Piecewise functions have been something my students have always struggled with. They don't always get they are taking parts of the function and graphing them on the same graph. They'd like to graph the whole graph of all functions on the same graph or they don't have an idea where to get the points to graph. So, I am changing up piecewise functions this year based on some suggestions from the Math Twitterblogosphere.

The first thing I did was introduce piecewise functions via

Mathalicious'

Domino Effect lesson. (shameless ad - I've met Karim and had wonderful conversation with him. He and his company are doing some great things to help teachers. It is worth the money to subscribe and have access to the lessons. Go check it out. I'll wait. :-) ) I had used this at

Hedge's suggestion - she had used it in her Algebra 2 classes to introduce piecewise functions.

On the second day, I adapted what

Maggie has done with her PreCalculus students when

introducing piecewise functions. She created an investigation where the students graphed the individual functions and cut out the pieces needed and put them together on a graph. What a great idea! Granted, right now we are working with piecewise linear functions, but the idea is fantastic. So, I took her idea and modified it to fit what we were doing with piecewise functions. Here is what I came up with:

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