Productive Pieces: Exploring Multiplication on the Overhead

In working with teachers in the primary grades, there are several mathematical topics that are frequently labeled as trouble spots or difficult topics to teach. One of these is multiplication. How can the concept of multiplication be developed meaningfully? How much time should be spent on developmental work before attention shifts to drill of facts? What model for multiplication is most effective? Should more than one model be used with young children? There are no hard and fast answers to these questions, but we have found a series of lessons using an array model to interpret multiplication to be very successful.