Real-Life Problem

Ms. Cookie conscientiously deletes ALL memory from her calculators: RAM, ROM, RIM, ROOM, and all the excellent APPS on the "school bus yellows" for the TAKS test. Ms. Cookie saved one calculator to the side and kept the programs/APPS on there. Ms. Cookie now wants to repopulate the other calculators. Once she does one, then she has 2, then 4, etc. Each repopulation takes 12 minutes (!!!! who knew!!!!). How long will it take her to "fix" all 74 calculators?

Culturally/Gender Biased Test Questions

We were practicing problems for our TAKS test, and 2 funny incidents came up.

First problem: a baseball diamond has 60 feet between the bases. How far is it from home plate to 2nd base?

Some of the girls in my class indicated that they did not know what a baseball diamond looked like. Now we were working on the Pythagorean Theorem, so it had to be a square ... but they didn't know the layout of the bases. We discussed it. Then, being a good teacher (cough), I wanted to link it to something, so I asked if they'd heard about boys getting to 1st base, etc. But I digress; the point is that if we hadn't happened upon this practice problem, and they got it on their exam, they may get it wrong not for not knowing the math, but for not knowing baseball.

Second problem: What information do you need to figure out to know how much material is needed for a basketball? (surface area? volume? ....)

I thought this was obvious (surface area), but then a child asked me why it wasn't volume. I started to explain, and then she said, "oh! there's no stuffing inside?" I'd never thought of that, and explained that it was just air inside. Then I thought about it. There are sports balls that have stuffing inside (baseballs, softballs, ...). We could think of 3 more in addition to those 2 when we brainstormed. Anyway, ARGH sports problems and non-sports people!

TAKS helpful hints

And so starts the crazy TAKS week. I made up a sheet for my 9th graders and printed it on pretty paper and discusses each tip with them. So in addition to doing algebra/TAKS practice MTW, we will talk about calculator skills, and these test taking skills. And we will cross our fingers that everything will be okay.

One student shared with me that someone at church had walked up front and was in tears (a junior) and asked people to pray for her because this week she was taking her math TAKS. Oh my goodness, what have we come to with all this testing stress.

Anyway, here's what I handed out (on a 1/2 sheet front and back):

Movies & Teacher Talk

I went to see "City Island" with my teacher friend today - my teacher friend that still works at my old "crazy" school. Loved the movie, loved spending time with my friend. She said something that resonated with me, "sometimes I just want to go do some volunteer work or something in another country with school children who still actually appreciate their education so that I don't get too far gone and cynical about the state of things."

She's dealing with kids that:
* just come to her class because it's a part of their probation,
* come to class and don't do anything but still expect to pass,
* don't show up on the day of their oral exam for no good reason and then expect to have time to do it again at their convenience.

I wonder if there are summer programs for teachers like this - 1-3 week programs where you can travel and volunteer and do something nice/beneficial for others in this "school" way and not have it be too much of a drain on your wallet. Maybe we should come up with something - the power of teachers.

Also, I'm wondering (and worrying) about Mrs. H and hope she's okay and just taking a blog break.

Perceptions and Circles

I started to "do the math" and it basically seems that barring tests and tests and finals and reviews and other-time-vacuums, I have basically 5 or so block days left of teaching each class. Panic!

In other news I had an interesting conversation with another math teacher in the copy room today. Unlike the other 2 schools I've taught in, at my current school, everyone is expected to go above and beyond, and it's just an ordinary thing and possibly commented on in some way if you don't ... or maybe that's just our new teacher perspective of things. Anyway, we were discussing the results of the math 8th grade TAKS scores .... that were phenomenal .... for any other school, but since they were not 100% passing, there's an undercurrent of "why not?". Yeesh, the pressure.

So our conversation took the turn of her saying, "I can't wait until summer; I'm so exhausted." .... and, "I always walk around, and it seems everyone else has their act together, and I'm scrambling to keep up". I could contribute that I don't think everyone DOES have their act together, they're just putting on a great facade and doing the best they can (based on other conversations I've had). That got me to thinking. We make these judgment calls based on our insecurity of how we're performing by looking at others, and if they look calm or "with it", maybe we think, "ackh ... I need to work harder ... why don't I have things done and planned and thought out yesterday?". Anyway .... maybe a reason to get out and talk to more teachers in depth instead of just surface, "hello, how's it going" conversations.

Finally, we started circles today in geometry. We barely scratched the surface, and again I didn't want them to copy definitions, so I did the matching game again. My twist this time was that I did a search on the internet, and found a cool website that showed me how to make envelopes that don't use glue. So I had the kids make them out of pretty paper, and they could store their cut out matching cards there (also on pretty paper) ... AND they could write the key on the back of the envelope. Nice.

Quadratic Formula

It's that time of the year in algebra, and I'm processing the right sequence that works for me on how to teach this. I have block classes, and even though that seems like, "whoa! 1.5 hours! You can cover HEAPS." It turns out that this is still a multiday process for me. Here's what I've done so far and where I'm going.

Previously on As the Algebra Turns:
Quadratics bla bla bla
Factoring bla bla bla
Finding Zeros of Quadratics by factoring
Linking Zeros of equations to graphs of parabolas.
TEST on some stuff

START of our Program:
Day 1: start the class with reviewing one problem of finding zeros by factoring and link it to the graph. Start them on the 2nd problem of trying to find the zero by factoring, and BOOM, falls apart. Ask them if they think this means it DOESN'T cross the x axis. Show them it does but the numbers aren't "nice". Show them a slow step by step process of how to use the never-fail quadratic formula to solve. Have time for 1 "nice" problem.
HWK: can't involve simplifying of radicals (haven't done that yet). Can't have the equation in a weird form yet ... must be in ax^2+bx+c=0 form.

Day 2: now they have a reason for simplifying of radicals. Spend most of the period on simplifying (just the stuff they need for the quadratic formula). Then have time for one quadratic formula problem where they solve AND simplify. I also threw in a problem to solve that looked like: ax^2 + c = bx to get them used to this.
HWK: mixed radical problems (some with and without denominators) and some quadratic formula problems.

This is where I am so far.

Now I'm thinking, they need practice of both radicals and more quadratic formula. I still want to link it to the graph. I'd like to throw in some word problems. I'm probably forgetting something, but that seems about it. So, sheesh, 4 block days on this. Why am I stressing about that? Better to do it well than just to rush through it. .... I guess I'm stressing because I still have/want to cover: more radicals (adding multiplying...), Pythagorean theorem use of radicals and to refresh their memory, midpoint and distance formulas .... more geometry and radicals. Will I have time for rational expressions?

Stay Tuned for the Next Episode.

Quadratics Review

Woot Woot! Our school participated in a 10K today (which I think of as a 10K+ since we walked to and from our bus to the race place), and I actually ran/walked the whole thing. Oh yea! I think I'm hooked now. It was fun with the bands along the way and the various people cheering us on from the side lines. It was my 1st race, and here were my fears before hand: oh no! I'll get trampled by the faster people at the start of the race, and it'll be a tragedy reported on the news. or... oh no! I'll be so slow that there won't be any other runners in sight, so I won't know the route and I'll veer off the course and get lost. or ... oh no! what about bathroom issues? or ... oh no! my pasty white chubby legs will blind the other runners and there'll be another tragic accident from the glare that will be reported on the news. It turned out that there were runners of all shapes and sizes and ages, and I am now home safe, and if anyone was blinded from the glare, I didn't hear any cries of agony. I think of a phrase I read on another blog (crazyauntpurl? or yarnharlot?) that my "deficiencies" will make others feel better about themselves ... it's just a small service I provide to the world.

Anyway, in algebra we (and by we, you know who I mean) will have a test this week on our beginnings of quadratics, so I've created this self-checking review sheet for the kiddies that I like. Once again, the box.net preview looks wonky, but it should download nicely. Also, the "English" of the sentence is probably cringe-worthy, but I didn't want to keep using the same words over again.

EDITED LATER: no matter HOW many times I checked this sheet, there apparently was still a mistake (which is now fixed on box.net). In the answer bank, the "-4x^6" should be "-4y^6". Thank you to a student with eagle eyes.

Great Intentions, Bad Execution

As with probably most school districts we have a dress code policy (though at the other school I worked at it didn't prevent me from having to see massive cleavage and feel uncomfortable about saying something). But maybe unlike many schools, at my current school, it's mostly enforced. Today I noticed a girl without shoes in my 1st period. I asked her what was up and where were her shoes and "put on your shoes". This was sort of a "drive by" on my part because I didn't expect any grief from her.

I started class, and then noticed a while later she still didn't have on her shoes, so I was more firm with "put on your shoes". "No," she said. Ding, ding, ding, warning bells. The whole class (in my memory) quiets down to see what'll happen. I stared at her wide-eyed in disbelief and asked her to step outside, which she did. I got the class to continue moving on with their work (the thrilling quest of finding zeros of quadratics, ooh, aah), and went in the hall to "discuss".

I asked her what was wrong and why she wasn't putting on her shoes and waited. I got no sensible response. I said that her options were to put on her shoes or to go to the office, and I asked her what her decision was. She opted for the office. This was at the beginning of a 1.5 hour block class. Then I had to simultaneously teach and figure out how to get word to the office without a disruption. I sent e-mail, and thankfully (I LOVE my administration this year!), I got an immediate response that it was being dealt with.

In the last 10 minutes of class, the administrator came back with the girl, and I found out what's what. Apparently, it's "A Day Without Shoes", and this girl was participating. Did she ask me? Did she explain to me? Did she have documentation about this? No. She waited all the way (even with the administrator) until she was facing suspension for insubordination before she explained in tears what she was doing.

Oh my goodness, 14 year old minds and their logic/decision-making-skills, etc.

PSA project idea

In our city once a year about this time, the art of the students from our school district is displayed in a building downtown. Apparently, the people that work in that building say it's something they look forward to every year. All grades from K-12 are showcased. I went to see it last Friday and was inspired by all the creativity. I'm even thinking of taking some art classes this summer.

There were all sorts of techniques, and being an art know-nothing, I don't know (shocking) the names of the styles. But. There were things made with aluminum foil and blackened; there were things painted on cloth. There were pictures and then an overlay of an overhead slide with another component to the drawing. Very fun to browse. One technique intrigued me, so I thought maybe I could incorporate it into a project for my kids.

They could create a PSA (public service announcement) for some things you never want to do in math or always want to do in math. For example, (x + 3)^2 = x^2 + 9 OBVIOUSLY in many of my students' minds. My thinking is that if they spend time making the PSA, and they're hanging up around the room and other students look at them, then maybe the correct thing to do will be triggered in their minds when they need to use/perform the math task.

Anyway, I made a mock up of an example today. I guess I'll think through the specs and see if it's something feasible.

Factoring Trick

I don't know if I mentioned this before last year when I taught algebra 1, but it worked so well this year, that I have factoring geniuses in class - even kids who have trouble elsewhere.

We just finished learning how to factor trinomials of the form axx + bx + c where a is not 1. My retired math teacher friend had taught me this trick (over chips and salsa and margaritas last year), and I tried it out with my class. I had to first prep the period with the following statements:

* I'm going to show you a trick today that's going to be your new BFF in math.
* First I'll predict how the class will go.
* You'll take notes on the process while we slowly go through it with an example and you take notes carefully like you're taking them for your best friend who's absent.
* You'll whine and say, "I'll NEVER like/use this trick. It'll NEVER be my BFF".
* After the 2nd problem you'll say, "okay, it's not so bad. I can be in the same room with this trick."
* After the third problem, you'll quietly wait for the 4th after you finish this current one a little faster.
* After the 4th problem, you'll be ready to marry this trick. Your NEW BFF.

We laughed and got down to business. And yes, I had to make fun of them for each of my predictions coming true. And yes, 2 or 3 classes later, when I came back to this kind of factoring, they almost all of them remembered it.

Miscommunication

Wednesday in algebra 1 we were exploring parabolas on the calculator. We're just getting into our groove with the calculators, and I'm slowly trying to introduce more capabilities of it. The question was, "when does the rocket reach 528 feet", and after we'd graphed the equation, I was showing them how they can put y2=528 and then find the intersection with the original rocket equation.

I tell them to press 2nd TRACE (though I always say, 2nd calculate, ... whatever), and go on to show them the intersect capability. Many kids ooh and aah, and move on to the next question.

One girl calls me over, "it doesn't work", and she's all frustrated and pushing 2nd and TRACE over and over. I walk up behind her and ask her to do what she's doing slowly. Then I couldn't help myself, I laughed. She was pushing down on the "2nd" button with all her might and annoyance and holding her finger there in the down position while simultaneously then pushing the TRACE button.

I'd never come across this before, but now that I think about it, why not? Never have I said, "push 2nd and release and THEN push TRACE". Aaaaaaah, good times.

Prisms & Polyhedrons

We started out unit on polyhedrons this week, and are learning first about volumes and surface areas of prisms. I know they've worked out volume and surface area with a vengeance in middle school, but I know they didn't do the "hard" problems. With all this in mind, I started with the information that is shown in "Discovering Geometry" about how the lattices of different substances that are made up of the same elements (carbon) can have way different properties (diamonds vs. graphite), and can behave counter intuitively (water expands when frozen and other things don't).

Then, instead of giving them definition upon definition to copy down (edge, vertex, lateral face...), I handed them 2 blue sheets, and we had a race of cutting out the squares (otherwise, la la la, I'll take my own sweet time to trim VERY neatly and NEVER get done). Then they had to match the cards. I didn't answer any questions (what's oblique mean?), and just said that they should use process of elimination. And, "why are there more than one hexagonal prism cards?" .... you'll figure it out. Here are the sheets. (note: for some reason, the "preview" on box.net comes out all wonky formatted, but it downloads nicely. I'm not sure why that happens.)





At the end, I gave them a key and let them keep these to put in a plastic baggy. I plan to do the same with pyramids, cones, cylinders, on different color paper. I also made sure we had a discussion about correctly describing right and oblique prisms.

Ways of Asking For Things

A student came in after school concerned about her algebra 1 grade. This 6 weeks, she was absent for maybe 2 days in one stretch, and then she basically never got back up to speed turning her in stuff (in any of her classes). Then, thank goodness for good parenting, she's now concerned about her grade because her birthday is coming up soon, and if her grades are stinky, well mom won't be too much in the birthday mood.

So I love how she tried to turn in some late work. First of all, she turned it in during class a while ago claiming it was absent work - about 3 week old work, so I gave it back to her and said it was too late (as is our school policy) (thank you sane administrators). Then she tried to turn in stuff after school today. Hmmmm, one had 2 problems out of 8 done, and another had 6 out of 8 done. She tried to do the "air quotes" thing with me claiming that she'd tried to turn them in earlier, but I wouldn't accept them so they were "air quotes" too late "air quotes".

Now I just have to laugh. I asked her why she hadn't done the work. "Well I didn't get it, so I thought I'd just turn it in for some credit (2 of 8 problems)". Then I asked why she hadn't come for tutoring. "Well .... excuse, excuse, excuse". Then I quickly disabused her of her air quotes and said, "hopefully you'll be in school for another 7 years (she's a freshman), and you'll have many teachers. Most likely when you're asking them for a favor, it probably won't do too well if you just come with an attitude, and ESPECIALLY if it looks like you're not even interested in learning the material. A better thing would be to say, 'well, it may be too late to turn this in, but can I still have help on knowing how it's done, and I can practice'".

So somehow, magically she could stay for tutoring on the spot, and we worked through some of the problems. She was a quick learner and showed improvement. Her funny statement then was, "why do I get it when I'm working here with you (she's NEVER been to tutoring), and I can't get it at home?". I asked if she was distracted at home when she was doing her homework. BINGO. "Well, I guess so, but don't tell my mom." We discussed that math was hard, and you had to think about things as you were doing them, and not just half pay attention to your homework.

Maybe she's seen a wee bit of light? Or .... most likely, this is the upswing of the see-saw that is a teenager's personality .... and her birthday incentive will be gone soon. ... I'll take what I can get.

Spring Break Almost Over

I remember how in the past someone had mentioned to me, "Students like routine. They want to have a sense of comfort of what to expect and such." I don't remember the context of the conversation, but I was thinking about it over break. I apparently like routine, too.

Break's all well and good - I slept about 8 or 9 hours every night, delicious; I got to go to bookstores during the day and browse and come upon great new books to read (hello, "Little Bee"). I went rollerblading 3 times in the afternoons (goodbye fish-white pallor ... almost), etc. But. I miss my routines. I missed my 2 favorite yoga classes for various reasons; tap dance class follows the school schedule, so it was canceled. I didn't run at 5am MWF, well, because, who in their right mind would get up at 5am if they didn't have to, I miss my Thursday morning treat of having breakfast out at a 24-hour diner before school and reading the paper and doing the puzzles. I miss the free exercise of being on the go all day and not having easy access to my refrigerator (hello tighter pants).

Waa waa waa. All that is to say, that though I won't like the stress, I'll be happy to go back on Monday and get back to my well-tuned-and-familiar routine. Then pretty soon I can start my finger countdown of weeks until summer .... and then I have to find other ways to resist the fridge and the sitting all day.

Differentiation Chapter 2

A key point of chapter 2 of the differentiation book I'm reading is that you can differentiate in one of 3 areas:
* content
* process
* product

Her examples are not from math classes (wait! there's one at the end of the chapter), so I have to brainstorm about how to differentiate content. Let's say I'm teaching solving inequalities in 2 variables. Maybe a content differentiation would be to have separate groups of kids: one with basic line inequalities (y=mx+b set-up), one with point-slope inequalities, and one with standard, point-slope, and basic all mixed. Or maybe a group with line equations given where there is some thinking involved to graph the line (the y-intercept is not an integer, or the "easy" point is off the grid I've given them). So then my thinking goes to: when do I separate them into groups? At the outset? After my initial spiel? After a day together? How do I gather them back at the end of class and make sure they learned? Do they have an opportunity to advance to another level if they mastered the basic ones? Is there enough time, or will we move on to the next topic?

Continuing on with the same example for process differentiation: this would be how they're originally learning the information (among other things). Maybe they could listen to me speak, or separate off and learn from the book, or maybe I have a sheet pre-typed out that goes through the process and prompts them to learn the concept.

For the product differentiation: hmmm, this always smacks of "project" to me, and I know it shouldn't. If I get away from a paper and pencil test, how will I allot the time to assess them orally or in other ways? How will I stop from giving them hints either with my body language or with actual words? How do I know they really know the material?

She does discuss starting your differentiating small and adding to your bag of tricks each year.

The Book...

Ode to Freshman Test Takers

Nine Questions. Blank blank blank blank, scribble times four, blank. Partial credit does not compute.

Let me practice writing my name. All over the paper. Curly, squirrely, poorly Q's. First and last name. Oops, ran out of time to complete many problems.

Week-long note on the board: TEST! solving by elimination, solving systems of inequalities, graphing inequalities in two variables. This was not code for DON'T STUDY.

Earnest note at the bottom of a half blank test, "do not understand this part. will come in for tutoring on Friday."

Many practice problems involved integers. Or. GASP. Minor fractions. One Half. GASP GASP. Negative one half.

Thus, my befuddlement at your "23/67" for an answer. And your gumption at following through and plugging in to get y - 2 and 17/93. Yay. Boo. Joy and Sorrow.

Checking Your Answer. Outrageous. Don't Fall For It. She's Tricking You Into Doing Needless Work. Mwa ha ha, Teacher Lady. I will NOT be fooled!

Blank Math Joke Sheet

I started thinking that is would be convenient to have some blank "joke sheets" ready to make a quick practice assignments for various math skills. I took my last geometry sheet and reworked it so that it's ready for a quick altering. In this one, I guess I'd have to find 12 problems that each have 2 parts, or I ask 2 different things, since there's an a and a b component. I guess I could easily rework it to make 24 problems, but I would have to reformat it. Let's see if it works.

Here's the downloadable version. And here's what it looks like:

Grading Projects

Some things I've come away with on my geometry project:

* Even if you don't get around to grading them immediately (say in a week or so), glance through them all and count them. If any students haven't turned the project in, notify them and their parents. I had one child inSIST she turned it in 1 day late in my mailbox - swearing up and down to her parents. I never saw the project. Luckily, the parents were supportive, and the child is turning it in WAY late, but turning it in .... well I say that, it's supposed to be tomorrow. We'll see.

* I like the "wow factor" component. I purposely left it vague, and just said, "wow me", and not everyone, but MANY students went beyond what I would have imagined.

* Put EVERY child's poster up if you're going to hang them .... and don't put them up in waves, do it all at once, or you'll hear about it.

* Don't assume they know how to draw "tilted rectangles" on a coordinate plane. Some just eyeballed the 90 degree angle, and didn't use slopes to force the 90 degrees.

Other than that .... spring break after tomorrow. Woo HOOOOOO. Sleep at last and movies and books and more sleep. I've also assigned a "castle project" to my IED (engineering class), and I have to build my castle on the Inventor program over break since I told them I'd do the project with them. ... Just got home from "Alice in Wonderland". Phenomenal. The creativity of people is very inspiring. It makes me want to go meditate and ponder on doing all sorts of fantastic things. The sky is apparently not the limit.

System of Inequalities

We just finished our unit on inequalities, and my students have a test next class. I'm thinking of putting the following question on it to gauge their understanding of what the solution graph really indicates. (sorry can't figure out a nice way to embed the document directly onto this page ... does anyone have a tried and true method?)

LATER: Thanks to a wonderful commenter, I learned a new skill of "screen shots" (after I asked him how to do it ... and then thought of "Google University"):

Special Triangles

We are just finishing up trigonometry and special triangles in geometry and moving on to areas, but as with all skills, they need to revisit the topic a few times. Here's a sheet I made up that I'll be giving my students next week.

EDITED LATER TO ADD: Well, after I made the sheet, I thought about how much I like the puzzle sheets with answer banks, so I improved it to make the following puzzle geometry sheet.