Perhaps not one of the most usual home educating activities, but we introduced our kids to the Dungeons & Dragons role-playing world.
This is a sample of their first ever encounter, using the "Heroes of Hesiod - a Monster Slayers Adventure" module for kids (aged 6+ apparently, but pfft. Lexi was 6 & Eli 3 when we did this), which is available as a free pdf here.
You can see that Lexi really warms up into the idea as she plays, and Eli gets distracted ;)
Possibly surprising to some, but D&D involves a fair amount of maths, lots of reading, problem solving, lateral thinking, role-playing and characterisation. And you can actually play it without killing anything too ;)