Math is a tool. A way of studying and understanding the world. The science of numbers and operations. A logical method for making complex things simple. A way to uncover the beauty of nature. A serious part of education that is essential for kids to master to be literate in our 21st century.
Sure. It is all those things. But, it is also imaginative. It doesn't have to be connected to anything. It can just be fun. A sense of play. It can be fictional. Schools tend to treat it as a non-fiction subject that is directly related to the real world, and you must master it because then you won't understand the world and if you don't understand how the world works then you will be missing a key indgredient in the recipe of life..... (why don't we say the same thing about painting?).
I remember coming across a great quote in The Mathematicians Lament by Paul Lockhart (if you haven't read, please do, you will not disappointed and it's only 25 pages!) when I was just in teachers college, and I jotted it down and stuck to the wall in my classroom, where it has been ever since:
I love this conception of math, and I try to include it in my math instruction whenever possible. Of course we spend the majority of our time on real-life things, like graphing results from surveys, measuring land to build a house, or finding the area to tile a kitchen floor (because those will be incredibly useful skills to have when they grow up, I re-tile my kitchen floor at least once a month, and I am constantly building houses, in random places and I just leave them there, I have no idea if anyone actually uses them or not, and as for surveys, I hand them out every weekend and analyze the data in my free time).
Sometimes, I like to pose a problem that has nothing to do with anything, has no real world value or application, but is purely intellectual, interesting, and downright puzzling. The kind of problem that leaves you scratching your head, but unable to look away. There is some great thinking in those types of puzzles. For an awesome treasure trove of such problems and questions see 101qs.
Math doesn't have to be about the real world. It can be an imaginative world, one of your own creation, like any fictional writing, but you are bound to rules and laws. Within those rules and laws, you can create or make anything that you wish. The book Flatland is a beautiful thought experiment of mathematical wonderfulness, but it is also a sharp criticism of the political climate of Victorian England. Mathematical thinking can be artistic.
When I asked my kids (and some partners down in Yokohama who we have regular math problem solving sessions with on skype) how many hot dogs could you stack one on top of another to go from the ground to the top of the Tokyo Sky Tree, I didn't care that the answer would have no value for them in their lives. It is a thought experiment, a way of playing with math in your head, testing yourself and what you know, making assumptions, understanding what information is relevant, choosing the next direction you will take on your own and not just blindly following a procedure or an algorithm, checking assumptions, seeing the multiplicity of mathematical ideas, etc.
My kids enjoy these types of questions (or at least they like posing them, we are working on the solving part!), and after the skype session was over, sitting in the cafeteria eating our lunch, we came up with more. How many grains of rice would it take to fill this cup? How many oranges could fit in this room? How many people could stand in this room shoulder to shoulder?
Play with it.
Leave the serious study to serious things, like painting and sculpting.