I remember years ago (circa 1997) using a scenario about Grant the Ant walking toward the door. Only one problem – Grant would always stop walking when he reached the point half way to the door. Then he would begin walking again. Stop half-way. And so on. I think the initial prompt was used for sequences and series. But Grant’s Adventures have evolved over the years.
One year in Algebra 2, I set this up as stations around the room. Students visited each, read the scenario and sketched the indicated graph. Once everyone had a chance to visit each scenario, teams were given poster paper and asked to create larger versions of their graphs.
We then did a gallery walk to indicate if we agree / disagree and offer written suggestions and ask questions on the posters. Several were fairly straightforward, but always a few they brought up some discussion. I had items available like erasers on a desk with a cup or even mini marshmallows, the pencil sharpener and students were taken to the hallway to walk / model Grant’s walk between two classrooms.
File with scenarios: Grant the Ant
Usually this lesson either followed-up or was followed by the Representing Functions of Everyday Situations from Math Shell – Painting the Bridge is always one of my favorite graphs to discuss as a class.
Its a great tool / visual to reference back to in future discussions are we went more in depth with studies of each function family.