The disparity (150/100) is based on the fact that growth depends on ionic content of the water–the purer the water the larger they grow. The very same Orbeez wll grow to a different size depending on the water purity. The number we chose ended up being a marketing decision (100 is a powerful figure) but we should have been consistent. It’s impossible to choose one accurate number.

This one is about a year old. It’s short and simple. As I recall, I used it for an opener problem and nothing more. In my development as a math teacher and curriculum developer, though, it has a lot of sentimental significance. In Leslie Knope’s Love Life, I wrote about my goal to draw inspiration closer to action through practice, practice, practice, and this is the result.

I was driving along, checking Maps on my iPhone for directions, and found it interesting how the blue tracking orb moves faster when you’re zoomed in close to the map and slower when you’re zoomed out. Reflexively, I turned it into a question: “how fast is the car going, given this particular orb?” Then I tweaked it: “Do we arrest this person for speeding?” (Crime doesn’t pay, but it’s more interesting to my students.) Then, just as reflexively, I knew the image I needed to create.

Just to be totally clear, I wouldn’t bring this video inside fifty feet of a classroom. I’m not recommending you use this video in a classroom. I’m recommending that when you see math in the world around you that you get in the practice of doing something about it – especially, that you turn it into a question.

Click through to view embedded content.

Don’t know how to do the black box and the censor beep? Just pause the video right before she answers her own question. Point being, the more you habituate this practice – even on lessons like this one that won’t go anywhere – the more often you’ll catch these moments.

Sorry to be all post-y today but reader Ryan Bavetta sent in a hot tip and I had to jump on it before Drudge did. Here’s Obama delivering his State of the Union address. Ryan says, “I don’t think they got the sizes of the circles right.”

So I go all Woodward and Bernstein with my compass and protractor. I measure off the diameters.

The ratio of the diameters is 2.45, which means the ratio of the areas is going to be (2.45)^2 or 6.00. But the ratio of America’s GDP to China’s GDP (14.6T/5.7T) is only 2.56! The US circle is too big! What’s the progressive propaganda machine trying to sell us here?!

Here’s how it should have looked:

For Classroom Use

I think you have to get rid of one of the quantities, ask the students to determine it, show them the full SOTU screenshot, and then encourage them to marvel at the difference. You can give them Obama’s circle and ask them to tell you what that should make the GDP.

Or you can give them the GDP and ask what that should make the circle.

I don’t know how to get excited about the difference when Jon Stewart’s probably trying to call my booking agent right now.

I’m really grateful for the deep bench I have on this blog, the readers who take the time to share with me the mathematical objects that intrigue them. Adam Poetzel, secondary math ed prof at the University of Illinois, sent along Orbeez, which is pretty aptly described by this commercial:

Basically, small things that grow big in water. The Orbeez website puts the volume increase at a factor of 100 while the instructional manual puts it at 150. Controversy! Which is right? Or are they both wrong?

I went to Toys R Us and bought a starter pack for $8.00.

I dunked ’em for a few hours and got this:

A few ideas here. Start informally. Move from the concrete to the abstract. The informal question is, “how many times bigger is it, really?” Ask the students to write down guesses. Write a few up on the board. Perhaps print that photo out and have them draw what they think “150 times the volume” would look like. (Am I alone in thinking this looks way way smaller than 150 times bigger?)

Ask them what information they need to answer the question exactly. Put up this photo.

Here’s the math:

Okay, Orbeez, just watch yourself, that’s all I’m saying.

Ideally, you’ll move from the relatively laborious calculation of volume to the relatively simple comparison of the diameters using scale proportions. ie. if the large volume is really 150 times the small, then the large radius has to be at least 150^(1/3) = 5.3 times the small.

This is the rare WCYDWT investigation that would be even better with real stuff rather than all these digital replications of real stuff. Buy some Orbeez off Amazon. Let your students dunk their own Orbeez on day one. Perform the investigation on day two.

2011 Jan 11: Sharon Cohen, the brand manager of Orbeez, stops by to drop some knowledge on us all.