This was the result (photo).
They hand-calculated about 1/2 of the numbers seen on this wall. This was great practice in multiple-digit addition and multiplication. Once they got to the higher numbers Skye showed him how to calculate exponents using a scientific calculator.
It didn't take him long to first notice how quickly numbers grow when you move from one base to another (somewhere around 3^6) and then the interesting relationships between base 2, base 4, base 8 and base 16.
They took a short detour into computer science to discuss how computers are based on a base 2 number system.
Fun!
For base-9 digits, Skye showed Austin that he can reduce every solution to 9, by adding up the digits and reducing them until only a single digit remains. For example, the solution to 9^9 is 387,420,489. 3+8+7+4+2+0+4+8+9 = 45; 4+5 = 9! This way, Austin can double-check to see if he has calculated the correct result.
Carla showed Austin that he can do the same for base-3 digits, and the final result will be 3, 6 or 9 (all multiples of 3).
Austin is enjoying exponents so much, that he has been teaching the concept to Aidan. Aidan is a good sport about it and is enjoying finding patterns on the grid.
I overheard Austin encouraging Aidan at one point. I hadn't heard what Aidan said, but I heard Austin say, "You ARE smart! You found patterns that even I hadn't noticed!" This teaching experience has been good for their relationship. In fact, I've noticed that they are getting along better, overall, these days. Hope it's not only because Santa's watching ;)
