66: Go Fish with Primes

3 William Carey, on a Dan Meyer post:

We play Prime fish with the sixth and seventh graders. You need a special deck of cards, but it’s an easy deck to make (edited, - ed.):

Ten cards with a "2" on them (or two fish)
Ten cards with a "3" on them (or three squid)
Eight cards with a "5" on them (or five eels)
Five cards with a "7" on them (or seven sea-slugs)
Two cards with a "11" on them (or eleven shrimp)

Each player draws four cards. They multiply their hand together, and announce only the product (!) to the group. They then play go-fish.

It’s fun to watch the kids debate whether there’s a strategy to the game. It’s more fun to watch them work out the strategy once they decide that there is a strategy. 

What's the strategy?

8: More Exponents

From Dan Meyer (via email):

Which is bigger: $60^{63}$ or $63^{60}$?


The beauty of this problem is that both sides are beyond the capability of a TI-84 so a reduction of some kind is called for. wolframalpha.com has no difficulty but the answer is startling.


Find Dan on Twitter @ddmeyer, too.

7: Exponents.

What's bigger?  $2^{100} or {100}^2$ ?

@MathCurmudgeon Can I suggest one? What's bigger, 2^100 or 100^2?
— Max Goldstein (@dethornSTEM) January 21, 2014