A few weeks ago I was in a training and during a break I sketched out an idea I have been playing with for a long time. Can you make a single graph that can display all the big ideas of Calculus in such a way that students can work through how and why they relate to one another?

I finally set out to make it real while ticking away the hours before AP scores released (more on that punch in the face later). The result is pretty nice:

The starting function can be whatever and the x-interval is adjustable. On screen is the y-value at each end of the interval, the slope of the graph at each of the interval, a short line segment indicating the slope at each end of the interval, the area accumulated in the interval, and the value of the second derivative at any point in the interval.

The idea is to use this to have a discuss early on in the process about some properties before we put a name to them. That's why other than the y-values the other numbers are unlabeled. This combines a lot of half-hearted attempts at this I've made on the fly in the past.

I have found my students have big problems visualizing how all of this stuff works together. Concavity in particular is a weird one, what with positive/negative readouts at seemingly arbitrary locations.

Play around with it and edit as you please: Calculus in One Picture.

AuthorJonathan Claydon

Next school year marks 10 in the business. You would think teaching is a very consistent career over that length of time. Not so much! I realized I accumulated a lot of different preps and duties over the years and wanted to see what it looked like mapped out.

This doesn't include the 3 or 4 things I considered doing or was asked to do and later didn't happen. With the kind of staff turnover you have in education, you never know what opportunities will become available.

Yes, this is a subtle announcement that I'm returning to coaching, though in a more limited capacity. A combination of staff turnover, limited replacement options, and what was best for the kids (since I'm not leaving any time soon).

AuthorJonathan Claydon

All of a sudden the third year of Varsity Math Summer Camp has come to a close. I had one group of 15 campers this year and it represented a more diverse set of incoming AP students. This year ran super smooth thanks to a decision last year to have a simple structure to each day (also I've got a stockpile of all the random junk I need). Every day would feature an opening competition, a main (1.5 hour) activity, and a game. Each one a little different and each one designed to give the kids a nice while to get into something and interact with one another. I was not going to get them excited about coming up here for the summer and then talk at them for 3 hours, no way.

Kids attending represent are future students in all of our AP options (Stats was only 7% of the population in 2017, similar in 2016):

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Day 1

Competition of the Day: BrainQuest 7th Grade Trivia

Activity: Algorithms
A borrowed a common idea from computer science courses. Given the ingredients, write very specific instructions for building a peanut butter and jelly sandwich. Kids worked with a partner and had a little while to construct their steps (ranging from 9 to 32!). Then they swapped with another pair who had to follow their instructions exactly as written.

This had some pretty funny results. From the "that's a lot of jelly" when the instructions said to squeeze for 3-5 seconds, to the group spreading peanut butter with the knife handle because the instructions never said HOW to grab the knife.

Second Activity: Drones
I have an ever growing fleet of drones of all price ranges ($40-1500) to demonstrate the general idea of quadcopters, and what spending a little more money gets you. All the kids got to fly the whole range of options. For once we didn't break anything.

Game of the Day: Spit on your Neighbor

Day 2

Competition of the Day: Make 24

Activity: Spreadsheets
A basic overview of some simple spreadsheet commands (average, sum, countif, etc) to assist with Wednesday's activity. We discussed spreadsheets as a simple database and how formulas help with problems that need to work at scale. Then they played with a demo database where they had to apply to some formulas to determine a set of information.

Second Activity of the Day: Flextangles

Game of the Day: Coup

Day 3

Competition of the Day: 4 4s, specifically, come up with as many combination of 4 4s to create 1-15.

Activity: Statistics
Almost half of the students attending this year are taking Statistics in the fall. Last year I added an intro lesson and it worked so well I had to do it again. As an introduction to variance and standard deviation, kids tear into candy bags and count the distribution of the various colors. We talk about patterns in the data and how to quantify just how far off center a given bag of candy might be by calculating the standard deviation of total candies in each bag and the total of each color in the bag. Though with only 11 bags of candy, we have to be careful about how we interpret our results.

Later on we collected heights and wingspans and did a similar analysis to figure out who represents the average person in the room, and how much the population varies.

Game of the Day: Trivia Murder Party
Despite the grim premise, this game is a huge hit with the kids because the questions are challenging, the minigames intense, and the narration really funny. One such minigame involves frantically doing simple math problems as fast as possible.

Up to 8 people play the game (much like Guesspionage) using phones or computers. With 15 campers they played as partners on a shared device.

Day 4

Competition of the Day: 5 x 5

Activity: Engineering
I do a brief talk about my time in the construction industry and show them architectural plans from a project I worked on. They have discussions about what each kind of drawing tells you about a particular room. Later, they participate in a bid/proposal exercise. I, an owner, am soliciting designs for a structure that suspends a tennis ball 11 inches above the table. Kids have two kinds of pasta ($1/each or $2/each depending on type) and three kinds of tape to choose from ($1/ft for masking, $6/ft for electrical, $10/ft for duct) as building materials. They have to track costs. After an hour, they have to present a structure that meets the requirements as the final cost for me to review.

A few projects didn't succeed at the task, and a few succeeded but didn't meet some of the requirements. We had a discussion about how in some cases requests for proposals are flexible. The owner might have one idea, but your presentation might convince them to go another route, depending on the project. The most successful (and clever) design was very expensive. A similar (though shorter) design came in at 43% of the price. What might the owner have to say about that?

Game of the Day: Jungle Adventure


A great time as always. It's very relaxing to just hang out with a group of kids with a flexible agenda. The kids enjoy the novelty of the topics and really have fun together by the end. One year I'm going to figure out how to have a longer camp.

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Still no love for poor mommy shark.

AuthorJonathan Claydon

Some goals/projects for the summer:


Something I've been meaning to do for years and couldn't make myself do. I'm going to try my hardest to keep from having to invent stuff as a go next school year. That means formalizing how I'm going to progress through topics and the relevant classwork that goes with it. And then, sticking with it. Like, minimal changes as we go along. For the most part I have a feel for how stuff should work, a major rewrite isn't necessary. Writing down all the hair brained things I've come up with a little more so.

Summer Camp

A random idea returns for Year 3 in a few days. I've got one batch of 21 campers entering at least one of our AP courses (Statistics, Calc AB, Calc BC). I've gotten a lot better at planning these mornings to give kids time to dive into the activities. Last year was a great success and I'm hoping for the same here. The main idea is to pose one interesting activity of the day, teach them a new skill, and show them a variety of games.


What started with one wall is now spreading all over the school. Enabled by our librarian who was a former art teacher, we adding some color and spirit around the school this summer. Work is already underway.


We have a variety of murals around the school. These will be a set of three, one on each floor. The school mascot will go in the white circle with the floor numbers indicated on the far right side.


Only one stop this year, TMC 18 in Cleveland, OH. I'm giving two presentations and possibly a My Favorite. Depends on what I can think of. My first presentation on July 20 is a rehash of a successful one from last year, Calculus for the Algebra Teacher. I'll walk through some ideas from middle school (slope of a line, composite area) and show where they reappear in a Calc 1 course. The next day on July 21 I'm tag-teaming with TMC keynoter Julie Reulbach for Assessmos, a look at how Desmos Activity Builder can be used for in class assessment tasks big and small. I'll be bringing my mega-giant Calculus benchmarks for you to play with.

Probably a wise idea to mute me the morning of July 22. I will be spitting incoherent nonsense about possible locations for TMC 19.

AuthorJonathan Claydon

Over the years I've tried to start incorporating financial literacy lessons into what I do. Seniors in particular get that "wasn't I supposed to learn this?" feeling about this kind of stuff and I aim to help a little bit. Especially to offer some perspective on the rent vs own debate. A majority of my students rent their living space and have heard all about how it's allegedly a waste of money. Even more are eager to save up for a car of their own and need some insight on the process.

Last year I formalized that into Let's Buy a House. Last year I had about 10 days with this lesson. I had students do a lot of comparison shopping, visit a make shift bank, and then organize their findings. I had waaaaaaay less time with this in Calculus after the AP test this year. More or less two class periods and then school was over. A condensed version was necessary.


Fast forward to your early 30s and assume you have the cash saved up for a car and a house. Find a new or used car for under $30,000. Find a house in certain zip codes for under $300,000 (not unreasonable for the area around school). Approximate the cost of property taxes for the house. Calculate the monthly payments and see what monthly income would be necessary to afford both. Answer some questions related to what you observed while researching.

All of students have Google Apps accounts and used my class set of Chromebooks to complete the task.

That's the short version. Here's what students were presented with:

Because of the limited time available, they only needed to run calculations and present their findings on 1 house and 1 car. 3.5 hours of class time over 3 days was allotted for this and most students finished in about 2.5 hours. This was their absolute last assignment of the year, finals started the day after this was due.



You'll have to make a copy of these files to use them.


Despite the rapid end of school approaching, students did a great job with this activity. They took their time and asked a lot of good questions along the way. Last year we spent a couple days building the payment calculator together. I didn't have the time this year so it was just given to them. Thanks to the suggestion of someone at TMC 17, I presented three credit rating scenarios for the car payments. That prompted a LOT of questions of what it takes to be considered in the Bad, OK, and Good camps. Students who had taken some of our finance electives were able to assist those that didn't understand it as well.

Many many students made good observations about how people in worse credit situations are often offered lower monthly payments not seeing the big disparity in money going towards interest. I think I successfully scared most of them off 30 year mortgages too.

A sample:


Earlier in the year I did the same exercise with College Algebra. We were nowhere near as constrained with deadlines so they had a much longer version of this project. They had to research 3 cars, run the calculations, and present their findings. Separately they had to find 5 houses, run the calculations, and present their findings. For their 5th house they were given a $4 million budget, just to give them an idea what the payments would be like for something like that. Collectively they were a little less organized, so in addition to giving me two presentations, they had to gather and submit their house findings on a worksheet:

They were a little dazzled about the kind of numbers that resulted from their "dream house:"

College Algebra spent about a week on each half of the project. It was part of a series of tasks they had to complete in the final grading period. As it was more of a self-paced environment, students worked on other things as they did this.


College Algebra found it useful, if a bit tedious. I may shorten their requirements for next year. Calculus did a great job despite the constrained schedule. Calc BC didn't do this activity at all because schedule quirks left us with even less time (1 class day really) and I had other things I wanted them to do. A majority of those students attended summer camp and did the exercise there anyway, so it wasn't a huge loss.

More than one student made me laugh out loud as I scanned through their presentations:

Many of them incorporated a "I don't wanna grow up" vibe that was adorable.

AuthorJonathan Claydon
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Seniors graduated a few days ago and I'm making an attempt to be a little more proactive about some things this summer. Mainly addressing some to do items that have been languishing for a few years. Before it starts in earnest, a few final thoughts about the year.

Ten years ago when I informed an advisor from college I was switching to education, his only comment was "well, will be interesting to see how you like teaching Algebra 2 forever." Interestingly enough, there was only a small run where I taught the same thing multiple years in a row. This year's biggest challenge was all the creation that was necessary. At the end, it all turned out pretty well.

College Algebra

I took a giant gamble in January where I decided to stop whole group instruction. Somehow, we made it through the entirety of the second semester and it really wasn't a problem. It required a lot of effort on my part to properly script moves. Accounting for the time kids would take on things was constantly in flux and I was always over or underestimating. Though it felt like there was a lot of wasted time, it could be argued it all evened out because even if it took forever to get kids started, they were doing something quite a lot of the time.

Essentially, I had 4 hours of class time each week and kids had about 3 hours of work to do (exploration, discussion with me, classwork). Early in the week a lot of time was burned with setup as I had to float around and give some introductory information and outline the requirements of the week. Each little pod took a different amount of time to buy what I was selling. In any given week maybe 8-10 kids out of 32 would finish their week's work early and not have a lot to do Friday. This was not ideal, but a reasonable trade off to allow the ones who needed longer to take longer. A mistake on my part is letting a particular group of students set the pacing for everyone some weeks. Often they were taking longer not because they needed to, but because they actively chose to. It was very hard to decide whether I should penalize them for taking forever (and thus make grades about compliance) or surrender the time now to avoid delays in the future (inevitability there'd be an assessment they had 0 clue how to do because I forced them to stop working on a topic). The long term benefit of having everyone in the same ballpark was more valuable than getting into a protracted skirmish with 4 kids (it was highly likely that weaponizing grades would've caused behavior problems from 1 of them).

I am teaching College Algebra again and I think starting with the small group model from the beginning will be interesting. There are a few procedures I can tighten up as well. In the end, teaching this class was a good experience and the students as a whole were very good. There is a lot of joy in helping seniors rediscover an interest in math when a lot of people have told them they aren't good at it.

Calculus AB

The eternal struggle. There's sort of three things going on. Vocab, concepts, and deep mechanical fluency. And you only have time to pick two. I have always chosen to focus on some core fundamentals to the detriment of smaller ones to improve the whole group proficiency. I just don't like leaving kids behind. As a group, there was a lot to like. Many many kids put in a good effort and showed promise during our AP reviews. What that will translate to in July remains to be seen. Last year saw sizable increases and the sense I had was more kids were prepared and at a better level of preparation than last year. Fingers crossed.

There are always new efficiencies to find and I think I've got some we can work on next year. Wrapping my head around presenting good, concise, mathematical arguments was a late game discovery this year, something that will be helpful if we can put it into practice for longer.

Post Exam reactions were fairly positive. The ones who I thought would do well didn't seem too frazzled and the free response questions were incredibly restrained and well within stuff my kids would've known how to do. As I said to them several times (with only a little snark), with 62 people taking the test, I would think more than 2 could pass.

My big goal this summer is to finalize my classwork. I change it so much each year that I think it's finally time to decide what I should be doing and stick with it, as a sanity saver throughout the next school year.

Calculus BC

Probably the biggest questions here. This was our first group of students taking it as a separate class. The sheer scope of the material caught up to a few of them at the end of the year. But they were all incredibly capable students. It would be almost impossible to pick a better group to start a class like this with. They really embraced the task at hand, validating the recommendations they were given to take it.

There was some mild complaining about free response with this group, but after seeing the question they were talking about (#6), I agree with their assessment. We didn't dive into series quite thoroughly enough, so there was a lot of surprise that could've happened in free response scenarios. The big relief was that as with AB, there were minimal comments otherwise. All the students felt like the material was accessible. We also had some very calming conversations about what it takes to show proficiency on this thing and I think that helped. I really hope some of them do well and that there are some universal good results for the whole group.

In their exit comments, they did mention that they'd like assessments to be a little more intense. Throughout the year all of their assessments were collaborative (sometimes with notes, sometimes without). In my mind it made the most sense for such a small group, with only 15 students the grades shouldn't be important, the focus should be on collective understanding. In effect, their request was for me to force them to be stronger individuals, as a few noted that while they understood what was going on, they found themselves becoming dependent on others. Interesting to seem them recognize this with no connection at all to the "I need to know I have a better grade than other people" mindset.

New Frontiers

As the old ones leave, it's time to start thinking about the ones that will come to take their place. I had a meeting with the BC students of 2018-19 and they all seem very excited. Especially when I said not only would they be getting their own personal calculator (not for keeps, but for use throughout the year), but that they could give it a goofy name. Varsity Math is proving a successful recruiting tool, with Statistics numbers finally headed to the right direction (30 next year, up from 9 this year) and kids pumped to be involved in all of our AP offerings. Summer Camp enters year three, and it continues to be a fun way to onboard kids into the Varsity Math universe.

AuthorJonathan Claydon

At long last it's AP Test Day. What started with a hurricane and some kids on the couch has finally finished. When I started teaching Calculus, I had a personal mandate to improve the results on the AP Exam. Though it is just a test, there was no reason in my mind our students couldn't be successful at it. They're more than capable of piecing that thing together.

I started trying to be very specific about predictions and found that in general that back fired. This year, the thought was, let's just look for promise. Who shows the indication they'll be able to make it work on May 15?


While I was able to do a significant amount of catch up despite the 12-day delay, a few things just never happened. In AB I still sacrifice things like related rates, in depth discussions of the mean value theorem, and an in depth look at solving differential equations. As a program we weren't grasping the basics anyway, so those fringe things weren't making a big difference. On top of that I just didn't have the time. I needed it for other things.

In BC we pretty much got it all, though I'd say they have some other fringe weaknesses. Mean value theorem, fiddling with Lagrange error bounds, and the more obscure convergence tests.

Despite the shortcomings, in our final review sessions there was very little practice exam material that was not within my students' grasp.

AB's Long Prep

A majority of my focus was on getting the AB group ready to go. Historically results have shown me that students struggle with free response. They lack some of the exacting finesse you need to make sufficient answers. Starting in March, I removed their standard assessment system and replaced it with released free response questions. In some cases students were given the use of a picture or calculator where normally it wasn't allowed because of where we were at in the material. Students completed 4 of these sets, composed of 9 full length FRQ on the subjects of particle motion, function/rate analysis, volume, and data tables. I tracked their results and some questions were used as follow ups once we had discussed some pitfalls.

If you're interested, Set 1 was 2012 #6, 2008 #4, 2009 #1; Set 2 was 2016 #3, 2017 #2, 2013 #1, Set 3 was 2013 #5, 2014 #2; and Set 4 was 2012 #2.

The goal was to expose them to the language and requirements of a free response questions early and often so that they were less intimated by them when the exam rolled around. In addition to these assessment items, they were given a pack of "ultimate" free response questions that I wrote myself a couple years ago. For College Board reasons I can't post them, but if you are a credentialed AP teacher, please get in touch.

We had many conversations about showing mathematical thought in their answers. There should be a clear setup (what information am I going to use?), work (what am I going to do with the information I chose?), and conclusion (how do I interpret my work?). Students who put the effort in improved dramatically at these as we got closer to the end. In some cases they exclaimed how easy the question was, something I had never heard before.

BC's Prep Integration

I exposed BC to released material early and often. We were doing free response questions since October. They worked through a full AB exam in December. My challenge with this group wasn't going to be language or organization, but grasping the sheer amount of material we had to cover.

When we got to their unique topics in the spring, I integrated AP-level material at every step of the way. Almost every topic discussion was ended with a look at relevant multiple choice and free response questions. They took a number of Desmos assessments that were structured like free response questions. These kids were very familiar with the requirements of a free response question.

Final Stages

Each version of Calc wrapped up new material in early April. On April 16, I started doing after school tutorials. My students have a number of commitments, so I made these flexible. AB students needed to see me once a week over the course of 4 weeks. For BC I reserved two Wednesday afternoons for us to discuss whatever they needed.

I posted sign up sheets for AB students.

Each week had a theme. In some cases I covered material we didn't have time for and the last two weeks we talked about exam strategies. My students have limited experience with big exams like this, and time management is something that needs improved. In addition, they will think themselves in circles for 10 minutes on a question they should probably skip. We discussed doing a full reading of the exam before starting any work, helping them to prioritize their time. Finally, we talked about what was really necessary for a passing score. Many many many students are unaware that 45% or so represents a passing standard on this exam.

Out of 62 AB exam takers, they showed up after school an average of 2.64 times. I can't make these things mandatory (I know the sign says mandatory, but that's for effect) or grade them for showing up or anything, so that's pretty good considering it was all voluntary. 40 students did what was requested and showed up 3 or 4 times.

All the BC students attended both of their sessions.


When we concluded new material I gave both groups a significant number of assignments to work through. Class time was work time for several weeks, with tutorials in the afternoons. Each group got several skills-based assignments and then separate AP-level material. BC worked through another full length exam. AB had a selection of multiple choice and their "utlimate" free response. We went over the AP-level material either in class or after school last week. Students were given access to answer keys.

What will happen in July? I don't really know. I have some good feelings based on my observations the last month. I tried to gauge things based on how students asked me questions. Most knew what to do and were seeking confirmation, with others it was apparent they were at step 0. Fortunately, I think that group was minimal.

I would be very amazed if any BC student got below a 2, they've all shown strong levels of comprehension all year. The BC cut lines are also a little more forgiving because of the content demands. A number (in my wildest dreams, all) of them will pass without question. AB feels like ~70% of them should register on the scale (2+). I scratched in some predictions for each kid, but I'm prepared to be surprised in either direction. Ultimately, I want the 1 to become the minority score in my AB results. How many can make the jump from 2 to 3+ will just have to wait. Fingers crossed for about 70 days.

AuthorJonathan Claydon
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Last week at NCTM 2018, I presented some thoughts from a radical Algebra II experiment I ran some years ago. While Algebra II was the center piece, the topic is broader. What story are you trying to tell with your curriculum? How do you integrate pieces so that students can see a theme in the skills and concepts they learn throughout the year? Why should what you teach in September matter in April?

This is a summary of those ideas from my talk.

The Script

The textbook models of Algebra II are pretty consistent. A whole parade of function types, done in isolation, over the course of a school year. Your experience probably looks something like this:

I dutifully followed a script similar to this for four years of Algebra II. But there were lingering problems. In the Fall of 2012, I included this as part of my final exam:

I made what I thought was a fair assumption: we had covered linear, linear systems, absolute value, and radical functions throughout the fall system and students should be able to work with them when mixed to together.

I was completely wrong. Students had forgotten fundamental algebra mechanics and were thrown trying to remember not only how the non-linear ones were dealt with differently, but even what they were in the first place. The topics we discussed had been so spaced out that students had made no valid connection that equation solving is a universal thought, different functions merely introduce new mechanics.

Second, we had this section in the book on parent functions. There was an activity that accompanied it:

Students spent a class period matching equations, words, and graphs together to form a parent function library of sorts. Then we never talked about this activity again. It served no purpose other than to say "ooh, activity!"

The Flip

I spent the summer of 2013 frustrated with Algebra II and determined to find a better way. There was good material in this course, but it was being handled in such an awful way. The messaging was all wrong. If you take the Texas State Standards for Algebra II and make a word cloud, you get something like this:

Clearly, the individual functions themselves are not the most important players here. Equations and Inequalities are the most frequently used terms. Incidentally, you see how small "real world" is there? Probably could stand to fix that too.

I revisited the parent function activity and thought: what if this was the entire course? What if we talked about parent functions at the very beginning of school and referenced it throughout the year? What if we focused on not just solving equations with one function at a time, but with many functions at time?

Pivot Algebra Two was born. Let's have students see how a set of skills play out with many different kinds of functions all at once. I divided the curriculum into two parts. Part 1: linear, radical, quadratic, and absolute value. Part 2: log, exponential, rational, polynomial. In each part, we would do overviews of the skills in play and slowly spiral up the difficulty.

In addition to taking tons of times to play with equation mechanics (roughly 6 weeks on linear, quadratic, absolute value, and root functions with increasingly higher difficulty), students got to see connections between their work and graphs. I don't know about you, but prior to this experiment, my kids hated graphing. It was a tedious process that seemed unrelated to anything. In this vision of Algebra II, I was going to give graphs a purpose.

The Motivation

When it was time to start a month of graphing, they groaned. As the ones that came before, they hated graphing and didn't understand the point. But then I took some classwork we had done previously. At this point they all agreed that solving equations was super easy. I graphed one side of the equation, and then graphed the other. I clicked the intersection points. MINDS BLOWN. The graph and the equations are related! I can check my answer easily! I don't need your help anymore!

It was a beautiful moment. I used it as a jumping off point to more complex algebra. In both our look at advanced quadratics and logarithms, we started with the graphs. We know that the intersection point of two graphs is equivalent to the solution of the equation. What algebra do we need to prove that?

Kids saw the power of the quadratic formula. They saw transformations for what they were, ways of manipulating various parent functions into equations.

Then we summarized what we learned about our first four functions:

The Payoff

The efficiencies in this system were apparent pretty quickly. I was no longer reteaching simple algebra moves. Kids had them down. We could tackle mechanics previously unheard of in Algebra II. We even put logarithm properties to good use with problems like this:

There is a lot of overhead in this problem. You have to understand how logarithms combine, how they are undone, that the resulting quadratic has two solutions, and that it's possible not all of those solutions are valid. And, to my sheer astonishment, the kids were telling me this was easy. Absolutely bonkers to think that this problem, which take a good 5-6 minutes of kid time to work, was easy! I'd ask if they need any help and they'd say, nope, I can just graph it.

These connections also help improve their ideas of equivalence. We could take any line in this process, graph it, and see that the intersection points had the same x-value. We were manipulating a log into an equivalent parabola.

The Longterm Lesson

This line of thinking, finding the story in my curriculum, continues to pay off. Because of this exercise, I have improved my ability to weave concepts together in other courses. I no longer teach Algebra II, now I'm primarily focused on Calculus, but the fundamental thought behind this experiment remains. Calculus has a story, and students should be able to see it.

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Calculus is even better suited to these ideas. Limits, Derivatives, and Integrals interplay with each other in all kinds of ways. What if students saw that relationship from the very beginning of the course? What if they didn't have to wait 4 months before they even heard the word "integral?" How much better could they be at seeing those relationships?

The Conclusion

I encourage you to take a hard look at what you teach. What are the big ideas? What should students be able to do when it's all over? How can you give them an overview of their year in the first month of school?

For more detailed information, I chronicled everything about my radical journey through Algebra II. Please contact me if you need anything.

AuthorJonathan Claydon

Every spring, during a brief period of time when it's very pleasant outside before the ravages of summer, a few hundred students venture outside and make over a half mile of public art. We call it Sidewalk Chalk Day.

Sidewalk Chalk Adventures
Return of Sidewalk Chalk
Sidewalk Chalk Three
Sidewalk Chalk, the Fourth One
Sidewalk Chalk Five
Sidewalk Chalk Six

Now etched into school tradition, Sidewalk Chalk Day features students from all kinds of math classes displaying graphs of whatever it is they have been learning recently. As one faculty member who was strolling outside as we worked put it, "I always know it's spring when the chalk goes down." The first iteration involved two sections of Pre-Cal. This year 11 classes (AB Calculus, BC Calculus, Pre-Calculus PreAP, Pre-Calculus, and College Algebra) went outside throughout the school day.


Myself and a colleague pick the day a couple weeks in advance. It's trickier to pick a day than you might think. Because of our bell schedule, only Tuesdays and Fridays work, and, as the subject that started the movement, it has to coincide with Pre-Calculus classes wrapping up Polar Equations. Go to early and the material isn't covered thoroughly enough. Wait too long and suddenly it's testing season and nothing works.


Day in mind, we incorporate a unit that will culminate with students graphing something. Pre-Calculus students create a pair of polar equations (rose curves/cardioids or something in between); AB Calc creates regions between curves with stated integrals for area and volume using that region; BC Calc creates polar equations with integrals of area for them; and College Algebra showed off logarithms and their corresponding inverses. Each student created their own set of equations/graphs that fit the requirements. They were given two panels (or one double panel) of sidewalk to show off their work. If complete, extra panels could be decorated however they like.

While students worked I flew around a drone and took pictures. Last year there I made a video compilation. The weather didn't cooperate this year, so I had to settle for pictures. Enjoy!

AuthorJonathan Claydon

I have always liked introducing games into the classroom. Often I take trips to Target just to see what kind of new games they have that might work with kids. Some are relevant to math, and some are just fun to play in big groups. With the advent of internet connected devices everywhere, a new kind of genre has opened up, trivia games played on a console or computer that lets students enter a room code and participate in front of everyone for fame and fabulous prizes (well, not so much the prizes). You know, like Kahoot, but better. WAY better.

I have gotten endless value from the Jackbox Party Pack, specifically Party Pack 3. For $25 you get 5 games, and two of them make FANTASTIC classroom games. Right before Spring Break, with a confluence of a blood drive, field trips, and general maybe-lets-not-introduce-something-new-right-before-a-giant-holiday, I played Guesspionage with all my classes. Participants take turns approximating answers to survey questions, the other players get an opportunity to decide whether the guess is much higher, higher, lower, or much lower. Points are awarded based on the accuracy of the guesser, and who correctly said higher or lower, with a bonus for much higher and much lower. In the final round, everyone is given the same question and has to choose the three most popular answers from a set of 9 (for example: which decade would people like to live in the most?).

Thanks to The Array™, I brought in my Nintendo Switch and we were off.

The questions are great. Every kid has an opinion and some of the answers will surprise you. There's also the collective FREAK OUT if a participant manages to get the question exactly right. Guesspionage allows 8 players to compete in the main game, with room for an audience who are also able to answer the questions. You can also set a family filter if you have a younger audience.

Here's a gameplay video:

Once kids understand the rules, the game runs itself. I just sit back and enjoy the arguing. When prompted to play a second round, every class was a unanimous "YES MORE GUESS NOW."

AuthorJonathan Claydon