"Students truly 'get' math when they see it applied in real-life ways they care about—in other words, when they see math as a tool they need and want. This motivation is not promoted in word problems about the number of books or the number of students in a classroom. However, when you give small groups of students 67 toothpicks and some index cards and then ask them to model the pizza party seating problem described earlier, they’ll build the experiential knowledge of a real-world situation where remainders are not helpful. When they consider dividing leftover pieces of pizza into parts, they will see that fractions or decimals are a valuable tool to make the pizza sharing process fair, whereas a 'remainder' would imply that perfectly good pieces of pizza sit in the box because there is no way to divide them."
The above excerpt is taken from the pages of Learning to Love Math, by Judy Willis. Chapter 1. Reversing Math Negativity with an Attitude Makeover can be read online here. This is one of the most important and impressive articles I’ve seen on math education in a very long time!