Complex Fractions in Algebra 2

I just came up with this warm up to spice up my lesson on simplifying complex fractions:


Suppose a mother and daughter decide to make a pie. 

(a)   A pecan pie to be specific.  The slave over it all day, and they are so engrossed by their pie baking that they forget to eat.  By the time the pie is ready, they’re both starving.  Suppose the mom eats twice as much as her daughter.  They’re both so hungry that they eat the whole pie.  There is 1 pie to be divided by 1 adult appetite and the little girl has ½ of an adult appetite. 


      (1)     Write a fraction that represents this situation
      (2)       How much of the pie will the mom get?  How much of the pie will the little girl get?

(b)  On another day, the mother daughter pair make an apple pie.  The father LOVES apple pie.  He comes home and shares in the eating with his wife and daughter.  So now there’s 1 pie, 2 adult appetites and a ½ an adult appetite.


   (1)       Write a fraction that represents this situation
   (2)       How much of the pie will the mom get?  How much will the dad get?  How much will the little girl get?

(c)   The mom and the dad have decided to have another baby.  This time, it’s a baby boy.  The baby boy also loves pie, but because he’s growing, the fraction of the pie that he can eat keeps changing, so let’s just let the fraction that he can eat be represented by 1/x.  The mom and the daughter again go back to pie baking and one day, they make a blueberry pie.  All four family members split the pie to match their appetites.


        (1)      Write a fraction that represents this situation
        (2)        Write an expression for how many pieces they’ll need to cut the pie into.

I like this warm up in that I think it shows pretty clearly why we would want to simplify complex fractions, but I'm thinking that it's going to be pretty time consuming, and won't even begin to address how to simplify complex fractions.  I so badly want to show students the why of math, but the how of math is all we have time for and that's what they're tested on.  


Note: I know this problem is a little sexist.  I thought I could insert students actual names when it came to teaching this so that it's not so blatantly- mom and daughter bake while father and son eat.

Passing Algebra 2

I spent last evening talking with a school counselor at a party.  She works at the big, over crowded public school nearby and she mentioned a few things I found incredibly interesting.

(1) Despite the fact that they laid off about a third of their staff last year, and they started school this year with 45 students to a class, there are going to be more cut backs for next year and she's not sure she'll still have a job.  Though she's a part time counselor, they have assigned 200 students to her, requiring her to work more than full time hours.  If she gets let go, the "full time" counselors will have maybe 500 students each?  Maybe more?

(2) The state of Oregon has changed its standards for this year. (I knew this already.  They took 4 or 5 simple standards for each high school class and ballooned them into hundreds.)  These standards will require all high schoolers to complete three years of math above algebra 1.  I'm not in opposition to students learning more math at all, so I hadn't thought too much about this requirement, but the counselor I was speaking to last night said that a huge percentage of students this year at her school (I think she said 50% of those enrolled in Alg 2 but I'm not sure, surely it can't be that high) failed the first semester of algebra 2.  This means that they can't progress to the second semester of algebra 2 and for now, her job is to look around and find easy online classes that will get them that half credit.  That's her fix for now.  Next year, once these new standards take effect, these students will have no recourse.  They will have to take algebra 2, but at this school, many of the students taking algebra 2 are seniors and they won't get another chance to retake it.  So I asked her if they can take an extra year to graduate and she said that 5th year seniors aren't allowed back.  They have to go to am alternative school to finish up their final year.

The big question that was rocketing around my head was "what's the point?"  What was our goal in creating this new standard?  The rationale must have gone something like this:

"Our students are constantly under-performing on their math standardized tests, what should we do?  We look bad compared to other states."

"Let's make the math requirement in high school more extensive.  If we require students to take more math classes, surely they'll learn more math and do better on tests."

But at least in this one public school, according to this counselor, the new math standard will leave a lot of students without what they need to graduate, so a lot of them probably won't.  Is the purpose of the standard to weed out the "bad" math students and to deny them any chance at graduation?  Shouldn't we ask ourselves what's wrong with the elementary and middle school math programs if high school students can't pass state math tests?  I asked her why students were failing in algebra 2 and not earlier on.  She said the students for the most part could scrape through algebra and geometry  with Ds, but then couldn't pull it off for algebra 2.  Why would they even let a kid who'd gotten Ds in both algebra and geometry into algebra 2?  Isn't that a bit of a red flag right there?  It just all seems so broken.  And it seems like a lot of kids are getting really hurt by the way this system is run.  Why can't we let them into consumer math, or math for future carpenters or something?  What's wrong with taking a math class targeted to the careers students may pursue later in life?  Does every kid need algebra 2?  Or rather, should passing algebra 2 be what determines whether or not they graduate?

(3) The third interesting thing from this conversation was her description of one algebra 2 teacher's methods. One algebra 2 teacher in the school requires that all her students pass each section of her tests.  If they fail a section- even if they got a passing grade on the test, she refuses to enter it into their grade and they have to redo that section.  If even one section is left as a fail, she refuses to give them a grade for the class until they have shown they mastered that material.  I thought this was kind of awesome because it's letting students slide by with a half-baked understanding of the material that leads them to fail as soon as real understanding is demanded of them.  This teacher makes sure that every student who passes her class knows all the material the course covered.  The counselor though, had a different take.  She said that she got 3 or 4 phone calls each week from desperate parents begging for their students just to be given a C and moved on.  Why are they desperate?  Because their student needs that credit to graduate.  All they care about is the credit and ultimately, the diploma.  So when we make these kinds of math standards- what are we doing to parents and students?  Are we really just teaching more math?

Exponent Rules Unit

I feel like getting up onto my little soap box. I don't know how justified my strong views of this subject are because I haven't ever talked to other math teachers about this, but in my limited experience I feel like my views are reasonable and therefore my rant will have some bearing on reality, maybe?  Exponents.  I love them.  But when I first came to work at my current school, none of my high schoolers knew their exponent rules.  I figured maybe we could just pick them up as we stumbled our way through algebra 2, pre-calculus and calculus.  Boy was I wrong.  Exponent rules came up all the time, in almost every topic we studied, and I tried to show the students how to use them because to me, they're pretty easy.  If you expand the expressions, the rules just become clear.  But the students forgot the rules, mixed them up, could never remember what a negative or rational exponent meant and for the life of me I couldn't get them to think about why the rules existed.  They would not simply expand the exponent and play with the expression until it simplified itself.  So when exponents came up in our pre-algebra textbook I was thrilled.  A chance to nip this problem in the bud.  If I could really rock exponents in pre-algebra, my students would not have these difficulties as they moved up through the classes.  So I threw myself into planning the perfect exponent unit.

The interesting thing is that I couldn't find exponent rules on our state standards, nor really in other pre-algebra textbooks, and I was having a lot of trouble finding resources online.  When a lot of people cover them, they cover them all at once: here's this list of 8 different rules to memorize.  A lot of the resources out there did show demonstrations of why the rules work, but I kept feeling like I didn't just want to give my students the rules because they would only remember the rules, not the proofs. My high schoolers love rules.  They love being able to just plug something in.  The problem is that there are too many rules and they were mixing them all up and they didn't really care that they mixed them up.  They had an answer that they got with a rule- presto- math is done!

I  feel that teaching the exponent rules slowly and well in pre-algebra is a bridge to successful math in high school.  We do this unit right after a basic algebra unit so it's a nice way to apply some of the skills they learned in algebra.  Teaching them the proofs of the rules is a nice way to show them how math is built on a logical, proof based system where everything has a reason and we need to seek out that reason to fully understand the math.  It cements their understanding of negative numbers because we have to play with negative exponents.  And finally, they learn the exponent rules which in my experience are really REALLY important for success in high school math.  This unit should do everything a math unit is supposed to do- draw in a ton of prior knowledge and show students how that stuff we studied before was useful, show them the logical foundations of math, and give them something new and cool to play with.  So why did there seem to be so little emphasis on exponent rules in state standards and textbooks (except for our book of course, impact mathematics, which is awesome but really hard to teach from).  Maybe it's just Oregon that doesn't give these rules the respect due to them?

Anyway, I'd like to share some of the stuff I've come up with to teach this unit.  This is my third time through and I think I'm getting better, but I'm still not satisfied that I have achieved my goals of the perfect exponent unit (I know its not possible, but I still want to rock it.  That is my ultimate goal.)  First of all, here's the document I drew up to help the students explore all the different rules: Exponent Rules Proof Worksheets

We do one of these a day.  I have different ways of presenting these to the students.  Sometimes I had them pair up and work through the sheet, sometimes I had them do it silently and alone, then pair up to compare answers.  Sometimes I timed them and gave them 1 minute to fill out a column, then they switched partners and had another minute to do the next column.  When they finished they cut out the box and taped it into their notebooks.  I think the students enjoyed it, and the best part was the sense of excitement I felt around the room as they discussed what was going to happen.  They seemed to enjoy the process of creating these rules for themselves.  After we do one of these worksheets, we discuss the rule, run through examples, then I give them practice problems from the book.  This is the lamer part of the unit, but they do need to just practice it right?

I have another few documents to share.  Before they start work on the quotient rules, I give them this worksheet I made to introduce canceling.  It follows a discussion we have as a class as to why we can say 1/2 is the same as 2/4 or as 3/6.  I keep pushing them until someone says that they're the same because we're multiplying by 1 and multiplying by 1 doesn't change a number.  Then it's pretty easy to show them how canceling works once they've made that connection.

Here's the canceling worksheet: Canceling Worksheet

As they add more rules on, the students tend to start mixing them up, so I've made a few games to try to help them practice using the different rules and practice combining them.  The first one is a simple karuta (this is the Japanese name, I don't know an English name) game. The students group into 3s or 4s and each group gets a deck of cards.  First, they need to just pair the answers to the questions, and we can discuss the harder problems.  Then they put the question cards to the side and spread the answer cards in front of them.  I put a problem up on the board and the first student to grab the correct answer card gets to keep it.  The person with the most cards at the end wins.  We then play again, but this time with the question cards.  I write the answer on the board and they have to find the question that matches it.

 Here are the game cards: Exponent Rules Karuta

This is a game I thought the students wouldn't like that much, but I thought it could be good at helping them analyze each others mistakes and pick out common mistakes.  I called it the Power Rangers game because I do it right after they learn the power rule.  Surprisingly, the kids LOVED it.  Every day they ask if they can play it again.  Maybe they liked it so much because I did play the intro song of the power rangers TV show before we played.  I had them form groups of 3.  Then of those three, one had to be a power ranger.  The power rangers came to the front and practiced some exponent problems.  In the meantime, the group members left behind were the evil nemeses of the power rangers.  Their job was to solve three exponent problems incorrectly on purpose.  Furthermore, because they wanted to foil the power rangers, they needed to make their answers look correct so that the power ranger would have trouble finding the error.  Once the nemeses work was done, the power rangers came back to their groups and they had to find the mistakes in the nemeses problems, then explain the to the nemeses why their answer was wrong.  The nemeses got to grade their power ranger on finding the mistakes and the clarity of their explanations. I don't know how educational it was, but my students keep demanding to play it again.

Here are the documents I used to play the Power Rangers game: Power Rangers Game

Finally, I started giving them quizzes to make sure they have the rules down.  From the first quiz I pulled out the problems students had the hardest time with.  I put the problems, along with students' incorrect answers on note cards.  I gave one note card to each student in class and asked them to tell me if the answer on the card is correct or incorrect, and if it's incorrect, explain what mistake the student made.  The students rotate cards and do this for about 10 incorrect problems (I don't tell them that all the cards are incorrect.)  Then they pair up and compare answers.  Then the pairs pair up and compare answers.  We keep doing this until students realize that all the answers were incorrect and we discuss common errors as a class.

Here's the first quiz I give: Exponents Quiz 1

Here's the second quiz I give: Exponents Quiz 2

So far, this unit has gone better than last year.  My students got an 87% average on their first exponents quiz, but there are still some students below the 80% mark and I want them all above it so that our next topics- exponential growth and decay and scientific notation- go smoothly.  I think I have a pretty cool project to finish the unit with, but I'll post that once we get there.

If anyone has any suggestions, I would love to have other games, resources or ideas to throw into this unit.  I know it's not quite rockin' yet.

Vertical Dilation

My algebra 2 students are learning about various function transformations and I was trying to think of a way to make this topic a little more engaging.  My students are all wild about silly bands (I'm not sure why... They're still pretty excited about the fact that the silly bands always maintain their shape no matter how stretched they become) so I thought it would be pretty fun to see if we could explore vertical dilation through silly bands.  This led to kind of a neat little warm up, but I think it was maybe a little more prep than the educational content was worth.

I cut out squares of cardboard and taped graph paper to them.  Then I let the students choose their own silly bands out of a selection:

The students had a lot of fun picking out their silly bands at least.  The robot shaped ones were the most popular.

I then had them put their silly bands against the graph paper and draw a coordinate axis.  They were told to plot at least 10 points that their silly bands went through.  I asked them to double all their y-values and plot the points on their cardboard graph paper with thumb tacks.  They then tried to stretch their silly bands over the tacks to see how the shapes of their rubber bands changed:

This was a cup cake shaped silly band.

It was a nice visual because in the past, I've had students get confused because a parabola that's been stretched vertically by a factor of 2 looks skinnier, so students thought that it must have been multiplied by 1/2 instead of 2.  This activity I think showed them that multiplying by a number bigger than 1 made the object taller and skinnier, while a multiplication by 1/2 would make it shorter and fatter.

It was kind of anti-climactic however when we just launched right into normal classwork after this activity.  I would love to find a way to pull this idea into a larger lesson plan rather than just a warm up problem.

How can I know if I'm any good?

So, my students tell me that they like my classes.  Some even tell me I'm the best math teacher ever.  But what do they know?  All they know is that I'm the only high school math teacher they have ever had.  That the teacher before me was primarily a biology teacher and didn't really know math so didn't teach it at all, so I must be better than that right?  And finally, that they like me personally (which is nice, but doesn't make me a good teacher.)  They don't know about the material that we don't get to, or the games that are out there that other teachers do but that I just haven't found yet, or how tired I am all of the time and how I probably could have explained a lot of what we just covered much more clearly if I didn't have a million preps.  Their comments are all I have to go off of and I keep thinking to myself- they have NOTHING to compare me to.  So how can I know if I really am doing the best job anyone could do in this situation, or if I'm actually terrible at teaching but personable (I think.  I must at least have this quality if my students like my classes.)  I did though, get an AMAZING e-mail today that makes me feel like at least, maybe I can do this job with some degree of competency and makes me feel that all the time I pour in is worth it.  This is from a former student from last year who is now going to a large university (probably going to major in theology but I wish he would major in math or science because he was so good at it.)

Hi!
I just wanted to tell you that I really miss your math class. I am taking
math 110 and the teacher is nowhere near as good as you are, even with a
smaller class.

Thank you for being the best math teacher I have ever had.

I love my students so much.  They are such good kids and they know when I need an e-mail like this.  

FOIL, Factoring and Quilting

I've spent my whole long weekend (Thursday, Friday, Sat and Sun.  We got a day an a half off due to rain.  I'm feeling guiltily giddy at having so much time to prep and to play) working on my next algebra 1 unit.  I've specifically been thinking about how to introduce FOIL and factoring.  I don't like the acronym FOIL very much either, but it is a better name than "multiplying binomials."

I've been trying to come up with a new way to introduce it.  I've played with using algebra blocks and I like the connection to area, but I find them a bit unwieldy.  The last two years I've just introduced it using this solid worksheet I found online somewhere (but I can't remember where.) Intro to FOIL Guided Notes I think working through this worksheet with my students has gotten the job done, but it's a little bit dull and unconnected to reality. Why would we be trying to find the area of random rectangles that we don't actually know the dimensions of so we have to write the dimensions as x+2 and x+3?  I know it's just a way to introduce the logic behind FOIL, but I find it a bit unsatisfying.  I do think it does a great job of showing how  and why the process works and my students have enjoyed learning FOIL this way.

So I threw together some ridiculous replacement activities modeled on this worksheet and on algebra blocks.  Mostly, I am just trying to give a tiny bit of context and some humor and silliness to this topic.  I may, though, have just confused the point.  The beauty of the above worksheet is  its simplicity and what I've thrown together is much more complicated.

I thought I'd start with the following algebra blocks that I made myself: Algebra Tiles for Teaching FOIL V2 I'd let the kids cut them out and play with them a little, then I'd have them work through the following "quilting activity" in pairs.

Algebra Tiles for Teaching FOIL Quilting Ws I've already changed the third rule of quilting to "all quilts must be formed with exactly four rectangular pieces of cloth" because I realized that without this rule, the kids would probably get pretty confused.

The purpose of this is just to try to introduce them to the idea of having rectangles with dimensions that have variables and to see if they can intuit FOIL for themselves.  I would follow this activity with a more conventional multiplying binomials lesson with some notes and some homework.  I'm unsure about this lesson.

The advantage is though that I was able to make a follow up activity for when the students start factoring that follows the same pattern, so doing FOIL this way, then factoring this way may help students connect the two processes with one silly context problem.  Here's the factoring worksheet: Algebra Tiles for Teaching FACTORING Quilting Ws I think I like this one a little bit more than the first one, but I'm still not sure if this is the best way to go about teaching these two topics.  Oh no, and I just noticed on the last page I put it's, not its.  I like to have correct grammar, I really do, but I can't hold good grammar and math together at the same time.  I'll go fix it on my originals...

The Name

I feel a slight need to justify, if only to myself, the reason I chose the name I did for this blog.  Yes, I know it's cliche and I also know that people looking for Douglas Adams websites rather than teacher websites will end up here and will click away in a huff perhaps when they discover the truth.  But I couldn't resist.

When I first got my job, I decided to make large, friendly signs in bubble letters to hang up on my walls.  One read "Don't Panic" and the other read "The Answer is 42".  I thought the students would probably find them kind of dorky, or may not get the reference at all, but I thought that these two signs represented much of my teaching philosophy.  (It turns out that these signs got about half my students reading Douglas Adams, which I think is a major success.)  I have always been an incredibly anxious math student.  I had a few terrible teachers, and never felt like I was all that good at it (probably because my older brother was a bit of a math prodigy and I could never compete). I took math in college because I enjoyed the challenge and the break from more writing based classes but again, I never considered myself a serious math student.  As I signed up for each new math class I would have moments of panic because my abilities to do math seemed magical and out of my own control and I thought they may leave me as the challenges I faced got harder.  I both loved and hated the fact that I could stare at something for hours and not be able to make any progress despite my best efforts, then mysteriously in the night the solution would come.  So I always felt that there would be a point where it just stopped working and I would be scared yet excited by each new math class and was always frightened out of my wits when tests came up.  Despite my anxiety I did quite well and am now using my math abilities professionally but I worry that the anxiety I experienced kept me from fully exploring this part of myself.  (I ended up majoring in history, not math even though I took enough math classes for a major.)  I think a sense of panic plagues many students as well and my greatest task is to help them relax, enjoy the math, and work through those moments when their brains refuse to get it no matter how much the students want to get it.

The answer is 42 part of it is more for my entertainment but I also think having this sign up is important.  Students will often jokingly suggest that they put down all their answers for a test as 42 and I tell them that it will make me laugh, but they won't get any credit for it.  Sill, though, I think they like the fact that they can just put something down when they don't know what to do.  When students are stuck on a problem, often times they leave their sheets blank.  I hate this because it seems so hopeless.  When I'm stuck on a problem I always try something, write something down, play with it, tease it until something resembling an answer comes out.  Almost always we can't immediately see to the end of a problem, but a lot of students just give up if they can't see the solution right away.  I like the idea that they always have something to put down, some way to break the white plane of paper that is so intimidating.  To break the graphite barrier and to play a little bit with math, even if it's just writing down a number.  Because I think that once pencil is to paper, it's harder to just give up and leave the problem untried.

Adding Like Monomials

I just spent the last three hours working on one algebra 1 lesson plan even though I have about 20 lesson plans I'm supposed to write this weekend.  Maybe not the most efficient use of my time, but I'm kind of excited about this one.  The topic is: adding like monomials.  Students understand pretty readily that they can't add expressions without variables to expressions with variables and they can't add two things that have different variables, but I've found they have a lot of trouble with understanding that they can't add an x expression to an x squared expression.  They won't take my word for it and it takes a lot of work to stop them from writing 2x+4x^2 as 6x or 6x^2.  Thinking about this, I threw together the following story worksheet/activity to see if it may help clarify the difference between an x and an x^2.  Any feed back would be awesome. Adding Like Monomials

Geometry Test on Congruent Triangles

By the way, here is the test I was going to give.  About half I wrote myself and half I pillaged from other geometry textbooks and test question banks.  Sorry for the goofy font.  I've tried to change the font back to a more professionally mathy font, but my students rebelled.  They insist that the font makes math less stressful for them.  If that's all I have to do to make math less stressful, count me in.Geometry Test over Triangle Congruence

Rain Day! And Proofs in Geometry

We have a day off today.  Oregon is flooding.  We would have much preferred the snow storm that was predicted but it is Oregon after all.  The funny thing is the rain doesn't seem to be coming down that hard, and if there's one thing us Oregonians should be used to by now it's the constant drizzle.  Here's the bridge in the town I teach (picture from the local newspaper: The Sheridan Sun)



I think the river has risen high enough that the water is already spilling over it's banks but I'm not sure.  It's only running a few feet below the bridge and as the weather prediction is more rain, water will over take the bridge.  Since I need this bridge to get to work, I'm probably not going to work for a while.  We'll see.

We were supposed to have a geometry test today over congruent triangles.  The first thing one of my students did when she learned of the school cancellation was to give me a call and bemoan the fact that she couldn't take her test because she was going to rock it.  Odd  but awesome phone call to receive.

This brings me to something I've been worrying about.  I decided to use Harold R. Jacob's Geometry: seeing, doing and understanding text book, but my school could only afford the 2nd edition.  I've been happily teaching out of it though because I love it.  Recently, to aid in test writing I got the 3rd edition to help me find test questions so that tests didn't take me a million years to write and much to my dismay I saw that he took a whole bunch of the proofs out of the 3rd edition.  He doesn't stress them nearly as heavily in this newer edition, while I, blindly, have been battering my students over the head with the rigorous proof based curriculum of the second edition.  I promised my students the proofs were important, engaging, that knowing how to do them would aid in understanding higher level math, and that learning to do proofs taught them much needed critical thinking skills.  Has all my pleading, wheedling and dragging all been in vain?  Do people not do proofs as much in geometry anymore?  When I was doing higher level math in college, it took me forever to catch on that if and only if statements had to be proved both ways because no one in high school ever mentioned conditional statements.  All of math is couched in the language of conditional statements and proofs.  Isn't it still important to teach this stuff?  But maybe the content of geometry itself is more important.  It is true that while trying to help my students truly understand proofs, our progress through the curriculum has slowed down.  But as a college prep school I don't know if I could live with myself if I didn't help students feel more prepared for college than I felt and I felt the lack of having done proofs keenly.

Well, I guess I'll use my day off to have all sorts of fun- like plan my next algebra 1 unit... Yay.

Getting Started

I've been following the f(t), Continuous Everywhere and Differentiable Nowhere, dy/dan, and Think Thank Thunk blogs for the last year or so and I've been blown away by how wonderful it is to read about teachers who are struggling with the same frustrations, joys and dilemmas as I, (me?  Hey, I'm a math teacher after all.)

I'm in a bit of a unique situation and stumbling into these blogs has returned my sanity and revitalized my love of teaching.  You see, I am all alone.  Totally and completely isolated from professionals in mathematics and I thought I would just have to suck it up and learn as much as I could all by myself.  I was hired at a tiny (88 student) rural college prep charter school and I am the only math teacher.  The reason my school was started in the middle of nowhere, Oregon is because the local college in the area had professors who had children who wanted to go to college.  There were also lawyers, doctors, waitresses, construction workers and basically, a lot of concerned parents who wanted their children to have rigorous programs so that their children had a fighting chance of getting into good universities and colleges.  The public schools in the area are routinely below the state average on state tests and can be less than wholesome environments for determined students (meth has taken over our area.)

The result: a charter school was created here in the early 1990s (originally it was a magnet and switched to charter 7 years ago.)  Our school is as rigorous and demanding as a private school, yet we make do on 85% of the funding a normal public school would get.  This means that with 88 students we have a total of 4 full time teachers.  I teach all levels of math from 7th-12th grades including pre-algebra, algebra 1, geometry, algebra 2, pre-calculus and calculus.  I also, (because we only have 4 teachers) have to teach the science classes which I'm totally hopeless at.  By the way, I also teach the art elective.  This is 9 preps.  Last year I had 14 preps.  The year before I had 15 preps.

If you're wondering how we ended up with 15 or so different levels of math, the reason is that the teacher before me was hired for her science teaching abilities (biology) not for math.  The students studied by themselves straight out of textbooks without anyone ever checking their work.  I walked in on my first day to high school math students who were from all different levels from pre-algebra through 2nd year calc clumped into the same two class periods (6 different levels in the same period).  In addition, those who were supposed to be in say, algebra 2 had been studying independently of each other and were all in different places of the curriculum.  Not to mention the fact that few of them had really learned much of the content they had "gotten through".

The last two and a half years I've been working in isolation, slowing trying to fill in holes, trying to pull kids into the same level with each other, and trying to keep up with so many different preps.  I had no other math teachers to talk to, no curriculum to go off of, and no time to think about looking for advice because I was barely keeping my head above water.  Now two an a half years in I've developed a full 7 year long math curriculum, I can keep up with the planning and grading, and my students are performing well above average on state tests (because of their determination.  I don't want to take credit because all I did was organize the curriculum.  I spent most of my time flopping around trying to feel my way blindly.  My kids are awesome.)

Yet despite things going pretty well, this year I've found it much harder to stay motivated.  Maybe because, now that I no longer have the panic and desperation of my first two years of teaching, I've been asking myself if I'm actually good at it.  Sometimes I think I'm doing pretty well, other days I spend all evening and sometimes all night obsessing over things I feel could have gone so much better but I don't know what else I could have done.  I didn't have time for this kind of self reflection before and now I realize that I am not capable of evaluating my own abilities as a teacher.  I need other people.  I need to vent, and I need criticism and advice.  I need a place where people know what I'm talking about and where I can get out what I need to say about teaching so that my husband and friends and family can talk to me about something else.  I also need to stay sane.  And have a life outside of school (90+ hour work weeks, but reading around other blogs makes me feel better because all of you seem to know what that's like.)  So even if no one reads this, at least some of these goals may be accomplished.

We will see.