I just created a 3-ACT task for infinite geometric series. Here is ACT 1:
The question I want students to answer is, “How much ice cream will I need/eat if I continue this process for the rest of time?” I didn’t want to make it obvious that the answer would be finite. For example, if I did something like I get half a carton of ice cream, then you get half of what is left and then that person gets half of what is left of that and so on and so on, students are likely to see right away that the answer is not infinity; with this video I don’t think it is that obvious.
ACT 2 I just have two pictures. One is the weight of one ice cream scoop in grams. The other picture shows the serving size (which works out to be about 1 scoop) and the total number of servings in one container. I could see students not even using this information and just sticking to “scoops of ice cream”.
ACT 3 is the best I could do to show infinite time elapsing.
I like this task because it starts informal. We aren’t talking about any formulas or weird notation; that stuff can make its way in at the end of the lesson. It has a low floor and decent height of a ceiling. As a sequel for students who finish early, you could ask, “What if I started with 9 scoops, then 3, then 1,ect?” or “What if I started with a 0.5 scoops, then 1, then 2, 4, ect.?” All of the files are on 101Qs.