So you've learned to juggle 3 or 4 balls, but 5 is way too difficult and you've run out of tricks to learn. Now what? It's math to the rescue. After seeing that juggling patterns are functions on the integers with certain properties, we encode them as sequences (known as Site Swap notation). This gives us many new juggling patterns to learn. It also opens up all kinds of questions, such as: What sequences constitute juggling patterns? How can one generate all the juggling sequences? How many juggling sequences are there, say, of length $l$ using $b$ balls? (Some of these questions will be answered.)