Flash as in really fast! I used a period today to assign a group project. I gave the kids (in teams of 3 or 4) about 40 minutes to:

- Pick a function from a list (e.g. u(x)=2*sqrt(10-x^2)+5)
- Figure out how to graph it in geogebra (the “sqrt” command was not obvious to them)
- Figure out how to get a table of values out of geogebra
- Figure out interesting things about it (my prompt suggested asking questions like “Are any points especially interesting or important,” and “What does the function do or look like?”, but they were encouraged to ask their own questions too)
- Graph the function “very well,”
- Make a poster describing the interesting parts they learned
- Give a 3-minute presentation to the class

The functions from which they could choose all had interesting features, like discontinuities, endpoints, etc. I was astonished at how focused the teams stayed throughout the period; I think the low amount of time helped a lot. Since the mathematical content was pretty simple (it would be, what, maybe 5 or 6 questions on a worksheet?) they could focus on finding interesting features, and I could encourage them during their work to find ways to convince the other students that these were interesting features. The small time limit made it so that they HAD to find a quick way to get the graph from geogebra on to graph paper, which meant that they HAD to identify the important characteristics and sketch on top of that guideline.

Never before has it occurred to me to slam through presentations like this, but honestly the quality of the presentations did not suffer too much (as compared with a week-long assignment) and the interest in the content was much higher. The kids had to remind themselves of deadlines every ten minutes or so (I put one student in each team in charge of the time) and I think they got a lot of practice prioritizing and working efficiently. The biggest benefit, of course, is that our treatment of domain and range in the upcoming week is practically covered already, and the students already have a refreshed understanding of numbers that can’t be fed into or gotten out of functions. And, they got practice zooming around in geogebra, making tables (one group figured out spreadsheet view!!), etc.

Fantastic!

Sounds like a very useful lesson! I did something similar with a Mechanics group a while back — they had 30 minutes, in groups, to pick a mechanics question, create an outline solution to it on a poster, and then present that question to the rest of the class.

You don’t lose all that much in quality, because, sadly, you often get almost as much concentrated work out of people if you give them a week as you do if you only give them 30 minutes!

Could you share the functions with us? I’m planning on doing a similar activity with one of my groups in the near future, and it’s always easier to cop… I mean revise and extend previous work :).

Here are several of the type I used. I’m just making them up:

f(x)=2sqrt(4-x)+2

g(x)=3sqrt(4+x)-5

h(x)=4sqrt(9-x^2)+6

u(x)=-sqrt(4-x)-3

All of the functions had a square root in them, so that they’d have at least one end point that the kids could find. Some with a sqrt of x^2 had two end points.