HodgePodge - we home educate, and my lot are quite a bit older than yours.
Here's where the child-related money goes, out of the single family income:
Home Ed groups (usually about £5 per family per day, which covers hall hire and materials for particular activities - these are usually run as a co-op between the families. We do one or two of these per week)
Clothes (because the hand-me-downs disappear once the kindly hand-me-downers' children begin to have worn their clothes to shreds before they can be passed on. Charity shops also have less and less available as the children get bigger for the same reason. I get stuff off Ebay, but it's still not free any more)
Educational/play materials that is truly valuable to our family (and yes, lots of it is charity shop stuff, but it's still often necessary to buy things that make it possible for a child to pursue a passion)
Plastic crap from charity shops or Ebay (because: children)
Food
Season tickets to cool places (we limit this to 2 or 3 per year, and then cycle around - zoo one year; national trust the next year) but it still adds up
Cost of regular sports activities with other home edders (costs me £30 a week at the moment, sometimes £35)
Petrol (I drive about 100 miles a week just to facilitate their education and social life - slightly far flung community of HE friends)
Cost of one-off educational trips (this week it'll be £20; sometimes we go for weeks without needing to pay for anything)
Random meals out (about £70 a month) when I wasn't organised enough to pack lunch but we are out for the day
There is an excellent barter system around home edders - I got a free, almost new, bike for one of mine recently from a friend who just said "oh, pass their old one onto someone for free and we'll call it quits". And of course there's lots of skills sharing. But even pretty frugal home edding has financial implications :D