Since 3rd grade math relies on the concepts that were learned during kindergarten, first and second grades, don't be afraid to start your child at a lower level.
Book knowledge is the ability to recognize book formats and purpose. Early readers learn how to hold a book properly, to read English from left to right, how pictures supplement the story, and that books have basic components such as a front and back, spine, pages, covers, and more. Children automatically learn these things at a conceptual level long before they understand the purpose of each component.
When you feel your child is physically ready to write, have your child use a stick or finger to draw in sand, rice, pudding, shaving cream, paint or oatmeal. Make simple lines and shapes and ask your child to copy them.
Many online math games are designed purely for entertainment and won't do much in terms of teaching your child. While these games can be fun and engaging for third graders, you want to choose games that will practice the skills being taught in school.