However, I think I'll start with a list of activities that are not computer based. I'll be the first to admit that I'm a little biased toward hands-on, not-virtual learning, especially for the primary grades; children's bodies really need to be involved in the learning process, especially math.
Also, although my kid has some computer skills, she is basically raising herself as a luddite, which is fine with me for now. She's never been drawn to the computer, even when I specifically show her something I think is fun or cool. So, many of the games and interactives listed in the online category, below, are places that I go to get activity ideas to adapt for her off-line lessons or to grow my own math understanding or just for inspiration.
I don't know where we'd be this year without the endless Shut the Box tournaments of last year. I attribute at least half her mental addition skills to rolling two dice (which can make up to 12) and finding different ways to make the rolled number.
I attribute the other half of my daughter's mental addition ability to UNO. It's a classic game that we played speed style all last year. And, at the end, the winner got to add up all the points she won from her
Peggy Kaye's book Games for Math has LOTS of easy and inexpensive ideas including Nine Men's Morris which is sort of like a more complex and moveable tic tac toe (strategy, logic).
Variations on "sort and count the change jar" along with "save and spend" from about the age of five means that now, at age seven, the child is a whiz at money math (also known as adding and subtracting 10s, 100s and 1000s).
And, of course, The Game That is Worth 1000 Worksheets from the Let's Play Math Blog -- for the littles all the way through high school. This fall we used a version that was a combination of sums and differences.
ONLINE GAMES & INTERACTIVES (NOT JUST NUMBERS)
Some of these are for you, lots for them, and some for the whole family (like Scale of the Universe 2 and the triangle interactive!!)
National Library of Virtual Manipulatives: Truly a class act and a challenge for all ages.
Math Pickle: This link takes you to a large library of interesting videos and ideas organized by grade level.
Kaleidograph: I first found this toy and played with it online, and then I bought the real thing for Christmas. Both the online and hands-on versions are great but, no surprise, I find more meaning in the actual toy.
From my childhood memory bank, a classic Sesame Street clip with a lovely song: Two Little Girls and Their Little Doll House. My adult eyes immediately saw one-to-one correspondence but my little girl heart remembered something different.
Scale of the Universe 2: I have no words for this interactive graphic other than just GO. You can turn off the music if you want.
I've included this link to Planet Seed/Math Puzzles for Kids because I don't want to forget about it. It was on a long list of bookmarks already. Puzzle topics include combinatorics, algebraic thinking, topology, probability, etc.
Games from Freudenthal Institute look great, and they even have a star interactive!
Make your own isometric dot graph paper here. These and the other dot graph paper you can print out are fun to leave around the house so kids can make designs whenever the mood strikes.
Math cats! Need I say more?
I personally love Symmetry Artist from Math is Fun and my daughter actually liked playing with it for a while. It's a great way to really experience the differences between line and rotation symmetries and you can print out the designs you make at the end.
And, you really cannot miss this triangle interactive from the Triangulation blog. Truly. Run, don't walk.
To close it out, here is a lovely and thought provoking classic Sesame Street animation with music by Phillip Glass called The Geometry of Circles.