I think you could also have multiple pipe cleaners coming from one number and students have to show multiple ways to add numbers to get to that number. Counting with pipe cleaners and beads. Great for fine motor development too.
Two preschool math activities using Duplo Legos. These are great for younger brother while the older ones do their schoolwork! Identify the next number in a series of numbers up to ten. Pre-school age 3 and 4
If You Give a Mouse A Cookie Math & Counting Activities from Still Playing School. This book incorporates math well. It isn't necessarily a math book, but can be very engaging for students. Students can learn addition and counting within this lesson.