I spent a solid 6 months teaching my 8 year old (now 9) fractions in the fall. We did ratios, proportions, addition, subtraction, multiplication and division, then common fractions to decimals and back again. We spent forever on fractions- learning when you can cross cancel, when you can simplify, when to use LCM or GCD to find common denominators or simplify. THEN we started AoPS Pre-Algebra in January. Fractions are really the only thing that I have "drilled and killed" into his head. I wanted automaticity so we could move on to the harder "what if" problems in AoPS.
I was recently telling a middle school math teacher about how I did it and she was shocked. "Why did you spend so much time on fractions? We do that in just a few weeks!" She could not believe that I "wasted" all that time. Yet, like the author pointed out, fractions are the base of everything that comes next. If you can't understand fractions, you can't really move on with any long-term success. I don't know why teachers don't spend more time on this!
