This is the primary way to teach to an elementary class, particularly if it is new material and it is as complex a subject as math. However, lecturing requires that a teacher be articulate; and since it does not encourage participation by the students, the teacher must know that the children are grasping the material. Furthermore, if a teacher uses the lecture method, he should prepare what he is going to say, and use notes to assure him that he stays on track.
Children should gain an appreciation for the relevancy of math in their daily lives rather than learning it through repetition and rote. Designing a project based on the material is one way to do that. As an example, most children are attracted by magic tricks, many of which are based on math. Let's say you're teaching multiplication. Write the numbers one through seven, then nine, on the blackboard, then ask one of your students to choose one. Unknown by your students, you have multiplied the chosen number by nine. Then ask the class to multiply the eight-digit number by the answer. Magically, the answer will be the number that they chose, in succession. For example, they choose three. Three times nine is 27; and when you multiply the number 12345679, the answer is 333333333.
Design math word problems for your class, then check how they arrived at that conclusion. The questions should be relevant to the interests of the class, while covering the intended material. For example, if you are teaching addition, you might ask them: "In round numbers, if Johnny had 254 baseball cards and was given 350 for his birthday, about how many would he have now?" Then ask each child his answer and how he arrived at it. Listen carefully for the methodology rather than the answer and correct him if he is on the wrong track.
This method is based on the premise that a student will learn new material if it is predicated on information assimilated in the past. The teacher should always frame the new information based on existing knowledge. An example of this method is demonstrated in the instruction of multiplication where the teacher always bases the new concepts by first mentioning the significance of adding one number to another, using material learned previously.