## Wednesday, May 16, 2012

### 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.

1. Very cool!

I am picturing some kind of rubric in my head that might require variety in the types of relations and quantity of relations to get to the highest levels. I'm also picturing this with inequalities if they'd like to color some of it in.

I am teaching a boatload of Algebra (different levels) next year...I better tag this post before I forget about it!

2. Nice idea. We too allow our students who scored well on the state test to be exempt from finals and those students can be a nightmare come this time of year.
I just might steal this project idea of yours for next year.

3. I did a graphing project like this for many years. I saved some of the ones I thought were impressive and I challenged the next group to top the best of last year. I found that every year the projects got better and better as a result.

4. If you have computer access you should try www.desmos.com . They have a great online graphing calculator for something like this.

5. Thank you all for the thoughtful comments. This is what I love about blogging! Within a few days of posting this project, I now know how to make it better for next time.

Matt, the calculator is fabulous! Thank you for the recommendation. I would like to use this for next time, but I am a little concerned that my students will try to copy or modify one of the drawings posted there. Any suggestions on how to make sure their work is original?

6. I teach Algebra 1 & Algebra 2. I don't do this as a final project, but in Algebra 1 they make a picture containing at least 8 straight lines. They have to find the equation for each line and identify the domain & range they used.
In Algebra 2 I did this first with piecewise parabolas (they really struggled with piecewise, so it helped a ton), and then later with conics. The students enjoyed it and it made them feel like they were practicing with a purpose.
Each project requires a math version and an artistic version, as well as a reflection. One overachiever did 47 parabolas, and then 54 conics!

7. Awesome idea and pictures! Love the way you open it up to include any kind of picture. In the past, I've had kids recreate flags of different nations. My favorite was a remarkably accurate rendition of Kenya.

The colored pencil is especially awesome -- forcing kids to connect a part of a picture to a particular equation.

Thanks for sharing such an awesome project!

8. I did this project this spring with my students because one of them actually asked to do it. "Hey, Miss B, since we've been doing all this piecewise function stuff, can we do a project where we use it to make those graph pictures?" Um, you're inventing a project that's totally tied into our content? Yes, please do it! Little did I know you'd posted the same thing here!

The part that impressed me most was that a few students researched types of graphs we hadn't studied this year because they needed other shapes!

It's a great project, and one I was even able to leave when I had a sub (after we'd spent time the previous day getting started).

Thanks for sharing! So happy I stumbled across your post via Pinterest.