In order for students to begin learning multiplication, they will need a strong foundational grasp of addition facts. It is this strong understanding and mastery of addition facts and concepts that multiplication will build upon. The three major steps for learning/teaching multiplication facts are developing an understanding of the operation and related number relationships, developing efficient strategies for fact retrieval, and drilling for rapid and accurate recall of facts. The strategies for developing the concepts of multiplication include repeated addition, the commutative property of multiplication, using zero and one, doubles, five facts, and some special helping facts. Teaching these strategies will consist of using concrete experiences (real-world problems), pictorial materials, and some drilling practices with clearly defined parameters. To develop an understanding of the multiplication operation and related number relationships, real-world problems should be modeled using manipulatives. This in turn can lead to a well-developed understanding of mathematical representation. Students can solve multiplication problems using beans and cups, story boards, unifix cubes, arrays, and fact finder grids. Students will also benefit from making up their own real-life multiplication problems, modeling them, and solving. Students might resonate with multiplications problems that could encounter in the real world. For example: If there are 12 students in a class and each eats 3 pieces of pizza during a class party, how many pieces did they eat altogether? When students use manipulatives to solve problems, they are making powerful connections from concrete ideas (12 rows and 3 columns make 36) to abstract mathematical concepts (12 x 3 = 36). Efficient strategies for fact retrieval should also be developed which include equal groups, commutativity, using zero and one, doubles, and fives facts. Equal groups can be demonstrated using arrays.
