Before teaching students how to find a limit on discontinuous, piecewise, and other complex graphs, first build your students’ understanding of a limit on a graph with a context they can talk about!
In this lesson, we explore 3 contexts:
• The changing body mass index of Miss America (which also serves as a review on domain/range and revising a model,
• The human potential for average speed in the 100m, 200m, 400m, 800m and 1500m races, and
• The average speeds of horses in the Kentucky Derby, Preakness Stakes, and Belmont Stakes
The “hook” videos include:
Usain Bolt’s 100m races when he broke the World Record (3 times!). Each race you hear the excitement of the crowd and the announcers as they cannot believe the WR has been broken...yet again! Is it possible it can be broken again? Will humans continue to get faster and faster or is there a limit to our potential?
Secretariat’s record-breaking Kentucky Derby time of 1:59.40 in the 1 ¼ mile. This happened in 1973! American Pharoah recently won the Triple Crown (2015) as did Secretariat, but when will another horse break the record time?
I hope this lesson helps your students understand and talk about limits. While I use this lesson in my AP Calculus class, it can also be used in an Algebra 1, Algebra 2, or Precalculus class for discussion on domain/range, end behavior in graphs, and discussion of fit of a model to a scatterplot.
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