By the time students reach third grade, they should have the mathematical foundation to learn and master long-division problems that divide a two-digit number by a single-digit number. Memorization of multiplication tables will help them determine multiples as they tackle division. Third-graders learn that the quotient (answer to a division problem) sometimes has a remainder, or a quantity left over.

Draw a bracket for division on the board. Remind students that division is the opposite or inverse of multiplication. Label each part of a division problem in the appropriate place. As you do this, tell students that the number that is divided, called the dividend, goes under the bracket. The divisor, or the number the dividend is divided by, goes to the left of the bracket. The answer, called the quotient, goes on top of the bracket. Write a simple division problem, using the division sign bracket, next to the labeled example, such as 10 divided by five. As you write the numbers, tell students 10 is the dividend, and five is the divisor. The problem is read, “Ten divided by five is __.” Ask the class for the answer, or quotient. Write the correct answer and say, “Ten divided by five equals two.” Demonstrate that division is the inverse operation of multiplication by multiplying the quotient by the divisor. The students will see that the answer to an addition problem or product is the same as the dividend. Tell them this method works to check the answers of division problems.

Draw a fraction bar on the board. Tell students this is another way to write a division problem. Label the parts of the problem. Write the dividend on top of the fraction bar, the divisor under the fraction bar and the quotient after the equal sign. Write the same problem, 10 divided by five, on the board. Tell the students 10 is the dividend, and five is the divisor. Ask the class for the quotient. Write the correct answer after the equal sign and say, “Ten divided by five equals two.”

Draw a slanted line (/) on the board. Tell students this is a third way to write a division problem. Label the parts of the problem, with the dividend to the left of the slanted line, the divisor to the right of the slanted line and the quotient after the equal sign. Write “10/5 =” on the board. Tell students 10 is the dividend, and five is the divisor. Ask the class for the quotient. Write the correct answer after the equal sign and say, “Ten divided by five equals two.” (10/5 = 2)

Draw the division sign, ÷, on the board. Tell the class there is a fourth way to write a division problem. Label the parts of the problem with the dividend to the left of the division sign, the divisor to the right of the division sign and the quotient after the equal sign. Write “10 ÷ 5 =” on the board. Tell students the dividend is 10, and the divisor is five. Ask the class for the quotient. Write the quotient after the equal sign and say, “Ten divided by five equals two.” (10 ÷ 5 = 2)

Practice more division problems, using numbers that divide evenly and all four ways to write division problems. Increase the value of the two-digit dividends, such as 15, 16, 18, etc. Ask students to tell you the names of the parts of each division problem.

Show students several problems where the divisor does not divide evenly into the dividend. Tell them what is left over is called the remainder. They will learn other ways to write the remainder later, but for now they should write an uppercase “R” after the quotient, and copy the remainder after the “R”. Practice division problems using remainders.

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