Category Archives: math

Daily Agendas on Google Docs

I’ve been doing this with a few classes for the past two years, but this year made the move to all: I keep a Google Doc with the day’s agenda for each class. This is useful as a central location from which all of the day’s activities can progress, with links to assignment documents, links to online quizzes, links to videos, and links to resources all embedded in there. In review surveys at the end of each class, this has consistently been a highlight and something they really appreciate. For example: “The links on the agenda and the directions that gave us to do what we had to do”, and “Somenthing that I really liked about this class was the agenda because if by any reason you was absent you just have to go to the online agenda and you can make up from your home.”

Because of these reviews, this year I’m moving to all classes having an online agenda. Combined with the fact that I’m a fan of the website for shortening and choosing your own url, I was laughing with a few of my students this afternoon that today I had my students use 5 different tinyurls for these agendas (and of course have to keep them straight in my head):


[Year 12, Day 2 post]



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Year 12, Day 0

This week teachers headed into school to prepare for next week and students’ return. This will be my twelfth year!

My teaching this year will include more computer science than ever before:

  • AP Computer Science Principles (full year)
  • AP Computer Science A (full year)
  • Foundations of Computer Science  (spring)
  • Computer Integrated Manufacturing (fall)
  • Precalculus independent study (fall, three students, three separate periods)

I’ll also be working with our new engineering teacher and our librarian+new-computer-science-teacher to help them with their lessons, and collaborating with two geometry teachers around standards-based-grading.

Extracurricular activities and competitions:

  • Coding Club (app development, cybersecurity, & more)
  • Women’s Transportation Seminar’s “Transportation You!” Mentoring Program
  • TRAC bridge builder competition
  • CyberPatriot competition
  • STEM Competition
  • possible (in my mind, I want to do each of these this year): Cyber Movie Mondays, Saturday AP & PLTW study groups, Girls Who Code club
  • probably several others…

Ongoing projects that will occupy some of my time this year include:

  • Comp Hydro (teaching hydrology and flooding through computational simulations & modeling, in partnership with the Baltimore Ecosystem Study)
  • MyDesign (engineering design process app and learning management system, in partnership with NSF & the University of Maryland)
  • Internet of Things project to measure air quality and other environmental factors in schools (in partnership with Cool Green Schools, Johns Hopkins University, and Morgan State University)
  • Continuing work toward my Master’s Degree in Computer Science (taking “Artificial Intelligence ” course this semester)
  • Baltimore City Engineering Alliance, a nonprofit 501(c)(3) we created to provide opportunities to Baltimore City students to further their engineering education, and for which I am treasurer

School starts for students on Tuesday, after Labor Day for the first time in my twelve years here teaching in Baltimore. Wish us luck!

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Pythagorean Triple Answers

As a follow-up to yesterday’s post, here are some answers and steps toward figuring out the scarcity (or frequency) of Pythagorean triple days (like yesterday 8/15/17) in a century:

I will mention I did not get the answer right away but needed some prompting (from a math-teacher colleague on Twitter), so I’ll take you through my thought processes.

  1. I have certain primitive Pythagorean triples memorized (like 9/40/41) — perhaps from several years of teaching geometry, or from studying number theory in college where integer (or rational) values for algebraic relations are important (cf. Euclid’s formula for Pythagorean triples, Diophantine Equations, & Fermat’s Last Theorem), or perhaps even a few recalled from taking high school geometry. In my head I tried these, saw several had occurred already in the past (5/12/13), while others were not interpretable as months days and years, like 9/40/41 (since there are max 31 days in a month). To go beyond the primitive triples, I tried multiplying each times 2, times 3, etc. In this way I discovered yet to come this century: 10/24/26 (twice 5/12/13) and 12/16/20 (quadruple 3/4/5).
  2. I thought I had them all, but had forgotten some primitive triples, like 7/24/25! At this point, referring to this list of primitive Pythagorean triples, I tried to systematically enumerate all with a≤12, then go through multiples of those until all values were larger than 12 (and therefore none could fill the month slot). I did this in Excel, color coding as blue dates already past, yellow yet to come, and red invalid date formats:excel1
  3. In creating that chart I did mentally transpose months and dates to see for example, that 12/5/13 could also work as a Pythagorean triple date in addition to 5/12/13. But this only yielded more in the past so I didn’t bother to write them out. My fatal flaw, though, was not permutating with the years also, so I neglected to find two more future dates: 7/25/24 and 10/26/24. After realizing this, I did add more to my Excel chart, going through each permutation that yielded a valid date in rows below the main ones:excel2
  4. I do believe this is now a complete list of past, present, and future Pythagorean triple days, written month/day/year. By my count there will be a total of 28 this century, 23 now past and 5 still in the future. Let me know if I missed any!


By the way, here’s an awesome interactive generator of Pythagorean triples by Vincent Pantaloni (shared on twitter).





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Happy Pythagorean Triple Day!

Today is 8/15/17 (abbreviating the year to two digits), which are three natural numbers that make up a Pythagorean triple! That is, three numbers that satisfy the equation from the Pythagorean Theorem a2 + b2 = c2 , and therefore make up valid integer side lengths on a right triangle.

Try it! 82 is 64, plus 152 (225), makes 289, which is 172 .

In fact, 8/15/17 is even more special than other Pythagorean triple days like 6/8/10, or 12/9/15, since it is a primitive Pythagorean triple: that is, its numbers share no common factor (e.g. 6/8/10 all share a 2, which if factored out yields the more familiar 3/4/5).


A great question to ponder: how many more Pythagorean triple days will we have this century? (question and image from Chris Smith, on Twitter)



Also, how many already occurred (and perhaps we didn’t even realize it)?


Will post answers to these questions tomorrow…

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Pi Day Snow Day!

After a winter with no snow (no snow that’s stuck, anyway, there’ve been flakes in the air a few times), it’s a pi day miracle: a snow day!

Last night, when the call was made, we were predicted to get 6-12″, but with more sleet than snow, we’re on the low end of that range or a bit less. Here’s a joke I’m stealing from my friend Matt:

In honor of pi day, and with the extra free time of a snow day, I baked a quiche pi!


I tried to arrange the broccoli in the shape of the symbol π (pi), which you can see if you look closely 🙂 I’ve outlined it below.


And, of course, I had to break out my pi cutter to slice it with!


If you’re more ambitious than I am with your pi day baking needs, you could  try a “celebrity chef” pie, or Vi Hart’s Venn Pi-agram (she has both a dessert pie and a pizza pie version):

In Pi Day news, there have now been over 22 trillion digits of pi calculated! Hooray!

Whether or not you, too, are snowed in, have a wonderful pi day, and check out some of the following links!

Even though there are skeptics out there,

I agree with Cookie Monster:

Me love pi (and pie)!

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New Year

Greetings readers, and happy new (school) year! This is year number eleven for me (who knows where the time goes?).

This year I shall be teaching the following subjects:

  • Computer Integrated Manufacturing (my tenth year with this, my most-frequently-taught class) – Fall, two sections
  • Foundations of Computer Science – Spring (ninth graders, to be recruited)
  • Precalculus – Spring
  • AP Computer Science Principles (a brand new AP course this year, though it has been in the works and piloted for several years, including last year by me) – Full Year

Here’s the College Board’s Intro Video to the new CSP course:

I’m super-excited for the new year, and the new CSP course in particular (if you’d like to follow along with our daily agenda, it will be updated each day at ).

This year I am thinking I shall try to keep up with #teach180 on Twitter, posting a photo tweet every school day (more explanation here). We’ll see if I can keep that up, after my abysmal recent record of updating this blog. 🙂

I’ve also just started my fall course from Georgia Tech, Computer Vision. I’m very much looking forward to it, and learning how computers can make sense of what they “see”!

To all the other teachers out there, hope you have a great year!

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Happy (Round-Up) Pi Day!

Greetings once again, one and all!


Pi Pies (photo by djwtwo on Flickr)

It is PI DAY, y’all – gather round and roll out the red carpet for that most glorious of numbers,


a.k.a π,

a.k.a pi.


In fact, though we made a big deal of last year’s celebration as the “Ultimate Pi Day”, or the “Pi Day of the Century”, a case can be made that today is even more special! Today’s date, 3/14/16, is a rounded-up version of pi to four decimal places (rather than a truncated version like last year); it also only comes around only once a century; and in fact 3.1416 is about nine times closer to the actual value of pi than 3.1415 is! 😉

If you’re a little bummed out that we won’t have a “pi day of the century” next year (after all, 3.1417 doesn’t seem too special), check out this article (via MAA) which proves that, for some norm other than the Euclidean distance, there is a “pi” for that norm that will match that year–thus every pi day can be the “pi day of the century”!

I wore a shirt with a similar message today! (Image via Cliff Pickover)

I wore a shirt with a similar message today! (Image via Cliff Pickover)

OK, here’s your round-up of cool pi links:

Apple Pi (Image by elips, via Cliff Pickover)

Apple Pi (Image by elips, via Cliff Pickover)

HAPPY PI DAY !!!!!!!!!!!!!!!!!!!!!!/!!!!!!!

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