VHS Algebra CP 1 & Geometry CP
Mathematical Explorations Project
- This is a project where you are not graded on your correct answers—effort, imagination, creativity and analysis are being graded.
- You select 6 of 20 Explorations that you think that you will like. If you don’t find an Exploration enjoyable and interesting, pick another one.
- The Explorations must be turned in on a rolling basis—the first two Exploartions are due by May 9th, the 3rd and 4th by May 23rd, and the 5th and 6th Explorations by June 6th.
- All work must be done individually but you can always ask Mr. Cashill for assistance.
- Unauthorized aid will result in a zero for the entire project.
Name: ______
“On my honor, I have neither given nor received any unauthorized aid on this assignment.”
Signature: ______
Introduction
Here’s the thing. I find math fascinating and I want you to have fun exploring math that isn’t really tied to the curriculum. I want you to enjoy learning about something mathematical that piques your interest—something that you select that will help make you see the beauty, fun and excitement in math. There are so many ways to find interesting mathematics and I want you to explore a few of them.
The point of this project is to allow you to explore mathematics that you are interested in. I want you to enjoy this. The tasks are not designed to be challenging. That isn’t the point of this. And I want to reward you for doing math for fun.
So this is what we’re doing…
The Task
By the end of the 4th Marking Period you will do 6 of the 20 explorations described on the next few pages. So you can be exposed to a variety of things, you should do six different explorations. However, if there is something that you simply get obsessed with and want to do more of, just talk with me. It shouldn’t be a problem.
The first two explorations must be turned in by Friday, May 9th. The 3rd and 4th Explorations are due on Friday, May 23rd and the 5th and 6th Explorations are due by Friday, June 6th. You can turn in more, of course, if you get on a roll and you can turn them in early as well! You are also welcome to do more than 6 Explorations and I will only grade your six best.
As the marking period continues, I may ask you to present an exploration you found interesting to the class. So we can hear from a number of students, you will be (strictly) limited to three minutes.
Grading
In terms of grading, these explorations are worth a total of 300 points or 50 points each. You are not being graded on whether you get right or wrong answers. You will, however, be graded on the effort you put into the investigations, the completeness of your work, your ability to describe what you did and how you went about it, and your thoughts on the investigations.
Remember that you are selecting investigations that you want to do—not ones that you have to do. You are, in essence, making a portfolio for next year and your grade will reflect the time and energy that goes into each investigation.
All reports must be typed but all mathematical work can be hand-written. Every report must include screen shots and/or printouts of what you accomplished. Every report should be self-contained—that is, a person who knows nothing about the exploration can read your report, find the exploration and follow your actions.
If you do the exploration and do a minimal job on it, you’ll get 0-10 points for it. If you do a solid job on it, you’ll get 20-25 points for it. If you do an excellent job, you’ll get 35-40 points for it. If you do a super-duper-excellent job on it, you will earn 50 points for it.
A grading rubric is attached to guide your work product.
Academic Integrity
All work must be done on an individual basis. You may ask Mr. Cashill for help at any time. Remember you are not being graded on how many/how much you get right so the need for unauthorized assistance should be nil. Should you succumb, however, to the dark side and you do receive unauthorized aid, all explorations will become null and void and you will receive a 0 out of a possible 300 points.
The Cashill Honor Pledge--“On my honor, I have neither given nor received any unauthorized aid on this assignment” must be written on each Exploration along with your signature. No pledge, no grade.
Exploration # / Exploration Name / ScoreOverall Score
The Explorations
Exploration #1: Sequences / Exploration #2: PatternsDo you like finding patterns? Do you find sequences interesting? Well if so, go to Visual Patterns (http://www.visualpatterns.org/) and pick two of the hundred patterns, and try to determine the number of objects in the 43rd figure. Submit your answers. Print out the visual patterns you were trying to solve, and include a brief write up of your logic of how you tried to find the 43rd figure. It’s okay if you aren’t right! /
Do you like creating things? Go to Visual Patterns, visit the gallery to see what other students came up with, and generate your own puzzles (you can take a photograph of it). Submit your puzzles and the write up of your solutions.
Exploration #3: Math Articles / Exploration #4: Graphing
Read two articles about mathematics or a mathematician in the New York Times. Submit a serious comment/analysis/summary that cogently expresses your thoughts about each article. Print out the article and your comments.
(http://topics.nytimes.com/top/news/science/topics/mathematics/) /
Visit Daily Desmos (http://dailydesmos.com/) and find two graphs that intrigue you. They are categorized into basic and advanced. Now try to reproduce the graphs using Desmos.com (an incredible, easy-to-use online graphing calculator--https://www.desmos.com/).
Submit a comment with your answers--or the closest you could get to your answer. Print out and submit the original Daily Desmos challenges, and your Desmos.com pages with your investigation.
Exploration #5: Estimating / Exploration #6: Hypotheticals
Do you like estimating how many jelly beans are in a jar? Go to Estimation 180 and pick three consecutive days of estimation challenges and take the challenge. After you submit your estimate, be sure to look at other estimates. Look at the answer. Print out the challenges, and write up three rationales as to how you came up with your three estimations, and also make sure to mention the true answer. It’s okay if you aren’t close to being right.
(http://www.estimation180.com/) / “How many unique English tweets are possible? How long would it take for the population of the world to read them all out loud?” If you like hypotheticals, go to xkcd’s “What If” archives and find two hypotheticals that interest you and have some math involved. (http://what-if.xkcd.com/1/)
Print out the “what ifs” you were intrigued by, rewrite the “solution” in your own words--additionally being sure to explain what drew you to the hypotheticals, what you found innovative/interesting about the solution, and what you were confused by in the solution.
Exploration #7: Museums / Exploration #8: Vi Hart
New York City is the home to the newly creation Museum of Math (MOMATH). Visit this museum! Submit a review of the museum. If you can, include a photograph for your review.
Alternatively, every so often the Museum has lectures for the public--called “Math Encounters.” Attend one of them, and write a review of the lecture you attended. (These fill up quickly, so register early if you want to go!)
(http://momath.org/)
/
Go to Vi Hart’s youtube page and find two videos that spark your imagination. Watch them. Submit a serious comment that cogently expresses your thoughts about each video--what you liked about it, what confused you about it, what inspired you about it. Print out the article and your comment.
(https://www.youtube.com/user/Vihart and http://vihart.com/)
Exploration #9: Math Stack Exchange / Exploration #10: Math Munch
One vibrant online community is the Math Stack Exchange: “a question and answer site for people studying math at any level and professionals in related fields.” It has a number of higher level math questions, but you can find high-school level questions too.
Go to this site and find an interesting question and some answers for it. (Frequently asked questions might be of interest.) Submit the problem, the answers, and a short description of what you understand about the problem and the solution.
Then, if there is a question about mathematics that you’ve been wondering but never understood (e.g. what does 00 mean, really?), post it and see if someone responds. Submit your question, and any responses you get (if any).
(http://math.stackexchange.com/) /
Math Munch (http://mathmunch.org/) is a ridiculously addictive weekly digest of all things mathematically interesting on the internet. Go to the website and browse the archives. There are a number of things that will have you DO, MAKE, WATCH, READ, and PLAY. Find something that interests you.
DO: Work on a puzzle, or solve a problem, or struggle with a problem.
MAKE: Re-create a piece of math art, or create your own artwork inspired by the original work.
WATCH: Watch a video and leave a comment on the site with what you learned and/or what questions you have.
READ: Read about a mathematician, write down why this mathematician was interesting to you, and compose two questions you’d like to ask this person.
PLAY: Play a math video game and then write a critique of it (likes, dislikes, suggestions, etc.)
For each of these, print out the original post and include your work (your solution, art, comment, critique, etc.)
Exploration #11: Math by Design / Exploration #12: Stop Disasters
Design a park or help build an environmental center at Math by Design. Keep detailed notes of your progress and take some screen shots to build a portfolio of your work.
(http://mathbydesign.thinkport.org/) /
Although not a true mathematics activity, Stop Disasters allows you to simulate disasters and ways to prevent them. Great fun. Select a disaster and keep track of what you do to minimize the damages.
(http://www.stopdisastersgame.org/en/home.html)
Exploration #13: Numberphile / Exploration #14: Movies, Comics & More
Numberphile is a great website that explores math and stuff through some very interesting videos. Watch any two videos that sparks your imagination. Submit a serious comment that describes the video and cogently expresses your thoughts about the video--what you liked about it, what confused you about it, what inspired you about it.
(http://www.numberphile.com/) /
Use your creativity to produce your own math movie or comic strip. Some great sites include:
Marvelkids.com (http://marvelkids.marvel.com/comics), Make Beliefs Comix (http://www.makebeliefscomix.com/) and, for animated movies, GoAnimate (http://goanimate.com/)
Exploration #15: Reddit / Exploration #16: TED or TEDx or TED-Ed
Are you a Redditor or simply love browsing Reddit? Visit the math subreddit. Find a thread that interests you. Submit a printout of the thread and comments, and an explanation of why the thread was interesting, what you took away from it, and what questions you are left with.
(http://www.reddit.com/search?q=math) /
TED is a nonprofit devoted to spreading ideas, usually in the form of short, powerful talks (18 minutes or less).
TEDx was created in the spirit of TED's mission, "ideas worth spreading." It supports independent organizers who want to create a TED-like event in their own community.
TED-Ed aims to amplify the voices and ideas of teachers and students around the world. TED-Ed’s commitment to creating lessons worth sharing is an extension of TED’s mission of spreading great ideas. With this philosophy in mind, and with the intention of supporting teachers and sparking the curiosity of learners around the world, TED-Ed is the newest of TED’s initiatives.
Watch one or two videos that interest you (must be a total length of 10 minutes or more.) Identify the speaker, describe the talk, the key points of the talk and what your opinion/comments are about what you have just heard.
https://www.ted.com/
http://ed.ted.com/lessons?category=mathematics
https://www.ted.com/watch/tedx-talks
Exploration #17: Brain Binders / Exploration #18: Yummy Math
Brain Binders contain a puzzle with a finished picture. The goal is to fold the puzzle into a shape with a solid color on each side. Simply print, cut out, and fold to match the finished picture...it sounds easy until you try it! Brain Binders--All you need is a sheet of paper and a brain.
Pick one puzzle each from the 2, 3, 4 and 5 fold puzzles. Bring in your completed puzzles to share with the class.
(http://www.teachnet.com/brainbinders/) /
Yummy Math provides students and teachers with an easy way to bring real-life into their math. It is our belief that when math is explored in contexts that are familiar and of interest to students, students will be more engaged to do math, reason, think critically, question and communicate. Pick a high school activity and do your best to solve the problem. See Mr. Cashill for help along the way.
(http://www.yummymath.com/)
Exploration #:19 Dare To Compare / Exploration #20: On Your Own
How do you compare with students nationally and from around the world?
Pick a subject (math, of course), a grade (8th or 12th) and how many questions you want to see (20), then click the Show Questions button. Print out your problems and your responses and how well you do against the rest of the world. Try a subject other than math as well.
(http://nces.ed.gov/nceskids/eyk/index.asp?flash=true) /
Do you have some other mathematical thing you’re interested in doing… or that you’re already doing? Do you have a math problem you’ve invented and are working on? Are you reading a book about a mathematician/mathematics? Do you want to research encryption and code breaking because you find it interesting? Great! It can count too!
Just talk with me and I’ll let you know how it can be part of this!
Mathematical Explorations Scoring Rubric
Excellent
10 Points / Good
8-9 Points / Fair
4-7 Points / Poor
0-3 Points
Display / Excellent
Creative display with a variety of materials and high creativity. / Good
Display with materials and some creativity. / Fair
Display with minimal materials and creativity. / Poor
Bare display created.
Math Ideas Explained / Excellent
Ideas labeled and fully explained, very easy to follow and understand. / Good
Ideas labeled and explained, but details are left out / Fair
Only Ideas labeled or explained, but not both. / Poor
No Idea labeled or explained
Math
Operations / Excellent
Numbers and operations are clear, correct and logical. / Good
Numbers and operations are clear and most are correct with some order shown. / Fair
Numbers and operations are attempted but out of order / Poor
Numbers and operations are not clear or correct
Written/Oral
Presentation / Excellent
Exploration is easily read and understood, spelling and organization are proper. Student easily explains Exploration and answers questions easily. / Good
Most of Exploration can be read and understood, spelling is correct, organization is mostly logical. Student can explain Exploration t, reads some of it but can answer questions easily. / Fair
Some of the Exploration could be read and understood, spelling and organization are confusing. Student has problems explaining Exploration. / Poor
Could not read or understand Exploration, words not spelled correctly, and project not organized. Student can't read or explain own Exploration.
Overall
Exploration
Quality / Excellent
/ Good
/ Fair
/ Poor
Exploration
Score