Often, my son will be working on something that will spur a question about some other matter. We get totally sidetracked from our original lesson while we hop around the internet or through books following the rabbit trail of questions.
For example, today he was working on his copy work. He was copying a short paragraph that talked about Hot Springs, Arkansas. He asked, "How hot are the Hot Springs there?" So we researched that. (143 degrees F.)
Then he wondered, "What makes the Hot Springs hot?" ("Geologists believe that just the right combination of rock types and old faults exists here to permit water to perculate deep, where it is heated by surrounding rock.")
Then my daughter asked, "What's a fault?" So we talked a little bit about the Earth's crust, plates, etc.
That led us to a discussion of Earthquakes.
I think after Earthquakes, we all decided it was time for lunch. We had spent a good thirty minutes researching something we didn't even know interested us when we started our day. Both children asked if we could study more about Earthquakes next week.
It's really wonderful to have the time to indulge and encourage their curiosity.