Snail's Pace

Last post, I shared a lesson (Woody's Raise) that included both Act 1 and Act 3. I asked you all to collaborate and design Act 2. Many of you came through like champs in the comments.
THANK YOU!

For this post, I only have an Act 1, leaving Act 2 even more open-ended. I'll admit, I only have Act 1 because I haven't invested the time necessary for Act 2 and Act 3. Here's my current Act 1.

I thought of this lesson many months ago while out walking in the morning, but wanted to capture it on video... no joke. So until that time actually comes along, I'll give you what I envisioned for Act 1, the video version. We start with Bill Conti's Gonna Fly Now (Theme from Rocky) as we take a couple close-up shots of the snail. The camera pans out to a bird's eye view of the snail starting at one side of the sidewalk, letting time elapse for about 15-20 seconds.

Back to the picture of the snail who has an increasingly long road ahead of him. I notice that he isn't taking the shortest path to the other side. I notice that there aren't any other snails to avoid. I notice the sidewalk is wet. I wonder what his path will be. Will his path be linear? curved? circular? other? I wonder what his rate will be. I wonder what the dimensions of the sidewalk are. I wonder if the Pythagorean Theorem could be used here. What do you wonder?

Head over to Dan Meyer's 101qs.com and enter a question (or skip it) so you can see my Teacher Notes for Act 2. You might need to log in. Thanks to Ignacio Mancera for linking a site with Speed of Animals. This will help assist our Act 2 adventure.

Here's what I have so far if you can't get into 101qs.

What initial conversation(s) would you have with students?
How would you have students work with Act 2 information (dimensions, rate of snail)?
Is this a waste of time?
Should we (I) shelf this idea for now? (or even toss it in the trash can?)

Slowly,
333

Dancing with the Functions

I'm honored and humbled to have been a (small) part of Christopher Danielson's online course The Mathematics in School Curriculum: Functions. There were some great tasks, discussions, and contributors. I now have a better misunderstanding of functions. However you interpret that last sentence, let me assure you that this two week course broke me down in order to give me a better perspective and idea of functions. Professor Triangleman moderated the course well, provided challenging tasks and opportunities that took me out of my comfort zone, encouraged us to think differently, and didn't hesitate to whip us into shape as you can see here:

He's referring to beating me down while informing the teacher's pet (Fawn) of his tactic.

Our choices for our final project were:

• a blog post,
• a lesson plan,
• an interpretive dance,
• a work of visual art,
• etc.

I thought writing a blog post was "too easy" in the sense that I could blog about anything ordinary at anytime. This class wasn't ordinary though, and I felt I'd rather try and give something back to the class, professor, and community in exchange for what I have received. No Fawn, not because I'm "too lazy." Therefore, I'm going to give you a lesson idea I have, based on an interpretive dance, which might be a work of visual art, all wrapped up in a blog post.

Interpretive dance really got me thinking. I thought back to the handful of dance lessons my wife (fiance at the time) and I took to practice for the First Dance at our wedding. My wife was a natural. As for me, well let's just say all the dance lessons in a lifetime wouldn't have helped. Here's a dance photo I have of us where it actually looks like I'm doing something worthy. Don't be fooled.

Don't worry, I won't torture you with video. Anyway, our dance instructor taught us many helpful tips and gave us a glimpse of dances like swing, salsa, the waltz, and the two-step box. We only did a few moves in our wedding dance, but it mainly revolved around the two-step box. We had a short song, thank goodness. I'm sure our guests would have taken their gifts back had they seen me dance any longer.

Here comes my lesson idea. I'd like to see the relationship between the number of steps taken in a dance over time. So let's make it a graphing story. Here's the first 30 seconds of a dance. Write a story for it. Even better, can you write the functions (along with any intervals, domains, ranges, etc)? Go here to Desmos to check your answers. I give you my interpretive dance.

Thanks to Sadie, Timon, and Michael Pershan for inviting me to their hangouts. I was honored to collaborate with you guys during one of the hangouts and bounce ideas off of each other. Thanks to Fawn for getting me in trouble, ratting me out to the teacher, and reminding me to submit my final project. Where would I be without you? Probably in class and not in the principal's office.

I would love some feedback on this lesson idea. Would you have your students dance? If so, what dance(s)? Would you have students come up with a function for each type of dance? What kind of relationships would you have your students look for? Would you consider "dancing" an applicable use of functions? I leave you with this clip. You must give these guys (Sean and John Scott) some crazy respect. They're insanely fantastic at tap-dancing. Just watch the first minute. Then make a graphing story.

Dance,
933

Distance, Rate, & Time [Giddy Up!]

Last week I finished Steve Leinwand's Accessible Mathematics. It's a quick, easy, informative, realistic, and applicable read. Get on that!
This week I planned on diving into Standards Based Grading while restructuring some things for next school year. Well, there's still time for SBG. Instead, I've been churning out some new 3 Act lessons with:

1. Some outtakes to the hexagonal Pencil Cup lesson and...
2. The beginning of some distance, rate, and time lessons

There's a plethora of resources out there dealing with d = rt. Therefore, I thought I'd try and put my little spin on the whole roundabout. Keep checking my Distance, Rate, & Time album for updates.
Giddy up to summer!

Ferrari Ride - Act 1 from Mr.Stadel on Vimeo.

Go the distance,

1140