Some explanations are easy. Cutting up the pie works for understanding fractions, and is tasty too.
But how do you explain to your child the practical meaning of dividing fractions by fractions? I struggled with this a couple of years ago until my math-savy mother-in-law loaned me two wonderful books:
Mathematics for Elementary Teachers offers different ways to explain the various components of elementary math, which is very useful for anyone teaching math to their child, or even to other people’s children. This book is wonderful because it helps you to explain, in practical terms, all the basics of math (logic, sets, probability, statistics, finance, geometry, matrices, exponentials, and calculus) with a bit of math history to boot.
Both of these books were written long before the idea of common core oozed from the depths, so they are heavily skewed towards teaching our children to actually be proficient in math.