**Artifact**

Can we use math modeling and/or equations to answer the question of when it becomes advantageous to **install a stoplight vs. a stop-sign**? Can we “ambush” students by having them **create equations without really knowing it**?

What are some of the things we need to know about this?

**Guiding Questions**

- How long does a car usually stop at a stop-sign? And how long does it take to start up again?
- How long is the red light at a stoplight? Can we adjust this?
- What’s the time gap between a red-to-green light transition? A couple seconds?
- How long does it take a car to pass through an intersection?
- What’s the speed limit here?

**Suggested Activities**

- Have students use their iPhones or flip-cams to
**conduct some tests**. For instance, here’s a couple of run-throughs through**stop-signs in my neighborhood**. Stopwatches at the ready! Improperly mashed-up music & driving video now!

(note: even though I’ve posted the videos, I would totally have students test it out on their own, hopefully with a stop-sign/light in their neighborhood that they find particularly ill-placed.)

Test 1

Test 2

Test 3

Test 4

(note: the speed limit WHICH I WAS DRIVING is 30 mph for this neighborhood, if that helps)

Each test took me about 10 to 15 seconds to slow down, come to a complete stop (as I’m sure all your students do) and then get back up to full speed. So it seems reasonable to assume that a stop sign will cause each vehicle about a 15 second delay, even if there are no cars around.

**Potential Solutions and Possibly Foolish Assumptions**

**Assumption #1**: *It takes 15 seconds to go from full speed, to fully stopped, to full speed again.*

If there were another car in front of us, there would be an additional wait time. Let’s say 10 seconds per car in front of us.

**Assumption #2**: *We wait 10 seconds per each car that is also at the stop-sign.*

**Assumption #3**: *No matter the direction the other car is coming from, we wait 10 seconds to advance.*

At this point, our equation may look like this:

**Wait time for my car** = (15 seconds) + (10 seconds) * (# of cars)

What about the total wait time for *all* cars? We’d have to multiply by the number of cars.

**Wait time for all cars** = (15 seconds)*(# of cars) + (10 seconds)*(# of cars)^2

Or, if we let y be the wait time for all cars and x be the number of cars,

*y=15x + 10x^2*

I’m going to cut things off and **let you ponder this a bit**. I’m sure I’ve made **mistakes** and **false assumptions**. I’m also going to let you guys think a bit about how we could represent the wait time for all **cars at a stop light**.

Couldn’t you see this sprawling into a really interesting Algebra project? Imagine students developing this model and bringing it to a community meeting or city planning gathering of some sort. It could happen.

**Stay tuned for Part 2**, and be sure to **correct my math** in the comments below!

Interesting problem. I don’t have a solution for you but I do have something else that may change the mix. What if you included roundabouts? We have just had a pile of them installed in our area to replace both stop lights and stop signs. I was skeptical at first but now I like them and actually think they are more efficient at managing traffic.

http://www.tc.gc.ca/eng/roadsafety/tp-tp14787-menu-179.htm

Hi David,

I thought about that. There are a couple roundabouts near my house I’ll need to “test out”. Seems like they’re gaining favor in communities around here….

That might be a good Part 3.

Pingback: A stop-sign vs. a stoplight; when does each make sense? (Part 2, Math modeling) | emergent math

Pingback: Math to Social Studies: “We’re not so different, you and me.” | emergent math