This is easily one of my favourite problems that I have come up with. Mainly because of the back story. I handed a student this calculator, and he told me that it didn't work. The numbers weren't working. I showed someone else and they decided to throw it out, but I couldn't help but think that something more than broken buttons was the problem.
Act 1 - The Brokenness
So ask the students: "What is wrong with this calculator?" or "What is this broken calculator going to give us for '433+233'?"
Act 2 - Examples
Okay full disclosure here, this is not really what I want to give my students, but as a low tech version (and one that you can use as well), I have made these...
What I really want students to do is to explore their own numbers and find patterns on their own. In order to do this, I want to program a base 5 calculator that kids can use on the school netbooks, BUT I don't know how to program. If anyone has ideas about how I could put this calculator into my students hands without telling them that it is a different base please put them in the comments.
The other option is I just put my calculator under the document camera and have students ask and record class wide. That doesn't help you guys though, so this is what I have started with. If you think I need some more/better examples please tell me in the comments and I will make them (groups of four look nice).
Act 3 - The Reveal
This is a pretty pure mathematics WCYDWT so I can only think of standard sequels. (Please give me more ideas in the comments, these are pretty lame).
- How does multiplication work in this number system? Can you find some easy methods for solving basic multiplication statements?
- Pick a random base (2,7,12,4.5(?), 16), and create some problems, and share them with a partner. What is different and similar among different bases?
- From @trianglemancsd How would you represent 1/2, 1/4, and 1/10 as a "decimal" number? What does 1.3, 1.021, and 0.033 become as a fraction? (All sorts of headaches happen here, clarify a fraction in base 10 or base 5; what does 1/10 mean?