Unit 1: Properties of Functions

Project

Exploration Options (with links)

Read an article about mathematics or a mathematician in the New York Times. Submit a serious comment that cogently expresses your thoughts about the article. Print out or email the article and the comment you submitted. In addition, write a paragraph (at least 5 sentences) summarizing the main points that you got out of the article and your thoughts about what was written.

Visit Daily Desmos and find a graph that intrigues you. They are categorized into basic and advanced. Now try to reproduce that graph using Desmos.com (an incredible, incredible easy-to-use online graphing calculator). Submit a comment with your answer – or the closest you could get to your answer. Print out or email the original Daily Desmos challenge, and your Desmos.com page with your investigation to submit. In addition, write a paragraph (at least 5 sentences) explaining what you did for this activity. This can include your process, an explanation of errors you made, or your thoughts as you tried to do this.

Do you like finding patterns? Did you find sequences interesting? Well if so, go to Visual Patterns and pick one of the hundred patterns, and try to determine the number of objects in the 43rd figure. Submit your answer. Print out or email the visual pattern you were trying to solve, and a brief writeup (at least 3 sentences) 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 puzzle (you can take a photograph of it). Submit your puzzle and the writeup of your solution (at least 3 sentences).

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 or screen shot and email the challenges, and write up three rationales as to how you came up with your three estimations, and also make sure to mention to true answer (at least 3 sentences for each). It’s okay if you aren’t close to being right.

“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 a hypothetical that interests you and has some math involved.

Print out or email the what if you were intrigued by, rewrite the “solution” in your own words -- additionally being sure to explain what drew you to the hypothetical, what you found innovative/interesting about the solution, and what you were confused by in the solution (at least 6 sentences).

Go to Vi Hart’s youtube page and find a video that sparks your imagination. Watch it. Submit a serious comment that cogently expresses your thoughts about the video – what you liked about it, what confused you about it, what inspired you about it. Print out the article and your comment. (Your comment should be at least 5 sentences).

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 (at least 5 sentences).

Alternatively, 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). Write up the reasoning behind your choice of that question (at least 5 sentences).

Math Munch is a ridiculously addictive weekly digest of the mathematical 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.). For all but PLAY, you should include, at least, a 6 sentence reflection with your work. For PLAY, you critique should be at least 5 sentences.

Are you a Redditor or simply love browsing Reddit? Visit the math subreddit. Find a thread that interests you. Submit a printout 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 (at least 6 sentences).

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 RSA encryption 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!

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+ Unit 1: Properties of Functions

+ Unit 2: Rational and Logarithmic Equations

+ Unit 3: Right Triangle Trigonometry

+ Unit 4: Analytic Trigonometry

+ Unit 5: Conics

+ Unit 6: Vectors, Parametrics, and Polar

+ Unit 7: Sequences, Series, and Limits

+ Unit 8: Functions and Modeling

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