The mathematical expression 3 5 represents three groups with five items in each group. To find the product, students can build a model of three groups with five items in each group as shown below.
Students can also use repeated addition to find the product. They can add 3 five times: 3 + 3 + 3 + 3 + 3 = 15.
Remember that multiplication undoes division and division undoes multiplication. In other words, since 3 5 = 15, then 15 5 = 3. Since division and multiplication are inverse operations, students can use models similar to the models used in multiplication, to divide. In the expression 15 3, you begin with fifteen items and want to know how many groups you can make with three items in each group. The answer, or quotient, is the number of groups.
15 3 = 5
Since multiplication is a form of repeated addition, division is a form of repeated subtraction. For example, 15 3 asks you to repeatedly subtract 3 from 15 until you reach zero: c15 - 3 = 12 - 3 = 9 - 3 = 6 - 3 = 3 - 3 = 0. This process required 3 to be subtracted 5 consecutive times, so again we see that
As students master their basic division facts, the need will arise for students to learn how to divide larger dividends. It would be prudent to begin with 2-digit dividends by 1-digit divisor to introduce the long division algorithm. Although students may know the quotient for the problem, the need to carefully learn the division algorithm will allow students to quickly move to larger numbers. Look at the division problem below.
It is sometimes very helpful if you think of division as multiplication. The above division problem can be written as
When beginning the long division algorithm, realize that you are asking questions such as "what number times 6 is less than or equal to 300?" Remember that the 3 is in the hundreds place. Since the answer is 5 tens, or 50, a 5 can be written above the 0 in the tens place as shown below. Since