Unbeatable! Combining a Greek myth with an investigation with a reward attached!
We start our investigation of patterns every year with this contest offered by Mathpickle:
http://mathpickle.com/project/daedalus-and-icarus-try-to-escape/
We start with any youtube video of the tale of Icarus. Then we show the video from mathpickle (link above). They claim to be offering a $1,000,000 prize to any child who can find a number that does NOT end with one when we follow these 2 rules: RULES: Choose any number.
- If the number is even, divide by 2.
- If the number is odd, multiply by 3 and add 1. Repeat until the chain works its way down to ONE.
Talk about a buzz! 
What we appreciate about this activity is that everyone can get into it, and it involves a practice of multiplication and division that is fairly painless.
Some students got 
so excited (partly by the challenge, partly by the prize money!) that they stayed in at lunch and tried larger and larger numbers.
A group of 3 are still coming, day after day, chipping away at the problem.
Here are 2 significant insights:
- In order to end with ONE, every number must at some point go to a power of 2. (This lead to an investigation of binary numbers, in case they might hold the key to figuring this out)
- All the powers of 2 they’ve investigated are preceded by an ODD number that end in one or five! (Something I’ve never noticed before!)
They’re set on continuing this challenge – we’ll keep you posted!
Of course the powers of 2 descend to 1, but the numbers BEFORE that are odd, and can only be odd. And only every OTHER power of 2 works, and the odds show a pattern of 1, 5, 1, 5, 1, … in the ones place!
We’ll keep you updated!
ODD: POWER OF 2:
341 -> 1024
512
85 -> 256
128
21 -> 64
32
5 -> 16
8
1 -> 4
2
1