I began by asking who knew a good tongue twister. Most of my students did, and we took a few minutes to share some. Then I explained:
“I am going to give each pair of you an unfamiliar tongue twister. One of you is going to repeat the tongue twister as many times as you can while the other one counts and watches the clock. You will time your partner for 10 seconds, 20 seconds, 30, 40, and 50 seconds, and record the number of times they say the tongue twister for each time in table. What I want to know is: do you think that table will show a proportional relationship?”
We had a good conversation about that. I was surprised that most of my students said no. They thought saying a tongue twister was just too unpredictable. You can challenge them to explain how they will know if it is or it isn’t, and see how much of the previous lessons they have understood and can apply on their own.
Then they got to work. We have just finished collecting the data. In conversations with pairs we looked at tables that seemed to not be proportional at first, but then seemed more proportional as we noticed other patterns. At one table we realized the number of times the student said the tongue twister was always 1 off from 1/5 of the seconds. At another it was always just above or just below. When we reconvene after our annual trip off-campus, I will be sharing all the tables with students, asking which tables have a constant of proportionality or something close, writing equations for those tables, and talking with them about the roles of approximation and modeling in applying math to science. I think this will be a great way to lock in some of the key concepts for this unit, and make them memorable.