Review (Lessons 8.3-8.4)

Unit 8 - Day 12

Quick Lesson Plan
Activity: Continuity Scavenger Hunt

     

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Lesson Handout

Recording Sheet

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Experience First

To prepare for today’s activity, print the scavenger hunt and post the papers around the room, being sure to mix them up and NOT post them in the same order as they appear in the file. We like to print them on colored cardstock.

 

Students should work individually or in pairs to work through the sequence of problems as they travel around the room. Students can start at any station and the answer choices will determine where they go next. Students should keep track of their work and record the letters of each station in the order that they visit them on the recording sheet.

 

Checking work is incredibly easy! The correct order of stations should spell T-H-E-O-L-Y-M-P-I-C-S. Since students can start at any station, their answer might start at a different letter and loop around (example: LYMPICSTHEO would be a correct solution). If students return to a station they already completed before having gotten to all the problems, they will know there is a mistake in their work somewhere.

Formalize Later

The stations our students struggled with the most were stations Y and S. In Station Y, students had a hard time recognizing the parking lot price structure as being a step function and thus demonstrating a jump continuity. Because of the nature of the scavenger hunt, I let students make that mistake, knowing they would have to come back later. It’s okay to get a little lost on the hunt! After a group’s second or third time at this station, you can offer a little more support. Generally I can do this with a few basic questions like “how much would you pay if you parked for 58 minutes? 59 minutes? Exactly 1 hour? 1.5 hours?”

 

In Station S, most students chose option M, that a=-3. Although this value would make the limit exist at x=-1, the function is not defined at x=-1 and thus will never be continuous unless an ordered pair were to be added to the graph at (-1, -3).