quadratics – emergent math

Hot Rod Quadratics: Let’s jump this jump!

Artifact

Hot Rod is one of those movies that’s incredibly dumb the first time watching it. The second time watching it, it’s still incredibly dumb, but it gets funnier with each passing viewing. It’s basically just an excuse for Andy Samberg to to Andy Samberg things for 90 minutes. I’m ok with that.

Anyway, this isn’t Rotten Tomatoes. Let’s get to our Entry Event:

The final stunt of the movie, cut ever-so-slightly short.

Suggested questions

The most obvious one: will Hot Rod land the jump? Or maybe better if you know how it ends: will he clear the jump?
You could get all physical on this question. Considering how high he is and how fast he’s going at liftoff might be some other options.

Activities

In a nod to Dan’s “Will it hit the hoop” task, I’d go with Geogebra here as well. In fact, let’s just use pretty much the same idea (side note: if anyone can rip a better quality video, I’d be interested).

In fact, I’m going to go ahead and toss it in after the Basketball task in my Algebra 1 curriculum map. I’d consider using the Hot Rod task as a way of solidifying conceptual understanding by removing some of the sliders on the Geogebra task, or removing it from Geogebra entirely and having groups do some hand-to-hand combat with it on paper. It’s times like this that a problem taxonomy could help: do you want to assess student learning or enhance prior learning?

The goods

The video (above)

A couple screen shots

Fig 1:

Figs 1 & 2 mashed together

The Geogebratube student worksheet

Aaaand the “reveal”:

On final monkey wrench:

Conservation of momentum?

A 90-yard punt ; Quadratics

Posted by Geoff in algebra, quadratics, tasks

So upon my call last week for quadratic activities, I got a ton of resources in my inbox. I’ll post them soon after I’ve had a chance to look through them. Until then, here’s something I cooked up that could go several different directions, depending on your students’ needs.

Artifact

This terribly grainy video of a famous “90 yard” punt (well, as famous as a punt could be) by NY Giants punter Rodney Williams. Get out your stopwatches.

http://www.youtube.com/watch?v=OQKHOMHKT00

Guiding Questions

How far did the punt travel?
How fast did the punt travel?
How high did the punt get?
Does the fact that the punt was in “Mile High” stadium in Denver have anything to do with this?

Suggested activities

Students sketch their basic anticipated path of the football. Something like this.

“Say that looks a lot like a parabola! Great job, students. You drew a parabola! What? You don’t know what a parabola is? Well, you just drew one….”

I hope the students had their stopwatch out. If not, they may have to see it again.

Or, for those without a stop-watch…

(side note: if you can find a better, less grainy video that would be fantastic. Sometimes they even put the hang-time right there on the screen in tenths of the second. That’s awesome.)

Looks like it had a hang time of 5 seconds. So, let’s try to answer some of the above questions.

Solutions

Even though the punt takes place way up in Denver, I’m going to assume that gravity is pretty much the same at sea level. So the acceleration due to gravity is -9.8 m/s2.

So in the vertical it takes 5 second to go from the punter’s foot (which we’ll assume is a lot like the ground) to the ground at the ~16 yard line.

So the ball’s initial velocity in the vertical direction was about 24.5 m/s. If we move things around a bit, we can find the top of the ball’s trajectory (i.e. the height it reached). At the height of the ball’s trajectory t=2.5, so we have the following:

So at the height of the ball’s path, it made it to almost 31 meters. Let’s do a quick diagram-recap.

Another thing we could do to this is use Geogebra to recreate the punt, here. (note: this worksheet represents the first minute-and-a-half I used Geogebra. It could be a lot better.)

Brainstorming Quadratics

Posted by Geoff in quadratics

I’d like to do for Quadratics what we did with Pythagorean’s Theorem. I put out the call on Pythagorean’s Theorem and had come up with several ideas, only a couple of which were by me.

So I’m putting up the bat signal again. Except in this case it’s the quadratic formula signal and asking for your help. Please comment, email, or tweet me ideas, resources, youtube videos, or stuff you’ve done.

So far here’s some stuff I thought up.

Cars crashing – use quadratics and the acceleration formula to determine who’s at fault.

Remote control cars accelerating and decelerating. Plot and find the acceleration and deceleration of the cars. (should be a quadratic)
NFL punts. Find a nice video of an NFL punt with good hangtime and do some stuff with it.
Related: let’s get a punter to nail the giant TV in the new Cowboys stadium.

Until then, here’s a post by Dan Meyer on quadratics that is way, way more interesting than anything I’ll do (here’s the how-to).