Every year I'm amazed at just how much there is to do at the end of the year. It's already time for the second year of Summer Camp. I mused last winter that offering an enrichment program to my existing students might be a hit, and they proved the theory correct. Despite the wandering topics, the kids had a great time. I had a great time. It was a great time.

After the first day last year I knew I was doing it again. 


Like last year, I want the students to dictate the agenda. If they want to wander down a rabbit hole, we will explore all there is to see. I'll lay out a few base objectives and go from there. I want to simplify the focus a bit and just have a few bullet points to hit.

  • financial literacy
  • spreadsheet/programming literacy
  • space
  • drones
  • games

A new component will be a game of the day. There are a billion non-phone non-video games out there, and the only one my kids seem to know is UNO. I think we can do better here. Last year's live action parser proved to be quite popular.


The surface objective is to explore some random stuff in the summer. The secondary objective is to focus on relationship building. All of these kids are enrolling in AP Math next fall. Unlike last year, about half of the campers will be new to me. This a unique opportunity to work with them prior to letting them experience the full insanity of Varsity Math.

The fascinating thing is just how many kids are super excited to do something in the summer. Most of my participants jump at the chance because their summers are fairly unremarkable or their parents want them to be up to something productive. I handed out 60 permission slips for about 50 spots. Two days after handing out the forms both sessions are half full. I expect camp will sell out before the deadline. It's awesome.

AuthorJonathan Claydon

A few years ago I hit upon this project for polar equations of conics. Objects orbiting stars can be modeled more or less as polar ellipses, with their host star as the focus point. With a little Wikipedia finagling, you can recreate our solar system.

It's pretty cool, and with new Desmos labeling abilities, it's easier to distinguish what's what. However, the project had a case of the samsies. Every kid or set of kids was making the same thing. There was a lack of creativity. I don't know why it took me so long, but this year I changed it up. I wrote up an explanatory document and let them design a solar system of their own.

We got some very nice and orderly systems, and some whose planets wouldn't survive very long before ramming each other to pieces. I encouraged creativity with the themes.

This one took a little longer than I thought (about 2 hours or so), but I find it important to relax a bit on time requirements if kids are putting in a lot of effort, and that was definitely the case here. Lots of good discussions about how to vary their objects, what various eccentricities would do, and how to manipulate orbits just so.

AuthorJonathan Claydon

It's a little baffling that this is our sixth adventure out on the sidewalk.

The complete archive:
Sidewalk Chalk Adventures
Return of Sidewalk Chalk
Sidewalk Chalk Three
Sidewalk Chalk, The Fourth One
Sidewalk Chalk Five


I'm a fan of big, obvious evidence that my classes have something to say. Sidewalk Chalk Day is one of the oldest ways we make that happen.

This year, about 250 students in Pre-Calculus and Calculus took to perimeter of our school and decorated the campus. For Pre-Cal, students were tasked with designing two types of polar equations. They graph the functions and write the equation responsible. Calculus has played along too, but never on the same day. Their task was to generate a slope field, region between curves, or f/f'/f'' family and immortalize it in chalk. Students use Desmos, print out their creation and bring to life like it's elementary school all over again.

Fly High

For the latest installment I brought along some new helpers:

It's always hard to capture the scope of this project as it has grown over the years. We cover about half a mile of sidewalk over the course of 5 hours and consume a small mountain of chalk. These spectacular views brought to you by my robot friends:

It's a great way to spend a spring day. Enjoy this fly-by:

AuthorJonathan Claydon

Fun milestone a couple weeks ago:

Sounds crazy right? Lots of people would have you believe the future of computers in the classroom is those dystopian pictures of kids in cubicles with headphones on. Turns out you have other choices. So what were we doing during this magical week?


We were wrapping up area between curves and various volume expressions. I figured it was a great opportunity to let them play with integral notation on Desmos. Super duper handy for expressions of volume/area with respect to the y-axis. TI-84s can't touch this.

Later in the week I gave them a pre-loaded set of regions with a request for a particular integral expression (area between curve, solid built with square cross-sections, etc) and had them enter their results into an activity builder.

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Student's ability to play with function notation here is awesome. Being able to collect math input through Desmos was a neat experiment.


What haven't we done on computers in Pre-Cal this year?

To start, we finished a study of three-dimensional vectors with an opportunity to make some 3D objects in Tinkercad.

With our study of vectors and polar coordinates, I offered students a glimpse at what spreadsheets can do faster than people. Namely, kick out a bunch of polar points and convert them to x-coordinates and y-coordinates.

Some students needed helpers:

Then, super quickly, and with several "ooooooooohh"s, we dropped the x/y table into Desmos for an initial look at the graphs of polar equations.

We refined the ideas present here through the use of an exploration activity made with Activity Builder.


In each situation the computers came out because they can perform the task better and faster than pencil and paper. In the case of Pre-Cal, they extended math to a place they didn't know it could exist before through spreadsheet formulas. Calculus got a chance to speed through volume because of the ability to see a region, talk through the logic of how to define an integral around it, and then see that integral computed in the same window. That took us a million button presses and a stack of copies previously, with no option for functions defined in terms of y.

A+++ would teach again.

AuthorJonathan Claydon

Maybe this isn't a big problem for you, oh Calculus teacher, but it's a yearly issue for me. What do you do about kids not taking the AP Exam? No one would fault you having them work through the remainder of the curriculum, because not taking the exam isn't an indicator the kid is woefully lost. However, the way I do things, if I advise a kid not to take the exam, or they've chosen not to, there's a lot of evidence behind that decision. It is very likely they need (and have needed) some help for a while.

Last year I didn't have a lot of these students. Coming up a with a list of practice assignments for them to complete was easy, and fielding their questions wasn't a big burden. They did their thing and, hopefully, they got to leave Calculus with at least some fundamental knowledge about the course.

This year the challenge is bigger, I have a significantly larger number of non-testers. My filtering process got stricter (on purpose), so it was a natural result.

To improve these students' ability to be self-sufficient, I generated assignments for them as before. However, I added a little treat. For years and years and years kids have been asking me to make a database of recordings. I struggled with workflows, file sizes, and practicality, ultimately deciding each time it wasn't worth it.

Enter iPad Pro.

I've had Wacom devices for years, and still use a Cintiq daily in my classroom, where working with a full computer makes sense. Here, I have a more focused purpose: short (<5 min) explanations for kids who already heard this once, with material relevant to a specific assignment. Enough to help them answer their own questions so I can focus on other tasks during class time. Generating things like has been tedious with those devices. Having a self-contained slab I can write on works better.

The workflow is dead simple. Attach iPad to a Mac, open QuickTime player, start a New Movie Recording, and select the iPad as the camera:

An external mic is optional, the internal microphone will probably do the job. Export the files as 720p movies, and plop them in Dropbox.

Their titles mirror that of the relevant review assignment. A non-tester grabs a computer, opens the shared folder link, and works at their own pace.

Some MAJOR clarifications about why I don't consider this in the same category as super buzzword-y "Personalized Learning":

  • This is a limited run engagement, kids are using this for 2 weeks while I address other issues with exam takers
  • They got live, in person exploration/explanations from me once before, these videos are not intended for first time learning, the kids using these have some working knowledge of the concepts in play
  • This is intended for use during class, I'm not explicitly requiring they do any of this at home
  • The videos were produced quickly (record video, export, done) with a laser focus objective: offer clarification through worked example if necessary
  • This is an opportunity for kids who have been behind the curve to feel some accomplishment and back track

I'm not replacing myself with videos any time soon. I stand by my belief that having kids work through an exhaustive database of tutorials, machine graded tasks, PDF worksheets, and whatnot is nowhere near a valid replacement for talking face to face, having in person discussions with peers, etc.

If you have access to sufficient devices and are considering some kind of tutorial database, use it sparingly. Find a specific use case and keep it simple.

AuthorJonathan Claydon

As a general rule, I don't like to let activities linger in a particular state. There are always subtle tweaks to make or the tough decision to cut something loose and try again. The advent of Chromebooks in my classroom has opened up a lot of opportunities we just didn't have before. Realized recently when it was time to talk about three dimensional vectors.

Historically, I turn the room into a giant coordinate system, we discuss how to orient ourselves in 3D space and I've had them build stuff out of straws. It was interesting at the time, though time consuming. Due to the nature of building things out of straws and electrical tape, the creations didn't last very long either.

Enter Tinkercad. I'd like to thank Autodesk for a monumental shift in the way they approach access to their software. Fifteen years ago, AutoCAD or the various things a college student might need were prohibitively expensive. It all came down to knowing the right person in the dorm who had license keys of a shifty nature. Since about 2010, they've done a total about face, making tons of great stuff available for free or cheap for students, teachers, or anyone who isn't a corporation. Tinkercad is a browser-based 3D modeling app that lets you mock up whatever you like. There are pre-built simple solids, and you can browse a whole library of community built objects and drop them into your design.

Rather than mess around with a bunch of straws and tape, I set my Pre-Cal kids loose on Tinkercad and gave them about 50 minutes to make something. The site's export options are intended for 3D printers, so we stuck with screenshots from a few different angles. We got some really awesome stuff.

Chromebook trackpads aren't the greatest, so this was a tad challenging for some. I do have touchscreen models, and kids with those were very happy with themselves. Wired mice can be had rather cheap in bulk, so that might be an idea for next year.

AuthorJonathan Claydon

Last year in Calculus I gave kids an open note assessment on volume with respect to the x and y-axis. There were two handouts. The regions and the questions.

It took.......forever. I had a lot going on here. We had had a jam packed week where we talked about the area between curves, cross-sections stacked on top of the region, AND solids of revolution. Plus there was the x-axis/y-axis context to wrap your head around.

This year I streamlined it a bit. We took our time and focused on area between curves. We did some extensive practice on identifying expressions for various x-axis and y-axis based regions. That was a huge problem last year. My kids weren't comfortable with simply defining the area, so slapping the volume idea on top just added to confusion. Since defining the area is really the hard part of any volume expression, it was important to invest our time here. Afterward we focused solely on built-up solids with known cross sections. We can save rotational solids for later.

To stream line the assessment process I prepared the regions in Desmos and shared the collection with them. I also requested far less information about each region: a single integral expression for each one, either an area or a volume.

For collection I set up an Activity Builder where they can type their integral and its result for submission.

I'm hoping the more methodical approach helps here. Gathering input through Activity Builder is promising as well. Integrating functions with respect to y is probably my favorite Desmos feature these days.

AuthorJonathan Claydon

After six years, I have put quite a bit of material online. I share tests, problem sets, lesson ideas, and have taken thousands of pictures. Some of that material has taken on a life of its own as teachers continue the great pursuit: what's something I can use tomorrow?

The teachers I watch on Twitter are in great contrast with the teachers I encounter locally. Little focus on the big issues, always looking for the next great idea starter or lesson resource. That seems to bear out in my statistics.

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Nothing on this list was written in the last two years. A certain subset of you seem interested in the most recent thing I have to say, which is awesome, I'm glad you like what I have to share. A vast majority are after the archives, the stuff they could potentially use tomorrow. In most cases they're finding their way here from Pinterest, the post in question collected on a board labeled "Teaching Ideas," "Pre-Cal lessons," or something similar.

What does this mean? I don't know, but it seems like there is a constant interest in what other people have to offer. I know I still go looking for it myself:

If you have an archive that's organized in anyway, I suggest making it available, there is certainly an ever present demand. We all have something to learn from each other.

AuthorJonathan Claydon

Here's a little reverse jinx I pulled:

I say reverse jinx because as Februarys go, this one wasn't too bad. Normally I have an increased work load from being soccer season, the push towards AP Exams, and it's all compounded by abysmal weather. With an absolute lack of winter around here, the work load felt a little more tolerable.

While it appears I've been pretty quiet, I have a lot going on:

Math Department

In October Varsity Math made a splash by taking over a blank wall in the hallway. It now features current class photos and our Hall of Fame. With a load of painting supplies on hand, I turned my attention to an old feature of our math department office.

It dates from the 80s, maybe? I took my painters and we're turning it into a unit circle:

A slow process (we have about 1 hour/week), but soon to be completed.

Summer Camp

It's almost time to start thinking about things for Varsity Math Summer Camp. Despite the random nature of the topics (from my point of view), all the kids consistently said they enjoyed themselves. One of them even made use of some things we talked about to work on a physics lab this year. I've done the initial advertisements to Pre-Cal students, and several are already convinced this is the thing for them. For $20 it's a pretty good deal.

Focus is the goal. Fewer topics and more time. I have a better idea of what you can accomplish in a 2.5 hour session now.


A big change is I have access to Chromebooks this year, making spreadsheets a more realistic tool at my disposal. I learned in Summer Camp that there's a real desire by kids to wrap their heads around spreadsheets. Most having no idea of all the math stuff you can do with them. Both Vectors and Polar Coordinates can make use of these. Recently we've walked through combining vector components and finding magnitudes and directions. A spreadsheet can do this quite nicely:

We jump over to Desmos, and with the help of super slick things like auto-connecting points and labels, we can quickly render our interaction:

It's almost time for the 6th Sidewalk Chalk Day. There's a possibility Calculus will get involved, allowing us to cover a truly massive amount of sidewalk.

Sidewalk Chalk means it's time for polar coordinates, a unit I started teaching after Vectors because so many of the concepts and math are identical. Traditionally I start polar coordinates with some hand calculation and plotting of points:

But computers are so much better at these things. Can we teach a computer to calculate polar coordinates? Let's used what we learned from vectors to speed up the process:

And thanks to the super bananas awesome data table pasting, we can get something far more sophisticated than our markers could accomplish:

Very excited to see how this goes.


Ugh, I don't know where to start here. It's time to register for the AP Exam, and as part of my five year plan, I said I wanted 80% (54 students) to register for the exam and have 30% pass. Well, determined to avoid the absolute fake out that happened to me last year (I had data to suggest that many many students would do well, it was wrong), I have tweaked the process. And well, ugh. But at the same time there are positives.

First, I learned I have a solid 20 kids who don't seem to have learned anything. It's late February. How did this happen? How much of that is my responsibility? At the same time, I have 25 who seemed to have learned everything. I'll spare you the details of my benchmarking calculations (the older a benchmark, the less it's weighted in a student's rating), but the data identified 8 highly proficient students last year. Using more difficult assignments, that same method has identified 16 individuals this year, with a higher average than the previous 8.

While there was a lot wrong about my methods last year, those top 8 all registered a 2+ on the exam. To have doubled that group is a positive.

The real disheartening thing is at the other end of the spectrum. 16 nailed it, another 9 did alright, and the remaining 55 are just wandering in the wilderness.

I have to make some hard decisions about what happens next and what is best for each student. My first year of teaching Calculus taught me that allowing kids to leave knowing nothing is a disservice. But slowing everyone down is a similar disservice.

Calculus BC

We identified 16 individuals willing to start the first full Calculus BC course in the history of my school. They're excited. I'm excited.


Lastly, in 3-4 weeks I'm getting all new furniture. It will be a bit more flexible than what I have now but will still let me establishing the grouping methods I have come to like. More on that when it arrives.

AuthorJonathan Claydon

Last year I had a pretty well thought out AP Review program. The intent was to give students exposure to the most common material. In the end, it proved somewhat effective, but time was the enemy. A big lesson I've learned in Calculus is knowing when to stop and let the students rehash through a bunch of material. Last year I gave them a huge stack of free response and integral/derivative mechanical work a few weeks before the exam hit. The eternal truth is that students take forever to do anything. As we progressed through the material students were waiting for my review sessions to get the answers straight from the source. Or they were working problems alongside the answer key, nodding along on the assumption they were doing all sorts of learning.

That learning didn't happen. I answered way too many questions. It was too late in the game to be answering so many rudimentary questions.

New strategy for this year, recognize that the review material I came up with is still good, but introduce it earlier. Force the kids to work through it before giving up the goods. Minimize questions. And more importantly, expose them to free response material in smaller batches, allowing them time to internalize some things.

Currently my kids are working through my big set of integral and derivative mechanics and two FRQs that are similar in scope. I allotted 3 class days plus a weekend for this. My observations so far is that kids are able to progress better on their own because a) the material is more current b) I haven't overloaded them and c) it's February and time is not yet the enemy.

If this goes well, I free up more precious time in April to let them work through a (now) less dense set of review material.

AuthorJonathan Claydon