In primary school, children are extensively taught how to divide in the abstract form while for us adult, we would simply reach for the calculator and voila! you have the answer. I pity the children.
Well, to teach division, I would take a 2 step approach. In fact, in any teaching of mathematics, these 2 approaches should be taken systematically.
Step 1: Concrete
*I would start simple. Give the child 4 marbles and 2 cups. Tell the child that he is supposed to SHARE the marbles between the 2 cups. Ask him to place the marbles into each cup one at a time in alternates.
*After this has been done, ask the child to tell you how many marbles are there in each cup. The answer would be 2 in each cup.
*Tell the child what they have done. The concept of SHARING is actually DIVISION.
*One point to highlight to the child would be that after SHARING/DIVIDING, the resultant or answer would be smaller than the number you start with.
*Let the child experience a few rounds of this hands-on or concrete activity until they get used to it.
** Extension - In this step you could give the child 5 marbles and ask him to SHARE them with 2 cups. What is left would be the REMAINDER. Explain the concept of remainder.
Step 2 : Pictorial
*For this step, the aim is to transfer the hands-on division onto paper. You can start by drawing 4 boxes and tell the child that they need to color these boxes. They need to share/divide the boxes into 2 colors.
*Give them 2 different color pencils and asked them to color one box at a time with one color.
*Ask them, how many boxes were in one color. The resultant and answer would give the pictorial representation of the answer.
*This step can be extended in may ways. It is up to your creativity. I am using boxes as it is similar to the over-used model approached. You can also used lines, circles, cartoon characters and what not in order to keep the interest of the child.
*Again, keep repeating this step until they are comfortable with it. Remember to introduce the concept of remainder.