# Conceptual Function Foundation Follow-up

One of my favorite parts about teaching is having the opportunity to see growth in myself and my students.  I love when a lesson I have used with success previously gets even better the next time around, especially when it is a lesson that exemplifies my teaching philosophy.

Last trimester, I used the New Visions for Public Schools’ Algebra 2 functions unit to help build a conceptual foundation.  I wrote about that experience here.

Day 1:  To start off this unit on functions, they were in pairs:  one partner facing the projector screen and one facing the back of the room.  I then drew an arbitrary function on an unlabeled set of axes.  The person facing the screen needed to use words only (no pointing, no gestures) to help their partner draw the graph.  The person drawing was not allowed to ask questions, just draw what they hear.  For example:

Follow-up question (before they turn and look): What could you tell your partner to help them improve their graph?

Afterward, we talked about what descriptions were helpful.  My goal was to turn those descriptors such as “hills” and “curvy lines” into more specific function features.  Classwork (with their group of 4) involved looking at specific graphical examples to define end behavior, turning points, positive and negative intervals, etc.

Day 2:  Gave students a set of 36 graphs.  They needed to sort the graphs into exactly four groups based on their function feature.  I then followed up by having them choose one graph that best represented each group.  Some examples of student work:

Next week, we will look at their groupings and decide which ones highlight important features of the graphs.  Then, we will see if we can add some specificity and some real-world.  Seriously, I love the way this progression helps my students make sense of the function features.  It sure beats standing at the front and going through examples.