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Well, numbertheory and arithmetic stuff with manipulatives is always fun. Then there's dominoes, dice games, dottodot pictures, Sudoku games, colorbynumber worksheets, doing fractions with baking. And then there's the less obviously mathematical stuff like checkers, chess, backgammon, tangrams, mighty minds, LEGOs, reading a clock, puzzles, mazes, etc.
And if she wants something more traditionallyacademic you could always work on mathematical reasoning or a math workbook (Kumon are good) with her. 
Well, numbertheory and arithmetic stuff with manipulatives is always fun. Then there's dominoes, dice games, dottodot pictures, Sudoku games, colorbynumber worksheets, doing fractions with baking. And then there's the less obviously mathematical stuff like checkers, chess, backgammon, tangrams, mighty minds, LEGOs, reading a clock, puzzles, mazes, etc.
And if she wants something more traditionallyacademic you could always work on mathematical reasoning or a math workbook (Kumon are good) with her. 
Thanks for the AoPS link! DD is going to love that.
I'm a big fan of the Montessori math methods. It's not because the manipulatives are so fun, I swear. You can easily gather secondhand or make many of these without it costing so much $. DS used to have a sticker Sudoku book when he was littler that was a way to do it with logic and not numbers. 
You might check out books like The Number Devil and Penrose the Mathematical Cat. They will cover concepts she will learn in school, but also concepts they never seem to get to in school more number theory and other discrete math topics that get shortchanged in current curricula.

Some "mathy" board games that my 5 year old enjoys are:
1. Monopoly Jr. 2. Parcheesi (uses two dice, great for addition and memorizing "math facts"). 3. Money Bags (teaches American coins, skip counting by 5s, 10s,25s, making change up to a dollar). The spinner will sometimes yield a result that says you cannot use a certain coin to collect your change, so it forces you to add in interesting ways. It's a very short board game. 4. Dino Math Tracks (teaches place value by 1s, 10s, 100s and 1000s). Right now, we are playing a simplified version of the game and omitting 1000s, for my 5 year old's sake. In this version, the child rolls 3 dice and arranges them in any way he wants to make a number, then breaks it down into 1s, 10s and 100s by marching his dinosaurs down various paths. I don't have workbook recs, because my 5 year old is not fond of them. But the games we play are excellent for teaching and reinforcing math concepts, particularly for the handson child. HTH. 
She has less patience for the games, and wants to do problems versus learn by playing games type of stuff. 
Oh, what about math + music? Are there any songs that have math in them?
Dd loves singing and listening to music. We have the DVD of Schoolhouse Rock, which I'm going to dig out and I know it has math songs in it that she might really like. But I was wondering if there were other songs about math? 
If she really gets into it, this really makes me worried about K, because she's already reading and she's going be 6 by the time she enters into school. If she's going to walk in there with more than a basic understanding of math, I might really have to push for a grade skip for her. 
i am soooooooo excited. this just worked out for me.
i have a 3rd grader and 6th grader teaching my first grade dd math. yesterday evening they were sitting in the park with his 3rd grade gate math book and going over problems with my dd. i couldnt have asked for a better teacher. teachers. so much so that my dd doesnt really want to study math with me. she loves telling me what she has learnt. the 3rd grader is doing algebra with her and the 6th grader is teaching her the 9 times table using his fingers in a pattern which i want to learn too as its so cool. 
If she's covered K math and K reading by the fall, I'd encourage you to look at a mixed grade classroom if not acceleration. My personal experience with entering grades K and 1 with all the academic skills mastered was that I was pretty much on my own for 2 years. 
From what I can tell, she's at about a 2nd grade reading level now.
I'm just going to have to wait and see what happens. Her social anxiety might preclude a grade skip, but I will do what I can and definitely work with the teacher. She does have an IEP in place for the selective mutism, but I'd like to see if I can't broaden it somehow to include gifted enrichment as well. 
Mom to a teenager and a middle schooler.
She'll only be a month younger than the potential youngest according to the cutoff?
Seriously, I think you should talk to whoever at the school/district about a skip. IMO, her social anxiety may be alleviated by finding true peers, which she may be more likely to find in an older cohort. 

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