The first step to teaching the above is strengthening the small muscles in the hands and wrists that are used in handwriting. This process is often referred to as building fine motor skills. You can encourage fine motor development by having your child use art supplies like crayons, paints, markers, glue and scissors.
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.
By the time your child is ready for kindergarten or school, they should be able to recognize their own name and other simple written words. The sounds of each letter of the alphabet should be familiar to your child, and they should understand the principle of reading from left to right, which way to hold a book, and possibly even be starting to read three and four-letter words.
Look for games and puzzles that are part of an adaptive learning program. This means that the online games are well-thought out and match the same set of skills that are being taught in the third grade curriculum. The program is structured toward each individual student and fills in the gaps where the child is struggling.