We've moved on to solving literal equations for a variable. I like this transition because it reinforces the same skills they've been working on forEVER. One thing came up in my first of 3 classes to teach it this year that made me change tactics for the next 2 classes.
We were all about "isolating the variable" and "undoing what's done to the variable you're solving for" and such. Then as I'm walking around, lo and behold, a student was actually moving the variable. She wanted to get it to the other side. What was she doing?! Don't touch that variable!
That led to the following in my next 2 classes. Suppose the problem is
Solve 3A = 2w + 4p for w.
I first made them get out another colored pen/pencil, and then identify the variable they were solving for. Then they had to write that variable in a DIFFERENT color:
3A = 2w + 4p
Then I made them draw an arrow to the w and write in their notes, "DON'T TOUCH THIS" while humming the M.C. Hammer song of the same name. We continued on, and most everyone successfully colored the "solve for" variables and left them alone in the remaining problems.
Wednesday, October 28, 2009
Saturday, October 24, 2009
"Subtracting or Negative"
In the course of getting my algebra 1 kids up to speed on solving equations and inequalities, they have to combine like terms, and I'm getting the above question too often for comfort. Sometimes after they combine the terms, they'll squish them all together and instead of something like 6x - 5, it will be 6x-5, where that's a teeny tiny negative sign and not a subtraction sign. I hadn't clued into this until a kid wrote "7x4" instead of "7x + 4" because in her mind, it was a positive 4 that remained after combining the like terms, and not an adding of the 4.
So I'm trying to be careful to say things like: you're keeping track of all the steps you're doing, for example subtracting 5 and then adding 18, so at the end of the day, you haven't seen all the intermediate steps, and if you had just done it in one step, you might as well have just added 13 (and not "positive 13").
Also, in my continual attempt to bring in problems in context, I had interesting conversations with the kids about this problem I gave them:
1. Two cell phone plans Verizon offers are as follows. You can have a monthly fee of $40 and pay $0.20 per text message, or you can have a select plan costing $60 and unlimited texting. Consider the inequality
40 + 0.20t > 60
a. What does the t represent (give units)?
b. What is the person trying to find out by solving this inequality?
c. Solve for t and explain what this means in the context of the problem.
d. Cell Phone Sally has tons of friends and wants to see if her texting habits would be too expensive under the 1st plan. If she texts about 10 messages per day, what would her bill be per month under the 1st plan mentioned?
e. How many texts do you send per day? What would that be per month?
f. What would your monthly bill be under the 1st plan?
I had gone online to the Verizon website, and got that accurate information. I was very careful to have them do only a couple of problems and stop them. Invariably they answered "text messages" for a. Then we had to have a discussion about "what about the text messages? their length? their time? what?".
Then for problem b, practically everyone got it wrong. They said: they're trying to find out which plan is cheaper. So I asked them, okay what is your answer going to look like when you solve the inequality, and THAT'S going to tell you which one is cheaper? We held off on answering b until they did c.
Now note, my coworker and I decided to clump topics: solving equations and solving single variable inequalities one after another, because it would give the kids a chance to practice the same skills. Also note that we have not discussed linear equations and graphs and rates of change yet in the sense that they would not know how to set up the 40 + 0.20t if just the words were given to them.
So, my students solved c. And the answer is t > 100. So we had to have a discussion about what this means. Some kids had $100, some kids said "this means the left plan is more expensive", etc. We finally got to: if someone sends more than 100 text messages, then the first plan is more expensive. I asked what the t values were the solution to this problem, and they said "all t greater than 100", so I asked, would t = 101.3 work? and they said, no, it has to be an integer in this case. good.
d was also a problem that started discussion. There were kids that just started working it without asking me how many days in a month, so that was a good check of their careful reading.
And the last two were GREAT big eye-openers for me. I don't have a cell phone, so silly me, I knew "10 messages a day" was low, but I didn't know HOW low. Some of my students reported out that they sent anywhere from 100 - 500 - in one case 1000 text messages a day? Hmmmmm, I had to ask how many hours a day they were doing this, and we had to do the math to see if this was even physically possible. Holy Moly.
So I'm trying to be careful to say things like: you're keeping track of all the steps you're doing, for example subtracting 5 and then adding 18, so at the end of the day, you haven't seen all the intermediate steps, and if you had just done it in one step, you might as well have just added 13 (and not "positive 13").
Also, in my continual attempt to bring in problems in context, I had interesting conversations with the kids about this problem I gave them:
1. Two cell phone plans Verizon offers are as follows. You can have a monthly fee of $40 and pay $0.20 per text message, or you can have a select plan costing $60 and unlimited texting. Consider the inequality
40 + 0.20t > 60
a. What does the t represent (give units)?
b. What is the person trying to find out by solving this inequality?
c. Solve for t and explain what this means in the context of the problem.
d. Cell Phone Sally has tons of friends and wants to see if her texting habits would be too expensive under the 1st plan. If she texts about 10 messages per day, what would her bill be per month under the 1st plan mentioned?
e. How many texts do you send per day? What would that be per month?
f. What would your monthly bill be under the 1st plan?
I had gone online to the Verizon website, and got that accurate information. I was very careful to have them do only a couple of problems and stop them. Invariably they answered "text messages" for a. Then we had to have a discussion about "what about the text messages? their length? their time? what?".
Then for problem b, practically everyone got it wrong. They said: they're trying to find out which plan is cheaper. So I asked them, okay what is your answer going to look like when you solve the inequality, and THAT'S going to tell you which one is cheaper? We held off on answering b until they did c.
Now note, my coworker and I decided to clump topics: solving equations and solving single variable inequalities one after another, because it would give the kids a chance to practice the same skills. Also note that we have not discussed linear equations and graphs and rates of change yet in the sense that they would not know how to set up the 40 + 0.20t if just the words were given to them.
So, my students solved c. And the answer is t > 100. So we had to have a discussion about what this means. Some kids had $100, some kids said "this means the left plan is more expensive", etc. We finally got to: if someone sends more than 100 text messages, then the first plan is more expensive. I asked what the t values were the solution to this problem, and they said "all t greater than 100", so I asked, would t = 101.3 work? and they said, no, it has to be an integer in this case. good.
d was also a problem that started discussion. There were kids that just started working it without asking me how many days in a month, so that was a good check of their careful reading.
And the last two were GREAT big eye-openers for me. I don't have a cell phone, so silly me, I knew "10 messages a day" was low, but I didn't know HOW low. Some of my students reported out that they sent anywhere from 100 - 500 - in one case 1000 text messages a day? Hmmmmm, I had to ask how many hours a day they were doing this, and we had to do the math to see if this was even physically possible. Holy Moly.
Sunday, October 18, 2009
Duties and Conversations
Most likely, just like other schools, I have extra duties and guilt that sometimes makes me volunteer for EXTRA one time duties. And, just like other teachers, there's probably a fair bit of grumbling under my breath about how I don't have TIME for this and I need my time to prepare and on and on.
On the other hand, there are some nice perks that go along with my morning duty. The 2 other teachers I share it with teach different subjects and different grade levels, and I never see them other places. So my 15 minute morning duty allows me to chat with and get to know them and feel more connected to our school's "family".
Along the same lines, I volunteered to give up my lunch time to help sell t-shirts the other day. Not so bad, since I could eat my lunch at the same time, and I have the next period off, so I didn't feel too stressed. At this duty I got a chance to talk with yet a 3rd teacher I never see (new also this year) that teaches a foreign language. This conversation was super helpful to both of us. I shared with her some of the snippy behavior and struggles I'm having with a few of my students, and she mentioned that the same was happening with her. We talked about another student that's not doing so well in either of our classes, and I think we both left with the feeling of, "Whew! it's not just me.".
It's so easy to feel isolated and stressed and feel like the ONLY one that may be having certain troubles, that it's nice to commiserate with others that are going through the same thing ... not that I'd wish it on them, but you know...
On the other hand, there are some nice perks that go along with my morning duty. The 2 other teachers I share it with teach different subjects and different grade levels, and I never see them other places. So my 15 minute morning duty allows me to chat with and get to know them and feel more connected to our school's "family".
Along the same lines, I volunteered to give up my lunch time to help sell t-shirts the other day. Not so bad, since I could eat my lunch at the same time, and I have the next period off, so I didn't feel too stressed. At this duty I got a chance to talk with yet a 3rd teacher I never see (new also this year) that teaches a foreign language. This conversation was super helpful to both of us. I shared with her some of the snippy behavior and struggles I'm having with a few of my students, and she mentioned that the same was happening with her. We talked about another student that's not doing so well in either of our classes, and I think we both left with the feeling of, "Whew! it's not just me.".
It's so easy to feel isolated and stressed and feel like the ONLY one that may be having certain troubles, that it's nice to commiserate with others that are going through the same thing ... not that I'd wish it on them, but you know...
Wednesday, October 14, 2009
Regrading Issues
Yeesh! I thought I was careful, brought on by bad experiences and lots of practice, but today ....
Way back when in the early days of teaching, when I'd grade a test/quiz/homework, and something was missing (a problem not done, a justification, some work), I learned pretty quickly to make sure to look carefully at ALL the blank space around it, and if there was, say a blank side of the page, I'd draw a diagonal mark through it to indicate I'd noted it, and also to prevent the kiddies from later on, after they'd got the paper back, ADDING something to that blank space and then claim that it'd been there all along, and then demand/request/beg more points because it was MY mistake. Ditto for blank parts of pages and such.
I know I make mistakes ... still happens ... daily ... so this marking and covering up of blank space cut down these instances dramatically. It also cut down my 2nd guessing myself that I'd missed something.
Well, we had a ton of swine flu absences a few weeks ago, and many students missed many days, and some are still making up old tests and homework. One student had come in last week to make up a geometry test. I had a meeting after school, so I put her in a windowed smaller room that I glanced in on periodically and had her work. She took forever, and it looked as if she had not studied. I think she was assuming I'd give her the same version as everyone else and not a make-up version, and she had used a friend's returned test to study the answers instead of studying concepts. She finally handed it in, and I graded it. 68/100. Ewww. On one unchanged problem, she MAGICALLY produced the answer and none of her work supported it. On another, she showed some work, but then guessed and checked an answer .... but didn't check the geometry constraints.
On a third problem, the one I had "regrading issues" with, I had made a table where students were supposed to fill in 7 cells. She left a whole column blank - 4 cells (logic symbols). I circled the whole column and put a question mark through it and graded on. Today she came to talk to me. Amongst other things, she showed me that she had written those missing answers in small letters in another column (this was a logic section, and the answers were like " p->q " and such). Hmmmmm, I didn't outright accuse her of lying, but I questioned her as to why she didn't put those answers in the right column. She had some story about how she had written them there to help her with another problem, and she didn't know what I was expecting in this problem's column titled "symbols".
I know I'm overly cynical about such things at times, and about 50% of the time I'm wrong, and I'd HATE to accuse someone of outright lying if it weren't true (it happened to me in high school with a teacher and I still remember it to this day). So, I didn't say more and gave her 1/2 the points back, but now I'll have to remember this and be more careful in the future.
Way back when in the early days of teaching, when I'd grade a test/quiz/homework, and something was missing (a problem not done, a justification, some work), I learned pretty quickly to make sure to look carefully at ALL the blank space around it, and if there was, say a blank side of the page, I'd draw a diagonal mark through it to indicate I'd noted it, and also to prevent the kiddies from later on, after they'd got the paper back, ADDING something to that blank space and then claim that it'd been there all along, and then demand/request/beg more points because it was MY mistake. Ditto for blank parts of pages and such.
I know I make mistakes ... still happens ... daily ... so this marking and covering up of blank space cut down these instances dramatically. It also cut down my 2nd guessing myself that I'd missed something.
Well, we had a ton of swine flu absences a few weeks ago, and many students missed many days, and some are still making up old tests and homework. One student had come in last week to make up a geometry test. I had a meeting after school, so I put her in a windowed smaller room that I glanced in on periodically and had her work. She took forever, and it looked as if she had not studied. I think she was assuming I'd give her the same version as everyone else and not a make-up version, and she had used a friend's returned test to study the answers instead of studying concepts. She finally handed it in, and I graded it. 68/100. Ewww. On one unchanged problem, she MAGICALLY produced the answer and none of her work supported it. On another, she showed some work, but then guessed and checked an answer .... but didn't check the geometry constraints.
On a third problem, the one I had "regrading issues" with, I had made a table where students were supposed to fill in 7 cells. She left a whole column blank - 4 cells (logic symbols). I circled the whole column and put a question mark through it and graded on. Today she came to talk to me. Amongst other things, she showed me that she had written those missing answers in small letters in another column (this was a logic section, and the answers were like " p->q " and such). Hmmmmm, I didn't outright accuse her of lying, but I questioned her as to why she didn't put those answers in the right column. She had some story about how she had written them there to help her with another problem, and she didn't know what I was expecting in this problem's column titled "symbols".
I know I'm overly cynical about such things at times, and about 50% of the time I'm wrong, and I'd HATE to accuse someone of outright lying if it weren't true (it happened to me in high school with a teacher and I still remember it to this day). So, I didn't say more and gave her 1/2 the points back, but now I'll have to remember this and be more careful in the future.
Friday, October 09, 2009
Linear Word Problems
Whew! In algebra 1 I've finished the initial introducing of solving a variety of linear equations: one-step, two-step, multi-step, weird distributive action, variables on both sides. Now it's just a matter of having them practice their hearts out until most/all of them are successful. Yesterday, I wanted to have them see how these problems could be used in real life, and after scanning through books and such, I saw that a lot of people were fascinated with how many coins someone has, or how much of a certain type of mixture to use, or which 2 consecutive numbers add to another number.
Then, whew! I scanned throught he Hughes-Hallett book of "Functions Model Change" and adapted some of their ideas that were written in table form to use as linear equation problems. There's one problems about carbon-14 dating which I know is not linear, but, boom, call it a "model", and it can become a linear situation. Then there was one about weight of a person vs. calories burned doing various exercises. Finally there was one about the years since 1970 vs population of a town.
I liked my adaptations because I've altered the scales on the variables, so that the kids have to think about what the numbers mean in terms of units. Also, these are in-context types of problems, not "math world" type. Also, the kids didn't need a calculator, since I made the numbers "doable". We had a discussion about estimating. For example, for the fossils, t represented time the tree had been dead in 1000's of years. An answer came up as t=3 & 2/11, and I asked them what that meant. We discussed approximating 2/11 by 2/10 and having t=3.2 and they finally got to the point to see that was 3,200 years. I also liked that in 2c below, they had to think to put in w=1.4 instead of 140, for example.
Here's an example of one problem I adapted:
2. Exercise physiologists tested many people, and have come up with an equation that shows the number of calories used per minute as a function of body weight for various activities. For walking they calculated the equation
b – 4.6 = 3(w – 1.7)
where b represents the calories burned in one minute, and w is the weight in 100’s of pounds of the person.
a. If w is found to be 1.6, what does that person weigh? (don’t solve; interpret w=1.6)
b. If b is found to be 5.4, what does that mean? (don’t solve; interpret b=5.4)
c. Suppose a person weighs 140 pounds, how many calories did they burn walking in one minute? In 30 minutes?
d. Suppose someone burns 5.2 calories a minute, how much do they weigh?
Then, whew! I scanned throught he Hughes-Hallett book of "Functions Model Change" and adapted some of their ideas that were written in table form to use as linear equation problems. There's one problems about carbon-14 dating which I know is not linear, but, boom, call it a "model", and it can become a linear situation. Then there was one about weight of a person vs. calories burned doing various exercises. Finally there was one about the years since 1970 vs population of a town.
I liked my adaptations because I've altered the scales on the variables, so that the kids have to think about what the numbers mean in terms of units. Also, these are in-context types of problems, not "math world" type. Also, the kids didn't need a calculator, since I made the numbers "doable". We had a discussion about estimating. For example, for the fossils, t represented time the tree had been dead in 1000's of years. An answer came up as t=3 & 2/11, and I asked them what that meant. We discussed approximating 2/11 by 2/10 and having t=3.2 and they finally got to the point to see that was 3,200 years. I also liked that in 2c below, they had to think to put in w=1.4 instead of 140, for example.
Here's an example of one problem I adapted:
2. Exercise physiologists tested many people, and have come up with an equation that shows the number of calories used per minute as a function of body weight for various activities. For walking they calculated the equation
b – 4.6 = 3(w – 1.7)
where b represents the calories burned in one minute, and w is the weight in 100’s of pounds of the person.
a. If w is found to be 1.6, what does that person weigh? (don’t solve; interpret w=1.6)
b. If b is found to be 5.4, what does that mean? (don’t solve; interpret b=5.4)
c. Suppose a person weighs 140 pounds, how many calories did they burn walking in one minute? In 30 minutes?
d. Suppose someone burns 5.2 calories a minute, how much do they weigh?
Sunday, October 04, 2009
Studying for Math Tests
Blach! I'm having an inner cursing and outer cursing with lots of hand gesturing and bad facial expressions weekend as I grade my Algebra 1 tests. This was their first true test on algebra (the other one was on topics they've seen since the womb: positive and negative numbers, fractions, simple graphing). During Friday I'd started grading my 1st set of exams (with inner grumbling and outer professionalism while my 2nd set of kiddies took the exam).
Then before my 3rd class started their exam, I had a quick informal vote: how many people did problems from scratch to study for this test (thumbs up or thumbs down)? How many people started studying before last night? How many people read through their notes? Hmmmm, the number of thumbs down was heart breaking.
Maybe it's an experience they have to go through: horrible test grades to see that they actually have to study. On a positive note, the way their grades are weighted with homework and tests, it doesn't HORRIBLY bring down their grades, but it does lower it (sometimes up to 6% points depending).
With a hope of helping them in the future, I've made up a document that I'm going to hand out to them a week before their next test. It walks through the steps of how to study for a math test. Hopefully, this will work.
Then before my 3rd class started their exam, I had a quick informal vote: how many people did problems from scratch to study for this test (thumbs up or thumbs down)? How many people started studying before last night? How many people read through their notes? Hmmmm, the number of thumbs down was heart breaking.
Maybe it's an experience they have to go through: horrible test grades to see that they actually have to study. On a positive note, the way their grades are weighted with homework and tests, it doesn't HORRIBLY bring down their grades, but it does lower it (sometimes up to 6% points depending).
With a hope of helping them in the future, I've made up a document that I'm going to hand out to them a week before their next test. It walks through the steps of how to study for a math test. Hopefully, this will work.
Monday, September 28, 2009
Memorable Classes
I started thinking about this when a *way* former student (2001-2002 school year) "friended" me on Facebook yesterday. I immediately knew who he was and what class he was in and what year and most all of the other students in that class.
Then I started thinking that this wouldn't be true with many other students and classes. Sure, some stand out and I can remember their names and faces, but ... let's see, roughly 12 years times an average of 6 classes times roughly 25 kids per class (and by "roughly" I mean I'm blotting out the recent years of 38, 40, 36, .... and 25 is easy to multiply by ... and I'm ignoring the fact that I had some students for more than one class) ... so ... 1800 students????? Is that right? Holy Moly.
So, I'm guessing it's a good bet that I wouldn't remember the bulk of them. And, I've been "attempt friended" recently by recent grads, and it feels weird, and I ignore it and move on. But back to the student in question. He's graduated from college now I guess and is working in a tech field. ...
Here are the reasons this class was memorable. It was a gifted & talented class of juniors, and they were smart as a whip. They started out kind of wary of me and the class, and were resistant, but we grew on each other. I would just throw the most obscure problems at them and put on my "game face" of "what? of COURSE I expect you to solve this .... what? you don't think you can?" and then I'd wait, and sure enough, they would come back with answers. It was also one of my smaller classes ... 14 or so. We also had a ton of laughs together over the silliest things. And ... well, after that year was over, right before their senior year started, one of the nicest, sweetest, kindest, most honorable girls from that class (and from the school) died in a car wreck on a rainy night. I'm choking up just thinking about it, and it happened, what, 7 years ago. Boy did I cry during her memorial. Their senior year was a bit more somber because of that, and the valedictorian was a girl in my former class, and her graduation speech wove that event in through her talk and about how it altered her thoughts and actions of that year.
I'm guessing that the most traumatic things are the most memorable. Like when you try to remember your earliest memory from childhood, and invariable it seems to be of some injury or something scary that happened. ...
Anyway, it's nice to see/hear about the kids that are now "adults" and having their next part of their lives. ... Maybe if I stay in one school long enough, I'll have the kids of my current kids?! Yeesh. Or at my advanced years ... maybe I'd be in dentures and Depends by then and too old to terrorize the little kiddies any more.
Then I started thinking that this wouldn't be true with many other students and classes. Sure, some stand out and I can remember their names and faces, but ... let's see, roughly 12 years times an average of 6 classes times roughly 25 kids per class (and by "roughly" I mean I'm blotting out the recent years of 38, 40, 36, .... and 25 is easy to multiply by ... and I'm ignoring the fact that I had some students for more than one class) ... so ... 1800 students????? Is that right? Holy Moly.
So, I'm guessing it's a good bet that I wouldn't remember the bulk of them. And, I've been "attempt friended" recently by recent grads, and it feels weird, and I ignore it and move on. But back to the student in question. He's graduated from college now I guess and is working in a tech field. ...
Here are the reasons this class was memorable. It was a gifted & talented class of juniors, and they were smart as a whip. They started out kind of wary of me and the class, and were resistant, but we grew on each other. I would just throw the most obscure problems at them and put on my "game face" of "what? of COURSE I expect you to solve this .... what? you don't think you can?" and then I'd wait, and sure enough, they would come back with answers. It was also one of my smaller classes ... 14 or so. We also had a ton of laughs together over the silliest things. And ... well, after that year was over, right before their senior year started, one of the nicest, sweetest, kindest, most honorable girls from that class (and from the school) died in a car wreck on a rainy night. I'm choking up just thinking about it, and it happened, what, 7 years ago. Boy did I cry during her memorial. Their senior year was a bit more somber because of that, and the valedictorian was a girl in my former class, and her graduation speech wove that event in through her talk and about how it altered her thoughts and actions of that year.
I'm guessing that the most traumatic things are the most memorable. Like when you try to remember your earliest memory from childhood, and invariable it seems to be of some injury or something scary that happened. ...
Anyway, it's nice to see/hear about the kids that are now "adults" and having their next part of their lives. ... Maybe if I stay in one school long enough, I'll have the kids of my current kids?! Yeesh. Or at my advanced years ... maybe I'd be in dentures and Depends by then and too old to terrorize the little kiddies any more.
Friday, September 25, 2009
"69"
Argh! The dreaded number for a high school teacher. And what is it, that if you just make a problem up on the fly ... out of the infinite possible results that could come out, THIS one does.
Anyway, at my "new" school (when will I stop starting a sentence with that?), the kids are pretty well-behaved, and I don't really have many situations where I either inwardly or outwardly roll my eyes at their adolescent-ness. In one class, I have some 2 girls that are classified for special ed because of learning disabilities. Once or twice in the past when I'm making up problems on the fly, to "engage" them more in the process, I ask generally, "what is your favorite number?", and the first one to call one out, gets that number in the current part of the problem. This one particular girl shouted out as her favorite number, "69" amongst the other one digit numbers I was hearing. I didn't make a big deal of it then and just moved on, but I thought at home about an effective way I could address it.
In the past it was boys that did it, and I would just roll my eyes in front of the class and say, "high school boys!" and move on. Here .... girl yelling out .... weird. I couldn't get a grasp on whether she was doing it for effect or if she actually knew what it meant or was just cognizent of the fact that it got a reaction. Anyhow ... it happened again today, and I was ready. I turned to her and said, "you need to stop calling out this number. You probably don't realize it, but you are making yourself out to be a person you REALLY don't want to be mistaken for." or something to that effect and moved on. ... Let's see if this works in the future.
Anyway, at my "new" school (when will I stop starting a sentence with that?), the kids are pretty well-behaved, and I don't really have many situations where I either inwardly or outwardly roll my eyes at their adolescent-ness. In one class, I have some 2 girls that are classified for special ed because of learning disabilities. Once or twice in the past when I'm making up problems on the fly, to "engage" them more in the process, I ask generally, "what is your favorite number?", and the first one to call one out, gets that number in the current part of the problem. This one particular girl shouted out as her favorite number, "69" amongst the other one digit numbers I was hearing. I didn't make a big deal of it then and just moved on, but I thought at home about an effective way I could address it.
In the past it was boys that did it, and I would just roll my eyes in front of the class and say, "high school boys!" and move on. Here .... girl yelling out .... weird. I couldn't get a grasp on whether she was doing it for effect or if she actually knew what it meant or was just cognizent of the fact that it got a reaction. Anyhow ... it happened again today, and I was ready. I turned to her and said, "you need to stop calling out this number. You probably don't realize it, but you are making yourself out to be a person you REALLY don't want to be mistaken for." or something to that effect and moved on. ... Let's see if this works in the future.
Sunday, September 20, 2009
New Kid on the Block
Blach! I think last Thursday and Friday were the 1st 2 days in a row that I had a completely good day. All the other days have been filled with either snippy looks from certain students because I dared move their seats, or second guessing myself because all the other teachers seem to be clicking and I'm not chatting with them, or rush rush rushing to get all my things ready to teach my 3 different preps and not feeling as prepared as I'd like to be and semi-winging it. And just general "blahness".
On Thursday I decided to kill my students with kindness. Instead of just scanning their homework for completeness, I wrote little notes on them ... something positive: "great work", "you really get it", "your handwriting is so neat and easy to read", that sort of thing. That was in my snippy student class with the seat changes. Well, miracle of miracles, we had a good day together. They actually worked and laughed at my lame jokes, and nary a snippy look passed.
Then another teacher sat down with me and we mapped out the algebra course we're teaching and that was good and I felt like I belonged. Then I actually had time to think things through about how I'd teach a concept (the dreaded "5-2(x-3)" type of situation where they DON'T want to distribute the negative (or subtraction) in front of the 2.
Then there was teenage girl drama on Friday, and I happened to walk in on it, and I think I was part of their solution. This was with a group of friends that were clashing, and some of the girls were my snippy students, so maybe we've made progress towards forming a better relationship.
So, WooHoo, I'm on the up part of the inevitable rollercoaster.
On Thursday I decided to kill my students with kindness. Instead of just scanning their homework for completeness, I wrote little notes on them ... something positive: "great work", "you really get it", "your handwriting is so neat and easy to read", that sort of thing. That was in my snippy student class with the seat changes. Well, miracle of miracles, we had a good day together. They actually worked and laughed at my lame jokes, and nary a snippy look passed.
Then another teacher sat down with me and we mapped out the algebra course we're teaching and that was good and I felt like I belonged. Then I actually had time to think things through about how I'd teach a concept (the dreaded "5-2(x-3)" type of situation where they DON'T want to distribute the negative (or subtraction) in front of the 2.
Then there was teenage girl drama on Friday, and I happened to walk in on it, and I think I was part of their solution. This was with a group of friends that were clashing, and some of the girls were my snippy students, so maybe we've made progress towards forming a better relationship.
So, WooHoo, I'm on the up part of the inevitable rollercoaster.
Tuesday, September 15, 2009
Absent Students on Test Day
I got my first taste on how things work at my new school in the cases where kids are absent on a test day. In my old school after I'd been there a while, I found what the culture of the school was and what it would take for the kids to finally make up a test (so that a week or so hasn't passed and they then finally meander in after school to make it up). I announced firmly at the start of school and frequently after that (right before test day) that if they were absent during a test, then I would put them in the hall the next class and they would finish/take the test. This stopped people from being spontaneously sick during test day. It also stopped people from taking forever and 2 days to make it up.
Well, at my new school, I just gave my first test. To be fair, a ton of kids have been out with the flu and such. So basically I had about 2 kids per class that missed a test over the span of 2 block days. Hmmm, I was told the kids were pretty good about coming in and being proactive about taking care of business. Supposedly, they were to come to me of their own initiative and make up the tests. Did not happen. Then the next class day I asked them separately when they could come in after school. Hmmm, mumble mumble. Still did not come in. Finally, I entered a 0 in the electronic gradebook for the absentees' test columns, and it brought their averages WAY down.
Our students and their parents have access to the gradebook. The advisory classes were also to check grades today. And magically, 3 students showed up after school today to make up their tests without any extra prompting from me. Coincidence? Well, either that, or I don't have to keep nagging. If they choose to keep the zero, okay. .... Well, what if later on after TOO much time passes, THEN they want to make it up. I guess I'll wait and see what happens to see if I'll change my strategy.
On another note. One of my classes was getting TOO chatty, and I was crabby in class because of it. New seating today. Poof! Quiet class (for now!) and poof poof: happy teacher that could actually crack some jokes because she wasn't monitoring their rude behavior. I even threw in some off-topic math that they actually found cool (who knew). I was making up problems and asking for numbers, at one point someone called "6". Then I had to say, "you know, 6 is a perfect number". Then went on to tell them what the definition of a perfect number is. Then shockingly (I guess it shouldn't be, but remember, this was my trouble class), they started to wonder out loud about other numbers and their perfectness. Ahhhh, I'll take this one bright spot with this class as it was our best time together since the start of school. Hopefully, it will happen more often.
Well, at my new school, I just gave my first test. To be fair, a ton of kids have been out with the flu and such. So basically I had about 2 kids per class that missed a test over the span of 2 block days. Hmmm, I was told the kids were pretty good about coming in and being proactive about taking care of business. Supposedly, they were to come to me of their own initiative and make up the tests. Did not happen. Then the next class day I asked them separately when they could come in after school. Hmmm, mumble mumble. Still did not come in. Finally, I entered a 0 in the electronic gradebook for the absentees' test columns, and it brought their averages WAY down.
Our students and their parents have access to the gradebook. The advisory classes were also to check grades today. And magically, 3 students showed up after school today to make up their tests without any extra prompting from me. Coincidence? Well, either that, or I don't have to keep nagging. If they choose to keep the zero, okay. .... Well, what if later on after TOO much time passes, THEN they want to make it up. I guess I'll wait and see what happens to see if I'll change my strategy.
On another note. One of my classes was getting TOO chatty, and I was crabby in class because of it. New seating today. Poof! Quiet class (for now!) and poof poof: happy teacher that could actually crack some jokes because she wasn't monitoring their rude behavior. I even threw in some off-topic math that they actually found cool (who knew). I was making up problems and asking for numbers, at one point someone called "6". Then I had to say, "you know, 6 is a perfect number". Then went on to tell them what the definition of a perfect number is. Then shockingly (I guess it shouldn't be, but remember, this was my trouble class), they started to wonder out loud about other numbers and their perfectness. Ahhhh, I'll take this one bright spot with this class as it was our best time together since the start of school. Hopefully, it will happen more often.
Friday, September 11, 2009
Algebra 1 Surprises
This is only the 2nd year I've taught algebra 1 as a one-year course (in New Jersey we had a slower paced 2 year course of which 1 taught the 1st year). Recently, some interesting things have come to my attention that I'll be aware of the next time I teach it.
We've just started "baby graphing" ... I give them an equation, and x values, and then they find the y values and plot the points. They're still at the stage where they don't know if they should connect the points or not. When I prompted them on a linear graph as to whether they should connect them or not, I got "yes because they go up at a constant rate" or "yes, they follow a pattern". We'll fix that later. But here are some more immediate things that I need to address.
On the 2nd day we were doing this, I then did NOT give them x values. Oh HOLD THE PHONE! What should we do???? Oh no!!! We got that straightened out with the "rule of thumb" (then I had to tell them the origin of that phrase). Then here's the problem, sometimes I had given them a preset grid, and OH NO, the points they chose did not fit. They didn't figure out that they could change the scale, or NOT plot that particular point. So ... new buggaboos that I'm learning to address in the course of this unit.
Then, here's the more interesting one. I saw with alarming frequency that apparently, 10 divided by 20 is 2. I know. Who knew?! Then I realized, they did not know that if they saw "10 div 20" (where the div is the division sign) that that was the same as 10/20 or 20 into 10 (under the long division symbol). They didn't know what went where.
And finally, I'll have to come up with a clever way to make stick that if you're given: y = -x^2, and you plug in x=3, then that's NOT (-3)(-3). or similarly, if you plug in x=-5, then that's not (--5)^2 or 25. I'm thinking "x box": put a box around the x physically and follow PEMDAS. ... Another teacher today said that a student of hers suggested, "oh! y=-x^2 can just be written as y = 0 - x^2". Then they would follow PEMDAS more easily. Maybe I should try that.
We've just started "baby graphing" ... I give them an equation, and x values, and then they find the y values and plot the points. They're still at the stage where they don't know if they should connect the points or not. When I prompted them on a linear graph as to whether they should connect them or not, I got "yes because they go up at a constant rate" or "yes, they follow a pattern". We'll fix that later. But here are some more immediate things that I need to address.
On the 2nd day we were doing this, I then did NOT give them x values. Oh HOLD THE PHONE! What should we do???? Oh no!!! We got that straightened out with the "rule of thumb" (then I had to tell them the origin of that phrase). Then here's the problem, sometimes I had given them a preset grid, and OH NO, the points they chose did not fit. They didn't figure out that they could change the scale, or NOT plot that particular point. So ... new buggaboos that I'm learning to address in the course of this unit.
Then, here's the more interesting one. I saw with alarming frequency that apparently, 10 divided by 20 is 2. I know. Who knew?! Then I realized, they did not know that if they saw "10 div 20" (where the div is the division sign) that that was the same as 10/20 or 20 into 10 (under the long division symbol). They didn't know what went where.
And finally, I'll have to come up with a clever way to make stick that if you're given: y = -x^2, and you plug in x=3, then that's NOT (-3)(-3). or similarly, if you plug in x=-5, then that's not (--5)^2 or 25. I'm thinking "x box": put a box around the x physically and follow PEMDAS. ... Another teacher today said that a student of hers suggested, "oh! y=-x^2 can just be written as y = 0 - x^2". Then they would follow PEMDAS more easily. Maybe I should try that.
Saturday, September 05, 2009
Sitting at Tables
This is the 1st time in my teaching career that the students sit 4 at a table. I've always had desks that have been arranged in groups of 4 (facing forward). Now the kids are 2 on each side facing each other, and the tables are angled towards the front, so that everyone can see the board.
Well, this past week I gave my 1st quizzes, and I was pondering what to do about wandering eyes. I didn't have enough time to make a big table divider, and doing nothing didn't sit well with me since I can't monitor all students at all times. So I remembered what I'd heard about manila folders propped up in front of each student.
I was passing out the folders to my 9th graders, and some of them started to act offended. I don't know if it was a show or real offense, but the comments were, "we haven't done this since the 6th grade", "this is so childish", etc. Hmph. I've SEEN 9th grade eyes wandering. I presented it as, "humor me. This is so I don't wrongly accuse you of cheating, and it makes me feel better." But seriously, the seats/papers are too close together to not have issues. I wonder what other people do? I guess I'll ask at my school.
Well, this past week I gave my 1st quizzes, and I was pondering what to do about wandering eyes. I didn't have enough time to make a big table divider, and doing nothing didn't sit well with me since I can't monitor all students at all times. So I remembered what I'd heard about manila folders propped up in front of each student.
I was passing out the folders to my 9th graders, and some of them started to act offended. I don't know if it was a show or real offense, but the comments were, "we haven't done this since the 6th grade", "this is so childish", etc. Hmph. I've SEEN 9th grade eyes wandering. I presented it as, "humor me. This is so I don't wrongly accuse you of cheating, and it makes me feel better." But seriously, the seats/papers are too close together to not have issues. I wonder what other people do? I guess I'll ask at my school.
Tuesday, September 01, 2009
Answer Banks
Still loving the new school, but not loving the last minute scrambling to get everything together. Guess I'll figure it out soon (or it will be June and a moot point). The school philosophy sort of discourages the use of textbooks for homework problems, and we're to create our own thing. I'm fine with that because mostly that's what I do, but this year with basically 3 classes to get materials ready for, it's a challenge.
Anyway, wa wa wa. What I am pleased about is how my algebra 1 homeworks are going. I know when I'm learning something new, I like to have immediate feedback on my correctness. At the same time, if I'm a high school student that may quickly look at the answer without struggling with the problem first, that wouldn't benefit me. Therefore, I've been giving about 10 problems per homework and then putting an extra box on the bottom of the sheet with all the answers in mixed order. So they have to do all problems and cross them all off and will know soon if something is amiss.
I had feedback today as I was handing out the next assignment. One girl looked at the sheet and whooped, "YES! Thank you for the answer bank!".
I guess for algebra (not the line graphing) it'll be pretty easy to keep this up, but the geometry ... hmmmm, will have to think about it.
Anyway, wa wa wa. What I am pleased about is how my algebra 1 homeworks are going. I know when I'm learning something new, I like to have immediate feedback on my correctness. At the same time, if I'm a high school student that may quickly look at the answer without struggling with the problem first, that wouldn't benefit me. Therefore, I've been giving about 10 problems per homework and then putting an extra box on the bottom of the sheet with all the answers in mixed order. So they have to do all problems and cross them all off and will know soon if something is amiss.
I had feedback today as I was handing out the next assignment. One girl looked at the sheet and whooped, "YES! Thank you for the answer bank!".
I guess for algebra (not the line graphing) it'll be pretty easy to keep this up, but the geometry ... hmmmm, will have to think about it.
Saturday, August 29, 2009
Psychology of Pricing
I had an epiphany the other day about how much each homework was worth. In our grading program we can assign different weights for different types of things: homework, tests, projects, etc. I have a totally independent category for homework and it was worth 25% of their total grade. Now since this is the only type of object in this category, it doesn't matter what each homework is worth if they're all worth the same: each 2 points, each 100 points, etc. It all comes out in the wash. My homeworks were worth 2 points each, and I deducted points (or partial points) as needed, so you could still earn 100% or 80% or so on on an assignment.
I don't know why the 2 points always worked for me. Maybe I fell prey to the psychology of pricing, too, and subconsciously I thought that tests were where you really showed your stuff, so those were worth 40 or 50 points or what have you, so the homeworks should be worth 2 points.
Anyway, at my new school, all the 9th grade classes have to have the same percentages: 45% homework/classwork and 55% tests/projects. There was some extra wording about deducting 5 points for various homework infractions, and so being new on the block and wanting to at least try things the way everyone else is doing them, I'm deciding this year to have each homework be worth 100 points. Again it shouldn't matter because it's in its own category.
So here was my epiphany. In my old school maybe part of the reason why kids were lacksadaisical about turning in their homework was because, "hey, it's only worth 2 points. no biggie if I don't turn it in." When in reality, it was a big deal because those 0's started to add up. I'm wondering if they would have had a different attitude if I'd assigned each homework 2000 points, just to mess with their minds or to get them to think about how the math all works out.
In other news, how's my new school going? Well, I think all the staff I've encountered have come from a different planet: the planet of graciousness and kindness and hard work. Oh my goodness, I can't tell you how many nice e-mails or cards or words I've gotten from other staff just to welcome me (and other new teachers, I'm sure) and check to see if I'm okay and to see if I have any questions or need anything. I'm so blessed this year. WootWoot.
I don't know why the 2 points always worked for me. Maybe I fell prey to the psychology of pricing, too, and subconsciously I thought that tests were where you really showed your stuff, so those were worth 40 or 50 points or what have you, so the homeworks should be worth 2 points.
Anyway, at my new school, all the 9th grade classes have to have the same percentages: 45% homework/classwork and 55% tests/projects. There was some extra wording about deducting 5 points for various homework infractions, and so being new on the block and wanting to at least try things the way everyone else is doing them, I'm deciding this year to have each homework be worth 100 points. Again it shouldn't matter because it's in its own category.
So here was my epiphany. In my old school maybe part of the reason why kids were lacksadaisical about turning in their homework was because, "hey, it's only worth 2 points. no biggie if I don't turn it in." When in reality, it was a big deal because those 0's started to add up. I'm wondering if they would have had a different attitude if I'd assigned each homework 2000 points, just to mess with their minds or to get them to think about how the math all works out.
In other news, how's my new school going? Well, I think all the staff I've encountered have come from a different planet: the planet of graciousness and kindness and hard work. Oh my goodness, I can't tell you how many nice e-mails or cards or words I've gotten from other staff just to welcome me (and other new teachers, I'm sure) and check to see if I'm okay and to see if I have any questions or need anything. I'm so blessed this year. WootWoot.
Saturday, August 22, 2009
Creating Your Own Thing
In this crazy week of prepping for the start of school, I've been in a few situations where I keep thinking about the book "Why We Teach", well really about one essay in particular. The teacher described her growing up years and the need for her to find her own voice and opinions. She got to the point where she didn't want to have a discussion with others or listen to other people's opinions on something before she had a chance to digest things and form her own opinion or method of doing something. Otherwise, she felt that she was just going along with the crowd or that her thoughts would either be stifled or not formed or swayed by what others thought.
So I periodically thought about this as I was coming up with a syllabus or a first day activity or how to decorate my room or procedures I want to put into place. Maybe it's not a "la la la la I don't hear you" type of situation where I think "it's my way or the highway, baby", but more of a reminder to think my own thoughts, then gather other opinions, then go back and reflect about how I think things should be done that carry my personality stamp.
Here's one new idea I'm trying, and who knows if it'll work. For the past many years I have taken a picture of each group of students on the 1st day of school and during that 1st class I had them fill out a seating chart AND print their names on a small sticky note. Then that 1st night I go print the pictures, and with double-sided tape I put their sticky notes on their picture. This helps me learn their names, and I also put all the pictures up in the room. They love to look at them at odd times during the semester.
Because I've seen that they SO love to go up and glance at all the pictures and discuss things and point certain things out (ooh, I just realized one reason why ... this helps them also to see who everyone is). Anyway, because of this, I'm going to ask them to bring in a favorite picture of themselves that 1st week (that I'll return to them later), and I'll use the awesome stikki clips to put them up as a border around either the blackboard or a bulletin board.
So I periodically thought about this as I was coming up with a syllabus or a first day activity or how to decorate my room or procedures I want to put into place. Maybe it's not a "la la la la I don't hear you" type of situation where I think "it's my way or the highway, baby", but more of a reminder to think my own thoughts, then gather other opinions, then go back and reflect about how I think things should be done that carry my personality stamp.
Here's one new idea I'm trying, and who knows if it'll work. For the past many years I have taken a picture of each group of students on the 1st day of school and during that 1st class I had them fill out a seating chart AND print their names on a small sticky note. Then that 1st night I go print the pictures, and with double-sided tape I put their sticky notes on their picture. This helps me learn their names, and I also put all the pictures up in the room. They love to look at them at odd times during the semester.
Because I've seen that they SO love to go up and glance at all the pictures and discuss things and point certain things out (ooh, I just realized one reason why ... this helps them also to see who everyone is). Anyway, because of this, I'm going to ask them to bring in a favorite picture of themselves that 1st week (that I'll return to them later), and I'll use the awesome stikki clips to put them up as a border around either the blackboard or a bulletin board.
Tuesday, August 18, 2009
New Toy
I was recently at training and learned about fun ways to present information such as:
A Movie I Made (I see a side job forming)
I could see it getting old, but it's a nice thing to throw in the mix.
I've also met amazing people at my new school. It's only been open for 2 years, so they're still inventing who they are and what they are capable of doing. They seem genuine and smart and committed. BUT.
Information Overload. I'm totally at the stage of, "I'll never remember to do all this", and "Argh, what if I screw up, and they secretly shake their heads at the mistake they made hiring me", and "Oh My GOD, I'll never be ready come Monday". You know, the usual jitters (and don't forget: they have only HOW MANY copiers? What, no work/eating/microwave room?, etc.)
I'm teaching 4 different preps this year ... well, 3.5 (one is a type of study hall). And I've agreed to be some sort of team leader and occasional yoga instructor. I must be woozy from lack of sleep. Must. Learn. To. Say. No. I practiced a bit today when an afternoon robotics team leader position presented itself: no. Whew! Go me. Baby steps.
A Movie I Made (I see a side job forming)
I could see it getting old, but it's a nice thing to throw in the mix.
I've also met amazing people at my new school. It's only been open for 2 years, so they're still inventing who they are and what they are capable of doing. They seem genuine and smart and committed. BUT.
Information Overload. I'm totally at the stage of, "I'll never remember to do all this", and "Argh, what if I screw up, and they secretly shake their heads at the mistake they made hiring me", and "Oh My GOD, I'll never be ready come Monday". You know, the usual jitters (and don't forget: they have only HOW MANY copiers? What, no work/eating/microwave room?, etc.)
I'm teaching 4 different preps this year ... well, 3.5 (one is a type of study hall). And I've agreed to be some sort of team leader and occasional yoga instructor. I must be woozy from lack of sleep. Must. Learn. To. Say. No. I practiced a bit today when an afternoon robotics team leader position presented itself: no. Whew! Go me. Baby steps.
Tuesday, August 04, 2009
Words to Ponder and Chew Over
I recently came across a chart that contained these comparisons, while I was searching various high school websites. (hmmm, the formatting is wonky, but ...)
Comparing Solution Building with Problem Solving
Solution Building vs. Problem Solving
Ooh, 7 makes me wince because in some of my classes, that's what I did sometimes. Off the top of my head: if students were having continual problems understanding, I would tell myself that I was ALWAYS available after school and they had every opportunity to come to tutoring. Yet every year, there are kids who for a variety of reasons don't come to tutoring and STILL fail to understand various topics. Maybe I need to enhance my toolbox of skills so that more kids understand more topics in class or have different avenues of seeking help other than coming to my tutoring.
Anyway, more stuff to reflect on.
Comparing Solution Building with Problem Solving
Solution Building vs. Problem Solving
1. "How did you do that?" vs. "Why did you do that?"
2. Focus on the future without the problem vs. Emphasis on past with the problem
3. Solution talk vs. Problem talk
4. Attention on what is working vs. Attention on what is wrong
5. Student is capable. vs. Student is flawed.
6. Teacher skilled at "not knowing." vs. Teacher is "all knowing."
7. If it works, do more of it. vs. Just keep using what you think should work until it, hopefully, does.
8. Change is inevitable. vs. People cannot change.
This resonated with me and it's been popping in and out of my mind for the last few days. If I scan down the list, this past year I could count 5 of the 8 where I was more focused on what was wrong at my school than just rotating my thinking and concentrating on what I could change or fix or be a part of making better.Ooh, 7 makes me wince because in some of my classes, that's what I did sometimes. Off the top of my head: if students were having continual problems understanding, I would tell myself that I was ALWAYS available after school and they had every opportunity to come to tutoring. Yet every year, there are kids who for a variety of reasons don't come to tutoring and STILL fail to understand various topics. Maybe I need to enhance my toolbox of skills so that more kids understand more topics in class or have different avenues of seeking help other than coming to my tutoring.
Anyway, more stuff to reflect on.
Wednesday, July 29, 2009
Learned & Reaffirmed Things
After a slew of math workshops all crammed together in one summer, I can generate a list of things I've either learned or relearned from my experiences:
1. Your math text is NOT your curriculum. Not for what you should teach, not for how you should teach, not for why you should teach something.
2. Every workshop seems to have the same set of characters (other than perfect people like me ... cough cough):
- the know-it-all that has to shout out all the answers quickly just to show they know things.
- the on-the-sly-constant texter
- the nary-a-peeper
- the challenged learner that asks TONS of questions
- the I-know-this-&-am-too-cool-to-REALLY-process-what-you're-saying person who will probably be unpleasantly surprised when they have to actually apply this current knowledge next year.
3. I'm set in my ways. Before my 1st out of town workshop, I was stressing, "oh no, I won't have my favorite tea, my vegetarian food, my own bed, ..." waa waa waa. I *mostly* had a change of attitude and used it as an opportunity to try new things ...... mostly.
4. I love my new school-provided laptop. When I was getting homesick, I could stream our local NPR station, and I could Skype my husband, and I could send e-mail and impatiently wait for replies to feel connected to friends.
5. "yelp.com" is a great new asset in my traveling life. I could just type in a city and "thai restaurant" or "breakfast" and get tons of opinions to scroll through to find places to go.
6. "mathforum.org" has a section called "math tools" and you can enter the subject you teach and the topic you're interested in, and it returns a list of resources for you to browse through to use: applets, calculator tasks, worksheets.
1. Your math text is NOT your curriculum. Not for what you should teach, not for how you should teach, not for why you should teach something.
2. Every workshop seems to have the same set of characters (other than perfect people like me ... cough cough):
- the know-it-all that has to shout out all the answers quickly just to show they know things.
- the on-the-sly-constant texter
- the nary-a-peeper
- the challenged learner that asks TONS of questions
- the I-know-this-&-am-too-cool-to-REALLY-process-what-you're-saying person who will probably be unpleasantly surprised when they have to actually apply this current knowledge next year.
3. I'm set in my ways. Before my 1st out of town workshop, I was stressing, "oh no, I won't have my favorite tea, my vegetarian food, my own bed, ..." waa waa waa. I *mostly* had a change of attitude and used it as an opportunity to try new things ...... mostly.
4. I love my new school-provided laptop. When I was getting homesick, I could stream our local NPR station, and I could Skype my husband, and I could send e-mail and impatiently wait for replies to feel connected to friends.
5. "yelp.com" is a great new asset in my traveling life. I could just type in a city and "thai restaurant" or "breakfast" and get tons of opinions to scroll through to find places to go.
6. "mathforum.org" has a section called "math tools" and you can enter the subject you teach and the topic you're interested in, and it returns a list of resources for you to browse through to use: applets, calculator tasks, worksheets.
Saturday, July 25, 2009
Even Better Calculator Trick
We explored a "different ways of payment" problem and learned a new calculator trick to boot. Suppose plan A gives you $20 the 1st day and increases your salary by $1 per day. Suppose plan B gives you $0.01 the 1st day and doubles your salary every day.
Calculator:
{1, 20, 0.01} (to represent 1st day, plan A, plan B)
ENTER
{ANS(1)+1,ANS(2)+1,ANS(3)*2}
ENTER, ENTER, ENTER, ..... to keep seeing current day, plan A, plan B updates.
Nice. And sandwiched between 2 nice pictures of a recent trip.
Tuesday, July 21, 2009
Ooh Cool Calculator Skill
Today at my math workshop, I learned some new-to-me calculator skills that I believe I'll use this year.
Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:
{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.
Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.
Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:
{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.
Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:
seq(x,x,1,100,1)--> L1
I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.
Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.
Let's say you want to compare 2 functions at various values. They don't need to be, but for ease sake here I'll assume the x values are integers, and the y values linear, say some geometric patterns where x represents the pattern number, and y represents the number of sides. In the main window type:
{1, 3, 7} and ENTER
This would mean: 1=1st pattern, 3=#sides for one shape in 1st pattern, and 7=#sides for 2nd shape in 1st pattern.
Then TYPE/GET
ANS + {1, 2, 6} and ENTER
This would mean you're adding 1 to the 1st number (1) in list, adding 2 to the 2nd number (3) in list, and adding 6 to the 3rd number (7) in list.
Now you can keep hitting ENTER, and you have a nice way of visualizing what pattern number you're at without keeping track of how many times you pushed ENTER, and what the 2 other functions are, so this list would look like:
{1,3,7}
{2,5,13}
{3,7,19}
{4,9,25}, etc.
Second skill: you know how sometimes you're populating L1 and L2 where L1 is just integers and L2 is some function of the integers? Well, in the past, I would just go to L1 and physically type in 1,2,3,4,5,... then type in the equation at the header of L2. Well. In your main window you can easily populate L1 by:
seq(x,x,1,100,1)--> L1
I guess it would only be quicker this way for large amounts of integers. "seq" is found under LIST>OPS.
The first value is your expression/function,
the 2nd value is the variable,
the 3rd value is where you want to start,
the 4th value is where you want to end, and
the 5th value is what you want to increment the input by.
Now the ironic thing would be if I "learned" this in the past, and just don't remember it because I haven't used it.
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