Tag Archives: math teaching

Roots of Unity Final Projects


These are the results created last November for the art/math integration project described here.


By the way, happy pi week everyone!

Pi Week

Pi Week

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Art Integration: Roots of Unity & String Art

I talked with an art teacher this afternoon about ways to integrate art and math into a project. She had some great ideas, plus we came up with more ideas in the course of our discussion, many of which I plan to try for Algebra 2 or Precalculus (both which I teach this year, fall and spring respectively). Geeking out while discussing the intersection of math and art reminded me of this awesome collaboration and its result from a few years ago!

Our first idea (in terms of implementing soon) was some colorful string art crossed with a discussion of the roots of unity, since my students are (today) using and graphing complex numbers for the first time. Math teachers, art teachers, and any interested others, check out this rough draft of the project and let me know any thoughts and advice:

Roots of Unity Project


Colorful "string" art on the 17 th roots of unity

Colorful “string” art on the 17 th roots of unity


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It’s Pi Day!!!.

It’s that time of year again: spring is almost here, and you can almost feel a warm mathematical breeze on the air. It’s…

Pi Day!!!.

Since the number pi (π) is approximately 3.14, and today is 3/14, today is sort of a mathematical holiday. (You may have noticed that I’ve included approximately 3.14 exclamation points above and in the post title!)

I started my celebration this morning with some coffee iced with pi-shaped ice cubes:

Pi Iced Coffee

Pi Iced Coffee

Additionally, I noticed today that I follow exactly 314 people on twitter:

Hey look - I'm following about 100pi people!

Hey look – I’m following about 100pi people!

(OK, I admit, I followed one new person today to get that to work out 🙂 )

Today, in addition to celebrating both the number pi and all sorts of mathematics, it’s time to start getting ready for the best pi day celebration of our lifetimes, which will be held in two years: 3/14/15 at time 9:26:53. This will be a much more accurate representation of pi than we celebrated just over an hour ago (at 3/14 1:59). Though perhaps we missed an even bigger party four centuries ago on 3/14/1592 6:53:58.

A few notes, links, and cool things for this pi day:

  • Math geeks can even talk about their mania for this amazing number in the form of a palindrome: “I PREFER PI”!
  • It seems that pi day is getting more popular: Companies like Oreo and GE are getting in on the action!
  • Check out this video, where a few people use actual pies to calculate pi (from http://www.numberphile.com/videos/pie_with_pies.html) :

Lastly, I hope you all can read (and would agree with) the following t-shirt, tweeted by NSBE:

Picture from NSBE

Picture from NSBE

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Happy 12-12-12 Day!

Perhaps it could be called duodecimal day if you look at the numbers, or ternary day if you look at the digits. In either case, have a wonderful 12-12-12 day!

After being treated to a dozen similar days over the last few years (here, e.g.), we must now alas face a desert stretch of a few weeks longer than eighty-eight years until the next time the month, date, and year will all align.

Though at least we’ll have 11/12/13 next year, and 12/13/14 the year after. And of course the best pi day of our lives on 3/14/15 (at 9:26:53am). So I guess, even without repeated numbers, we still have a few good years ahead of us 🙂 .

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Phi Project

So, as I explained yesterday, I decided to create a project centered around golden ratio, phi (φ) ≈ 1.6180339887, and the associated Fibonacci sequence 0,1,1,2,3,5,8,13,…. My classroom has computers, so I had students go back and forth between watching parts of Vi Hart’s videos (123) on the subject, and doing or reflecting on something mathematical, artistic, or biological.

Here is my project:

I think it’s a little bit lighter weight than some of my other projects. But it does connect to our work with quadratic equations (which we are just wrapping up). And it gives my students a chance not just to see math in the world, but also to think about why our world is mathematical.

The students seem to enjoy working on the project so far. Either that or they just liked the pineapple we ate (after, of course, counting the spirals on it!).

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Math is in the Air!

Math is in the air this week as we close in on that most special of mathematical holidays, pi day.

Pi Day is only a week away, and I for one can’t wait! I’ve emailed our school secretary so pi day will be included in our weekly bulletin. I’m trying to consciously make students appreciate some of the cool things about math (I try to do this all the time, but sometimes get stuck on autopilot teaching procedures and projects).

In preparation for Pi Day, I’ll be posting some links to amazing mathematics over the next week.

To begin, you all remember the interdisciplinary geometry-art project on fractals I did last year? Well, these middle schoolers have gone even deeper into the world of fractals and produced some beautiful works of art, as part of their Fractal Club! Go to this link and check out the video. (Thanks to Ceilon Aspensen for sharing the link on facebook.)

Have a great pi week, and I’ll see you again soon!

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Good PD

Like many teachers, I have suffered through some pretty awful professional development (PD) days. Some where we are read to off a PowerPoint slideshow, one of the techniques we are told is not good teaching practice. Others are more interactive (e.g. think-pair-share) but still boring and/or not relevant to actual teachers.

I am a firm believer that PD needs to be much more self-directed to be effective. We, as teachers, are professionals. As such, we can be trusted to work toward our own professional growth.

I get so much out of reading blogs by and tweeting with other math teachers–including lesson ideas, projects, worksheets, innovative techniques, clear explanations, and feedback on my ideas. Mythagon does a great job explaining the value of the math blogging/tweeting community here. The engineering education community is smaller, but I’ve worked to create and find spaces for that collaboration to occur as well, including by creating an online course to share resources with other engineering teachers in Baltimore City, and by starting this very blog.

In an official PD Day setting, where teachers have school but kids don’t, what could a more self-directed PD look like? It could include time to develop and grow a virtual professional learning community (blogs, twitter, as described above). It could include time to collaborate with other teachers in the building or district, self-selecting colleagues in your subject area or outside it, and deciding as a group what topics need to be discussed. It could include a variety of seminars/presentations, each led by teachers, of which you can pick which ones to attend that you need the most development in.

The best PD is that which I can use in the classroom the next day or week or month. Some of the best days of PD for me personally have come from a series of workshops organized specifically for PLTW engineering teachers, through the Community College of Baltimore County and the Time Center. They’ve been offering these trainings for the past several years, and recently received an NSF grant to expand their ongoing-PD model to other schools and states across the country.

Crane, built from FischerTechnik parts and programmed via RoboPro

I attended one of these PD’s a few weeks ago about using and programming with FischerTechniks and RoboPro. We learned advanced programming techniques (variables, subroutines, displays, inputs/outputs, commands & operators, branches and wait fors). We applied some of these techniques to arithmetic operations, and some to operating the crane you see above.

For the second half of the day, we had time to complete a project of our own choosing. I needed some help and practice time with pneumatics, as they were not part of my original training in the Principles of Engineering and Computer Integrated Manufacturing courses but have since been added to the curriculum in both. To use the new curricula, we had to purchase supplemental kits, since our FischerTechnik kits did not come with pneumatic components. So this was still pretty new to me, and I really valued the time I had to explore, learn, and get help from both the professor and a teacher-classmate. We built the simple pneumatic system you see below, which will store compressed air in the tank using a motor and cylinder pump system, then convert the pressurized air to vertical or lateral motion. This has been especially useful, since I’ve been using the instructional resources provided that day, plus my greater understanding of this topic, to teach pneumatics and fluid power to my CIM students this week!

Our pneumatic system

I shall be attending another PD this Friday at CCBC to improve my skills in using Autodesk Inventor, a 3D modeling software.


It’s down to the home stretch for both Mustaches For Kids and #NaBloPoMo!

Please support my moustache & Baltimore students by donating at DonorsChoose via my page. Plus, if you give now, you can use the codeword JOLLY and have your donation matched!

Also please support my partners in Baltimore’s NaBloPoMo by visiting and commenting at their blogs:

Only one day left in November – we’re almost through!

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