There are mentions of 'methods' but no actual example of one. #3

I think it would be a great idea to explain exactly what a method is right after introducing Objects.
99.next looks like magic. But if you show that it's actually a method that can look like this:

class Integer
  def next
    self + 1
  end
end

... it removes some of the mystery. Plus there are opportunities to use methods in later examples, like n bottles of beer on the wall. Why start with 99? Pass whatever you want into a method. Even better, recursive method.