If you want to up your game, but don't have the dispoable income to do anything really crazy, may I suggest a very cheap asset. I bought a scanner a couple summers ago and it comes in handy all the time. If you don't have one yet, I have no idea what you're waiting for, they are so inexpensive. Mac OS X even has a scanner friendly app pre-installed that allows output to PDF. Windows probably has something similar, but I have no idea. Even with the amazing things computers can do, sometimes you can do something faster by hand. Especially true if you spend most of your creative energy in Word. I know the drawing tools are pretty good, but probably not as good as you would like. A nice high-res scan of a hand drawn graph can really be the key to a nice product. Two examples from this year. I was going to be out and didn't want my Pre-Cal kids to languish. They had work from the previous day to finish but I knew it wouldn't take the whole time. So I prepared some notes on tangent functions for them:


Now, I don't know about you, but when I'm out it's usually unplanned and I don't have a lot of time to prepare what will be needed. So I had a choice. Knowing full well that when I'm out only 40% of what I want gets done, should I spend the 15 minutes to write these out, 20 minutes to type them out, and find something to make nicely labeled tan(x) graphs with (15-30 minutes)? Or spend 15 minutes writing it and 2 minutes scanning it and e-mailing it to my student teacher?

Second example came from a second self-teaching exercise. I wanted them to determine how to solve logarithmic equations. I wanted to have examples. I had limited time. Formatting a typed step-by-step example was doable, but would take way longer than I had and I couldn't annotate as well as I wanted (kids like arrows, you see). A few minutes with a pen and I had what I wanted. You owe it to yourself to get a scanner. And one day, spring for a graphics package that will help exploit it.

AuthorJonathan Claydon

At some point the fall semester ended. It seems unreal given how many things went on and the fact that due to start dates, this is the latest school has let out since Texas moved to a unified start date. Christmas is like, Tuesday. I have a thousand things floating around in my head that need to get written and I think now I have some time to do so. Soccer season has been in swing for almost a month already, so big To Do™ item is purge that list right now because in January/February I won't have time. But, that's later. A simple debrief of Fall 2012:


  • Mentored a student teacher, he helped make a lot of crazy ideas this year possible.
  • Did a decent job keeping up a 180 Photo Blog.
  • Learned a lot of SBG implementation from the many academic level teachers who tried it at my school this year.
  • Managed to make iPads in the classroom work for some neatthings.
  • Made headway with more inquiry-based openings.
  • Rejiggered my room to accomodate 33 kids, replaced every old school desk with a table.


  • Not sure the Algebra II curriculum flow is quite right.
  • Not sure paper tests are the sole way I should be assessing students.
  • Not quite satisfied with the level of iPad access my kids have.
  • Not sure how to pace my Algebra II sections next semester, one is head and shoulders more with it than the other.
  • Not finding the relevance to many sections of the Pre-Cal curriculum. Really, double angle formulas, really?
  • Not sure if all this table wizardry I did in the room is helping my kids' ability to focus when I'm talking.

Final note, for those of you who find Word to be the be-all end-all of classroom item creativity, you can get your foot in the door with all those Adobe applications you stand in awe of (Photoshop, Illustrator, etc) for ridiculously steep discounts. I recently snagged CS6 Design Standard Bundle (Photoshop, Illustrator, InDesign, Acrobat) for a mere $349 because I'm a teacher. Now I know, you're like, $349!? I got kids to feed! Considering that normal people have to drop $1,299 for the same thing, it's a steal. Anyway, think about it.


AuthorJonathan Claydon

Lost in the shuffle of the "are iPads effective in the classroom or not?" debate and all the rosy videos of kids happily staring at Khan Academy all day is the back end of all this technology. There is an infrastructure required to support all these devices. There is maintenance that has to be done. These devices are not intended to stay in a steady-state for 10 years, like your standard issue TI-84. Operating systems are updated, apps are updated, and eventually, operating systems and apps are no longer supported. A 2010 iPad was supported by iOS 3, 4, and 5. An iPad 2 runs iOS 4, 5, 6, and you'd hope 7. New apps are already starting to require iOS 6 which doesn't run on a 2010 iPad. So what are these technology deployments going to look like in 2017 when it's the same batch of iPad 2s, iOS 11 is standard issue, and the last time someone released an app for an iPad 2 was in 2014?

People working in the technology industry may not be aware that schools don't have the resources to buy a brand new batch of iPads every two years. Some might, but most don't. iPads aren't even close to standard issue anywhere, and forget about 1:1 being the norm. Seems like the same problems we had 10 years ago when every kid in Maine got an iBook. What was that like 3 years into the program?

The folks behind app development need to keep the lights on, so the product has to stay fresh, and a healthy app is a maintained app. Which creates this constant nightmare:

Screen Shot 2012-12-15 at 12.41.20 PM.png

When it's your personal computer, no big deal. Maybe let the updates accumulate a little and knock them out at once. Two computers? Slightly more annoying because you're probably running the same stuff on each which means "yes I know that was updated, my other computer told me, just go away already." Keeping things up to date on 13 iPads? OMG. I don't even have much loaded on my student iPads (~10 apps) and in the 4 months since they were given to me, I'm not sure a week has gone by without SOMETHING demanding to be updated and there was the iOS 5 --> 6 transition. Right now each student iPad says 11 things need tending to, plus "iOS 6.0.1 is available, would you like to install?"

Is anyone forcing me to manage this? No. Will anything break if I don't update? Probably not. But in the "go go go" world of app development, the people behind this stuff are sure making it SEEM like you need to, lest you get left behind with a version they no longer care about supporting.

For right now, everything's fine. I have an infrastructue in place for working with iPads. We do some neat things from time to time. But is this sustainable for another year? 2? 5? Who is responsible for maintaining these things? The overstretched IT staff? The teacher?

Education seems incompatible with the bleeding edge. Texas Instruments is totally ok with this.

AuthorJonathan Claydon

As we approach the coming of Fall Finals, you may find yourself with a little extra class time on your hands. Maybe one of your sections is ahead of the rest, maybe you have an early dismissal looming, maybe you have a ton of kids who are exempting your final. Watching movies may or may not be frowned upon where you are, or you are short on something they would enjoy watching. I humbly suggest Straw-based engineering challenges. It's extremely successful every time I do it, and there are tons of ways to mix up the rules. Only rarely will you find a group unwilling to do it or fall flat on their face.

Long ago when I was in AP Physics, we took a field trip to a university on a Saturday. They were holding a design competition and they were giving away scholarships for the winners. We had no idea what to expect and hey, who doesn't like field trips? The contest was to build a straw tower that optimized various categories (weight, height, etc) and could support a tennis ball for a certain amount of time. This project is extremely similar to the popular marshmallow tower challenge. I have done the marshmallow challenge at times, though it can get a little messy, and sometimes I have more than 15 minutes to kill.

Over four years, I have presented the task in a number of different ways:

Version 1

50 full length straws

1m of tape

Build Time: 2 hours

build the tallest structure that supports a tennis ball for 60s

Version 2

50 full length straws

1m of tape

Build Time: 1.5 hours

build a structure at least 18in tall that supports a tennis ball for 60s

Version 3

30 full length straws

1m of tape

Build Time: 1 hour

build a structure at least 18in tall that supports a tennis ball for 30s

Version 4

30 short straws (~3", coffee stirrers that are a tad thicker than usual, found a box of 1000 for $4 at Office Depot)

1m of tape

Build Time: 25 minutes

build the tallest struture you can that supports a tennis ball for 60s

Version 5

45 short straws

1m of tape

plastic bag

Build Time: 25 minutes

build a structure that supports a tennis ball within a defined volume but no straws may touch the table inside that volume

This year I did Version 4 with an Algebra II class and Version 5 with my Pre Cal students. Version 5 is the most recent and one of the more interesting variations. The official instructions were they could use only what I gave them, and they could mutilate the straws in any way they wanted. If they asked to use the bag, I let them use the bag. Of the three class periods that did this version, one did not ask about the bag. The "no straw zone" was a 1ft x 3in area marked on their tables. No straws could sit on the table in this area. I did not set a minimum table clearance and probably will in the future. I did not forbid them from taping straws to the table and probably will ban the practice in the future.

Some results:


This last one year in particular got me thinking that I should've set a height clearance, but kudos to them for exploring the boundaries of the rules. Also a big hats off to the group that had the genius idea of situating the tennis ball inside the bag. Again, a minimum height clearance would've made that strategy more challenging to implement, but bravo to them.

My favorite part is how tense they get when it's time to test their structure. It doesn't matter if they finished early and have had the ball sitting there calmly for minutes on end. Somewhere deep down they're afraid the structure will explode when they're on the clock. It's hilarious.

AuthorJonathan Claydon

A theme this year has been to build in novel activities or situations for my students to deal with other than just give them a handout everyday. Now, I do have plenty of handouts when it's time to put things into practice, but I want at least half our time to be spent doing unique things where I'm not just talking. I also have 1 block day with every class per week and I want to take advantage of the added time other than just "oh I can teach TWO textbook sections today!" So I've expended a lot of energy trying to make "long day" (in kid parlance) a meaningful part of the week. Earlier in the year we made quadratic model videos as an introduction. We did it on long day. I came up with the idea the night before while randomly driving around. Log War was long day. Now, meet Inverse Trig War.

Struggling yet again to find a suitable use for long day, around 9pm while randomly driving around this happened:

@samjshah omg, picture @k8nowak 's log war activity but with inverse unit circle trig

— Jonathan (@ultrarawr) December 5, 2012

And thus, Inverse Trig War was born. I whipped up a list of 40 simple trig equations (things like sin x = 1, 2cos x = 1) and assembled them the same way as the log cards. Now, this game is a little more involved, as determining the value of the card is not as quick. So I had the kids divide up the cards, determine the values as a hivemind like "answer key" and then play. We had been working on Trig Equations earlier in the week and they had struggled with Unit Circle Inverse Trig anyway (especially tangents) so this was some nice reinforcement. Since each card has two angles associated with it, I had them set the "card value" at the highest angle. So if your solutions were 60 and 300, the card is worth 300. You could also play a variant where the lowest value wins.


PreCal kids being the good little soldiers that they are, took the task well. A few groups got invested in the game, some got bored after 10 minutes. But, still interesting and something that might only need minor tweaks. Before I started the games, we did a little collective checking of the answer key just to make sure. They still get weirded out by things like sin x = 1 since normally these things have two answers and a problem like tan x = 1 is solved waaaaaay differently.

Trig War Cards (Word), Trig War Cards (PDF)

AuthorJonathan Claydon
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Over the summer I stumbled upon this post about playing war with logarithms. The idea is simple. Evaluate the log, the person with the biggest card wins. In the event of a tie, there is a 1-card tiebreak. I didn't observe stacking tiebreaks, although I'm sure it's possible. Prior to playing the game, we talked about logarithms as the inverse of exponents and how 3^x = 9 equates to log_3 (9) with the answer to both being 2. Anyway, rumor is that kids love this game so I was optimistic. I took the cards that Kate Nowak links to and modified them a little bit to make a better distribution of numbers (most of the cards in their sets evaluate to 2). I finished with a set of 40 logs, printed them on mailing labels and had my student teacher affix them to index cards that had been cut in half. I gave each color group their appropriate color deck of cards. We had a brief demo and then I let them loose.

I'm not sure how to describe it properly, but watching the results were A-MAZING.


Now, I had a couple boo-boos on the cards but that didn't turn out to be a big deal. Doing spot checks it seems they were evaluating them properly and letting the correct person win. I told them the game was over when one person was totally out of cards. Every group played a couple games without getting bored. The only consistent thing I noticed is they were counting the zeroes when comparing log 1000000 (6) and log 10000000 (7). A few times I noticed they would think it was a tie until I pointed it out.

More interesting in action (and a nice way to test YouTube auto-blur, which seems to think hands are faces at times):

If you're interested in the set I used (boo-boos and all), poke around my Algebra II resources.

AuthorJonathan Claydon
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Standards Based Grading is intended to get kids thinking about their strengths and building confidence that can help them through their weaknesses. Rather than reference obscure sections of the textbook, you get them talking about topics. I learned out of a textbook, so I always filed my math learning away under whatever chapter it had been filed under in the textbook. When I started teaching I taught this way, using a textbook for reference and even titling my tests based on whatever chapter we were on. In my second year I started organizing my planning a little bit and used a long form calendar to map out my thoughts. A sample:


Notice my references to textbook sections. Now if you were someone making use of this, would you have any idea what Section 1.8 was? Why does Section 2.2 need two days? Is it especially hard? Wait, what is it again? This particular calendar was from my first full year of SBG, so I had the tests broken out into topic numbers. Separately I kept a list of what they were and I had this complicated mix of planning with textbook sections, identifying the topics, and then molding the textbook content to that topic. After running through Pre-Cal and Algebra II in SBG form, I now have a much deeper sense of the content because I think it terms of topics, not chapters. These days the calendar looks like this:


Much easier for an outside observer to determine what's going on. More importantly, I'm making myself think the way I want the kids to think. Who cares if they know anything about Section 4-2? In college their math class will be organized completely different from mine, and if a professor starts talking about "matrix multiplication" it doesn't serve them well to sit there and think "now was that Chapter 4 or Chapter 5?" Math is supposed to be universal, the mechanics work the same no matter where you go to school. So why not think more universally?

Don't let the textbook own you.

AuthorJonathan Claydon


We continue our discussion of harmonic waves, what relevant units of ampltiude are (I use dB and V) and how to disect Hz. We have a bit of a side discussion on how useful a second is when you're talking about a 800Hz wave and its 0.00125s cycle time. Oh hey, milliseconds! And for the extreme, microseconds. These discussions are great and all but again, do they understand what cycling really means? What does it look like? I had this idea of showing a video of cars and their out of sync turn signals or bulbs blinking or something. Sadly, the internet let me down. So I cranked out a couple animations:


I let them stare at it for a while, a few will shout observations. Then I ask a few questions: Which light has the highest frequency? The lowest? Where do the rest of them fall? A contentious debate arose about whether the top center or bottom left had the higher frequency (top center repeats every 3 frames, bottom left every 2).

Next, what does it mean to be out of sync?


Grasping a 180º shift is a little easier than a 90º but once I have them count the different colors the 90º image is going through they start to pick up on the pattern. We make some analogies to running/walking around a track in PE. Then I set them to work on the supplementary task. I present them with two signal waves that may or may not have different amplitudes, frequencies, and phase shifts. They graph one on top of the other and then describe. I leave a structure for the paragraph on the board. How can I expect them to write a proper mathematical observation if they've never seen what one looks like? Classic trap teachers fall in. I know how to do this and have for years and it's so simple, why don't you and your inferior knowledge and lack of experience not know how to do this already?

Photo Nov 14, 3 52 55 PM.jpg

I liked the result, discussing phase shift as a unit of time I think helped with the translation aspect. When you're graphing sin/cos in terms of pi, I don't think the concept of cycling comes across as well because it's obscure and overly mathematician like to talk about distance or time in terms of pi. No one does this. Stop acting like they do.


If you want something that addresses the same concept but sucks all the fun out of the room, by all means, try the textbook version:


I'm so excited to try Exercise 55!

Going Further

An idea on the table for next year is taking this project further. I think there's room in the schedule to start trigonometry a little earlier to leave room for more in depth exploration. If time weren't an issue, instead of hand feeding them amplitudes and periods, I'd have them take something like my blinking lights GIF and see if they could determine what the values should be for the picture. It needs some time to marinate though, I haven't quite determined how I would frame the questions. Something I'm really started to get frustrated with is how dependent a lot of them are on me to do the thinking, even with all these introductory tasks and things. This came to a head in a project on right triangles that followed a few days later.

AuthorJonathan Claydon

Like all teachers on the internet, I use standard based grading with my classes. I'm at the point where I would never go back and my math department is having success deploying it to most of our academic level preps. Every time I grade tests though, one little bit nags me. Though the idea of SBG is to move us towards learning for learning sake, at the end of the day, I have to assign grades. I use a 0-4 scale that translates into 0-80 (with a 4+4=5, and 5=100 context). The level that really nags me is the 3, a 60% on the scale, and I have a little modification where 3+3=70. Ideally, the scale should feel like this:


There's a nice, relaxed transition between each level. Mastery is clearly identified at one end, and deficiences at the other. A kid should be able to quickly look at their scores and see how they're faring. I really only give a 0 for leaving it blank, 1 for minimal effort, 2 for taking the first step at least once, and 4 for absolute correctness or minor mistakes. But then there's 3. How do you define being at a 3/5 proficiency level? Doing 3 out of 4 problems flawlessly with the 4th blank, that's easy. But what if all four problems are attempted, and the same error is present in all of them? What if all problems are attempted and there's a major error in just one? What if it's very clear the student understands the first step, but may not be clear with the conclusion, or wasn't quite sure how to interpret the answer? What if they did one part of the directions flawlessly but forgot to write a complete sentence like you asked, even if you're 1000% sure that kid probably just forgot and does indeed know how to answer it?

That's where the scale starts to feel like this:


The 0, 1, and 2 levels are very identifiable. And 4 should be special, leaving this HUGE gray area to be covered by 3. But do all those scenarios really represent 60% mastery? This isn't a huge problem in Algebra, the skills are defined clearly enough to where there's not a lot of interpretation to be done when I grade. But when I grade Pre-Cal it happens ALL THE TIME. One kid's 3 feels like sweet glorious mercy and another kid's 3 is due to unfortunate technicalties even if I know they know the material. The topics in Pre Cal are so much denser that I have a lot of students who can show me the math but can't quite handle the interpretation, or forget a niggling detail on all of their graphs. What's the solution? Go from 0-8? Where 8+8=10? What about 9? At a certain point that slippery slope gets you right back to grading things out of 100.

Perhaps the answer lies in putting the gradiation right where I need it, at the 3 level:


I can show a little mercy on the kids who have a clear grasp on the beginning but not the end with a 3-, and reward those who are clearly showing proficiency minus a labeled x-axis with the 3+. Perhaps 3- = 50/55 and 3+ = 70? And I scrap the double three rule and go with double 3+ = 75?

I could also scrap the 3- concept and just include 3+. It's worth experimenting with. Although I feel like with as many topics as I have within a six weeks that these things aren't really costing a kid the difference between an A and a B on a report card all that often. And any SBG system should be simple and transparent to avoid all the junk that exists when debating the differences between an 82 and a 86.

Perhaps it becomes a special Pre Cal rule? Time will tell.

AuthorJonathan Claydon
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The Abstract

Around October we start digging into trigonometry in Pre Cal. The way curriculum is structured here, this is the first time they really play with sin/cos/tan outside of a brief exposure in Geometry. Once upon a time trigonometry was a foundation of Algebra II, but not anymore. It starts with the unit circle and moves into graphs. I present an image similar to this:


We discuss what we see. Are there any trends? I show them another bill from about 9 months later. Does this appear to be predictable? Almost always someone will point out that the summer months are much higher because you're running the air conditioner. Then we make some jokes about the weather in Texas (weather jokes, they're great!). Next, I have them peak at their unit circle and plot the points associated with sin/cos for various angles around the circle. We compare the result to the power bills we were looking at. At this point we discuss amplitude and period and I assign them a graphing task.

Photo Nov 08, 12 08 24 PM.jpg

The assignment is to draw at least two periods of their given function, identifying the amplitude and period. This year's version of the taks doesn't look much different than last year's. My intent was to add a more in depth writing component and to require them to overlay their new function on top of the parent function. However, a few things conspired against this project and it got rushed. My initial day for conducting the poster portion got pushed and I wasn't at school for a couple days immediately after, so the result suffered a bit. Now, the results were still good but there's room for improvement. So that inspired what came next.

The Relevant

So graphing sin/cos waves (and as a supplement, tangent waves) is great and all. But something gets lost when you're marking an x-axis with numbers in terms of pi. What does that mean? Nobody thinks in terms of pi. In our discussion of these functions, I always mention the high-voltage power lines that run near the school. In the right weather conditions you can hear them hum. I ask if any of them have noticed. This leads to a discussion about how electricity works, AC/DC, why their phone has this huge power brick, etc. Then we talk about sound. I pull up a tone generator (only seems to like Firefox).

Screen Shot 2012-11-17 at 4.55.38 PM.png

If I mess with the volume, what aspect am I changing? If I adjust the frequency, what aspect am I changing? What's the highest frequency you can hear? Why can you hear 18kHz, but I can't? What's the lowest frequency we can hear? So, that's how dog whistles work? It was an interesting discussion. I tune it to 60Hz so they can hear how electricity "sounds." We make some connections to physics, as these words get thrown around in there too. One or two of them might realize that there might be something to this science stuff.

Continued in Part 2: Signals, Phase Shifting, and High Level Thinking

AuthorJonathan Claydon