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!

This is good. Real good.

People consume large amounts of caffeine on Friday and Saturday?

This might also be a question to ask in a Stats class. Can two people using the same data create histograms that look different? How? And I’m not talking about the last graph.

What would the graph look like if the variable was request per millisecond or per day/month/year or, if you want to get into it, requests per 1 Planck time? Is the request rate an instantaneous request rate? Is there such a thing?

Why would anyone design a graph that looks like the one in the picture? What goes through a programmer’s or designer’s mind?

You might like this geogebra applet on resource collection rate in Starcraft 2.

I really like that you included the last graph and asked students to reconcile it with the graphs above it. In my post, I included screenshots that showed spent and unspent resources, but you got to ask a more interesting question because of how the previous graphs look. Love it!

Thanks for the comments – I only wish I still taught calculus so I could really use these prompts. I like the idea of asking about the design decision the programmers made. It makes natural the question, “how else might we have displayed this data?”

@ Shawn – WORD. Riley this is dynamite for a calc or a stats class. I’ve never taught stats so my mind goes to the calculus lesson. I feel like this is a real intuition-builder for the fundamental theorem.