Distribute multiplication tables. These can be used for both multiplication and division. Teach your students that when a number from the left-most column is multiplied by a number from the highest row, the product is the number in the row and column of the two numbers being multiplied. But if your students begin with a number from the middle of the multiplication table, they can divide it by the number in the left-most column and the quotient will be the number at the top of the same column as the original number.
Reveal patterns to your students. For example, any number multiplied or divided by 10 will always have a last digit of zero, and any number multiplied or divided by five will have a last digit of five. Show them the nine rule. Have your students hold out all 10 fingers. If the problem is 9 x 4, have them put down their fourth finger. There are three fingers remaining on the left and six fingers on the right. The answer is 36. This works for all numbers one through nine.
Use flash cards. Flash cards are a great way for children to memorize products and quotients. Write the problem on one side of the card and the answer on the other. Now, students can look at problems, attempt to solve them, and turn the card over to determine if they got the correct answer.
Play games. Give students incentives to learn their multiplication and division tables, and using competition and rewards to do so always works. Games are great ways to get children excited about learning their tables.