# I’m back

Hey everyone.

I took a two year hiatus from blogging. Life got busy and I let the blog slide. I’m sorry.

But I’m back, and my New Year’s Resolution for 2017 is to post at least once a month!

Here’s what I’ve been up to over the last two years:

• Twitter. When people ask why I haven’t blogged, I say “twitter ate my blog.” It’s true. Twitter keeps feeding me brilliant things to read, engaging me in wonderful conversations, and providing the amazing fellowship of the MTBoS.
• James Key. I consistently receive mathematical distractions from my colleague and friend, James, who has a revolutionary view on math education and a keen love for geometry. This won’t be the last time I mention his work. Go check out his blog and let’s start the revolution.

with my nerdy friends named James

• My Masters. I finally finished my 5-year long masters program at Johns Hopkins. I now have a MS in Applied and Computational Mathematics…whatever that means!
• Life. My wife and I had our second daughter, Heidi. We’re super involved in our church. I tutor two nights a week. Sue me for having a life! 🙂

family photo

• New curriculum. In our district, like many others, we’ve been rolling out new Common Core aligned curriculum. This has been good for our district, but also a monumental chore. I’m a huge fan of the new math standards, and I’d love to chat with you about the positive transitions that come with the CCSS.
• Curriculum development. I’ve been working with our district, helping review curriculum, write assessments, and I even helped James Key make some video resources for teachers.
• Books. Here are a few I’ve read in the last few months: The Joy of x, Mathematical Mindsets, The Mathematical Tourist, Principles to Actions
• Math Newsletters. Do you get the newsletters from Chris Smith or James Tanton (did you know he’s pushing three essays on us these days?). Email these guys and they’ll put you on their mailing list immediately.
• Growing. I’ve grown a lot as a teacher in the last two years. For example, my desks are finally in groups. See?

my classroom

• Pi day puzzle hunt! Two years ago we started a new annual tradition. To correspond with the “big” pi-day back in 2015, we launched a giant puzzle hunt that involves dozens of teams of players in a multi-day scavenger hunt. Each year we outdo ourselves. Check out some of the puzzles we’ve done in the last two years.
• Quora. This question/answer site is awesome, but careful. You’ll be on the site and an hour later you’ll look up and wonder what happened. Here are some of the answers I’ve written recently, most of which are math-related. I know, I know, I should have been pouring that energy into blog posts. I promise I won’t do it again.
• National Math Festival. Two years ago we had the first ever National Math Festival on the mall in DC. It was a huge success. I helped coordinate volunteers for MoMATH and I’ll be doing it again this year. See you downtown on April 22!

famous mathematicians you might run into at the National Math Festival

Now you’ll hopefully find me more regularly hanging out here on my blog. I have some posts in mind that I think you’ll like, and I also invited my colleague Will Rose to write some guest posts here on the blog. Please give him a warm welcome.

Thanks for all the love and comments on recent posts. Be assured that Random Walks is back in business!

# Looking back on 299 random walks

This is my 300th post and I’m feeling all nostalgic. Here are some of the popular threads that have appeared on my blog over the last few years. If you’ve missed them, now’s your chance to check them out:

Thanks for randomly walking with me over these last few years (though, some say it’s a “drunken walk” 🙂 ). Either way, I’ll raise a glass to another 300 posts!

# Challenge Problems

Want to enrich your Precalculus course with difficult problems? Look no further!

I teach a high-octane version of Precalculus to students in our magnet program. Our course, like most Precalculus courses, covers a very wide variety of topics. As often as possible, I like to give them more difficult problems that enrich the material from the book. These documents are a work in progress, but feel free to steal them (just email me a copy if you improve them!):

If you want solutions for any of these, shoot me an email.

These aren’t 100% polished by any means, but I’m sharing them anyway! Long live the spirit of sharing :-).

By the way, many of these problems are collected from other sources but I’m too far removed from those sources to properly attribute the problem-creator. My sincere apologies!

# Guess who!

In an effort to share more of my resources through this blog, here’s another installment.

This time I’m sharing a little worksheet that I created called Guess Who? It’s a short activity–a warm up, or an exit card–and students should be able to do it in 5 minutes or so. I do this in my Precalculus class at the beginning of the year, but depending on the timing and the context, it could be appropriate in an Algebra 2 or Calculus class as well.

The functions and the questions have a one-to-one correspondence and there is a unique solution to the worksheet.

These 12 functions might seem a bit strange, but they are the “12 basic functions” named by our Precalculus textbook authors.

Here are two additional activities that can go with a discussion of functions and their properties:

1. I have all the functions printed out on 8.5″x11″ paper and backed with colored paper so they look nice. I get twelve volunteers to go up to the front and hold the functions. Then we can play all sorts of games. We can ask all the functions that have an asymptote to step forward. We can ask all the odd functions to step forward. Which functions are bounded? Which functions are always increasing? Which functions have a range of all real numbers? But we can also play a guessing game: A student in the audience picks a function and writes it down without telling everyone. The other students in the audience ask yes-no questions about their function, like “Is your function continuous for all real numbers?” Each time, functions that don’t qualify step back and only a few functions remain. This is repeated until the chosen function is the only one that remains.
2. Another fun game idea comes from one of my colleagues. I love this: Have a bunch of “name tags” made up for all your students. The name tags will be one of the 12 basic functions and students will wear these on their backs, without knowing what their function is. They then have to walk around the room and ask other students yes-no questions about the features of their function until they can identify which function they are. I think I’ve played a version of this with celebrities or something. But it’s perfect for the math classroom, too!

Okay, that’s my contribution to the MTBoS for the day :-).

# Math on Quora

I may not have been very active on my blog recently (sorry for the three-month hiatus), but it’s not because I haven’t been actively doing math. And in fact, I’ve also found other outlets to share about math.

Have you used Quora yet?

Quora, at least in principle, is a grown-up version of yahoo answers. It’s like stackoverflow, but more philosophical and less technical. You’ll (usually) find thoughtful questions and thoughtful answers. Like most question-answer sites, you can ‘up-vote’ an answer, so the best answers generally appear at the top of the feed.

The best part about Quora is that it somehow attracts really high quality respondents, including: Ashton Kutcher, Jimmy Wales, Jermey Lin, and even Barack Obama. Many other mayors, famous athletes, CEOs, and the like, seem to darken the halls of Quora. For a list of famous folks on Quora, check out this Quora question (how meta!).

Also contributing quality answers is none other than me. It’s still a new space for me, but I’ve made my foray into Quora in a few small ways. Check out the following questions for which I’ve contributed answers, and give me some up-votes, or start a comment battle with me or something :-).

And here are a few posts where my comments appear:

# I ♥ Icosahedra

Do you love icosahedra?

I do. On Sunday, I talked with a friend about an icosahedron for over an hour. Icosahedra, along with other polyhedra, are a wonderfully accessible entry point into math–and not just simple math, but deep math that gets you pretty far into geometry and topology, too! Just see my previous post about Matthew Wright’s guest lecture.)

A regular icosahedron is one of the five regular surfaces (“Platonic Solids”). It has twenty sides, all congruent, equilateral triangles. Here are three icosahedra:

Here’s a question which is easy to ask but hard to answer:

How many ways can you color an icosahedron with one of n colors per face?

If you think the answer is $n^{20}$, that’s a good start–there are $n$ choices of color for 20 faces, so you just multiply, right?–but that’s not correct. Here we’re talking about an unoriented icosahedron that is free to rotate in space. For example, do the three icosahedra above have the same coloring? It’s hard to tell, right?

Solving this problem requires taking the symmetry of the icosahedron into account. In particular, it requires a result known as Burnside’s Lemma.

For the full solution to this problem, I’ll refer you to my article, authored together with friends Matthew Wright and Brian Bargh, which appears in this month’s issue of MAA’s Math Horizons Magazine here (JSTOR access required).

I’m very excited that I’m a published author!

# A TOK Lecture on Mathematical Thinking

Students in our International Baccalaureate program here at RM are required to take a core class called Theory of Knowledge (TOK) which is kind of a philosophy class for high school students–or, at least the epistemology piece.

In some schools, this course is taught by math teachers. Here at RM, no math teachers currently teach TOK, which is too bad. So I volunteered to put together a guest lecture on Mathematical Thinking. I’ve tried it out once with a TOK class and I gave the lecture for some of my math teacher colleagues today after school. I plan to give the lecture to more TOK classes this spring.

I thought I’d share it with the MTBoS as well, so here it is. Feel free to read, comment on, or borrow my materials. I think other IB math teachers would especially benefit: