A long-awaited solution (featuring Geogebra)

So, a while back, I posted “Circles from Cedar Street” with an intriguing (at least to me) picture designed to kick off the conversation about rotations.

Then, I left it alone. Like, literally. I didn’t solve it. I should have solved it. I let you down.

I especially let guys like Dan down, who also found the problem intriguing. Sorry about that.

But I realized today that it’s never too late to make it right. So, using Geogebra, here’s is one possible solution to the Circles from Cedar Street problem from back in August of 2013.


Physics, a helicopter and cameras

First watch this (and be amazed… well, if you’re anything like I am.)

So, when the students can get past the idea that there is some foul play involved, then it becomes a wonderful opportunities to discuss the idea of frequency.

Frequency is an odd discussion because it’s got a strange unit. The “per time” can be a little challenging for students to wrap their heads around.

And the opportunity that this video provides is that here, we don’t need to immediately concern ourselves with the quantitative value of the frequency (maybe 300 RPM for the helicopter rotor, for example, or 5 frames per second on the camera), but we can begin with the qualitative value of the frequency (that the frequencies, whatever they are, are the same.)

And then it opens the door for them discussing some quantitative issues. For example, the fact that the standard unit of frequency (the “per unit time”), obviously isn’t constant. So, the helicopter rotor is RPM and the camera shudder is typically in frames per second (at least, I think. Not a photographer…) So, you’ve got some nice dimensional analysis opportunities.

Where could you take this next?

One thing’s for sure, I’d hate to waste a video like this. Fully captivating, and it only costs your 30 seconds of class time.

Source: I owe TwistedSifter credit for blogging about this video first.

Simple Leadership Advice

I’m going to attempt to model this my internalization of a bit of advice that I received recently.

Leadership is about trust. You want your people to trust you?

Speak plainly and keep your word.

By speak plainly, I mean say what you mean in a way that designed to be heard and fully-processed by those who hear it. Trust corrodes when those you are leading feel the need to constantly read between the lines of your statements.

By keep your word, I mean if you commit to doing something, then do it.

The advice I received was from Mark Wilson, but his was directed at goal-setting. Goals should be simple and easily understood. He didn’t mean that they should be low-level goals. But they should be able to be stated simply.

All of our students will be safe in our school.

All of our freshman will successfully complete all of their classes.

All of our new students will get a complete orientation to our school community before they attend a single class.

These are not-simple goals, but they are stated simply. That makes them easier to follow. Easier to implement. Easier to assess.

And it also makes it easier to keep your word. Here’s what I said I would do. Did I do it?

Well, if your goals sound more like this…

“To support the ever-dynamic pressures of a 21st century global economy, we will consistently find new and innovative learning experiences to blend with classical best practices to provide the highest-quality academic pathways for our diverse learners to produce successful work- and college-ready graduates.”

… then it becomes quite a challenge to evaluate whether or not you did what you said you do. This goal is not necessarily more complicated than “All of our freshman will successfully complete all of their classes”, but it is much less likely to become the unifying slogan around which we focus our energy. And isn’t that the point of stating the goal?


To close, all of this talk about speaking plainly has me thinking of this delightful scene from Shrek the Third