# A High School Math-Science Journal

In my first year of teaching, fresh from my haze from history grad school, I remember approaching the history and English department chairs about creating a high school level journal for those subjects. I mean, our school has a literary magazine, and also even a publication for works in foreign languages (seriously!). But nothing for amazing critical analyses and interpretations in English and history. I figured having something like this might encourage students to revise already excellent work for publication, and also make the audience of their paper be an audience of more than one. I even contacted the literary magazine student editors to see if they would feel like the journal would encroach on their domain (they said no). For reasons that are still quite beyond my understanding (because I still think it’s an amazing idea), both department heads rebuffed my idea. (Also, if they said yes, they would have gotten an enthusiastic first year teacher who would have taken on all this work!)

And so, I let this idea pass. One of many that I have, think are awesome, and then languish and die, either due to my own laziness or due to external circumstances beyond my control.

Until last year. When I was thinking: I’m a math teacher. Why not start a math and science journal? It’s so obvious that I don’t know why the idea didn’t hit me over the head years ago. So I found a science teacher compatriot who I knew would be interested, and we came up with an initial plan. And at the end of last year, we presented it to some students who we thought might have been interested (as this was something that is something that has to be for them, by them… if they don’t want it, there’s not point in doing it… it’s not about us…). They were, and we were officially off to the races.

We shared with the students the following document we made, with a brief outline of one vision for the journal. But with the understanding that this was their thing so their ideas reign supreme. This was, in some sense, a mock-up that the science teacher and I made to show them one possibility. The one thing that the science teacher and I were really aiming for in our mock-up was that the journal shouldn’t just be for superstar students. We wanted to come up with an journal that has a low barrier of entry for students submitting to the journal, and that if a student has interest or a passion for math or science, that’s really all they need to get started. To do this, original and deep research wasn’t really the primary focus of the journal. So here’s our brief proposal:

The additional benefit of having this journal is hopefully it will cause curricular changes. Teachers will hopefully feel moved to create assignments that go “outside of the box” — and that could result in things being submitted. Students who express an interest in some math-y or science-y idea (like why is 0/0 undefined… something that came up in calculus this week) could have a teacher say “hey, that’s great… why don’t you look it up and do a 3 minute presentation on what you find tomorrow?” … and if they do a good job, encourage them to write it up for the journal. Or a teacher might assign a group project on nuclear disasters, and encourages the students who do extraordinary work to submit their project to the journal. (Which can be showcased by teachers the following year!) Or a student who notices a neat pattern, or comes up with an innovative explanation for something, or who wants to try to create their own sudoku puzzle, or decides to research fractions that satisfy $\frac{1}{a}+\frac{1}{b}=\frac{2}{a+b}$. Or whatever. Knowing there is a publication you can direct the student to, as a way to say “hey, you’re doing something awesome… seriously… so awesome I think you kind of have to share it with others!” is going to be so cool for teachers. (As a random aside, I was thinking I could enlist the help of the art and photography teachers, because of the overlap between math and art… They might make an assignment based around something mathematical/geometrical, which students can submit…)

I honestly have no idea how this is going to turn out. What’s going to happen. How the word is going to get out. If anything will be submitted. If kids get excited about it. Lots of questions. But I have a deep feeling that the answers will come and good things are going to happen with this.

I’m soliciting in the comments any thoughts you might have about this. If your school does a math journal, a science journal, or a math-science journal, what does it look like? What works and what doesn’t? Do you have a website/sample we could look at? If you don’t have one, and you are inspired and think of awesome things kids could put in there (e.g. kids submitting their own puzzles! kids writing book reviews of popular math/science books, or biographies of mathematicians/scientists! getting kids to create photographs or computer images of science or data visualization or just making geometrical graphing designs! trust me — brainstorming this is super fun!) I’d love to share any and all ideas with the kids involved with this project at my school.

# My 2012-2013 School Planner

I know it is Thursday, but I have never really been good with working on a schedule. (I am not the teacher that has a unit outline and homework to give my kids at the start of each week, because how the heck am I going to know where we are in five days let alone one?) So forgive me this fault of posting my Made4Math Monday on Thursday.

Anyway, I’ve posted about this each year. I figure I’ll do it again. My school has a rotating schedule, where we meet kids four times a week (50 minutes each). We’ve had this schedule for the five years I’ve been teaching at my school, and I still don’t know it by heart. I have gotten the class period start-end times down, but which class I’m meeting when is always a mystery. Also, with my brain, scheduling meetings with kids is something that has to happen in my planner so I don’t double book.

To help me out, I designed and published my own 88-page weekly planner. A copy of my weekly schedule for 2012-2013 is below (missing, of course, the 10th grade team meeting, the two “duties” I will be assigned, math club, and the weekly meetings I have to schedule with the other Calculus and the other Pre-Calculus teacher… so don’t be so jealous of all the free time… it’s really not there.)

The cover for the planner is:

Simplicity.

What’s nice is after my first year, there were a few other people who wanted to order planners too, so I have put up a blank planner (meaning: without my classes inputted in them) for them to buy. I don’t make any money off it or anything.

## How I Made & Ordered Them

In order to make them, I had to use Adobe InDesign, which I had never used (the school laptops which we are issued come with it already installed). So I spent hours, years ago, making the original grid, picking the fonts, and working on the design. [1] But those hours were worth it, because even though bits and pieces change each year, I have been super happy with the look of it. (I created the file to be A4 paper size, because I wanted it to be slightly bigger than regular paper so I could slip a sheet of regular paper in there without it sticking out.) Then you convert your file to PDF. Just remember: if you’re going to design your own, make sure you have a blank sheet before you start your calendar pages. This way the entire week will be on facing pages.

So after I made the planner, I used lulu.com to order it. You just upload your PDF and specify what you want. I get saddle stitch (fancy way of saying heavy-duty staples). Designing your cover on lulu is really annoying — their “cover wizard” is difficult as all heck to use. But even if you order a black and white planner (as I do), a color cover comes with it. And if you are a photo person, you can have a photo background! Each year, the price of printing between $7-$9. With shipping it comes to around $15 plus or minus a few bucks. And viola! Your own fancy planner! ## How I Use It I basically just use it to schedule my time. A page from my planner from two years ago: Also, because of my horrible brain, I require kids to email me to set up a meeting. I’ll have none of the coming up to me after class asking to set up a meeting (usually I have to run to another class, so that doesn’t work for me), or accosting me in the halls. I simply don’t know when I’m free. So they email me with all their free periods for three days and I find the first common free that works for both of us. (Usually it is the next day… rarely I have to go a couple days in the future, if our schedules are so opposite.) And that’s it! My planner, from creation to use. [1] You simply need to upload a PDF file to lulu.com to get it published, so if you are good with Word, you could even create something nice in there! # Business Cards, Stickers, and Cards: Oh my! There has recently been this awesome arts & crafts trend that has been happening with math teachers on blogs. Lots of talk about hobby lobby and the container store and puff paints and spray paint chalkboards. I used to be crafty, but no more. I’m too manly to be crafty. [1] But I do feel like I have a fairly good sense of design. So I figured I’d join in with my first installment of Made 4 Math Monday. I should probably preface this by saying this is not math specific. I went to one of those personalization stationary websites, and ordered a lot of stuff. My favorite of the things I ordered were specially designed business cards. I ordered some fun ones for me to use when I’m out on the town, but I also designed some for me to carry around the school, in the classroom or outside the classroom. It’s definitely a novelty thing that will wear off, but I’m amused by them. Can you imagine being a kid and having a teacher sort of flick you a card as you’re leaving? Or just hand you one in the hallway? Or if you were being funny bad (but not seriously bad), have someone hand you one of these? The first card is more like a motto I want to instill in my kids, especially because I’m doing standards based grading. In order to get free shipping, I had to order more. So I designed stickers (I’m getting 24 of each sticker). I should say I had limited time to design them so they aren’t exactly the best things I could have come up with. But they’re good enough. Now that I’m looking at these, I’m wondering if I couldn’t make better stickers which weren’t all about achievement. But maybe a sticker for someone who just bombed something… something to make them smile, and feel encouraged. Or for someone who clearly put a ton of effort into something even if they didn’t do superduper. Anyway, thoughts for the future. I still had a little more money to spend for my free shipping, so I also ordered 10 cards (the outside, then the inside). The card is not my favorite, because I could have done a much better job and come up with a much better concept if I had more time. But here’s the thing. I always keep blank fancy cards at my desk to write thank you notes to people who have helped me out in small and large ways. Unfortunately, I forget I have them, so it hasn’t become normalized behavior. But since I will have fancy personalized cards, I think I will be more excited to use them and so I have high hopes this could become a thing that I do, instead of just intend on doing. I hate having to wait to see how all this merchandise looks (it’s going to take up to two weeks to get to me!), but I’m uber excited about it. As for costs, I had a groupon that cost$20 for $80 worth of merchandise. But for some reason, I had$10 off my groupon. I also had to order an extra $25 for free shipping. So for all of this (I ordered eleven different business cards, even though I only showed a few here), I only ended up paying$35.

And with that, my first Made 4 Math Monday is out.

[1] False.

# Algebra Bootcamp in Calculus

So it was the Old Math Dog who pointed out that I never wrote a post explaining how I deal with the issue of kids not knowing basic algebra in calculus. I started this practice two years ago (when I also started standards based grading) and I have seen a remarkable difference in how my classes go from my life pre-bootcamps to my life post-bootcamps…

An issue in any calculus course — and I don’t care if you’re talking about non-AP Calculus or AP Calculus — is the student’s algebra skills. They might see $\frac{1}{4}x+\pi x -4=0$ and have no idea how to solve that. Or they might not know how to find $\tan(\pi/6)$. Or they might cancel out the -1s in $\frac{x^2-1}{x-1}$ to get $\frac{x^2}{x}$. It depends on where they are coming from, but I can pretty much guarantee you that every calculus teacher says the same thing to their classes on the first day:

Calculus is easy. Algebra is hard.

In my first three years of teaching calculus, I started with how all the books started, and all my calculus teacher friends started: a precalculus review. Then we went into limits.

The problem with that is that we might review some basic trigonometry, and then we wouldn’t see it again for months. And by then, they had forgotten it. And who could blame them. The precalculus review unit at the beginning of the course wasn’t working.

As I transitioned into Standards Based Grading, I looked at everything I taught really closely, and I honed in on the particular skills/concepts I was going to be testing. And since I’d taught calculus for a number of years prior, I knew exactly where the algebra sticking points were. Thus was born The Algebra Bootcamp.

Before our first unit on limits, I carefully analyzed what things I needed students to know to understand limits to the depth I required. I then looked at all the skills and thought of all the algebraic things, and all the old concepts, they would need in order to understand limits. And from that, I crafted an algebra bootcamp, and I made SBG skills out of just those limited skills.

For example, here was our first bootcamp (which, admittedly, was longer than most of the others, because we were settling in and I was gauging where the kids were at):

and I did the same for other units… just the targeted prior knowledge that they tended to not know or struggle with…

Notice how they tend to be very concrete and specific? Like “rationalize the numerator” (because I knew we were going to be doing that when using the formal definition of the derivative) or “expand $(x+h)^n$ using the binomial theorem. Very specific things that they should know that they are going to be using in the following unit. It’s kind of funny because it is a hodgepodge of little (and often unconnected) things, and they have no idea why we’re doing a lot of what we’re doing (why are we rationalizing the numerator? why are we doing the binomial theorem?) and I don’t tell them. I say “it’s our bootcamp… once training is over you’ll see why these tools are useful.”

It is called “bootcamp” because I am not reteaching it from scratch. I’m reviewing it, and I go through things quickly. I only do a few of them in the first quarter and maybe the start of the second quarter. By that point, we’ve done what we needed to do, and they die off.

The reason that this has been so effective for me is because students aren’t having to relearn old topics/algebraic skills while concurrently learning the ideas of calculus. We review these very specific things beforehand so that when we approach the calculus topics, the focus is not on the algebraic manipulation or remembering how to find the trig values of special angles or what a piecewise function is… but  on the larger picture…. the calculus.

Remember: calculus is easy, it’s the algebra which is hard.

So we took care of the algebra beforehand, so we can see how easy calculus is.

My kids in the past two years have made so many fewer mistakes, and we’ve been able to really delve into the concepts more, because I’m no longer fielding questions like “could you review how to do X?” Doing this has also forced me to think about what the purpose of calculus class is. The more I teach it, the more I take the algebraic stuff out and the more I put the conceptual stuff in. For example, I don’t use $\cot(x)$, $\sec(x)$, and $\csc(x)$ in my course anymore  [1], because I wasn’t trying to test them on their knowledge of trigonometry. Doing these bootcamps coupled with standards based grading has forced me to keep my eye on what I really care about. Students deeply understanding the fundamental concepts of calculus. And I think you can do that without knowing how to integrate $\sec(x)\tan(x)$ just fine. [2]

[1] With the exception of $\sec^2(x)$ for the derivative of $\tan(x)$.

[2] I teach a non-AP calculus, so I have this luxury. But it’s nice. Each year I strip more and more stuff off the course and add in more and more depth. And I am glad that I understand depth to mean something other than “more complicated algebra in the same old calculus problems.”

# Optimization: An Introductory Activity & Project

I switched things around with optimization in calculus this year, and I realized if I had the time, I would spend a month on it. [1] I wonder if this shouldn’t be a crux of the class. Not the stupid “maximization and minimization” problems but finding some real good ones — in economics, physics, chemistry, ordinary situations. There have got to be tons of non-crappy ones!

Anyway, I wanted to share with you two things.

First, how I introduced the idea of optimization to my kids. Instead of going for the algebra/calculus approach, I wanted them to toy with the idea of maxima and minima, so I had them spend 35-40 minutes working on this in class:

[doc]

I thought it was pretty cool to see my kids engaged. I rarely do things like this, but I did it (I was being videotaped during this lesson… and I had never done it before… and I had the idea to create it the night before…). It was fun! And although I cut the debrief the next day short (ugh, why?), I enjoyed seeing kids engaged in problem solving through various strategies. And there was a healthy level of competition. (The winners for the 1st and 2nd tasks got a package of jelly beans, but they were so gross I threw them out! One student gave them to his rabbit who likes jelly beans, and even the rabbit didn’t like them!) But when it came down to it, it drove home the idea that optimization was something that trial and error is good for, sometimes we do it intuitively, sometimes our intuition is terrible and sometimes it is good, and sometimes we get an answer but we don’t know how to prove there isn’t a better answer (e.g. in problem #3). Some kids liked that this felt more “real world” than this world of algebra and graphing that we’ve been meandering in.

Second, I have allotted a few days for students to work on this project during class (it’s the week before Spring Break and kids are overburdened, so I didn’t want to have them do something which involved a lot of at-home time). They’ve been working on it this week, and I’ve heard some good conversations thus far. (They’re doing this in pairs, and I have one group of three.) The fundamental question is: with a given surface area, what are the dimensions of a cylinder with maximal volume?

Now I don’t quite know how their posters will turn out yet, or whether students will have truly gotten a lot of “mathematical” knowledge out of it. But each day, I’ve had a couple kids say things that indicate that this isn’t a terrible project. (I don’t do projects, so that’s why I’m very conscientious about it.) A few said something equivalent to “Wow, the companies could be giving me x% more creamed corn!” or how they like doing artsy-crafty things. At the very least, I can pretty much be assured that students — if I ask them if there is any question that calculus can answer at the grocery store — will be able to say yes.

Next year I will probably add the reverse component (for a given volume of liquid you want to contain, how can we package it in a cylinder to minimize cost… what about a rectangular prism… what about a cube… what about a sphere… etc.?).

[1] The one thing I found in this book my friend gave me (on science and calculus) was an experiment where you shoot a laser at some height at some angle into an aquarium, so that it hits a penny at the bottom (remember the laser beam will “change” angles as it hits the water) to minimize the time it takes for the photon to travel from the laser to the penny. I almost did it, but deciding to do it was too last minue.

# Two crazy good Do Nows

Recently, I’ve been trying to be super duper conscientious of every part of my lesson. For example, I wrote out comprehensive solutions to some calculus homework, paired my kids up, handed each pair a single solution set, and had them discuss their own work/the places they got stuck/the solutions. I actually had made enough copies for each person, but I very intentionally gave each pair a single solution set. It got kids talking. (Afterwards, I told them I actually had copies for each of them.) That’s what I’m talking about — the craft of teaching. I don’t always think this deeply about my actions, but when I do, the classes always go so much better.

In that vein, of super thoughtful intentional stuffs, I wanted to share two crazy good “do nows” from last week. Not because they’re deep, but because they were so thought-out.

For one calculus class, I needed my kids to remember how to solve $5\ln(x)+1=0$ (that equation was going to pop up later in the lesson and they were going to have to know how to solve it). I also know my kids are terrified of logs, but they actually do know how to solve them.

I threw the slide below up, I gave them 2 minutes, and by the end, all my kids knew how to solve it. I didn’t say a word to them. Most didn’t say a word to anyone else.

How I got them to remember how to solve that in 120 seconds, without any talking, when they are terrified of logarithms and haven’t seen them in a looong while?

I can’t quite articulate it, but I’m more proud of this single slide than a lot of other things I’ve made as a teacher. (Which is pretty much everything.)  Not deep, I know. It’s not teaching logs or getting at the underlying concept, I know. But for what I intended to do, recall prior knowledge, this was utter perfection. The flow from each problem to the next… it’s subtle. To me, anyway, it was a thing of perfection and beauty.

The second slide is below, and I threw it up before we started talking about absolute maximums/minimum in calculus.

As you can imagine, we had some good conversations. We talked about (again) whether 0.9999999… is equal to 1 or not (it is). We talked about a property of the real numbers that between any two numbers you can always find another number (dense!). I even mentioned the idea of nonstandard analysis and hyperreal numbers.

So I know it isn’t anything “special” but I was proud of these and wanted to share.

# Infection Points: The Shape of a Graph

Everyone here knows that I think Bowman Dickson is the bee’s knees, the cat’s pajamas, ovaltine! Recently he posted about how he introduces inflections points in his calculus class… and just a couple days later, I was about to introduce how we use calculus to find out what a function looks like.

Usually, I introduce this in a really unengaging lecture-format. But he inspired me to … copy him. And so I did, extending some of his work, and I have had an amazing few days in calculus. So I thought I’d share it with you.

The Main Point of this Post: By creating the need for a word to talk about inflection points on graphs, we actually saw the math arise naturally. And through interrogating inflection points, we were able to articulate a general understanding of concavity. In other words… the activity we did motivated the need for more general mathematical concepts.

First, definitely read Bowman’s post. All I did was formalize it, and extend it in a few ways, by making a worksheet. I put my kids in pairs and I had them work on it (.docx):

What naturally will happen when students generate their graphs is they will get a logistic function. (Which has a beautiful inflection point! But they don’t know the word… they just see the graph.)

So here we are. The students have a graph, and they’ve been asked to explain their graph for (a) the layperson and (b) the mathematician. Most get some of it done with their partners, and then they take it home to finish individually.

The next day, at the start of class, I assign students to work in groups of 3 (with different people than their partners the previous day). They are asked to take a giant whiteboard and:

(Now I want to give credit where credit is due. I have really been struggling with using the giant whiteboards well, and having students present their work effectively and efficiently. My dear friend Susanna, when I told her about this activity, suggested the groups, the underlining of the mathy words, etc.)

This worked splendedly.

(click to enlarge)

And they had such great observations. Some groups picked up on that change where the function was increasing in one way to increasing a different way. Others talked about how the rate of change (of infected over time) was greatest. Others talked about how the function was “exponential” for the first thing, seemingly linear for the middle third, and “something else” for the last third.

Those gave rise to good short discussions, and we came up with the language for inflection points (which I call INFECTION POINTS!!! GET IT!?!) and concave up/down.

After they had a sense what those words meant, I had students work in partners on the following (.docx):

The point was to get students comfortable with the ideas before we delve into the heavy mathematical lifting. It was powerful. Especially the last page, which got students thinking about patterns, exceptions, and ways to generalize. Our big conclusions:

And with that, I’m too exhausted to type more. But that’s the general sense of what went on in an attempt to teach how to use calculus to analyze the shape of a function.

# Next Semester

You know my philosophy about blogging… blog only when you want to blog. If you put pressure on yourself, it becomes a chore. And why would I make myself do a chore? More than that, it would be like a chore I created just to make my life harder. Like: every day, make sure you windex the windows to your apartment. (FYI: I have never windexed the windows to my apartment since moving in two and a half years ago.) (That’s what rain is for.) (And curtains.)

However, now that it’s been over a month since I’ve blogged, I wonder what’s going on?

We did have two weeks off, so it’s not like I could blog about school stuff when we didn’t even have school…

True. But that’s me rationalizing. Or how about…

I don’t have time because I’m just so busy…

I think. But this year I’m no busier than previous years. In fact, I might be less busy with school stuff. (However, I should say that I’m making good on my school year motto this year: “I’m doing me.“)

Actually, I think that is the problem. I wonder if I’ve gone stale, like that moldy bread in the back of my fridge? I only think it’s moldy, actually. I keep on putting things in front of it, because I’m scared to take it out, but I don’t want to look at it. It’s like smelling milk that might have gone bad. I don’t do it. I just throw it out, because the mere thought of smelling rancid milk makes me want to puke. Where was I going… oh yes, feeling stale. I’ve grown accustomed to having my SmartBoards that I slaved over years ago, and my worksheets and packets that I created ages ago. I’m tweaking. I’m not inventing. Or really even reinventing. I don’t have much to post because I haven’t been doing a lot of creation. And that’s always when I feel excited about posting. Invigorated about what I’m doing.

Now that I know this, I have an easy fix. Recreate. Invent. Reinvent. I’m also meeting with my department head on Friday to talk about course assignments for next year, and I’m going to ask to teach a course that will be new for me next year.

With all this mind, I’m going to keep a list (that I will update) with possible ideas/goals for next semester, which will be starting in a little over a week.

• In Algebra II, remember to do group work, and do more “participation quizzes” during that group work.  I did a bunch in the first quarter, and then the groupwork dropped off in the second quarter. Booooo, me! Keep it going, and strong!
• In Algebra II, remember to utilize the Park School of Baltimore curriculum, especially when working on Quadratics, Transformations, and Exponential Functions. It didn’t quite fit in with our 2nd quarter material, but it will align with our 3rd and 4th quarters.
• In Algebra II — since we don’t have a midterm for students to see a broad view and get a review of all the 1st and 2nd quarter’s material — have the 3rd and 4th quarter problem sets include “review problems” from topics from the first semester. Or if not, have review problem assignments, in addition to the problem sets.
• In Algebra II, do a written “final exam study guide” project again, to continue having kids work on their writing skills. Provide feedback, and an opportunity to do revisions, and fix errors. (Video study guides from years ago, paper study guides more recently.)
• Create this “pencils and eraser” station for kids who forget pencils.
• In Calculus, continue having kids work in groups on challenging problems every so often.
• In Calculus, do problem sets in the 3rd and 4th quarters, but make them shorter and give less class time than the 2nd quarter. Continue to make the problem sets have a “group” component and an “individual” component.
• I finally got large whiteboards for my students. I’m struggling to use them. So in the 2nd semester: use them. Even if it doesn’t go well, I need to keep using them. I need to have some practice and experience with them, even if to show me what works and what doesn’t work.
• Now that we’re starting the 2nd semester, have built in time to review the course expectations, and collaboration guidelines for all of my classes.
• Consider making changes with my Binder Checks in Algebra II? More frequent? Have kids leave their binders in class, and have time set aside for them to organize themselves? This year their binders are not improving much. It may be that I need to baby them. Some things might include: putting “correct the home enjoyment that we went over today” each day on the course conference (the place where I post the nightly work), having binder checks every two weeks instead of every five weeks (or random “homework correction checks” in addition to the five week binder checks), making test corrections a homework assignment (instead of just telling them they need to have it done by the binder check date), and showing kids how to create their own “checklist” to make sure they have everything in the binder done. I am a little surprised that sophomores and juniors are still finding this so challenging.

Some things I need to do regarding this blog:

• Blog about problem sets in Calculus and Algebra II
• Blog (briefly) about the change I made to Standards Based Grading in Calculus (scale is now out of 5). And also how this year is going compared to last year (read: better). And what still feels like it’s missing…
• Blog about achieving my goal from last new year’s… to read 52 books. And how I did it (short answer: I don’t know. It feels kind of miraculous.)
• Make a new Favorite Tweets (even though I haven’t been on twitter lately so it will be short)
• Update the Virtual Filing Cabinet

That is all.

# The Buttons, They Have Arrived

The top two I made last year. The bottom four I made this year.

That is all.

# Review Activity for Rational Equations

Last year, I did a review game that I got from Sue Van Hattum. I wrote that:

[this game] forces students to ask themselves: what do I know and how confident am I in what I know? (It’s meta-cognitive like that).

I set kids up in pre-chosen pairs, and they are asked to work together. In fact, I gave kids their new seats for the quarter, so this was their introduction to their new seat partner! They then are given a booklet with problems — and each pair is asked to work only on ONE problem at a time. (For those who finish a problem before others, I have alternative problems for them to work on.) When I see almost all pairs are done, I’ll give a one minute warning… Then I ask all students to put their pencils down and pick up a pen. We go over each problem, kids correct their own work, and using the honor system, they figure out how many points they have. (Scoring below.)

You can see three sample questions from our review game below…

[The .pdf and .doc file of the 6 questions are linked.]

I explained in my last post how scoring worked…

Each group started with 100 points to wager — and they lost the points if they got the question wrong, and the gained the points if they got the question right.

Some possible game trajectories:

100 –> 150 –> 250 –> 490 etc.

100 –> 10 –> 15 –> 30 etc.

Anyway, what was great was that the game really got students engaged and talking. Each student tended to work on the problem individually, and then when they were done, they would compare with their partner.

(If you try this, you have to make sure that students know NOT to skip ahead… everyone is working on one problem at a time. Then you go over the problem, and THEN everyone starts the next problem.)

So there you go… I don’t do reviews a lot, but for rational expressions, rational equations, and circuit problems, I figured we’d need a day to tie things up. And since this is one review I think works amazingly, I figure I’d share it a second time! Thanks Sue!