Graph Theory Projects

Out of the nine math teachers at my school, I'm one of two math teachers that is lucky enough to teach a course called discrete math. Although the other teachers argue it's not a "real math class" and some students do too, I absolutely adore teaching this course. I especially love that this class allows all students to be successful because they don't need any prior knowledge on the topics to do well. Since all students start off with knowing very little about any of the topics we will be studying, it levels the playing field among students. 

In discrete math we study a lot of discrete topics, hence the name. Some of the units of study in this course include: election theory, fair division, graph theory, probability, recursion, and matrices. My favorite topics are those on graph theory. In fact, we just spent the past seven weeks covering various graph theory topics and I'm a little sad to be moving on to probability today.  (I didn't realize we had been on graph theory that long - I just looked at my notebook and saw we started the unit on September 30...crazy!)

The majority of students in this class are just trying to get their 4th math credit to meet North Carolina's graduation requirements, so I try to make this course as fun as possible. Fortunately for me, these topics lend themselves to projects. We culminate every topic with a project and a test. I typically give students 1-2 days to work in class on these projects and if needed, an additional day or two at home. Here are a few of the projects my students completed this semester. For the most part, my students put a lot of time and effort into their projects. I enjoy seeing a students creativity and personality come out through their projects.  

Project Planning (Critical Path Analysis)
Students have to plan and organize an event/task that has time-sensitive operations, in order to find the minimal amount of time needed to complete the task.

Planning the Homecoming Dance - A booklet with graphs on transparency sheets
so that you can see each part individually or all at once. 

Planning a Wedding - Each layer of cake had a different part of the project. 

Conflict Resolution Graphs
Students have to create scenario that involve multiple interest groups, each of whom may have multiple interests, and minimize the conflicts between the groups.

Traveling Salesman Problem (TSP)
College Visits - Students had to find distances between their house and four colleges they are interested in attending. Then they had to plan out the quickest way to visit all 4 colleges once, when beginning and ending at their house. 

Expression Trees (Post Order Traversals)
Students have write a favorite quote on a binary expression tree so that it reads as a post order traversal.

I grade projects on a rubric based on meeting the project requirements and being mathematically correct.  However, since there are 26 students in my class this semester, I always have a few not-so-good projects or I have projects that look great but the math is wrong. To work on eliminating the latter problem, I've started putting a check system into my projects. Students are responsible for getting another student to look over their rough draft before they can begin making their final project. It counts as part of their project grade for both students (the student doing the check and the students work being checked.) That has helped but it hasn't completely gotten rid of the problem. 

I know there are very few online resources for discrete math at the high school level so I'm working on getting my discrete math files uploaded to box.com but it's a slow process. Maybe between thanksgiving break and winter break, I'll be able to get this done before the end of the year! If you want any of my graph theory project files/grading rubrics before then, send me an email.

Introduction

My first post told you why I am starting a math blog, so I figured my second post should give you a little background information about who I am. 


My name is Jennifer Williams and I am in my 7th year of teaching math in the northwest mountains of North Carolina. For the past four years, I had the joy of teaching 8th grade math at the middle school in my county.  Luckily, for my sanity, this year I have been transferred back to the high school where I initially began my teaching career. (Let me just say that middle school teachers are crazy, loyal, and hard working. That career path is not for the faint of heart!)


I am married to my wonderful husband, Jamie, and we live about 30 minutes outside of Boone, NC. Jamie works as an insurance agent and is extremely supportive of my job as a teacher. We do not have any children but we have two nieces and two nephews that we love to spend our free time with. I love being “Aunt Jennifer,” as they bring me so much pride and joy! 

Jamie & I - October 2009

I am originally from Durham, NC and moved to the mountains of North Carolina to attended college at Appalachian State University. I graduated from AppState with my Bachelor of Science (2008) and Master of Arts (2009) in Mathematics Education. As a full time graduate student at AppState, I had a graduate assistantship with two professors that worked with rural math educators in the surrounding counties. That's how I found out about the school system where I'm currently employed. Even though I had lived in NC my entire life, I had never heard of this county before. In fact, my first time here was the day of my interview. Now, I can't imagine leaving. 

My school system is relatively small (for the state of North Carolina) and has approximately 3200 students in three elementary schools, a middle school and a high school. I am blessed to live in such a beautiful part of our great state. This area is known for its abundance of Christmas tree farms and we are lucky enough to experience all four seasons. I love calling these mountains my home!

The math department dressed up for "Character Day" during Homecoming week.

I am obsessed with making math as fun as possible. I am continuously thinking of how to get my students out of their seats and how to incorporate graphic organizers into my lessons. I try to make things as hands-on as possible. I’m am constantly making changes to benefit my students. I have a passion for math and teaching students. It’s my honor to work with each and every student that comes through my classroom door. My goal is to build a trusting relationship with my students and as a byproduct help them learn math. This year I am teaching Discrete Math and Math 1.


When I’m not teaching, I enjoy biking, skiing, baking desserts, reading nonfiction books, and cross-stitching. I also enjoy doing math for fun. (For some reason, my students find this weird!) I am a self-proclaimed nerd and proud of it! I am the director of my church’s T&T Awana club for 3rd-6th graders and am also the faculty sponsor at my school for CRU- Campus Crusade for Christ.

Jamie & I before the Fletcher Flyer 100K - April 2015

That's all I can think of for now. :)  Feel free to introduce yourself! I'm excited about connecting with more math educators in the MTBoS!

Why I'm Blogging

I am beginning to blog about my math classroom as a part of the MTBoS. I've been reading math blogs for the past few years and they have had a great influence on my teaching. I could always turn to these trusted sites to get ideas for graphic organizers or activities to use with my lessons. But I was too bogged down with teaching and coaching to start sharing my own ideas (or so I thought.)

However, during this past summer my school system started encouraging teachers to share what they are doing using social media. As a result, I created a Twitter account and I immediately started following a few of my favorite math bloggers. Then Sarah posted on her blog about using the hashtag #teach180. The goal was to take a picture of your classroom everyday and tweet about it. It was AWESOME! Immediately, I was able to view into a lot of other classrooms and even began to share snippets of my own. Sometime in October, Sarah tweeted about the MTBoS mentoring program and I decided to take the plunge into the blogging world. 

My hope for blogging is to share what I'm doing in my class and give back to the math community that has inspired me to be a better teacher.  

So here it goes...