This school year has been a bit weird. I scaled back my duties yet I still have a lot of work to do outside of school. What gives? Well, each of my preps has presented some interesting challenges.

College Algebra

By far the class I underestimated the most. Not from a material point of view, but how the students would consume it. Turns out, whole group instruction doesn't really work here, I could blab all I want and some percentage is still going to need an individual explanation. In January, I started catering to that need. The challenge has been creating material that offers students a script they can follow and leaves me opportunities to have a conceptual discussion with them. I do not want it to devolve into a "do this, ok great, moving on" kind of thing. I want to retain the discussion aspect and that is requiring a lot of energy, as I have the same conversation 4 times in a class period. Pacing is still weird, many finishing assignments quickly, others taking their time (distracting themselves has started to play a part in this).

But on the plus side, the group in general is understanding new concepts, I'm probably saving time by cutting out the note taking, and it keeps the atmosphere really casual. Everyone still gets tons of time to work and enough face time with me than they can stand.

Calculus AB

Though we are slowly turning a corner, there's a lot of work to do here. I'm using yet another assessment system, and employ Desmos for benchmarks. Until we reach some future performance nirvana, I'm going to keep tweaking my approach in this course. Despite missing all that time at the beginning of the year and then another two days for ice, I think we're in a good place. It's that magical time of year when all the concepts finally start to make sense and you can discuss free response questions without major headaches. In a couple weeks I'll see if I was able to grow my exam participation (last year was 50%).

Calculus BC

We've entered uncharted water. We cruised through the AB material with little problem and now we have to tackle the material that's unique for them. It feels like we have eons of time to get ready. Since the class is small and they're all doing great, there isn't same benchmark mechanic necessary here, they're all taking the exam. As much as it pained me, I decided to bite the bullet and jump into sequences and series now before it starts to feel like we're running out of time. It is my weakest content area, so there's been a lot of studying and restudying and restudying to try and make sure I have it all straight. I knew it was going to be a rough period. But slowly, the light at the end approaches.

Common Theme

What's the problem really then? I have to make TONS of stuff. College Algebra is loosely based on my last attempts at Algebra 2 but the "no talking" structure of the class has really made me rethink a lot of things. Pacing still throws me. Calculus BC is all new territory as I relearn the material myself AND come up with ways to teach it. Calc AB is the one comfort zone, I know what I need to do, but there's still a lot of retooling required.

One day I will take a summer and write some kind of definitive practice book I can use throughout the school year, but that day has yet to come.


AuthorJonathan Claydon

A friendly reminder that we all have our days.

Friday was fairly straightforward, Calc AB and College Algebra had assessments, and we were going to fiddle with Taylor Series in Calc BC. Easy, right?

First I'm five minutes late. I also haven't made copies of anything I need for the day. So, open the room, wave the kids in, dash up to the copier. All this as the first late bell is ringing. On the way up to the copier two kids are trying to make a run for it out an exterior door. Got them back inside and shoo'd about 15 others who were trying to sneak in to avoid being late, a common problem we have.

Copy room! No line! Yes! Except the first machine I try throws a bunch of errors. Don't have time, move on to another. I get things copied and cut, and at this point it's almost 8:00, nearly 15 minutes into class. My first class needs to take the assessment that is currently in my hands. Fortunately it's short (Calc AB takes ~30 minute assessments that they check at the end). I manage to check homework and get them started such that they have plenty of time to work.

I didn't make the answer key in advance (each AB class has their own version of the test for which there are 2 sub versions, so 1 AB test = 6 keys), so I work on that while they work. Time's up, we check, no errors on my part.

Second Calc AB group comes in. Things are calmer now that I'm ready. Check homework, pass stuff out, work on their answer key. Time's up, we check, aaaaand I screwed up a couple of them. A small riot breaks out because kids are very adamant that there's no way what I have is the answer. And good for them being confident in their work enough to call me out. This will be important later.

Fortunately there's enough time before they leave to correct the mistake. They calm down and are able to check their stuff accurately. The rest of the day passes with minimal incident. College Algebra and Calc BC proceed with no problems.

Last class of the day! I even made the answer key while College Algebra was working so I didn't have to scramble. I chill out while they work. Time's up, let's check!

"um, what...?"
"I'm going to cry..."

Actually, I don't remember anyone boo'ing, but there was, simply put, a scene. I don't know what funky logic I was using while completing their key, but MAN, there were some problems. Unfortunately there was not enough time to figure out everything that was wrong, so they were only able to accurately gauge a couple of them.

It all worked out in the end, I found all the errors in the various keys, kids got graded accurately and there was a greater calm on Monday when I passed them back (kids do an initial check, I then verify and assign a score).

You never know when these moments of crisis will arise, the important thing is to trust the procedures you have in place. Kids were confident enough in their work to call me out. I was confident enough in them to take a second look, and not so confident that I can't admit fault in front of them. It's fine for kids to know that yes, you bleed.

AuthorJonathan Claydon

Though I don't write about it much, I've been teaching College Algebra this year. The kids aren't earning college credit for it, it's more of an alternative to Pre Cal we're offering for students that need another year of algebra. The Pre Cal we teach isn't like some places where you're doing Algebra 2 all over again, so our version of College Algebra makes a nice option.

Interestingly enough, I have two very small sections, 18 and 16 kids in each. It's been a long time since I've had classes this small. We had a bit of a population boom since I started and some quirks happened to bring class sizes down this year despite a very high overall population. The biggest lesson I learned from those early years with small classes is that they were totally wasted on early teaching me. I always wanted a chance to do a better job with that kind of environment.

The first challenge was their work pace. These kids are great, but they're all over the place. I developed a technique for dealing with that last semester.

The new challenge became holding their attention. For whatever reason, they aren't interesting in listening to me speak in front of the group in a traditional sense. I noticed this back in 2013 when I reframed Algebra II around lots and lots and lots of classwork. The kids got so used to knowing math class would require them to do something, that listening became problematic. They just wanted the classwork and it was crazy. Same thing here, this College Algebra crew eats up their classwork. But lecturing? Forget it.


How did I fix it? Let's look at a multi-part assignment I gave for inverses:

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On the surface, this looks like bad textbook worksheet moves. Steps are labeled. Kids follow the steps. Repeat.

The Mini Lesson

As mentioned, these groups work at varying paces. As the semester has gone on, they've gravitated to sitting with kids who move at their same pace. Generally, I know which table is going to finish first and which takes some time. This frees me to wander, stop, and initiate a discussion.

This multi-part assignment came with three discussion phases. As a group finished a part, we discussed what they learned. In Part 1, we made some observations about the data points from the table. We ironed out the relationship I asked them to observe, many noticing right away that it looked like some kind of reflection. I floated around and had the Part 1 discussion several times, with audiences of 3-6 kids each time.

For Part 2, we expanded the idea. Can entire equations be reflections of one another? Do the observations about points still hold true? Are the points of one equation just reflections of another? Could we come up with a counter example?

Part 3 is a culmination of the first two discussions. Now that we seem to have a definition of inverses in general, can you determine them on your own and check your work with a graph.


My classroom is uniquely designed for this kind of set up. Near each table is a screen replicating my teaching computer. I can carry a keyboard and trackpad with me to manipulate stuff from wherever. I can also make use of their work as we talk since it's right there with us at their table.

I think it went really well. It was easy to get the kids to focus because there's no hiding when it's a group of three, or even six. The kids were eager to share their observations and made some good ones, all catching on quickly. The pacing allowed kids to work independently and have a piece of my attention. In this classwork heavy setting, I have been very free to offer more face time than these kids could ever want.

From an outside perspective it probably looks chaotic. From a breakthrough perspective it's not that special. It's just some scripted tasks leading kids towards an observation. Kids do some work, practice some things, get tested over those things. The key part I think is that the teaching element hasn't gone away. I'm still their main source of information, rather than videos or whatever. I'm still facilitating discussion and offering new ideas even if the tasks aren't particularly exciting, such is the nitty gritty algebra sometimes. And the kids are more than willing to give everything a try, mistakes are no big deal when it's just a few people sitting around a table.

I like where this is going.

AuthorJonathan Claydon

Have you resolved to document more of your classroom experience this year? Or do you want to start making some more organized reflections? Let me offer some unspoken policies about how I operate around here. Maybe these will help you find your own voice. This is not some set in stone set of rules and feel free to ignore one or any of them, but it's the pattern I've settled into.


Write about the good things. A lesson that went well, a positive moment in your career, or a positive development you've made in planning something long term. If you're going to be negative, make it about something that was in your control. A procedure that could use work, an end product that's missing an extra something, or a better seating arrangement. Being negative has its place, and I certainly write about lessons that don't go well, but the intimate ins and outs of events on your campus may not be best suited for the internet at large. Dealing with local issues is usually best done locally. I have work place ups and downs, but this isn't the place for them.


I write up lessons and projects that I do throughout the year. I include some information about what happened before, what the goal of the project was, and how it might be an iteration of a version that came before. I document lessons so I can track their evolution over the year. Nothing pushes you to better ideas than looking back on the ones from last year and seeing what can be done differently. These are the bulk of my posts and done for my benefit primarily. They help me remember things for school years in the future and help me compile evidence for end of the year appraisals. If someone wants to see how I'm making use of Chromebooks and they didn't happen to see it during an in person observation, I can have 6 links ready to go in 5 minutes because I spent the year keeping track. Since starting a site, submitting stuff for appraisals has been an absolute breeze.


I keep the opinions to things I have control over. I have opinions on lessons I gave, what was done well and what was not. I have opinions on content, what's important and what could be done better. I have opinions on curriculum, and how it can be worked through better. I also have opinions about local on campus issues, but again, local problems are best dealt with locally. The internet is not the place for me to go on a rant about class size, or cafeteria menus, or whatever. Unless it's "I tried the school lunch fried chicken and let me tell you, WOW!"


I don't write up stuff in exchange for money. I don't write up stuff because an enterprising ed-tech person e-mailed me about it. If I discover or am directed to a product and I believe in it, I'll write about my experiences. I also don't have intentions of offering stuff for sale or taking donations. I'm in this for the betterment of my practice and the practice of others.


Lessons and projects are great, but I also play around with themes. Maybe I do a series on Pre Cal lessons that have worked well. Maybe I talk out loud about a new way to organize a class. Maybe I make a post about what's inside my classroom closet (which has totally happened and probably needs a version 2). There is no set requirement about what makes something worth writing about. If I'm in the mood to write it up, it gets written up.


I am the primary consumer of my site. You will be the same. Write what you want to write. Write what's interesting to you at the moment. Write what will help you the most. If you need to write up a million lessons to work through some things, do it. If you want to write about classroom furniture, do it. If you just want to post a daily picture with a caption to help you remember sequencing or something, do it. Your platform is yours and it should please you the most. If other people start to enjoy it, that's a bonus.

AuthorJonathan Claydon

Part of my Calculus procedure has been taking some benchmark data on my kids throughout the years. Other than improving student attitudes about Calculus, the second big priority is making sure students have an informed opinion about how they might do on the AP Exam. Kids are always free to do what they want, but I want to make sure if they're going to spend the money on that thing that they have a shot. Our results have been creeping upwards, and we are poised for a breakthrough, at least I hope so.

My data collection schemes have been problematic though. I think I've been a little too aggressive, giving questions that students probably aren't ready for in December. With the significant hurricane delay, we weren't even ready for what I've tried in the past, so I needed a new scheme. And with 75 students in AB, I needed something that'd be efficient to process so students could get feedback quickly.


A public version of the activity can be found here: Calculus Gauntlet Public

I wanted to test three things: Fundamentals (trig values, limits, continuity), Interpretation (curve sketching), and Skills (derivatives rules, Riemann sums). Roughly 12-20 items per section. I wasn't going to belabor any skills, if you can do it once you can do it ten times I figure. I sketched out what I wanted in each section:

To gather all the information, I was going to use Desmos Activity Builder. I didn't want to juggle a lot of papers, and I wanted a better idea of what items were causing problems. With previous benchmarks I had a vague idea of which questions didn't go well, this time I wanted to know for sure.

I included a mix of items: entering answers, typing short answers, multiple choice, plucking data off a graph, sketching on top of a graph, and some screens where problems were presented that students would complete on little cards they'd hand in. I wanted to assess their ability to determine a limit/derivative without making math entry fluency a limiting factor.


I initially planned 3 versions with 6 codes, but the reality of sifting through all the dashboards made me reconsider. I settled on 3 versions with 3 codes, randomly distributed among my class periods. There were 44 screens total, and 25 kids on each code.

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The "version numbers" are just arbitrary hexadecimal numbers (go ahead, convert them, see how dumb I am) designed to obscure the number of versions. I was giving this to a lot of kids all day long over multiple days, I knew they were going to discuss it, but I wanted to make it a tiny bit less likely that they could figure out who they were sharing versions with.

Again for data collection simplicity, kids would access the same activity across multiple days. We use Chromebooks with school Google accounts, so linking their accounts to Desmos took 2 seconds and was done earlier in the year. I used pacing to restrict them to the section of the day:

This was one of those features I knew was going to come through, but didn't totally trust until I saw it in action. There wasn't a single technical issue over the three days. Each day the Activity Builder remembered the kid had previously accessed the activity and jumped them right to the section of the day. It was really elegant. Sketch slides with a trackpad still kinda stink, but I was not super critical of the results.

Data Use

At the completion of each day, I did some right/wrong (I was pretty unforgiving here) tallying in a spreadsheet, and determined raw scores for the various sections. I also tallied up incorrect answers to see how questions performed. I would eventually throw out the worst performing questions in each section:

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After three days of data collection, I set out to determine my final product. What were students going to get about their performance on this giant activity?

The intent of the activity was not to assign a grade based on their raw performance, merely to give them a snapshot of where they stood on December 11-13. Yes, this assessment would factor into their course grade somehow, but I wasn't going to cackle in delight as I failed tons of them, that's not what this was here to do.

Being able to click through dashboard screens and tally results was quicker than I thought, maybe 1 hour a day. Generating something meaningful from the data and formatting it nicely took another couple hours.

The other nice thing about this collection method is I could quickly check for version bias. Each of the three versions had questions that were identical, but others that were modified. Codes were distributed at random, and for whatever reason one version registered a higher average raw score. I curved the other two versions up, roughly 1.16x (normal College Board is 1.20x), so that the group average was the same as the highest average. I took the resulting adjusted score, divided it by max points available, which gave each student a percentage and quartile.

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From left to right: class period, fundamentals raw (max 20), curve sketching raw (max 13), skills raw (max 18), raw total (max 48, three questions were deleted), version adjusted total (if required), percentage, quartile. Average was right under 70%. Seven students earned 100%.

I told the students about 10 times, that the percentage was NOT their grade on the assessment, it was merely a tool to see where they landed in the overall population. My message was this is one data point in a series of many and that we would be doing these again. I also wanted to communicate that 1st and 2nd quarter implied you were doing a good job, 3rd quarter meant you needed to study more, and 4th quarter should have been a little wake up call.

After handing out the slips I floated around and had a quick chat with each kid, affirming their work or letting the lower ones know that this number was not a personal judgement, but that something more is required of them.


This went pretty well. The kids took it seriously, the majority of students did well, and I think all of them got useful information out of it. More importantly, this activity was easy to build, easy to manage, and easy to score.

A great experience start to finish.

AuthorJonathan Claydon

As I've progressed through the career, I have tried to keep track of my base principles. What should always be true about the way I work? What should always be true about the way I run the classroom? And how do you keep it simple to avoid a self-induced pressure cooker?

Know the Content

Above all, I need to know what I'm talking about. I don't want to regurgitate something from a text. I want to make sure I understand a topic, how it works in general, how it might connect to something students have seen before, and how it connects to where I want to go. I want my content to tell a story. It's not necessary that the kids even know they're in the middle of a story, just that they can trust me to talk about things in a logical way that flows nicely. That we don't just study things at random because some curriculum guide told us to do so.

Initially, this was the hard part of the job. I am so upset if I teach something incorrectly, in a tricksy manner, or in an obtuse way. Really grinding away at the content early on has had the biggest payoff. I can sing you the ballad of Pre-Cal complete with a dramatic Third Act in my sleep now. But knowing the content doesn't mean you have to be perfect.

Know the Flaws

I screw up. I admit this to the kids. I make them keep an eye out for my mistakes, because they will happen. I try to model a good attitude when it comes to mistakes. They are ok! Even college educated adults make them! You would not believe the countless mistakes I have made on homework solutions, assessments solutions, and live in the middle of some topic. I recognize that I am going to make mistakes with the math and accept it. I try to minimize them sure, but I don't beat myself up over it. On the off chance I do cover something in a weird or incorrect way, I profusely apologize to the students and make it right.

I also know the flaws of my teaching style. I ramble. I get side tracked. I tell silly stories. The kids know this and in some cases are good at purposely triggering me into a distraction. I have gotten better at recognizing this in the moment and try to minimize the distraction. I don't stop, it makes class fun. It gets the kids to open up and usually leads to each class developing something funny that's uniquely theirs. I have classes that happily sing happy birthday to each and every office aide that wanders in, and that's fantastic.

I misinterpret kids questions and give answers they didn't ask for. I ask questions they don't understand. I think kids are talking to me or about me when that's not the case all the time. I trip over my words. I do all kinds of silly imperfect things. But that's cool, everyone does. It's ok to be a real person in front of students.

Know the People

In 7th grade for whatever reason I approached my art teacher and said very boldly "do you even know my name?" In a true pro move she smiled and said "Jonathan we need to talk about a drawing I want you to make for a contest..." not only deflecting my sorta rude question, but showing me that "ok punk, not only do I know your name, I know you're talented too."

The school I attended in 6th grade had been larger and I felt lost in my big classes (each around 30+). I suppose it was natural to think this teacher generally didn't know me much like the others. And for whatever reason this incident has stuck with me for 20 years. I greatly appreciated all of my teachers who took a moment to acknowledge, yes kid, I know who you are and what you bring to the table.

That's probably the biggest of my base principles. I need to be tight when it comes to presenting and teaching, but I need to be tight on my soft skills too. Each kid should feel like it's ok to talk to me, that we can have a conversation, however brief, that it can be about whatever, and that they know I'm aware of what they're up to and how I might improve things. I have structured so many of my classroom procedures out of building in time for me to get to know the students. If I'm talking 45 minutes a day, every day of the week, that can't happen as well as when I hand out some classwork, turn on the music, and go wandering.

AuthorJonathan Claydon

Year Four of Varsity Math. Every year there seem to be weird things that make each group unique, adding new features to our brand. Last year saw the juggernaut of Baby Shark. And boy is that sucker still going strong. We also constructed a Hall of Fame. What's new this year?

Varsity Math has become a brand unto itself and brands have to be managed. You have to keep them in the public eye. The hardest part for us is that 99% of the members graduate. This year we had 0 returning students. For 2018-19 there will be 3. Summer Camp has served as a great on boarding tool, bringing kids into the program in a fun way and hopefully making them that much more excited for the start of the school year. But what about during the school year? How do you get all the kids who didn't go to summer camp and who might only vaguely remember seeing goofy dorks with t-shirts running around?

Promote the crap out of it. Collecting money and generating merchandise takes some time, but once it all arrives I like to have a Nerd Day. A couple weeks ago was the 2017 edition. All the AP kids wear their shirts and patches and stickers on the same day. It gets people talking when ~100 kids not on a sports team all dress alike. At the kids' request I diversified the merchandise and added custom sunglasses:

And in what is by far the goofiest stunt I've heard of, a bunch of them had a parade of sorts at lunch. I was clueless it happened until after the fact when 10 or so kids ran to my room to tell me what they did. It was pretty simple, they did a lap of the cafeteria, sung a poor unsuspecting kid happy birthday and took a group photo:

The contingent that eats lunch earlier in the day was sorely upset that they missed out.

Recognizing that this is the future and something doesn't happen unless it gets recorded on social media, I bought a Snapchat filter for the day. It was geofenced to the classroom and cafeteria sections of the school and I told kids to post, post, post. They did not disappoint:

And the stats were pretty impressive:

I collected as many of them as I could and assembled a giant collage for posting out on the Hall of Fame (2 of 9 pages shown):

The parade was a little silly and over the top, but a sign of how much fun the kids were having. And were you to hang out in my room, you'd find that "over the top" is kind of the status quo anyway. To have the kids in AP math excited to be a part of it is one thing, but the fact that we can generate buzz around the school at large is so awesome. AP math as the cool kids club, who knew?

AuthorJonathan Claydon

In July I spent some time at Desmos HQ driving Eli's Lambo and shooting the breeze with people about how they incorporate Activity Builder and how the Desmos staff see as the role of Activity Builder in the classroom. Two things stuck with me: be thoughtful in AB design, and see how could change the way I assess.

Prior to my visit I had decided to experiment with Activity Builder more. I saw a lot of great work with Pre-Cal kids having to explain their thinking more, and Calculus kids could certainly use the same. The language barriers for making mathematical arguments have been a barrier for my students in the past, and I want to start being more picky about that kind of thing. I also want to push my kids to better understand how the regular Desmos calculator works with regard to restrictions, notation, and such.

In 11 weeks I've done 9 actual, premeditated Desmos activities between Calc AB & BC. There's at least another half dozen instances where they used it to make a project or annotated a pre-made calculator page. Here's a small sample of stuff I tried:

Calc AB

Being a math-based LMS, having access to notation is great. Here I asked AB a series of questions about derivative methods:

Being able to let kids sketch is also nice. For an activity on curve sketching, I provided the first derivative and they had to sketch the original function as well as the second derivative:

I really like slides where something has to be added to a graph, makes it easy to see how much a misconception has propagated. Here I can quickly tell that two students misinterpreted the initial picture has f(x) rather than f'(x). Were they working together? Did this idea manifest in separate parts of the room? I can figure it out fast.

Calc BC

For BC my built activities are part of their regular assessment program. I also incorporate it into their classwork a lot. While doing area between curves and volume, I was able to share a calculator page with them and have them add integrals to it. At regular intervals they complete Activity Builders as closed notes (though collaborative) assessments.

Here they shaded regions of a velocity curve where speed was increasing versus when speed was decreasing:

It's also been easy to adapt free response questions to the format:

Since it's a smaller group we've been able to learn a lot of nitty gritty things about the calculator. How to use folders, make dynamic labels, define variables, etc.


In all cases I make sure the activities are short and sweet, usually less than 10 screens. I consider what the activities let me do that's not possible with paper (for instance, compute nasty integrals). I also make sure the kids get to see the data that gets collected. In BC for example, we always go over their assessment when it's finished. I'll call up the dashboard and scroll through interesting answers or demonstrate common issues. At no point are kids being called out to mock them for getting something wrong, rather we use it an opportunity to discuss what mistake they might have made and how what we can all learn from it. Kind of like a digital "my favorite no" kind of thing.

There are still some scaling issues I'm working on. For the most part paper assessments are still faster for AB given the size (75), but there's potential there. So far it's working great. Kids can use the system well, I get useful information from it, and the technology gets out of the way.

AuthorJonathan Claydon

As an avid reader of Teacher Internet™, you may think it's all wild innovation and maker spaces in the math universe. Not so! Every day we all have very uninteresting procedures we have to implement, the real workhorse of any classroom. It's the inescapable part you don't read much about. At some point, you have to put away the VR goggles and 3D printers and give an assignment. In my attempt at College Algebra this year, I do exactly that, a lot.

My audience is ~30 kids split into two classes. That's really small, for me anyway. When there's only 15 people in the room, everyone gets face time for as long as any kid could possibly want.

And some of them take all they can get. Another feature of this audience is they're all extremely capable, but we're all over the place in terms of how long it takes for stuff to click and get assignments done. One kid is over and done with the task at hand in 10 seconds, where another needs 5 minutes. Adding to the challenge is just who is super speedy varies depending on the task. It is a weird environment.

Number one message I send to this group is I don't care at all how long it takes you to do something, I want you to understand what you're doing at the end of the task. If that means we're in 15 different places some times, that's fine. Most of these kids have been fighting the speed thing for years, I think it's time to give them a break.

How do you accommodate such a group? With work time, tons of it. I think I stand and talk in front of this group like 20 minutes a week, tops. The rest of the time they're working on problem sets. It is, by far, incredibly uninteresting. But uninteresting != boring.

Yeah, they work all the time, but the tasks are varied. There's some solving, some listing, some writing, and some graphing depending on what we're doing. And at no point are they working on a task to the point of exhaustion. Enter my go to format this year: 9-6-3.

Take a skill, have them perform it on 9 items, do an extension on 6 of those items, and finish with an analysis task for 3 items. Based on my observations the first few weeks of the year, this format keeps everyone at a similar overall pace despite their varied work speeds. 95% of the kids can complete all of that in the time allotted. Although 5% won't quite finish, they really get the ones they dd because they were given the time to sit and contemplate for a while. There's like 10-15% who finish pretty fast and without any prompting by me will be helping other kids around them.

I think the biggest success in this format is other than the initial "do this for all 9" the remainder of the choices are up to the kid. I'll do similar tasks with "here are 6, pick 4." I'm sure there's something in here about choice theory or something, but the kids put up no protests under this system. The kids take ownership here, managing their time to make sure they can do what's expected. That's the other big component, an inspection always comes and they know it. My inspections aren't a big deal, but it's a little thing that sends a big signal: I want you to try something and I want to see how you tried.

In the end all the kids get in reps, they aren't exhausted, and the ones who need to ask a ton of questions have ample time to ask their questions.

AuthorJonathan Claydon

A couple weeks ago I had a little fun with BC on Halloween. I liked the mechanics of tying a math problem to some bigger puzzle. This is no different than those escape box kits you can buy for way too much money.

For the first time we were looking at a week off for Thanksgiving, so I wanted something to do on Friday that would be a nice closure. Most people go test here, but I was not in the mood to take a big to do list home. In AB we had made some good progress of curve sketching. Students knew how to start at an original and sketch the two "lower" functions as well as start at a second derivative and sketch the "upper" functions. We'd talked about critical points of the first and second derivative as well as what they represent.


In this activity students would work with a partner and be given a random 5th degree polynomial as a starting point. On the back was a word, seemingly random.

I started with 5th degree polynomials because it offered a lot of variety. I mixed up the types of behaviors, repeated x-intercepts, and included some with their reflections to ensure students took the time to analyze the functions as we had done. The students objective was to start with their randomly assigned original, find its first derivative from a bank of choices, and then find the second derivative from another bank of choices. All their cards would have a word on the back.


The hallway set up like this:

Minimums and maximums were marked on the f cards. Minimums, maximums, and x-intercepts were marked on the f' cards. X-intercepts were marked on the f'' cards. As I made a lot of similar functions on purpose, I wanted some anchor to help students determine if they were on the right track. They'd have to find the functions with the appropriately matching critical points as well as behavior in order to complete their set.

My largest AB class has 28 students, so there were 14 sets. SOURCE GRAPHS

In Action

How would they know if they had completed their set?

The words on the back of the cards are seemingly random, but they aren't at all. Some time ago I watched a video on the Remote Associates Test (RAT), a mechanism for studying intuition. When presented with three words, they trigger a related fourth word as a response. Some fourth words are more difficult to determine than others. Sets that comply with the RAT methodology are available right here. Students wishing to validate their set would read me the three words they collected. If they formed a valid RAT item, I proceeded to let them guess the fourth word. If one of the words was incorrect, I would tell them which one.

For example, if a student told me ACTOR, FALLING, DUST they had a valid set. The hurdle to their prize was to correctly guess STAR from the prize wall.


Now in an official RAT test, it's not a multiple choice thing. I wasn't really out to do any kind of behavioral study here, so all the 14 possible final words were available for them to see. To prevent random guessing, students had two chances to guess their fourth word. Failure to do so and they forfeit the prize. If they successfully guessed the fourth word, they could open the locker and retrieve the candy inside.


Students would take pictures of their original and walk between the f' and f'' sets while having discussions. Some would retreat to the classroom and sketch the set and go hunting for something that matched. Some theorized they could try to reproduce the function in Desmos, though most abandoned that idea when they realized there were faster methods. The idea was for them have a discussion about function behavior and how f, f', and f'' are linked by critical points.

All students were able to claim their prize, some in as little as 10 minutes. The longest anyone took was about 20 minutes. Most groups produced a valid set on their first try, those failing to do so usually had the second derivative incorrect. In a handful of cases students made a mistake at the first derivative but found the corresponding (though overall wrong) second derivative, meaning their 2nd and 3rd words, while matching each other, were not valid when grouped with their 1st word. One poor kid had the set right the entire time, but had misremembered the first word, leading me to intervene to figure out what the heck happened.

As a point of comparison, I let BC loose on the task too (mostly because I over bought candy and needed a way to get rid of it). They did curve sketching a solid month ago so I was curious to see what they remembered. Unsurprisingly, all of them cracked it in 5 minutes or less.


This passed with flying colors. Wrapping my head around the decoding scheme took some time, but the use of RAT was really clutch here, a ready made puzzle that provided just enough of a pause point to add a nice challenge at the end. Some students spent many many minutes deliberating what their fourth word was, dancing around it the whole time. The two guess rule really put the pressure on. Designing functions that were similar but not too similar took the most time, as well as all the screenshotting, printing, and cutting. Oh, and a lot of nervous labeling. One misplaced word could derail the whole thing, so would losing the sets I used. I clutched that sucker TIGHT.

Loved it though. I'm not sure I've had a first time task go so smoothly.

AuthorJonathan Claydon