We can add and multiply numbers, but there are other things we can add and multiply, too! For example, we say that "odd + odd = even". What were we exactly adding here? Are there other categories of numbers other than odd and even that we can add and multiply together? Join us on this journey into an entirely new ways of thinking about addition and multiplication which leads us to draw triangles, squares, and stars on clocks, discover divisibility rules for numbers, know what day of the week it will be in exactly one million days, and figure out the last digit of 9 to the power of 100.