Experience First

We spend the first chunk of class time going over assessments whenever students take a quiz or test. Students work in their groups to make corrections with a different colored pen. We have a rule that every group member needs to be getting help or giving help, and not just sitting idly. At this point in the year, they do not need me hardly at all during this time as they are used to providing support to each other. Students do not earn back points for their corrections but we frame the time as instrumental to our learning.

Today’s lesson is a low-floor and somewhat silly introduction to continuity. During the activity, students consider various nightmares that could happen at an engagement party, each correlating to a different type of continuity. In the last question, we ask students to come up with their own definition of continuity just based on these examples. We are always surprised how close they are to the formal definition, even though we haven’t talked about the concept at all yet!

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Formalize Later

The debrief to today’s activity adds all the formal notation and vocabulary related to continuity. Emphasize to students that each type of discontinuity has a specific limit description. While classifying the type of discontinuity is an important first step, justifying their answer becomes the greater goal.

It can be useful to talk about the three nightmares in terms of “most bad” or “most severe”. Removable discontinuities (the chef not showing up) are fixable and thus less severe. The people are already gathered together which is the true intention of the party. The limit does exist! Getting food from somewhere else would complete the party (remove the discontinuity). Tomorrow’s activity will give students much more practice with how to remove the discontinuity. Nightmare 3 is obviously the most severe as the bride and groom break up forever. At an infinite discontinuity, the function value is undefined AND the limit does not exist.