This is a graph of the activity on ActiveGrade for the last 24 hours.

It’s Saturday at around noon right now, so you can see that maybe a couple of people have been entering grades this morning, and a bunch of people were entering grades over the course of Friday – petering out around 8 PM (ugh – I feel for you). The units here are a little complex – the vertical axis marks “requests per second,” which is proportional to “the number of things that are happening in ActiveGrade per second.” When the line is at 0.3 requests per second, it means that about 3 things (maybe entering an assessment, looking up grades, changing a grading policy) were happening every ten seconds. On average, of course.

I don’t think many of my students could really understand this graph. It’s deceptively complex. How many requests do you think ActiveGrade got total in the last 24 hours? How many requests do you think are in a single spike? What does it even mean to be getting a request per second at a particular instant in time – less than a second long? Do you think you could say when the most people were logged on?

Still, it’s easy to see when the program was the busiest. That’s useful.

But look at this graph, which covers the last 48 hours:

At first glance, it looks like activity levels were lower in the first 24 hours and higher in the second 24 hours. The requests per second stay around 0.05 for the first bit, and are frequently up over 0.1 on the second day.

How many of you would look at this next graph, of the last *four* days…

… and guess at the distribution of visits shown below?

This is the same data. Wednesday had WAY MORE activity than Friday! Could this be right? Is there a problem with the graphs?

So here are the questions:

- What is going on with these graphs? Why does Friday, which looks so busy, do so poorly in the final count?
- Is the line graph an appropriate model for reporting this data?
- How many total requests have we gotten here?
- Is the business going to succeed?

How would you structure a lesson to give students the fluency they need to ask, and answer, these questions? Graphs with these characteristics will probably not appear in your textbook.

If you don’t teach calculus, does this kind of question (“hey wait a minute, wtf at these graphs?”) have a place in your class?

Please leave your thoughts in the comments!