Kitten and I covered triangular numbers a couple months ago in our Competition Math for Middle School book, but I think it’s time to revisit the topic. I like the method James Tanton gives in this new video:
How Do You Count Infinity?
Tanton continues to play with triangular numbers in the next video, which is probably too abstract for Kitten, but I enjoyed it. The triangular numbers are countably infinite, as are the square numbers. But if you look at it another way…
Denise Gaskins' Let's Play Math 
Thanks for these videos! I’m always looking for ways to make math fun and interesting. 🙂