Division may not be everyone's favorite math activity, but teaching the process to children isn’t difficult when you begin with concrete examples and manipulatives. These help the students understand the concept behind the steps -- that division uses repeated subtraction to divide a whole into equal parts.
Setting the Stage
While you are introducing the concept of division to children, spend some time reinforcing their multiplication skills, keeping in mind that division is simply the opposite operation of a skill they have already mastered. A child certainly can learn to divide without having memorized all of the multiplication tables, but knowing those makes division much less stressful. Introduce the idea of division with children’s literature that involves dividing, such as “One Hundred Hungry Ants” by Elinor Pinczes and Bonnie MacKain, “The Great Divide” by Dayle Ann Dodds and Tracy Mitchell or Stuart Murphy and George Ulrich’s “Divide and Ride.” Next, have them create a KTWL chart to describe what they already know about division, what they think they know about it, what they want to learn and, for the end of the unit, a wrap-up of what they've learned.
Using Their Hands
Next, introduce hands-on tasks that divide real items into sets. Manipulatives help engage children's attention, and they make retention of knowledge simpler, particularly for those children who learn best through kinesthetic activities. Beads sorted into a muffin tin can introduce division by two, three, four, five or six, while you can use math cubes or other manipulatives for division by larger numbers. Begin by helping your child divide the manipulatives by two or three, starting with a number of beads or cubes that will divide evenly. When she has mastered even division by numbers up to nine, introduce the idea of remainders by starting with a set of manipulatives that cannot be divided evenly into the number of sets you are practicing. For example, give your child 11 beads and ask her to sort them into two spaces on the muffin tin, reminding her that each set should have the same number of beads. When she gets to the one left over, talk about remainders.
Putting It on Paper
Combine the hands-on manipulatives with pencil-and-paper tasks by starting with problems that include pictures your child can divide into groups with circles. Introduce both ways to write division problems -- horizontally and in the “garage” style. This format places the divisor to the left of a half-box, with the dividend underneath; the short vertical line is the "garage door," and the space under the horizontal line is the garage itself. Continue to use pictures or manipulatives to make the connection with very simple problems, such as 6/3 or 10/2. At this point, stick to division problems that are the reverse of multiplication tables facts, and help your child see the relationship -- that multiplication is combining multiple groups of the same size to make a whole -- whereas division is separating the whole into multiple groups of the same size. One way to do this is by having the child draw pictures or dots for the dividend -- the whole number -- and then circle sets equal in number to the divisor. For example, for 10/2, the child might draw 10 stars and then make circles around every two stars, to make a total of five sets. Reinforce the connection to multiplication by pointing out that the number of sets times the number in each equals the dividend.
Remembering the Steps
Now that your child understands what division is, he’s ready for the standard forms of the problems. For many children, the “garage” format is easier to master first, as it places all the numbers together visually. Have the child begin by checking to see if the divisor -- or the number you divide by -- is smaller than the first digit in the dividend, or the number being divided. If it is, let him put a small tick mark above that digit on the garage floor to mark where he should write his first answer. Help him work through the steps of a division problem: divide, multiply the answer times the divisor, subtract the multiplication result from the dividend, check to be sure the difference is smaller than the divisor and bring down the next digit. Teach him to remember the steps by using the first letters of the mnemonic sentence, “Drive My Super Cool Buggy,” to remind him of each step in order: divide, multiply, subtract, check and then bring down.
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