Will still has clumsy penmanship, so we taped together pieces of whopping one-inch graph paper for her chart. Then she wrote the numbers, with one digit per square, and I labeled them in small letters:
We knew the first few powers of ten, of course, but it wasn't long before we resorted to using the Really Big Number Machine for help (Willow often plays on this Math Cats site, by the way--she LOVES their online games).
There's a lot of great patterning that goes in writing the powers of ten:
- Using the graph paper, it's easy to see how each power of ten increases the number by one digit.
- When the numbers get bigger, the pattern of putting a comma after every three digits becomes clear.
- After a few iterations, you notice that the progression of names goes "one, ten, hundred." One quintillion becomes one hundred quintillion becomes one thousand quintillion becomes one sextillion.
- If you know your ancient languages OR your prefixes, you can predict the next name. BIllion becomes TRIllion becomes QUADrillion becomes QUINTillion becomes SEXtillion, etc.
Will's very intuitive about patterns, so she soaks this stuff right up. Except for that last one, of course--the ability to predict the next name is a treat just for nerdy old me!
One thing that I wish that I could do, to go along with this activity, is to have a concrete visualization of each number, ideally using Base Ten blocks. Except...I kind of doubt that even the warehouse of the factory that makes Base Ten blocks has a concrete visualization of one hundred sextillion, the largest number that Willow has written on her chart so far, on its shelves. One of my long-term projects is to make (or, rather, have my graphic designer partner and co-parent make) digital Base Ten blocks that we can use with Adobe Illustrator.
I still don't know if I'd get to one hundred sextillion that way, but one million is probably do-able in poster-size, right?