Skateboard Size
I wore a 13 shoe by age 13. Kids feet grow quickly. I recommend starting on an 8.0 width for 5-7 year olds. 7-13 Years old becomes more case by case. If you kid is 10 with smaller feet. Maybe an 8.0 is perfect. But if you child is 10 and his dads feet are a 13. I would go 8.5.
My personal recommendation is 8.0 minimum width for all students. The wider base, especially with the little guys, helps students to succeed on ramps quickly. If you are taller you may want to start your kid out wider to have them grow into the board not out of it.