Hot Rod Quadratics: Let’s jump this jump!


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.


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:

jump1 jump2

Figs 1 & 2 mashed together


The Geogebratube student worksheet

Aaaand the “reveal”:

On final monkey wrench:


Conservation of momentum?

Let them get it wrong: Caloric Quandary

Artifact & Facilitation

I must have cylinders on the brain. Maybe because they’re actually one of the few traditional geometric shapes that we actually interact with on a regular basis? Maybe it’s because they’re readily measured?

Anyway, here have a Coke can and one of those mini-Coke cans. Though it’s dependent on you exactly what information you’d like to black out.

You could black out one of the calorie counts and compare it to the fluid ounces.


You could black out one of the fluid ounces counts and compare it to the calorie counts.


You could eliminate the fluid ounces and one of the calorie counts to get at a really nice volume comparison (though, you’ll need additional dimensions – that’s good! Ask the kiddos what other dimensions you’ll need to procure?). 


While you’ll need other dimensions, I would actually withhold the dimensions of the base at the beginning. Why? Because students of all ages have a real tough time with scale factor and volume. Like, REAL tough. As in, I tell them straight up “when you increase the dimensions by a factor, the volume increases by that factor cubed” and then they totally forget that by the time I’m done saying it out loud.

So let students solve it using a simple proportion.


4/5=90/x –> x=112.5 calories

Then when you reveal the actual calorie count, we’re all like “wha?”




“WHAAAAAA??!?!??!! Math is wrong! You lied to us!” Or maybe they’ll claim corporate conspiracies to get us all fat. Either way: win-win.

This is the part when you swoop in with some additional dimensions to save the day. Find the volume relations of the two cylinders, the calorie counts, and you’re home free.



I also feel like there’s some way we can leverage this into some additional follow-ups/extensions: 

Or this.


I like having calorie counts as the final measuring stick for this task instead of volume.

Like I said, scale factor and volume (and area) were something my students would consistently get wrong. I think it’s indicative of the problem with front-loading instruction. Students don’t need to think deeply about the content because I’ve showed them how to do it in the “Scale Factor Unit” when it’s applicable, of course. Then, three months later, when we’re not in that unit any more, it’s out the window.

I’d suggest you read Frank’s post and watch the embedded Veritasium (@veritasium) video for more on allowing students to swim in their misconceptions a bit to enhance learning in the end.

What? How do YOU spend your two-hour school delays?, Water Content in a Snow Cylinder

As anyone in town for NCTM in Denver know, it’s been a bit snowy here this week. In fact, Fort Collins just had its biggest snowfall of the year. But how big?

We had a two hour school delay this morning as my daughter and I were greeted by this on our back doorstep.


“Wow that’s a lot of snow!” she says. But how much snow is it?  Go go gadget EmergentMath!


I got this ridiculously large [cola] mug at a white elephant gift exchange last Christmas. And now I have a chance to use it!


I asked her to make a prediction on how full the mug would be after it melted. We each made a prediction using her hair ties (hers on top, mine on bottom).


We took a couple measurements just for posterity’s sake.



I dunno, we might want them later. For now though, we just stuck with the predictions.

We then watched it melt. Slowly.

Sure enough, we were both way off:

013 015

Wow. All that snow and only that much actual moisture. I have some questions:

  • Is this typical? What if we redid this in the afternoon after the snow had packed a little more? 
  • What if we used different shapes? Could this be a sort of alternative to the how-full-is-the-weirdly-shaped-glass problem?
  • Going back to the original photo, how much water was on that table?

I also have a couple comments:

  • Want an easy way to build buy in? Have kids make predictions on something and make sure it *takes a long time* for them to see if they’re right. Like I said, our delay was a couple hours and this pretty much took up the entire time. This was sort of analogous to Dan Meyer’s now-famous water tank filling task.
  • This seems ripe for Estimations 180.
  • I’m not sure what you could do if you live in a non-snow state. What would Texas use? Sand? Cicadas?

My daughter and I could have gone into the volume of the near-cylinder, which dimensions were useful and that sort of thing. But our two hours were up. It was time to go to school.

Update 4/16: I’ve got my Facebook friends eating out of the palm of my hand. *maniacal laugh*



Sort of related: a couple atmospheric scientist friends of mine started a Facebook page crowdsourcing, archiving, displaying, and discussing clouds: Community Cloud Atlas 

You should join their Facebook page and tell them to get a twitter account.

Here are your Algebra 1 and Geometry Problem Based Learning curriculum maps.

Yes, you can do wall-to-wall PrBL. Yes, you can align your PrBL curriculum to Common Core standards. Yes, you can do it all with the help and goodwill of the math twitterblogosphere.

Note that these are just the tasks. They are not the facilitation notes, the scaffolding, the assessment. Just the tasks and problems provided for students that you could potentially work through. Also, this is just the free stuff. So that means no Dana Center, no Mathalicious, though I’d encourage you to check out both resources and consider paying them for the quality work they produce.

Check it out.

And with that, it’s probably time to shutter the Great Inquiry Based Math Curriculum Mapping Project. It hasn’t gotten too much traffic lately. And honestly, we’re past the point of just ideas for problems. It’s time to create and improve them.


Inheriting the wind; these are two of my favorite books about math


Baseball Prospectus

I never liked baseball as a kid. Maybe it’s because I wasn’t any good at it. Maybe it’s cause I never went to a professional game. Maybe it’s because it is quite boring when you watch it on TV. Then in the late 90’s the sabermetric revolution upended the stuck-in-the-50’s baseball establishment by using data to prove and disprove various myths that were pervasive in the game. From roster construction to in-game tactics, the sabermetric community was one or two steps ahead of the rest of the game. It was this data-driven analysis that served as my entry point into the game. Eventually the data-movement coalesced under the Baseball Prospectus name. Housed at, the writers produce an annual that is my notice that Spring has arrived.


The annual contains copious amounts of raw numbers, advanced metrics, data tables, projections, as well as an approachable and easy-to-digest writing style that I blast through every March. This year was no different. This is one of my favorite books to read every year.


Here we have another book grounded in mathematics: Paul Lockhart’s Measurement. Here we have a rich text of mathematical creativity and imagination. In fact, pretty much everything in the book is developed in the author and reader’s imagination.


The problems posed (some of which even have Lockhart’s proof to accompany them), are decidedly abstract in nature. The problems rely on ingenuity for a solution. Lockhart is more likely to use mental shape-folding than a two-column proof to describe a mathematical concept, let alone a spreadsheet of data. This is one of my favorite books.

Both of these books (in Baseball Prospectus’ case, the annual publication) are quite dear to me. They also represent two entry paths through mathematics. One uses messy numbers and data to explain why things are the way they are. The other uses clean, imaginary shapes to explain why things are the way they are in our imagination. They both feature clever, humorous, conversational writing including analogies and storytelling.

Inherit the Wind

Then there is the final scene of Inherit the Wind. After psuedo-successfully defending a high school teacher who dared to teach evolution in the classroom, the protagonist of the true-story, defense attorney Henry Drummond picks up the Bible in one hand, Darwin’s The Descent of Man in the other, and exits the courtroom. Both of these books reveal things about the nature of man, and you’d be a fool to entirely discard either.

There are context-rich ways of posing mathematical tasks. There are entirely abstract ways of posing mathematical tasks. There are interesting and engaging ways of posing problems. There are dry and uninteresting ways of posing math problems.

I hated math in high school. All the way up until my integrated Physics/Calculus class threw an old computer off the football stadium and recorded it on video and we were able to successfully approximate the gravitational constant. I’m not sure if I had been presented abstract math in more interesting ways I’d have latched on to it. I was a pretty detached kid. It’s possible, but I was also more prone to think about mid-90’s Indians baseball and Carlos Baerga’s VORP. That would have been a way for me to engage with mathematics in High School. In fact, I did engage in it when Rob Neyer would publish a new column. But that was me.

I’m not saying that every task needs to be grounded in the real world. But the number of contextual mathematical tasks that should be provided any given year is certainly greater than zero. It’s probably greater than 10. Maybe the tasks need not even be that authentic. I mean, is throwing a computer off a building a “real-world” situation? Or was it just a fun thing to do that we then did a bunch of math on? It was “real-world” in the sense that we saw it happen. We interacted with it physically, visually, inter-personally  and mentally. I have not, to this day, had a professional reason to toss a computer off a stadium.

Mathematics is so wonderful and ubiquitous that anyone can have some sort of entry point into the subject. It’s too vast to be constrained to a single context or a single person’s imagination. Our access points to the subject change from person to person, from age to age. You’d be foolish to eschew context-dependent scenarios to explore mathematics. You’d be foolish to toss aside all imagination from the content. You’d be foolish not to explore any and all avenues of all ways to provide access to this remarkable subject to your diverse students. You’d be inheriting the wind.