Piecewise Functions

The objective of the Senior Topics course I teach is to review/extend math concepts my seniors have learned before, and to prepare them to do well on college Accuplacer exams. There is a lot of flexibility in the topics I teach and I am always looking for new fun ways to approach each concept, especially since the students will have seen some of the topics (like systems of equations) at least three times already.

When getting ready to review writing equations of lines this year, I decided to approach the topic from the standpoint of piecewise functions, a topic I knew they had never seen before. I adapted my lesson activity from X Y Pi and divided students into groups. I told each group that a girl named Ann was going on a seven hour walk, and gave them each one piece of the story. Some groups were given two hours of the story. The task: write and graph an equation to represent the hour of her journey you were given. I cut large graph paper into skinny columns and marked the y axis so that each group would use the same scale.

When they had finished, we pieced the graphs together on the board to make one large function. Then we talked about the number of pieces we were looking at, and how we had seven different equations. And how what they just did created what’s called a piecewise function.

There were some oohs and aahs and even one “That makes so much sense!” When I passed out another graph, they immediately jumped into action to find the equation of each of six pieces that comprised the new given function. Definitely an activity I will be doing again.

Here are the stories I passed out to each group (adapted from a Pre-AP Laying the Foundation Module 1 Activity):