Helen has flat out refused to log on to the Rock Stars Times Tables site her school has provided all students access to, because — going by the demonstration and explanation of it they were given in assembly — she thinks it is about high scores and competition. This is of course tricky, because some children like the competitive element.
I'm a bit worried that the school is going to obsess over times tables (there's a new National Year 4 test) and that that may dent student enthusiasm. Helen tells me that some children in her class already think mathematics is "the worst thing", which suggests to me they are being asked to do too much — or the wrong things — too early. (I do realise this is a lot harder to avoid with thirty children than one; and it's not the school's fault the government is determined to cram specific things into everyone from as early an age as possible, even when it's clearly counterproductive.)
In general I think games are a fantastic way to learn mathematics — and, even more importantly, mathematical thinking. I'm in agreement with Sunil Singh, who suggests "a holy trinity of number, graph and game" at this age, and quotes Paul Lockhart's A Mathematicians Lament:
Play games! Teach them Chess and Go, Hex and Backgammon, Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary. Don’t worry about notation and technique, help them to become active and creative mathematical thinkers.
Christmas and birthday brought some new games. Shut the Box is a simple addition game with a tiny bit of strategy, too easy now to challenge Helen much. IQ Fit is a 3D shape placement game. Rush Hour is a block movement game (we also have this as an app). And Sushi Go! was such a huge hit we also got the construct-your-own game Sushi Go Party!. (We also got a set of Quirkle cubes, but haven't done much with them yet. And I really should teach Helen chess.)
On the app front, Piko's Blocks is a three-dimensional visualisation game involving rotating and placing or removing blocks. Jeffrey Weeks has published two free apps Helen really likes. I've mentioned the Kaleidopaint drawing app before — this allows free drawing with the imposition of one of the seventeen plane symmetries. The other is Torus Games, a bundle of common games — Apples, tic-tac-toe, etc. — played on a torus instead of a bounded board. Both of these are likely to appeal to adults.
Then there are the arithmetic games: the DragonBox Numbers and Algebra games are fun, but I like the recently found Sumaze Primary (free) which ostensibily teaches elementary arithmetic but is actually about planning ahead and structuring sequences of operations, so ideal preparation for computer programming (there's also a secondary school version, which I enjoyed doing myself). And, on the subject of programming, Camilla has taken Helen to her first Scratch course, in the council library.
I've also done a tiny bit of "formal" mathematics instruction, after Helen asked about the book I was reading, Mathematics and its History and on a whim I decided to try explaining the Kuratowski Theorem. I haven't actually stated that yet, but we've got as far as drawing representations of the graphs Kₘ and Kₘ,ₙ for small m and n (tip: draw the vertices in a different colour to the edges, both for clear logical separation and to avoid confusion with intersecting edges), understanding what it means for a graph to be planar, and getting some feel for the sub-graph relationship, so we're almost there.
Note: someone recommended another 3D visualisation app, Perspecto, and Helen's enjoying that so far.