PIeces (Final) Project

Students at our school can opt out of second semester final exams by doing well on state assessments. Most of my students fall into that category. Given the choice to take finals or get out of school two days early, you can imagine what most high school students will choose. With no exams, trying to convince students to review at the end of the year is next to impossible.

A few years ago, I switched to a final project instead:  Create a picture using parent functions (and/or conics) and their transformations along with restricted domains or ranges. I like how it encompasses so many things we have learned this year. Review, without looking at all like a painful study guide.

Leading up to this project, I do a week-long mini-unit reviewing all the different types of graphs we've studied this year -- linear, absolute value, quadratic, exponential, rational, polynomial, and conics. We work on their transformations, and then add in restricted domains and ranges. We sketch simple piecewise functions using known functions, and then more complex ones using a graphing calculator.

At the end of the unit, they do this outline of Texas using a graphing calculator.  (I wish I knew where this came from. Someone gave it to me and it became the inspiration for this project).

Now students are primed to make their own picture.

Here are the project requirements, rubric, and final product sheet.

Some questions/discussions that come naturally out of this activity:  How do I make the vertex of x^2 hit the point (5, 2)? How do I make x^2 skinnier? How to I find where this straight line intersects this parabola?  How do I restrict this domain/range to get half of the ellipse?  And (yikes!) how do I write the equation for this straight line?

Here are a few student samples from a previous year. I loved the penguin!

I've received a few projects already this year that are okay. Students are looking for ways to keep it as simple as possible and still meet all the requirements. I am not disappointed, really. They are doing exactly what I have asked them to do. For next time, I think I will edit the project a bit to require that more variety in graph selection be used.

Over all, it isn't a bad way to end the year. I like that students are still working on math up to the last day. They are being creative and I hear mathy conversations taking place. And I am not pulling my hair out trying to convince anybody to review for an exam they aren't going to take.