PS - Your island would also need Internet, wifi, laptops, smartphones, tablets, AND a way to charge everything. So... yeah.
Number 1: Feedly
Additionally, since working with Steve Olivo on a middle school team I've decided that the best way to hold students accountable for their writing is to have them blog. They are publishing their work to me, each other, and the world. What better motivation to build a portfolio that tracks one's own progress? They may not realize that they are building an online portfolio when they create the blog at age 13, but when they look back as 16-year-old sophomores they are astonished at their own growth over 3 short years. Feedly is an easy way for me to read their writing every day from my classroom laptop or from my iPad while I sit in the Social Studies Department room sipping coffee during my prep period.
Number 2: QR Code Generator
A QR reader and creator is essential. The fastest way for students to access your in-class presentation, an online video clip, a scholarly article, or just about anything else you can think of that can be digitized is via a QR code. I've also used QR codes to build parent interest at Back to School Nights (see the sample above). They look fancy hanging around your classroom when administrators "visit" too!
Ok, so if the public relations approach doesn't appeal to you, how about a quick way to answer the daily question: "Mrs. InsertYourNameHere, I lost the sheet. What am I supposed to do?" Your answer would involve pointing to a posted QR code. Student scans said QR code. Directions magically appear on student's smartphone screen. Game over.
Number 3: Quizlet
The basics of any unit in any subject area can only be absorbed by students if they have acquired the vocabulary to discuss the information. Recently, when teaching the Protestant Reformation, I felt like I needed a fresh way to teach vocabulary words like indulgences, heretic, excommunicate, and recant. Enter Quizlet. I type in the words and definitions with context. Students enter my room, log into Quizlet and start playing games on their phones/tablets/laptops. 15 minutes into the class period and I've taken attendance, checked homework, and even caught up on a couple of emails in the midst of peace and quiet. I ask them to pause their games and start telling the story of Martin Luther, asking them to fill in the blanks with the meanings of the words I'm using and THEY CAN DO IT! Nuf said.
So, yeah, there are a few more apps I can't live without both personally and professionally. These three Google Chrome apps are clicked almost daily, though. They make my day go more smoothly. They help my students submit and access information faster. They let us, student and teacher, get to the real business of learning and teaching.