As the students enter, hide the opening PowerPoint slide pulled up on the projector. Once the whole class is seated, flash the slide and roll out the opening problem. Give the students very little time to pick which option they believe will be better – I would say that the tone in the classroom needs to be similar to if they had just won a drawing on the radio, and had to make a split second decision on the airwaves.
Direct students who believe Option A is a better deal to one side of the room, and the students who think Option B is better to the other side. Once the sides are chosen, I hand the students one piece of chart paper per 3 people in the group – that is, I construct subgroups of students on the fly out of the two larger groups. Each subgroup of 2 or 3 also gets a marker to show their calculations.
I ask both groups to find out how much money they will have at the end of the 2 week prize pay-out. I encourage groups to go ahead and list the first few terms, but to try to use the type of series they are working with as an indicator to which sum formula they should use. Giving the students 3-4 minutes to work, I rotate the classroom in an effort to help individual students with the task at hand. At the end of this time, I tell each group that they have 2 minutes to compare answers with others in their group to see how everyone aligns – as well as look at different methods of solution (if any arise). Finally, each of the two prize option groups nominates 1 subgroup to show their work on the board. The class will see that the geometric series outperforms the arithmetic series by $58.83 over the two week period.
Optional Extension (great if you have time): Ask the students “When would the two prize options would be equal?”… That is, if a local radio station wanted to offer a similar prize package, but wanted the two options to be equal, how could we mathematically calculate and insure this?