We read children's books about how math is useful, how number systems were invented, and we made our own abacus and calculated with it. To show the meaning of equations we used colored snap-together cubes, and we played around with building blocks and pattern block puzzles. The critical aspect of motivating Emily was to make learning basic arithmetic fun and relevant to her life. Once she caught on to the basics, her confidence and skill improved dramatically. Now Emily is proud to be working arithmetic problems two grade levels above her counterparts in public school, and she likes math.
Grades typically have a bad connotation amongst homeschoolers.
Homeschoolers don't forge ahead until the child masters whatever he's learning, so grades are not really necessary. Then they lavishly adorn their papers with stickers and hang them up for all to see. We may not have official grades, but we do have review tests to help us find out how much we've learned. Because I create my own curriculum from a variety of sources, it helps us integrate what we've learned to pull together the most significant information to be all in one place. The test serves as a review as well as a record of our sources and coverage.