The concept of multiplication is described and illustrated using several different representational systems. A conceptual approach to teaching mathematics is compared with the procedural approach commonly found in the school curriculum. Four different methods of representing the multiplication process with numbers larger than ten are presented: combinations of coins, stories in which quantities are counted by grouping them, recording numbers in a way that is congruent with operations on quantities, and using multiplication as a procedure to solve problems involving estimations of weights. Each of these methods is related to the conventional algorithm for multiplying large numbers. Children's work is used to illustrate how they respond to each approach. (Author)