the AP asked me what was next. She didn't ask if I wanted to stay. maybe she assumed I wanted back in my old school ... or just my old borough on the other side of the bridge.
Which brings us back to randomness and inevitability. I went back to my old school during the summer for Regents Review classes, and subbing for a little spending money. One of my former colleagues was 8 months pregnant. She would be out on the first day of school. The AP of school organization started the paperwork to get me back on a temporary basis, and I was happy to go back. The only problem was that I hadn't a clue how long I would be back for. No one seemed to know how much time she would be taking. It was going to be six weeks plus whatever sick leave she had saved up (as far as I could guess) but I hadn't a clue how much that would be. Three months? A semester? Two marking periods, it turns out.
And here I am. Ready to leave again. Probably for the last time. I don't seem them -- at this moment -- turning things around. I don't see them expanding the student population, and with it, the budget. How long do I stay in the ATR pool? Sooner or later, I will have to find a position. Sooner or later, I will be subbing in a good school and I'll seek a position. (And maybe even regret not seeking last year's position again.) But in the meantime, I can count on two things:
A high probability of randomness, and an absolute certainly of zero lesson plans.
Everything in Arithmetic seemed to be about finding the answer. Let me add emphasis to that: THE Answer. Then along came Algebra, and, suddenly, THE Answer wasn't as important anymore. Don't get me wrong -- it was still important. However, how we got the answer and why it was correct seemed to matter more. Just writing, for example, "5" on the paper in that big, empty space wasn't good enough. Even if it was "obvious" that it was 5. Why? Because the next problem might not be so "obvious", so we still needed to know the rules so we could attack the next one, and the one after that, and so on, as they got more complicated.
But even as we showed our work and checked our answer, we knew one thing for sure: There are AN answer. One. Singular. The value that makes the equation True.
Until inequalities came along. Why did we even start that chapter? How could there be problems with not only more than one answer, but an infinite number of them, an entire range of values, shooting off into infinity. The answer isn't seven, it's greater than seven. Does that mean it's eight? Well, yes, but it's also nine, ten, eleven, twenty-seven, thirty-one and a half, the square root of 92, a googol (not a search engine). It's all those real numbers. The ones bigger than seven.
Okay, so equations have one answer (or maybe two?? -- what do you mean, "we'll talk about that?"), and inequalities have arrows that point to the left or the right and go on forever. That's it, right?
Weeeeeellllllll . . . .
Do you know how in English class (or ELA or whatever), you can have compound sentences, which are two sentences joined together by a conjunction. (Cue: Schoolhouse Rock's "Conjunction Junction".) Those conjunctions are "AND", "BUT", and "OR". In math, we can have compound inequalities, and they can be joined by "AND" or "OR". What about "BUT"? Here's a secret for you: "AND" and "BUT" mean the same thing:
I went to the store, but it was closed.
So we don't use "BUT" in Algebra. ("What about when talking about someone's face?" "That's just wrong, Gordo." -- and now because it's rude, so much as that would be misspelled.) Likewise, "OR" isn't a conjunction in math. It's something called a disjunction, and we'll address that later. One topic per day, please.
If you wanted to get a "B" on your report card, you would need to score AT LEAST 80 and LESS THAN 90. (Exactly 90 or higher would be an "A", and while that would be great, let's be realistic here: A's are tough to get. But aim high.)
This is an example of a compound inequality. If we were to graph all the averages that result in a grade of B, there wouldn't be an arrow. Sure, x > 80 would have a closed circle above 80 and an arrow pointing to the right. And x < 90 would have an open circle and an arrow pointing to the left. However, the "AND" in the condition tells us that we only want the points that make both true, the area that they overlap. So we wind up with a line segment with one closed endpoint and one open endpoint, representing a range of numbers -- still infinite! -- that are solutions to the inequality x > 80 AND x < 90.
One last thing. Compound inequalities with AND can be written without the AND. Look at the endpoints. The minimum number (80) has to be less than or equal to the actual average (the variable) and that has to be less than the maximum score (90), so we could write it as 80 < x < 90.
Confused yet? Don't worry, you'll get the hang of it.
And that almost fell apart on Day 1. It's late in the evening, and I'm exhausted. So I've punted and given you an introduction post announcing my intent without actually getting started. I've fulfilled the obligation with more noise and less content.
Noise and content, as we know, are inversely proportional in blog posts, as well as message boards and other forums. The more of one, the less of the other. Bob McAllister, host of the old -- old -- kid show Wonderama, used to sing "The more you Fingel, the less you Heimer, The less you Heimer, the more you Fingel" when he introduced his character, Professor Fingelheimer. That was probably my first real exposure to the concept of inverse proportion even though it didn't mean a fingel-thing!
With noise and content, you really can't have one without the other. Well, you can, theoretically, but 100% content is boring and bland while 100% noise would be ... should I name names? You know which blogs those are: lists of 20 random things required 72 clicks to get through.
So this is mostly noise and nostalgia, and tomorrow will be some wonderfully thought out piece about inequalities that might even merit a second draft.
Unless a comic comes to me in the next hour or so that just can't wait. Or my work schedule demands a little bit more of me.
Which would leave you with a little bit less of me.
