## Tuesday, April 7, 2009

### Real World Once Again Inconvenient

Here are three attempts to model "Will the Ball Hit the Can?" in Sketchpad:

Attempt 1: I try to make the grid scale match the given scale. (1 unit = 1 yard? Or close to it?) This requires the coefficient of the squared to term to be waaaay to small for clumsy freshman fingers.

Attempt #2: Make the scale very large. Now the leading coefficient is a little more friendly, but by comparison I have to make the constant coefficient slider way too short.

Attempt #3: Using a rectangular grid, so that the y axis is a relatively smaller scale than the x axis. Now all three coefficients are lengths I think the freshmen can handle. The catch? We can't even pretend this function means anything any more.
I'm going with #3, but it will bother me; I feel like I am perpetrating a ruse. On the other hand, I have learned way more about the behavior of the standard form of a parabola than I would have had I not bothered to try.
Feel free to email me if you want the sketchpad file to play with. It's 32MB.

Dan Meyer said...

This is freshman Algebra? Or Algebra II?

I really wanted to model the equation and talk about parameters but I think I sensed it was trying to pile too much math on a flimsy image and just stuck with the objective, "students will understand that parabolas show up in life and will get a clue about their symmetry."

Less ambitious than yours. Thanks for posting your outcomes.

Kate Nowak said...

This is Algebra 1 (freshmen). We are done with parabolas, I was just going to do something fun on the last day before break. My goal is to have them investigate the effects of the coefficients on the graph, with an outcome that is interesting. I'll update about how it goes after I run the lesson.

For Algebra 2, I'm hoping to be able to use it for a quadratic regression. I haven't played with that yet though to see how it will work out.

Dan Meyer said...

I tell you I am going positively crazy on this game here (I mean, it uses theta and v-sub-0 fer crying out loud!) but hell if I can figure out how best to package it up as a lesson.

If I taught Algebra II, though, I'd make it my mission to figure it out. I could probably burn a week on this thing.

Kate Nowak said...

That game is awesome. (Around these parts, it would be more appropriate for precalc, but still, awesome.)

I don't think it would be too hard. I wonder what units that velocity is in. Once you know that you would have to do some testing and measuring to figure out distances in that picture. I wonder if distances are consistent on consecutive boards.

Jackie Ballarini said...

Kate,

I'd love the Sketchpad file (jackie.ballarini at gmail)

I'm wondering if there's a way to scale it so that the -16x^2 is in there. If not, my seniors will rip it apart as not being true.

Kate Nowak said...

mmm...well...the 16 is relevant when you are talking about height vs time, yes? not height vs lateral distance?

file on the way (as soon as i get to school tomorrow)

Scott said...

Kate, you don't *need* to sacrifice the length of your sliders for #s 1 and 2.

Select each slider, Properties:
Slider tab
Slider section: make the width 500. (or so)

You can also change the increments of the variable on that tab.

So I would stick with #1. Make the sliders big (and thick, I had trouble seeing them on Dan's original).

Kate Nowak said...

Ooh, Scott, I didn't know you could do that. (In Sketchpad? Really? This is sketchpad, not Geogebra...) I'll try it when I get to school.

Scott said...

Ah, no, I thought you were using Geogebra... sorry!

I highly recommend making the switch! There's very little that sketchpad has the advantage in, and Geogebra has the huge advantage of being free and open source.

Kate Nowak said...

OK so technicalities: I ended up just using Dan's Geogebra files. (And, by the way, Way To Go Geogebra for the web launch thing.) Sketchpad is annoying because when you copy a photo in, the quality is degraded. Also, Geogebra has nicer sliders. Also, I didn't have to worry about the grid.

Dan, some kids recognized you from graphing stories. No lie.

As for the lesson...as successful as it was going to get, the day before break. I kept the script simple...what would we need to figure out where the ball lands...the axis of symmetry or roots...well how to do we find those...oh wait, we need the equation...here's a laptop. It kept their attention for almost the whole period, and my quick recap indicated that they remembered how a, b, and c affected the shape of the graph. Both classes were 3/4 on guessing whether the ball hit the can. That one with all the altitude (C) is tough - they all thought it would be too long. Also they thought the last one was a rotten trick (the one that fell behind the can).

Kate Nowak said...

Also, Scott, I thought of a way to make it work in Sketchpad...I'd have to construct another segment that was dependent on the "a" segment that was scaled up. Hide "a" and manipulate its inflated brother.