Calculus: Derivative Project Ideas

AP Calculus AB is typically the highest course for many high school students. Coming up with a possible Calculus project has been challenging. Not because the course is hard. It has been challenging because my desire to keep the project authentic and connected to the major concepts of the subject. Every time I create a project, I want it to be real-world work. I also want to have students think deeply about the "power standards" of the subject.

Identifying the power standards for Calculus was simple. I agree with Steve Strogatz's post in The NY Times,  "Calculus is the mathematics of change. The subject is gargantuan - and so are its textbooks. But within that bulk you'll find two ideas shining through. Those two ideas are the 'derivative' and the 'integral'."  Although knowing that a project on derivates or integrals was easy to identify, the real world application of it has been much harder. Every time I run into a person whose profession is mathematics based such as an engineer, I would ask them how do they use calculus in their work. They would often laugh and say they don't. 

Despite these roadblocks, I am determined to find an authentic use of calculus in the workplace. After searching, I think I have some ideas for a derivative project. The main criteria I am using in thinking of ideas is that there are multiple solutions. Please let me know what you think of them and please add other possible projects in the comments below. 

• Drug Flow: Healthcare is huge topic today. It is a constant discussion at dinner tables. One aspect of healthcare is drugs. Many people do not understand the affects of these on the body. The Center for Policy Analysis wants to educate the public on how various drugs affects the body so that people will be more empowered about their health care. They want to explain their website to include this information. It must include how to calculate the effects in layperson's terms (idea is adapted from extended applications in Calculs with Applications by Lial, Greenwell and Ritchey).
• Classic Box: Kellogg is in the process of repackaging their cereal boxes to respond to market demands. Increase in gas over the last decade has caused the company to increase the cost of cereal. However, recent changes in tax code is lowering Americans ability to pay increases in cereal. The company wants to redesign the boxes to achieve maximum volume but cost less to produce. The company's director of product development is requesting a proposal to meet the company's needs. It must include calculations of the cost to produce and the volumes of the new products (idea is adapted from the classic box problem in most calculus textbooks. There is also an activity by TI-Instruments with their TI-Nspire calculator).
• Start-up Company: Terri Miller has left her position as a manger of a local company to start her own business. She makes lady handbags. The demand has really taken off and she is in full production. She needs to get more capital to expand but that requires creating a proposal that details various financial aspects of the business. Investors are wanting a lot of information including her marginal cost, revenue and profit for the organization. She is small and don't have the staffing to help with the creation of this document. She is seeking assistance to help grow her business (idea is adapted from Calculs with Applications by Lial, Greenwell and Ritchey).

Please Join Me

I have taken a semester off from school to work on creating projects for all grade levels. I ask that you join me in helping shape this work. Your help is really simple, you can do any of the following:

• Share likes
• Give a suggestion of how to improve
• Try it out

Any and all comments are welcome. This is the biggest endeavor of my life. I hope you will join me in the adventure.

Smith Project-Day 1

The class began with a review of the format of my class, rules and expectations. The day I started the project was the second day of getting all new students. Originally, I was teaching Geometry and Algebra II. Now, I am only teaching Algebra II. I had to catch up the new students but also review some information regarding systems with the old group. The class ended with the introduction of their first project.

To understand how I introduced the project, you must understand the set up of my classroom. Some of my readers know about my classroom. However, for those of you who are not familiar with my classroom, it is a fictional corporation called Logic Inc. Students act as consultants and managers that solve real world problems of individuals or businesses. The mission of the company is to help people see math in all areas. In addition to helping clients, the students promote the company through a "company website" where they provide tutorials and information on math concepts.

Since my class is a company, the students get all their information from the company's intranet site (norfarlogic.pbworks.com). It is here the class gets information on the company's first "fictional" client. Students understand the clients are fictional right now so that they can gain experience solving problems. Students read the clients situation and their driving question. Students then created a concept map in mywebspiriation of what they know and didn't know about the clients problem.

To see the actual results of day one, check out the information below:

• This is the powerpoint presented in class-

Establishment of Class & Smith Client Project Introduced

• This is a web page link of the client problem information-http://norfarlogic.pbworks.com/September+18-Smith+Project
• This is a view of the concept map created and how it evolved through the project-http://mywebspiration.com/view/182956a2ba2d
  

Project in Full Swing

I am discovering quickly that once you start a project it is hard to sometimes stop and write about the flow of it. It is also difficult when all of your class dynamics change before you introduce the first project. One week ago today, the students were introduced to the Smith Project. Let me explain the situation regarding the Smith Project and the make-believe family in it.

Kate Smith is a single parent who lives in the area. Kate lost her job at the GM plant. Since losing her job, Kate has had three other jobs. She is now in a stable job at a local manufacturing business. However, Kate is not making as much money. While working at GM, Kate used to take her and her three daughters to the state fair. Since losing her job, they have not been to the state fair. She really wants to take the girls this year. The girls are teenagers and Kate wants to do as much with them as possible before they graduate. She heard we may be able to help her go to the fair on her limited budget. She has $150 that she can spend. The driving question(focus of the project): How can Smith make the most of her $150 budget for the state fair?

This is a very small almost seemingly easy answer at first. However, once students investigate the cost associated with the fair, it has some complexities to it. The goal of the project is to teach systems of equations and inequalities while also helping to get the students prepared to work in teams, think critically and talk mathematically.

I have several things I did to complete the project. The project ends Friday. I will discuss what occurred each day over the next few days. I can't wait to talk to you. Stay tuned for details and links to student work.

Presenting a PBL

This is the second portion to my video posting. Below is a video of me practicing presenting a PBL to a group of educators. The educators are pretending to be like my high school students.

Video on Getting Money for Education

Finally, I was able to find the time to make the videos from my filming at the IMSA institute. It is two different videos. Below is my information on getting funding for your professional development and classroom.

Contemplating Projects

There is absolutely to many things on my plate. I am a member of the alumni association of Northwest Classen High School. As a member, I agreed to produce the newsletter. I am five months behind producing the newsletter. I was supposed to have it out in April. I got completely caught up with understanding student council responsibilities and then a summer full of activities. As I sit trying to pull the articles together, my alarm sounds and I realize it is time to BLOG!

The funny part about this blog is along with completing the newsletter, I am trying to formulate all the projects that my students will complete this semester. I hope to have at least some ideas jotted down that match the standards I have to cover. I can't wait to get started but I have to get this newsletter done before our meeting tomorrow at 4:30 p.m.

Please make sure you check back into my blog to give me your advice on the projects I come up with tonight.

Great Meeting With Team

Yesterday, I discovered why it is great to work in teams. As I said in the earlier post, I was confused on the order to complete items. All of my colleagues are going to follow the book, chapter by chapter. This will help me with following an order even though I will still operate on concepts rather than specific chapters. I also found out that matrices are not as necessary of a skill for calculus preparation so I will be able to concentrate only on the other three methods to solving a system-graphing, substitution and elimination. I would rather teach a few ways that are strong then have students confused on a concept.

I also had a great lead for a project-circuits. I asked the team what is the emphasis for complex numbers. This lead to a possible project about electrical circuits. I have a colleague who is going to share with me what she does and I may be discussing soon how I will make it into a project. I am EXCITED!

Stuck on Order

I have come to the realization that I am officially overloaded. In the last two weeks, I created a manual for the new teachers at our school, helped conduct the new teacher orientation with colleagues, complete a student council retreat, found out how to use the online website for yearbook, informed teachers of pictures, as well as a host of other things I can't remember.

It is with this overloaded mindset that I find myself stuck on if I am making the right decision on the order of concepts to cover within the first 9 weeks of school. Part of the problem is my lack of experience. I am teaching Algebra II for the first time and Geometry which I haven't taught in two years.

Thankfully, I have the state standards and ACT standards to help me focus in on what is essential and enduring concepts to cover. After reading Larry Ainsworth's book on power standards, I am a firm believer that teachers have to be realistic on the fact that you can't teach all state standards in a year. We can cover them but it is unlikely that students will know anyone one thing in depth. In the book, Ainsworth describes power standards as those standards that are enduring (useful throughout life) and essential (critical for the next subject level). These power standards must be taught with depth and mastery. I have identified these standards and placed them in a concept map through mywebspiriation.

With my essential standards in hand, I am working on the first 9 weeks outlook. My teaching style is more about going from concept to concept then chapter to chapter. I start with an overview look of the main concepts to be covered and then go into details. Similar to flying around the forest before landing and examining the trees. I did this for the first time last year and found it very successful. I had 72% (39 out of 54) pass the state examination. This number is even higher when I only take into account students who had to take the exam seriously due to graduation requirements-91%.

As I prepare for the first 9 weeks, my school district divide the standards into 9 week increments. These concepts are apart of a benchmark the district uses to gauge if students are on track for the state exam (EOI-end of instruction). I have compiled the standards into topics and placed them in what I think will be a logical order. The topics and order are systems of equations and inequalities, parent graph of functions and function notation, complex numbers and quadratic equations and functions. I am starting off with systems of equations because it will reinforce their previous knowledge of lines from Algebra I and Geometry. We will then move to some of the core concepts of Algebra II which is polynomials, exponential and logarithmic. I decided to follow with parent graph of functions and notation because it will help lay a foundation to understanding the topics in depth at a later time. The focus of this unit is to recognize the graph, understand notation of the equations when they are a function and identify domain and range of various graphs. The 9 weeks will end with the study of quadratics in detail.

I am not sure this is the right way to approach the subject. There are teachers who have taught both subjects in the building with me. I am fortunate that we all have the same planning period we will be able to meet weekly. I know I will be able to get their insight as well. However, I would the insight from the international learning community as well. Please comment on whether I am on the right track. I am going to plan at least two project-based learning units based on this order.

Going to be a busy year

As I get ready to start the year, I am feeling behind and really excited. I hope I am not alone in this feeling. I have to admit part of my anxiety is due to taking on a new responsibility that will require more time. I also spent most of the summer doing professional development. I did not get a chance to work on curriculum like the previous summer. Despite my mixed feelings and thoughts, I had an amazing revelation while at school.

This revelation came almost at the end of the day when I realized I didn't get many of my classroom tasks completed. How is it I spent 8 hours at school and barely got my classroom tasks ready? It is the day before school and guess what I spent most of the day doing? Helping other people. Although I hate I didn't work some personal tasks accomplished, I realized that I am starting to love helping other teachers just as much as I love teaching students.

It is with this realization that I have made a greater commitment to keep up my blog. I know that the more I am consistent with this blog the more I am helping other teachers. I have placed in my iPhone an alert to make a post every Sunday and Wednesday. It is amazing how much I get done now that I place it in my iPhone.

To all you blog watchers out there, here is another info spot. I will continue to focus on project based learning with an integration of technology emphasis. However, I am going to discuss general technology information or teaching strategies. I will not only talk about how I am doing it in my math class but I will also share items that would be helpful for other subject areas. Please comment as much as possible to let me know I am providing helpful information.