When introducing the concept of multiplication, it is helpful for students if you tie it to something they already know. Students know addition, so first teach multiplication as repeated addition. Explain to students that 2 x 8 is like adding 8 two times, or the inverse, adding 2 eight times. For larger problems such as 7 x 6, help them to see that they can add 7 six times. If that is difficult for them, show them that you do not have to add all the sevens at once. Students can add 7 + 7 three different times, and then add the answers, 14 + 14 + 14. This is still the same as adding 7 six times.
Once students realize that multiplication is just repeated addition, the next logical step is teaching multiplication as skip counting. This works especially well for the 2, 5, and 10 times tables. If a student can easily skip count by a number, then they can quickly find the answer to a multiplication problem involving that number. For example the answer to 10 x 7 is simply found by skip counting by 10 seven times. Students get proficient at skip counting for many of the lower numbers, however it is much more difficult to skip count by some of the higher numbers, such as eight. Students should be taught that this strategy is just one that they can use, and they should be instructed only to use it with numbers that they are comfortable skip counting by. If they cannot comfortably skip count by eight, then they should use a different strategy for finding the answer to a problem with eight in it. The less comfortable they are with the skip counting, the more likely they are to make a mistake.
If a group of young children were given a pile of candy and told they had to share it equally, they would soon divide it amongst themselves in the easiest manner; "one for you, one for you, one for me." Students should be taught that this process of equal sharing is, in fact, division. When given a problem such as eight divided by two, lead students to look at this as eight things shared equally between two people. Stress to students that each "person" must receive the same amount for it to be divided equally. As students become more comfortable with this concept, help them to see that division is the opposite of multiplication.
Instruct students that if they cannot determine the answer to a problem using one of their strategies, they can always draw a picture to find the answer. If they are multiplying, they should draw what the problem says. For example 5 x 5 is five groups of five things. If they draw stars, then they should draw five groups of five stars each. They can then count all the stars they drew and get the answer of 25. Advise students to draw simple things, such as circles, stars or squares. Also remind them to draw carefully so they can easily count all the items at the end to get their answer. If a student is trying to find the answer to a division problem, such as 27 divided by three, they should first draw the total number of items in the problem. After drawing 27 of whatever item they choose, they should then circle the items in groups of three. They can then count up how many groups of three they circled to get the answer of nine. Drawing pictures is a strategy that students should be taught explicitly. However they should also be taught that this strategy has lots of room for error and should not be the preferred strategy they should employ.