Just as memorizing all of the basic multiplication facts (small multiplication problems all the way up to 12 times 12) is key to multiplying larger numbers, learning the basic division facts plays a crucial role in learning to divide larger numbers. Students must learn the basic multiples that go into products all the way up to 144. (See the first link in the "Resources" section for a sample worksheet; a typical problem would look like "72/9.") A teacher might ask, "How many nines are in 72?" to help the student answer.
Many math students can find it difficult to transform word problems into equations and mathematical symbols. Introducing word problems fairly early into the skill cycle will help students progress more quickly, however. An example might be: "Farmer Smith has 45 cows, and he has nine barns. How many cows sleep in each barn?"
Because multiplication is the inverse of division, you can use multiplication to check your work. For the problem with Farmer Smith's cows, if you ended up with an answer of 6, you would multiply 6 by 9 to see whether you get back to the original number. Unfortunately, 6 times 9 equals 54, so the student would need to try again to come up with the correct answer (5).
Not all division problems come out with an even number, of course. That's where fractions come from. However, you can divide any integer by another; you'll just end up with a remainder. If you divide 61 by 8, for example, on top of the division box above the "6" in 61, you'll write a 7, because only 8 times 8 is larger than 61. Then you'll multiply 7 times 8 to get 56. Write 56 below the 61, and subtract. The difference between 61 and 56 becomes your remainder, so if you divide 61 by 8, you get 7 remainder 5, or 7 5/8.