- The Order Property (Commutative Property): Often, it is not evident to children that the order in which the numbers of a multiplication sentence are ordered does not impact the solution. For example, at first children are not aware that 5 groups of 9 and 9 groups of 5 are the same. One method that can be used to help children see this property is the use of arrays. (Van de Walle and Folk 130).
- The Role of Zero and One in Multiplication: Children often have trouble with the fact that anything multiplied by zero is equal to zero. It is, therefore, much more beneficial to help children realize this in the form of problem solving rather than telling them the rule. By solving a problem, such as asking “how many grams of fat there are in 7 servings of celery with 0 grams of fat in each serving” (Van De Walle and Folk 131), they are more likely to understand the idea of why the answer would be zero. Multiplying something by one also tends to cause some confusion. Children should not be explicitly given the rules for these instances but should, instead, be encouraged to come to this conclusion on their own.
Van de Walle, John, and Folk, Sandra. Elementary and Middle School Mathematics - Teaching Developmentally. Canadian ed. Pearson Education Canada, 2005.