Having looked ahead in the curriculum when I’d sat down to plan out my year I knew that I had a unit on introduction to graphing coming up. I’d spent much time trying to think of things that I could do that we could graph, and would be interesting for the students. I’d considered trying to grow several plants in the window of the school and measuring the growth over time. I was far enough out that I could do it, but it wasn’t the growing season, and if anything happened to the plants I’d still be struggling.

Roumsii, my dog would go to class with me every day, and I had used her as an example in many stories. If I had known we could have charted her growth progress, right up until she became pregnant at six months old and stopped growing, but that is another story. I had this particular math class for two – two hour blocks and a one hour block each week (my work schedule was full days on Mondays and Tuesdays, a half day on Wednesdays, and then grading and planning the rest of the week).

Finally, about a week before it was time to give the lesson I came upon an idea. Rou had been chasing toads around our courtyard at night. There were thousands of toads, they got into everything and covered the ground like a carpet. The wells were all dry this time of year, and when my weekly water barrel would be delivered the first thing that I would have to do was take a cloth and filter out the toads so that none ended up in my barrel.

Watching Rou chase them, trying to catch them, but mostly mimicking their jumping action, I decided how I would introduce graphing. I told my students to bring in as many toads as they could to the next class. I would bring in a bucket and as many as I could as well.

Growing up we used to go to kla-ha-ya-days, a farm-style festival out near where my grandpa lived. There they would have frog jumping contests. You got to pick a frog and had to try to see how far you could get it to jump given three jumps. I remember the frogs – they were often erratic and unpredictable.

What I chose to do produced results that were much more entertaining than a single toad jumping. As the students walked into class we collected the toads in the bucket and then turned the bucket upside down. One student had a watch with a second hand. And I drew a chart up on the board. I found one student to be the recorder, and about ten to be the counters.

In the first row of the chart I wrote 0, 10, 20, 30, 40, 50, 60, 70, 80. We counted the number of toads, around 50, and flipped it back over. The kids were excited and involved, those in the front were having a difficult time staying seated so that those in the back could watch. We pushed their tables back and I drew out a circle around the overturned bucket, trying to keep it away from the wall as much as possible.

I had the recorder write the number of frogs currently under the bucket in the zero column and had the student with the watch count out ten second intervals. I told the counters to shot out the number of frogs remaining in the circle every time the student with the watch told us that ten seconds had passed and the student doing the recording to write that number down in the next column. We lifted the bucket off and all wildness broke loose.

We had toads leaping all over the classroom all at once. But the student with the watch, and the students doing the counting remained diligent to the task. Every ten seconds they had a new number that was dutifully written down on the board. We ended up waiting a minute and a half for the last toad to escape from our circle. I asked the students if they thought we should try it again.

Of course they said yes!

We switched up the roles and then rounded up the toads and ended up repeating this experiment another four times (this was a two-hour class), each time with a couple fewer toads than the time before.

After this we threw the toads out of the classroom, put the desks back in order and I started the lesson. I read the definition of the dependent variable and the students all quickly agreed that this should be the number of seconds that had passed. We drew up the graph with the data from our first experiment together, and then for an exercise they were to graph the remaining trials.

After about forty minutes of them eagerly working on their graphs I stopped them for a review of the graphing terminology. And with a few minutes left in class I asked them to guess how many frogs would be left in the circle after forty seconds if we had started with a similar amount of frogs and ran the experiment one more time. They all quickly came up with a range.

I asked them how confident they felt about this range. They were confident. They were also giggling. In one day I had taught my students about graphing in a way that they enjoyed, exposed them to exponential decay, and made them comfortable with the basics of probability.