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.
With adaptive learning, the programs won't move on to the next level until your child has a firm grasp on the current material. The online games will be a wonderful way for your child to catch up on basic arithmetic concepts and be comfortable using them across applications.
Just because your child will be playing fun online games doesn't mean the same value won't be there. Create a comfortable study zone. Turn off outside distractions such as cell phones, radios or TVs.
Textbooks, instruction manuals, and lesson plans are the basic foundation for any homeschooling program. Homeschooling does not have to be limited to the parents understanding of the material that the student is learning. Home school information and education should instead be based on the student's individual learning style and the materials that must be taught based on the students grade level and educational needs.