Act 1 - The Brokenness
Act 2 - Examples
Update: The awesome Jed Butler programmed this amazing base five calculator on Geogebra. If you are not plugged into the MTBoS, you need to get on that!
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).
Update: I have also begun having students exploreJames Tanton's Exploding Dots. This is a great intro into different number bases, and really stretches students, but is not completely out of the range of grade seven students. So much love for this.
Act 3 - The Reveal
- 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?