Experience First

Today’s review activity is inspired by Bryan Passwater’s Big 10 problem structure with all new problems written for the Precalculus level! Students should work in pairs to solve the ten problems and the solution to each problem will be a whole number between 0 and 9. No number will be repeated, so students have an easy way to catch mistakes. This activity garners great discussion among students and active debates often ensue--we’ve made it so that common mistakes are also whole number answers!

As you are monitoring students, be listening for common misconceptions and pay attention to how students are justifying whether a limit exists or not. Students may be comfortable with the procedures of evaluating limits but need to be coached on how to properly demonstrate their work.

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Formalize Later

Remaining class time can be spent debriefing difficult questions or discussing formal notation for evaluating limits. Question 4 is a great starting point to this discussion. Setting the two branches equal to each other is the correct procedural step but does not demonstrate the Calculus concepts involved. We like to have each student write a justification for their answer to question 4 on a notecard, then collect the cards, and look for common mistakes. We suggest writing various answers anonymously on the board and having students analyze what that response did well and how it could be improved. Creating a culture of safety around mistakes is critical--you may even get to the point where you don’t have to anonymize the cards. Mistakes will have become accepted and normalized.