Final “Exam” Parts I & II
Your task is to create an ad for a new roller coaster that’s being built at a local amusement park. The rollercoaster will follow the path of a piecewise-defined function, involving at least four different functions. Your ad should be mathematically correct, eye-catching, neat and organized!
You can work alone or in groups of up to three people.
Your ad must include:
A sketch of the path of the roller coaster
o Use at least four different functions with at least two different types of functions (linear, quadratic, exponential, logarithmic, etc.).
o Your roller coaster must be continuous at all transition points.
o Your roller coaster must be differentiable at a minimum of one transition point, and NOT differentiable at a minimum of one transition point.
A name for your rollercoaster & a tagline (it is an advertisement, after all)
A section of your work:
o Define the four (or more) functions and their domains.
o At the transition point(s) where the function is not differentiable, show how it is not differentiable. I need to see some work here – do not just say “corner,” “cusp,” etc.
A write up (on a separate sheet, or on the back of the poster)
o Explain what jobs you and your partner(s) took on. For example, who did the drawing? Who came up with the name? How did you choose your functions?
o Give me at least two mathematical concepts that you needed to take into consideration when creating the path of your rollercoaster. For example, one might say that their function was continuous because you couldn’t have a break in the roller coaster without endangering the lives of your riders… (don’t use that one – I already told you it had to be continuous)
o Explain to me what you found to be the easiest part of the project.
o Explain to me what you found to be the most challenging part of the project.
o Include at least two photos of you and your partners working – or a link for me to see the pictures online
Throughout the past four years, you have learned a lot of math. I want your group to pick one mathematical topic and create a song summarizing the topic. The topic must be approved by me, and each group must do a different topic. You can rewrite the chorus and three verses to a popular song. The song must be approved by me, but if you think you could play the original song for Mr. Bourn without being embarrassed, it should be fine. If changing the words to a preexisting song doesn’t work for your group, you can create your own song.
Your songs should include:
q what your topic is
q what your topic is used for
q when you learned about your topic
q who uses your topic in real life and when
q other important aspects of your topic, including
one mathematician who dealt your topic
You will hand in to me:
q The lyrics to your songs. I only want one copy of the lyrics per group.
q A video of your group performing the song OR a live performance of the song. The performance should include the three versus plus the chorus sung at least twice. Your song may be longer, if you’d like.
q A one-page summary of how you worked on the project. Each student in the group will write one paragraph explaining how they contributed to the group. There will also be a paragraph explaining when you met to work on the project, how you came up with the song lyrics, etc.
My website will have some resources for you…
http://www.norwood.k12.ma.us/nhs/ à Teacher Websites à Mullen, Laura à Calculus
You will be graded on:
Content and Accuracy:
· Are you discussing parabolas and don’t mention the vertex? Bad move.
· In your chorus, do you mention the slope formula? It had better be correct!
Inclusion of mathematicians:
· As part of your song, you must mention at least one mathematician who influenced the specific topic your group is discussing.
· Use the library, the internet, and your textbook as resources.
Creativity:
· Have fun with this project! Those students on YouTube clearly didn’t mind acting out a little bit for the benefit of the video.
Group work:
· Learn to work well with one another. You don’t have to start hanging out on the weekends together, but you must be able to work together to reach the common goal – a 100% on this project!
· Everyone must be a part of the group, and be a part of the one-page group write-up.
Presentation:
· All members of the group must take part in the presentation.
We must be able to hear and understand the words that are coming out of your mouths (whether on video or live)
· After viewing the performance, students in class will have the opportunity to ask members of the performing group questions about the material. Students must be able to answer questions relating to their topic asked by members of the class…or me.
A complete rubric is available on my website
BY / I NEEDThursday, May 4 / The Beginning Stages
· The name, tagline and rough draft of your rollercoaster’s path
· Your group members, topic, song
Wednesday, May 10 / Progress you’ve made on both projects
· Some work on how you know your function is/is not differentiable
· notes on topic, lyrics so far
Thursday, May 18 / Final products
· Ad, work, write up, pictures
· Video of your performance (or be prepared to perform on this day), lyrics, one page summary