Set of 8 limit description cards

Overview

This is the first of two review days to prepare for the unit 1 test. Today, students will be working in groups of 3 or 4 to create graphs on poster paper that satisfy the descriptions on the card assigned to their group. There are 6-7 limit and continuity statements written on each card. Once groups have finished, they will hang up their poster and their card next to each other, then travel to the other groups’ posters. Groups will then check each other’s work and either add a check mark if they agree that the poster has met all the requirements or post a sticky note with some feedback. Groups should visit at least 2 or 3 other posters to give feedback. At the end, students should return to their own poster, read the feedback, and make any changes that are necessary to their graph.

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Teaching Tips

We recommend having students sketch their graph on scratch paper before making their poster. It is rare that a group will meet all of the conditions on their first try. When you monitor the groups, encourage students to use precise mathematical vocabulary as they speak to each other and make sense of the limit descriptions. It will also be important for students to connect both the written descriptions and the limit statements to the various features on the graph.

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Student Misconceptions

This activity can be challenging for students because there is a lot of information to keep track of, and the limit descriptions are given in random order, not from left to right.
Students may struggle with the idea that a function can have a left-sided limit of infinity but a right-sided limit of some number. It is possible for there to be a point located on an asymptote, if that function is piecewise defined. Consider the example below.

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Suggested Homework

We will be assigning the Personal Progress Check (PPC) for Unit 1 that can be found when you log into AP Classroom.