I purposefully didn't mention the line-crossing algorithm, because I think (like other nearby commenters) that it's more of a mysterious trick than a visualizat

I purposefully didn't mention the line-crossing algorithm, because I think (like other nearby commenters) that it's more of a mysterious trick than a visualization that promotes deeper understanding. Maybe as they get older, it would be fun to present the line-crossing algorithm, and then ask them if they can explain why it works. My 7-year-old would not be able to do this, but she can easily relate to the multiplication-by-area analogy and its generalizations.