I love using Art of Problem Solving’s “Introduction to Number Theory” book as a way to help my younger son build number sense. We went through the book together a few years ago and he’s going through it on his own now.

Yesterday he worked on a section discussing perfect, deficient, and abundant numbers. These concepts are something that a kid can understand, but also come into play in unsolved problems in number theory. For a 4th grader I think the fun is in understanding the new ideas rather than their connection to the Riemann hypothesis: