Children learn best when they involve multiple senses. By giving them objects to manipulate they not only see how the amounts of things interact and can watch as piles grow bigger or smaller but they are physically involved in making those changes happen. Blocks, coins and even packaged food items make great teaching tools that children can use to figure out the answers to math problems and actually see and feel how the concepts of addition, subtraction and multiplication work.
Moving your body gets your brain engaged. Teaching math by letting children get up and be the things being added, the line segments being drawn or the shapes they are learning about make the activities fun and memorable. Students can even create their own groups or act as the director for the other students to make their own word problems.
Turn math problems into a game makes it fun to learn and practice the concepts. Set up several points in the room and have a starting point. Group the children and have them solve problems to get to a specific point. They should all have different points so they have to figure it out to get to the right one. You can have directions be simple like "go three feet to the left" or complicated like "divide 27 by 3 and go that many feet to the right. You can also have students mark their paths with painters tape so you can check their work.
In order to teach something to someone else you must have a full understanding of that thing yourself. Once you have taught the concept, have groups of students come up with a new way to explain it and create some examples. After they have taught the class the concept, have them come up with a quiz for the rest of the students to take. Students can use music, pictures, toys or anything else they can come up with as creative ways to explain the mathematical methods to the rest of the class.