Going the obvious route:

How many unique license plates can Costa Rica give out compared to California?

A little less obvious:

Perhaps compare the number of registered vehicles in Costa Rica to California. How many unique license configurations are left to give out?

Maybe with a little more digging you could even get your hands on how many new licenses are given out each year by each government. How long until they’re going to have to redesign their plate or numbering system?

Extension on the above: why would CA need such a great number of plate combos? This is like using these plates as primary documents in social science.
Set up how you make a comparison, the powers of observation needing to be at their strongest (Hocus Focus would work well for this, too).
Talk about format and requirements.
I’m sure there some kind of inductive/deductive reasoning lesson here.
Talk about tone, how formatting communicates a message, what each plate says about that country: the dirt, the vehicle material, the colors, etc.
On a related note, these plates are dying for a font study, in yearbook and journalism classes specifically.

I’m no math teacher but I might follow the above with something like this . . .

Give them some real data to chart the percentage increase of cars per year in CA. Use this data to forecast future license numbers needed.

At what point will CA need to change its license system?

What should the new system be in order to handle the calculated rate of growth without having to change the system for X years into the future?

–other extensions include using road and environmental data

At what point would driving become too painful to continue?
How many miles of new road would this kind of growth require? What would that cost? (are you taking inflation into account?)

How many neutral carbon credits would CA need to buy to neutralize the output of all these vehicles? What would that cost? etc. etc.

I agree with Todd that you could do a whole “personality” profile on areas based on the typography and design of the license plates.

I’ve seen the possible number combinations on license plats questions as an into activity in Saxon Math 76 (5th in Cali, 6 or 7th elsewhere). The photos make it MUCH better.

As earlier commenters suggested, I would have the class figure out combinations. I would just start with the Costa Rican plate in the first lesson (remember, we’re talking upper elementary, they will need more scaffolding for this).

You could do a Language Arts activity by having them create vanity plates, and limiting it to a certain number of positions, and/or # of numbers vs. letters to extend it.

Finding myself less intrigued by the numerical gymnastics (although I see that as the must-do if the plates themselves are the key variable in the 2 images).

Instead, I’m decidedly more curious about the contextual irony of the plates vs. how they are afixed to cars that seem to scream out: switched at birth.

I’d also add: the rust won me at the snapshot hello.

This texture-esque bit would lead me down a conversational road with my students of discussing the shared element of intuited authenticity throughout our worlds, as well as how often incongruity sparks intrigue.

As a writer or as a human being, the context which houses the variable shapes the ultimate meaning(s).

This I think would be a great way of discussing problem that seems simple at first but, is in fact in depth and would require much thought.

First of course start with some basic permutations of character sets and see how many plates would be possible in each.

Then throw a curve and add in readability requirements. This would eliminate confusing characters such as I and 1. What would this do to

After this you can introduce the problem of license plates spelling inappropriate words. To fix most of this problem just remove vowels and vowel lookalikes and you can no longer spell a word. You still have the problem of acronyms and slang terms. the only way to completely remove this issue is to have each letter isolated to where they can’t form meaningful strings of characters. This is probably why there is only one letter on that California plate.

This can be a fun class experiment add in the requirement that it the plates need to memorable. This is where you can summarize the theory of clumping in memory retention. So you can now create diffrent plate styles. for example is three letters, three numbers and a space between better then 7 characters.

I actually think this would be a great demonstration of how complex many real world problems are. It would fit into one of those “simple” problems you give at the beginning of class but the students find out the problems is not a simple as it looks.

Though I am a math/science guy, here’s a journaling topic for the english crowd, or a “think about this” for the tech-geeks.

Notice that the two license plates use different fonts. Some countries (areas in Netherlands) have begun to utilize different fonts based upon the readability of the fonts to OCR cameras. You know the ones that take a picture of your license plates, then kindly mail you a ticket for running a red light, or speeding.

“What is your opinion of using cameras to capture speeders, and possible flaws with the system, such as illegible fonts on license plates?”

As a physics teacher, I guess the appropriate discussion for my class would be to set up a hypothetical speed limit, and give a frame rate to my students. Then have my students calculate the displacement of the vehicle at given frame rate if the car were speeding. Expanding on this, how about the percent decrease in the font appearance at the relative distances.

I’m surprised nobody has mentioned this (maybe dan doesn’t have too many readers in CA) but that second plate is for commercial vehicles (pick-up trucks and SUVs included) only. A standard passenger car has the plate structure # LLL ###, giving many more permutations.

At some point in the early 80s, California switched from a ### LLL structure to its current one. Why?

When I bought my first (and only) new car in 1996, my license plate was 3SUB728. What is the newest plate that you have seen? How many cars have received new plates since then? How many cars have been newly registered per year since then? per month? per day? per hour? How does this compare to Costa Rica?

Also of note is the emissions testing sticker, which brings up both math and science questions.

Why is testing the emissions of vehicles important? When is the cutoff for when vehicles need to be tested every year? Who decided this cutoff?

I was going to point out that the California plate was a truck plate.

Obvious questions (at or about the 7th-8th grade level):

– What is the expected ratio of trucks to passenger cars, based on the license plate numbering schemes (0A00000 vs 0AAA000)?

– Assuming that the truck plates start with 0A00000, how many plates were issued before that one?

– Why doesn’t the Costa Rica license plate have any letters?

– When Costa Rica runs out of numbers, will they be better off with adding another digit to their plates, or making one of the digits be a letter?

– Why does the California plate have an Arizona frame?

This conversation is on the verge of a Lesson Study. With some focused organization and implementation, this could turn into a model for the future of teaching and learning about student learning. Kudos to Dan for a fantastic idea!

As for what I can do with this. . .

I am currently teaching Linear Programming in my Advanced Algebra class. It would be neat to see the costs in making each plate, the price the DMV charges to acquire the plate and perhaps do some cost benifit analysis of adding another character to the plate. At what point would the plate need to get longer or double stacked? How many plate numbers are recycled (if any) back into the mix because the car they belong to no longer exists. What information can you get from looking at a motorcycle plate, or a trailer plate, etc.? Based on seeing just one plate, can you give an accurate estimate of the number of registered cars in a state or country( +- 10, +- 100, +-1000, +- 10000, . . .)

It would be neat if this conversation would create a lesson, all of us teach that lesson and then come back and discuss the lesson and try to improve it. It could be something as simple as a daily warm up or a full blown lesson.

What a neat idea for a forum like this!

I meant numbers, not neighbors

Am I the only guy who’d be asking if we could track down the owners of the respective vehicles? Then ask about what other numbers are public information?

Oddly, (or maybe “Of course”) there is a site dedicated to something just like that called Road Sign Math.