I was trying to make limits more interesting for my students and promote better understanding, and I came across this blog post that compared limits a moment when you are watching a video (in this case a soccer game) and your computer goes black for “buffering”. Click on this link for a better explanation:
Putting these screen shots on separate slides, students used what they knew about minutes 3:58, 3:59, 4:01, and 4:02 to predict what happened at exactly minute 4:00.
This led to students making tables for functions and comparing”buffering” to ERROR (on the calculator).
After the first day, I noticed a few students who were exploring a limit as x approaches 4 by making a table with x-values 1, 2, 3, 4, 5, 6. I wanted to emphasize the importance of “zooming in” further. So on day two I made my own set of screen shots (this time using a volleyball game), and I showed screen shots of minutes 2:00, 3:00, 5:00 and 6:00. We discussed how screen shots of these moments was not enough info to predict what happened at 4:00. Too much could have happened between minute 3:00 and minute 5:00!
We were able to come back to the comparison between the soccer game and the volleyball game screen shots throughout the week.
Lastly, I want to mentioned that Bowman has a great blog post on limits with an activity that I also used one day: