I’ll post more later, but here’s a sneak preview of this year’s Pi Day Puzzle Hunt. We’ve been working on this for months, and it finally happens next week. Here we go!

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I’ll post more later, but here’s a sneak preview of this year’s Pi Day Puzzle Hunt. We’ve been working on this for months, and it finally happens next week. Here we go!

*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.**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! 🙂

**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?

**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!

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!

Have you been doing other things and failed to notice the origami world evolve without you? Have you fallen asleep and been left behind? **If you want to get caught up on what you’ve been missing in the world of origami, I suggest you visit Hannah’s origami blog, A Soul Made of Paper**. She’ll have you caught up in no time.

I especially like giving her blog a shout-out because Hannah is a student of mine. She often comes by my classroom to show me her latest paper creations. I like origami, and I’ve dabbled in it–stuck my toe in the stream, if you will–but Hannah is like a scuba diver in the origami world. She’s loves modular origami, but she’s also great at the artsy curved creations (like origami roses), textures, and tessellations.

If you haven’t clicked over to her blog yet, here are a few more pictures to whet your appetite.

Go get lost at A Soul Made of Paper. Maybe you can join her other 3000 followers on tumblr :-).

*All of the above are Hannah’s pieces and Hannah’s photos.

**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:

**Posts about the new Microsoft Equation Editor**: I’m a huge fan of the new equation editor in Microsoft Office and I’ve posted numerous times about its features, the first one here. I didn’t get it all out of my system and had to say more here. Many people complain that Cambria Math is the only available font, so I pointed you to other math fonts and work-arounds. I’m pretty handy with LaTeX, too, so I did a comparison in this post.**For some reason a**and this post is linked from a lot of teacher course pages.*lot*of people find this post about TI-Emulators**Philosophical posts about education**: Why Calculus still belongs at the top, Patient problem solving, In defense of Calculus, One thing that makes my class unique**The definition of trapezoids**. Need I say more?**Misconceptions**: PEMDAS problems, Do irrational roots come in pairs?, Asymptote misconceptions**Rants**: Rationalization Rant, Teaching domain and range incorrectly**Visitors to our school**: Glen Whitney, James Tanton, Matthew Wright**Some of my favorite resources I’ve created**: Halloween Calculus Worksheet, Challenge Problems, Guess who!, Theory of Knowledge Lecture**And of course, my Random Walk Mural**that just went up in the back of my classroom this summer! Check out the link for a video documentary about how it was made.

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!

I’ve been meaning to give the back wall of my classroom a makeover for a while. This summer I finally found some time to tackle the big project. I took down all the decorations and posters. I fixed up the wall and painted it a nice tan color. Then, I let loose the randomness!

I struggled with what the new mural would be–I’ve thought about it over the last few years. I considered doing some kind of fractal like the Mandelbrot Set. But it should have been obvious, given the name of my blog!! **What you see in the picture above is three two-dimensional random walks in green, blue, and red.** In the limiting case, one gets Brownian motion:

I honestly didn’t know what it was going to look like until I did it. I generated it as I went, rolling a die to determine the direction I would go each time. I weighted the left and right directions because of the shape of the wall (1,2=right; 3,4=left; 5=up; 6=down). For more details about the process of making it, here’s a documentary-style youtube video that explains all:

Actually, I lied–it doesn’t tell “all.” **If you really want to know more of my thought process and some of the math behind what I did, watch the Extended Edition video** which has way more mathematical commentary from me. I’ve also posted the time lapse footage of the individual green, blue, and red. Just for fun, here’s an animated random walk with 25,000 iterations:

I think the mural turned out pretty well! It was scary to be permanently marking my walls, not knowing where each path would take me, or how it would end up looking. At first I thought I would only do ONE random walk. However, the first random walk (in blue) went off the ceiling so I stopped. And then I decided to add two more random walks.

In retrospect, it actually makes complete sense. I teach three different courses (Algebra 2, Precalculus, and Calculus) and I’ve always associated with each of theses courses a “class color”–green, blue, and red, respectively. I use the class color to label their bins, to write their objective and homework on the board, and many other things.

The phrase “Where will mathematics take you?” was also a last-minute addition, if you can believe it. There just *happened* to be a big space between the blue and red random walks and it was begging for attention.

What a good question for our students. The random walks provide an interesting analogy for the classroom. I’d like to say I’m always organized in my teaching. But **some of the richest conversations come from a “random walk” into unexpected territory when interesting questions are raised.**

Speaking of interesting questions that are raised, here are a few:

- Can you figure out how many iterations occurred after looking at a “finished” random walk? Or perhaps a better question: What’s the probability that there were more than
*n*iterations if we see*m*line segments in the random walk? - Given probabilities of going in the four cardinal directions, can we predict how wide and how high the random walk will grow after
*n*iterations? Can we provide confidence intervals? (might be nice to share this info with the mural creator!) - After looking at a few random walks, can we detect any bias in a die? How many random walks would want to see in order to confidently claim that a die is biased in favor of “up” or “left”…etc?

Some of the questions are easy, some are hard. If you love this stuff, you might be interested in taking a few courses in Stochastic Processes. Any other questions you can think of?

**Where will math take you this coming academic year? Welcome back everyone!**

If you’re local, you should go check out the USA Science and Engineering Festival this weekend. It’s on the mall in DC and everything is free.

They will have tons of booths, free stuff, demonstrations, presentations, and performances. Go check it out!

For my report on the fest from two years ago, see this post. The USA Science and Engineering Festival is also responsible for bringing to our school, free of charge, the amazing James Tanton!

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 , that’s a good start–there are 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!