We’re deep into linears

We’ve established “rate” as “something per one something” and the y-intercept as our initial condition, all without using the terms “slope” or “y-intercept” or the variables “y” or “x.”… or Graphing Stories, for that matter, which at the time seemed like the quintessential introduction to linears, dammit. I can’t decide if I hate or love this part of my job.

Maybe you frown at that kind of corner cutting but a) you have no idea how gradually you’ve gotta introduce those abstractions at the level I teach, and b) that’s why I don’t read your blog.

So watch as I take my kids through this tech-drenched project-based assignment. Squint through crossed eyes and I might look like someone you’d see at NECC.

1. Set It Up

   If I fly 300 miles out of San Francisco, is the duration of my flight predictable? Is the cost? Would the graphs look predictable or random?

   
2. Give Them Laptops

   We have a mobile lab of 15 MacBooks. That’ll do.

3. Fly Out Of United Airlines

   Send them out of the same airport. (SFO is our local hub.) Have them pick fifteen one-way, non-stop destinations. Ask them if they have any international YouSpace or FaceTube friends they’d like to visit, thereby cementing your digital street cred.

   

   Baghdad, as many curious students found out, is somewhat inaccessible.

4. Record Flight Data In Hard Copy

   Have them record:

   • airport codes,
   • departure times,
   • arrival times,
   • flight durationsHave fun explaining why a flight takes off from San Francisco at 9:00 AM, lands in Honolulu at 11:30 AM, and lists a 5.5 hour flight time.,

   and most crucially:

   • distance in miles,
   • time in minutes, and
   • cost in dollars.

PDFs here! Getcher PDFs right he-ah!

5. Enter Flight Data Into Excel

   If you want to skip past the hard copy step straight to this one, just know you’ll need a continuous two hours.

   
6. Graph!
   

   Marvel a bit at how well Time v. Distance fits a regression line and how terribly Cost v. Distance does.

   
7. Discuss
   1. What does the rate mean for each? The plane flies at .11 minutes per mile, roughing out to 545 miles per hour. Each flight costs 22 cents per mile.
   2. What does the initial condition mean for each? This one’s truly fantastic, as you’d expect the initial condition for time to be zero. (A flight of zero miles oughtta last zero minutes.) Instead, that 36.9 minutes is the time the airline builds in for sitting on the deck, waiting to take off. Elsewhere, that $51.19 initial condition is the charge just for stepping onto the plane.
   3. What does it mean if a dot is above / below the line? The flight is longer / shorter than you’d expect for that distance. The flight is costlier / cheaper than you’d expect for that distance.
   4. Why is cost v. distance such a terrible fit? What does cost depend on if not distance? Why, for instance, does a short flight to podunk li’l Eureka, CA, cost more than a flight to LA at double the distance? TFJ pulled the answer to that one outta thin air, eyes darting back and forth, putting it all together in what has gotta be one of the most satisfying moments of my career, a moment in which I was pretty much wholly uninvolved: “There’re only one or two flights to Eureka.”

Occasionally I need to reassert myself as a math teacher, on this particular day because I realized Math Bloggers doesn’t include me in their tracker. Look! I am so a math blogger. So here’s what’s good lately:

Don’t Steal Nickels

I run this interlude in every age group. Awhile back some thieves got busted with a lot of nickels. The conversation on this one can’t be beat and eventually wraps itself around the idea that high cash value is great but has to balanced against the weight of a coin.

So you head over to Wikipedia and pick up coin images, then over to the treasury page detailing coin weights and you’re asking questions and taking bets constantly:

• Which would you steal right now? Knee-jerk reaction.
• Who’s on the face of a half dollar?
• Which is the lightest coin?
• [etc]

Then you have them calculate the ratios and you notice that one fantastic thing about the dime, quarter, and half dollar (consulting Slate if you’ve gotta) and you preface the whole thing with, “Let’s become smarter thieves.” Riveting.

Pick’s Theorem

Pick’s Theorem calculates the area of irregular, weird shapes using a grid for reference. I realized as the class bell rang I was only using boring irregular shapes (quadrilaterals that didn’t shake down into the usual categories) so I ran online, searched up Google Images for a fossilized footprint, put one dot down, and then copied-and-pasted-and-distributed-space-evenly the hell out of it until I had the picture above. All in a coupla minutes.

No image credit. I suck at that.

Fabulous Opener Numero Uno

Cherish the openers which a) span but one question, b) inspire fifteen minutes of sturdy work & discussion, c) incorporate real-world visuals, and e) play off their self-regard as savvy consumers.

Fabulous Opener Numero Dos

Those scamps took this one farther than even I wanted to, talking about subtracting the door’s and the window’s area from the surface area of each room, etc., etc.

Also, the third question didn’t show prices until I advanced the slide, so for a few seconds, we all argued violently over nothing more than carpet swatches, namecalling over color and texture.

Alright:

Well hopefully that settles that. I’ll see you all in a year or so.