What Can You Do With This: Yellow Lights

Naples Daily News:

According to county guidelines, yellow lights should be on one second for every 10 miles per hour of the speed limit. With a 45-mph limit on Collier Boulevard, the yellow light should have been on for 4.5 seconds. Instead, it was only about 3.8 seconds, Mogil said.

Yellow Lights – Kannapolis, North Carolina from Dan Meyer on Vimeo.

So I’m thinking about an ongoing classroom project, something that includes a wall map of the county, push-pins marking off claimed intersections, students collecting data with stopwatches or cameras, developing (what seems to them) a fair algorithm for the duration of yellow lights, then researching the county code to determine the actual algorithm, finally marching down to city hall to call the mayor on the carpet (if need be) for his reckless disregard for public safety in pursuit of a little extra revenue.

The math isn’t terribly difficult here – algorithm development, some discussion of domain, data visualization – but it’s the sort of project a) that takes place largely outside of class, and b) that stitches a class together, united against The Man, in a way that’s hard to reconcile with the usual instructional value calculus. (ie. how many hours of class time would you spend to create this kind of community out of your classroom? At their twenty-year reunion, will your students remember their investigation of cylinder surface area or the time they brought down city hall?)

Also, I should point out that the first thing I did when I rolled into Kannapolis, North Carolina, last Monday was shoot video of twenty traffic lights. Because I am often little more than a breathing apparatus and a set of limbs for whatever muse puts these ideas in front of me and I have to keep her happy.

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Just please tell me you’ll encourage the passengers to hold the gizmo while the teen driver, uh, drives.

  2. That is excellent video editing work.

    I would have ended up putting 20 individual stop light videos. This is why you are the master and I am but the learner.

    Someday the circle will be complete.

  3. This is a great project idea. I can see stretching the project over a unit on data analysis in my 7th grade math class. I teach in an urban setting, and there are many stop lights close to my school. Almost every student has a cell phone capable of captuing still and motion images. I can see the productive application of this ubiquitous hardware providing a great basis for data capture. Once they have the raw data feeds, they can work as a team to translate the information into graphical format. And then to take it a few steps further to do first order statistics and predictions based on them. WOW. Great idea. I’ll be on the lookout and start keeping my own set of real world application ideas.


  4. Taking down the man. That is the kind of project I like.

    “At their twenty-year reunion, will your students remember their investigation of cylinder surface area or the time they brought down city hall?” – So true. My students still talk about the Applebee’s lesson, and I’ve had parents bring up how much their kid loved calling Applebee’s and making a scene. It makes you feel like you’ve done something right.

    Beautiful idea.

  5. At the risk of sounding dumb…I’m not sure what you mean by algorithm in this case. Is it the mathematical equation that relates the yellow light time to the speed limit? So the kids would collect times and speed limits, graph them, find an equation from the data, compare it to the county’s equation, and spot any significant outliers?

    I love the idea, especially since the whole class works as a team. Creating a positive culture is key to get students to feel comfortable taking intellectual risks in class.

    BTW, it’s possible that the driver in the news article was at an intersection that had a “dilemma zone” and she was in it when the light turned yellow. If that was the case, she would have run the red light whether she hit the brakes or kept going. The Yellow Light Problem is a classic physics problem/lab activity. Here’s one: http://www.compadre.org/psrc/items/detail.cfm?ID=3809

  6. Great stuff, as always, Dan.

    A little frightening how many readers you have with father issues, however. Hard to believe that in the United States of America, so many people can be roused by the phrase “sticking it to the man.” My couch is now [OPEN].

    More seriously (well, I wasn’t completely kidding above), this seems much more on point than the Applebees lesson. Nailing government at the highest level appropriate when it is either dishonest or simply incompetent in its efforts to squeeze money from its citizenry is a noble task, on my view. Dropping this sort of data on the desk of the mayor (or the head of the traffic department or the agency that collects fines for violations, etc.) puts the ball squarely in the court(s) in which it belongs. Sending the same report to the local media pretty well guarantees that things won’t get buried.

    Sure, there are similar things going on in the corporate world, but if you’re going to complain, I think it should NOT be to small fry (wait staff, local managers of restaurants, etc.) who have no say in the slogans of their corporate masters and no time to check on their veracity or lack thereof.

    And yes, I get that kids are motivated by “sticking it to The Man”: I just want to be sure that they are actually doing that rather than blowing off steam to some poor schnook who is just trying to eke out survival wages at a local franchise.

    Math as part of raising social consciousness and appealing to the social conscience of people in a position to make change is a wonderful idea (and of course likely to tick off parents and others who don’t think that’s what school is supposed to be about – something that could provide many valuable lessons in civics in itself). But let’s not go off half-cocked with the notion that as long as we’ve found inaccuracy in public or private life that we should jump on the nearest person connected in any way to it. “Beating up on” workers isn’t exactly the way to accomplish the changes I’m sure we’d all like to see. Making things hot for the real bosses, however, is another matter entirely.

    An interesting book to look at in connection with all this might be Terry Southern’s THE MAGIC CHRISTIAN (if you can get hold of it). I love Guy Grand and his wicked propensity for “making things hot” for people. But I’m not sure all his targets were well chosen (too long since I last read it). Always worth taking a moment to think first.

  7. Great idea! I do this sort of thing a lot in my classroom. This summer I was summoned for jury duty and I came up with a ton of questions and probably a 2 day lesson and exploration that I will do with my students. (And I wasn’t even chosen for the jury!)

    Mind if I use this? I’ll send my other ideas your way. They involve creating a water tower for the new high school being built, creating a schedule with times and songs included for the local hit radio show, and many other ideas that are currently locked in my classroom.

  8. Kannapolis was NASCAR legend Dale Earnhardt’s hometown…I’m sure he ran a few yellow lights in his time!

    Great lesson idea as always.

  9. Whether sticking it to the man or not, I love traffic stuff. So here is a half-baked idea I used in a workshop once, and it really worked. Appropriate for drivers:

    You’re sitting at a red light and thinking, “Man, this light is badly timed. We shouldn’t have to sit here this long.” You may even know an intersection near your house or school that you think is particularly horrible.

    So apply the eternal measurement question: how bad is it? [Possibly working with a group] figure out a way to compute a number that measures how well or poorly a light is timed based on observations you can actually make at the intersection. Use your technique to compare intersections with one another and make an argument that your way does or does not reflect actual traffic light well-timed-ness.

    For example, one group counted the number of cars that were stopped, waiting to go when the light turned green, and compared it to the number of cars that got through the intersection in a whole light cycle.

    That in itself was kinda brilliant–finding something reasonably easy to count that could be translated into what you’re trying to get at–but then you get the symbolic-math payoff when you have to describe to others how you combine these numbers to calculate your index of goodness. All kinds of issues come up. Difference or ratio? Ratio of what? How do you make a good intersection get a larger number? Should a good intersection get a larger number? How well does the number translate from one intersection to another with more overal traffic–does it make a fair comparison?

  10. There are standard measures that are used by traffic engineers to determine whether traffic lights are reasonably set. It might be good to have students try to do some research to find out what those measures are. They can try to find stuff on the internet, but they might do better interviewing traffic engineers who work for the local governments. Talking to the engineers might also lead them to related questions: what different criteria have to be traded off when trying to optimize traffic light timing?

    One traffic light phenomenon that I’ve noticed is that traffic lights are often decidedly anti-pedestrian: a driver who arrives while the light is green will often get the cycle extended for them, but a pedestrian who misses the beginning of the cycle by a second is forced to wait for an entire light cycle. At some intersections, elimination of one crosswalk requires pedestrians to wait for two whole cycles to cross the street. Looking at average wait time for a pedestrian arriving at an intersection versus average wait time for motorists at the same intersection is an interesting exercise.

  11. Hey, thanks for the commentary, folks, and especially for the follow-up ideas from Paul, Tim, and gasstation.

    @Allison, I don’t know another way to make that video except with Adobe AfterEffects ($350) and Adobe Photoshop ($200). You can understand, perhaps, why I don’t do many Adobe tutorials from this site, though, if I knew of ten interested readers who had purchased both applications, I’d start putting together some seminar material.

    For this one, I shot sixteen videos with as stable a hand as I could manage. I put them all into AfterEffects as separate layers. I found the exact moment the light went from green to yellow. I synchronized all those moments. Then I created sixteen images that were entirely black except for a white square where I wanted that video to display. Add text. Add timecode. Nothing more than that.

  12. Any ideas for what unit(s) this activity could be incorporated into a high school Algebra II class? I love it!!!!!

  13. Thanks Dan for your explanation, I appreciate it. I teach high school physics, and since students often perceive physics as so foreign and insane, I want to incorporate real-life videos into my class.

    I was given a free flip camera, so I’ve filmed a couple things I plan to use in my class. If you think those two programs are worth the investment, I will consider purchasing them. I’ll be teaching physics for the next four years, so $550 is a small price to pay in the long-run.

  14. I think I’m going to use this in my physics class, just after we’ve learned about acceleration. That’s the straight-forward project that you’ve suggested – and it’s a solid one.

    But from my experience as a crash researcher, it seems that there is greater depth in using statistics. Present the issue of red-light cameras – are they for safety or revenue? Do a public records request (or see if NHTSA has data) on injury & non-injury crashes at those intersections. Do the red light cameras actually reduce the incidence of crashes? I know you can find the revenue from newspaper articles in most major cities, because this has been such a hot-button issue. The red-light timing can be another aspect to add to this project.

  15. Bill Bradley

    July 25, 2010 - 4:59 pm -

    I can’t believe that no one has mentioned Taxi’s “What does a yellow light mean?” yet

  16. I think the project you described on timing of yellow lights is great. Here’s something related that I’m considering pursuing.

    In my community, many of the street lights are being replaced with LED lights. It’s easy to understand the motivation in terms of energy saving (http://auto.howstuffworks.com/car-driving-safety/safety-regulatory-devices/question178.htm), but I have noticed that a significant number of the LEDs fail (leaving sometimes interesting patterns).

    I’m considering gathering data on one conjecture: LEDs of green lights fail significantly more that yellow or red. I believe this is true and the reason might relate to the amount of time green is on but it might also be color related (physics connect?). Also, if in fact the failure rate is as high as it seems (I think almost all lights in my community now have dead LEDs), is the energy savings commensurate with the replacement cost?

    An video of an LED traffic light along with an interesting observation from Holland about LEDs not melting snow can be found at

  17. Does anyone question the 1 second/10 mph of speed limit guideline? I think that this would be an interesting question to look into. Sometimes some of these oversimplified “rules of thumb” aren’t real great.

    A classic example from traffic that most students are familiar with is the two-second following distance rule. This rule assumes a kind of linear relationship that doesn’t really work well at higher speeds.

    Anecdotally I have always had a harder time making go/no go decisions at yellow lights that occur on higher speed roadways (we have one in our neighborhood on a 70 mph highway!). I’ve never timed it, but I don’t think the yellow light is 7 seconds long. How good are drivers at judging whether or not they can stop in time when driving at higher speeds?

    I see a lot of great questions and possibilities just wrapped up in questioning the guideline.

  18. This activity is fantastic, and similar to one that I do with my Physics class each year. We usually just do it with the one traffic light outside our school, but this year I’ll try sending students out to track other intersections and see if we can compare intersections that have cameras with ones that don’t. Such a nice extension. And my students will sure love to “stick it to the man” if they find a difference!

    The activity that Frank Noschese linked to is a lot closer to the Yellow Light Problem that I do with my students. I’m not sure how light times are set over there, but if the article is correct that “according to county guidelines, yellow lights should be on one second for every 10 miles per hour of the speed limit”, that doesn’t sound very safe to me! A safe yellow light time depends on both the speed limit and the length of the intersection, as it has to allow people to stop safely before the intersection AND to clear the intersection safely if they’re beyond the safe stopping distance.

    From my course’s assignment:

    “The Ministry of Transportation of Ontario (MTO) Traffic Branch Manual of Uniform Traffic Control allows for a REACTION time of 1.0 s for city driving and 1.8 s for provincial highways, where the speeds involved are greater.

    The BRAKING time is the time it takes the vehicle to come to a full stop once the brakes are applied. This time depends on the initial speed of the vehicle and negative acceleration of the vehicle. The MTO-predicted braking times are based on the assumption that vehicles are travelling at the posted speed limit and, for most purposes, the MTO uses a uniform acceleration of 3.0 m/s2 [back].”

  19. I just looked into it a bit more, and it looks like I was wrong! Since you only get a ticket for entering an intersection on a red (and not for simply being in the intersection at all when it turns red), the yellow light time doesn’t depend at all on the length of the intersection – the “all red” time does. So I guess the yellow light time would affect how many people get tickets, and the all red time might affect the number of accidents but not the number of red light tickets.

    I should really do my research! This will definitely make the activity a lot easier, though, as we won’t have to go block traffic again this year to measure the length of the intersection…