Evaluating Limits Graphically (Lesson 8.1 Day 2)
Unit 8 - Day 2
Evaluate limits using graphs
Connect expressions of limits across multiple representations
Quick Lesson Plan
To prep for today’s activities, print one copy of the quiz, quiz trade cards on cardstock and cut them into individual cards. For the card sort, print each card type (graph, equation, limit notation, continuity description) on a different colored cardstock. Make one set for each group of 3-4 students. Laminating these cards is really helpful, so you can keep reusing them year after year.
In Quiz, Quiz, Trade, each student is given a card with a unique graph. Without help from others, the student re-writes the limit expression on a sticky note and evaluates the limit. The sticky note is then attached to the back of the card. When directed, students form pairs and show each other the fronts of their cards. Each partner takes turns reading the limit expression of their partner’s card out loud and evaluating it using the graph. The person holding the card then checks their partner’s answer against the sticky note. When both parties agree on the correct limits, students exchange cards and seek a different partner. If changes are needed, students make corrections to their original answer before exchanging cards and finding a new partner. This process repeats several times. At the end of the activity, students should retrieve their original notecard and see if corrections or changes have been made.
You will want to model this process for students. Remind them they are listening for the correct value of the limit but also correct verbalization of the limit notation.
In the second half of the hour, have students work in groups on the card sort. The continuity cards are NOT needed today so direct students to leave those in the bag. Have students first match all the graphs with the limit statements. Groups that have accomplished this can then add in the equation cards. This part is significantly harder for students. Students should record their matches on the recording sheet to ease in checking.
You may choose to give feedback to each group individually or have a debrief at the end of class where you check the answers. Note that the # and % cards are identical and can be switched. As you are monitoring students ask questions like “How did you know these two go together?” or “Which ones are easiest/hardest to match?” Students can usually identify the piecewise functions but struggle with remembering how to determine the holes and vertical asymptotes of the rational functions. This will be discussed in depth in an upcoming lesson (8.2 Day 2).