Teaching Long Division to Kids: Step-by-Step Instructions
Long division is one of the most challenging math concepts that elementary school students encounter. However, if you teach it step-by-step, write down each step as you do it and require them to do the same when they work problems, they will pick it up faster. Just follow the process below.
Long Division Step-by-Step
Before You Begin
There are several things that you should do before you begin teaching long division:
1. Students need to know the multiplication tables up to 9 x 9 and basic division before they begin long division. Practice with flashcards, songs and games until your students know them inside out and upside down.
2. Find a way to help the kids remember the steps they need to follow (divide, multiple, subtract and bring down). For auditory - and sometimes kinesthetic - learners, you may want to use music; you can find several videos on YouTube of songs that other teachers have used. Alternatively, a mnemonic phrase can help, such as Does Max Sell Brains? If you want to add an R for the Remainder, you might use something like Dead Mice Stink Bad - Run! To help visual learners, write the phrase at the top of the board and refer to first letter of each word as you use the step it represents.
3. Let the children begin by doing their work on graph paper. This will help them line up the columns properly and put the right number in the right place as they work.
4. Begin with short simple problems - 2-digit dividends with 1-digit divisors and no remainder. After the students can easily do those, increase the dividend by one digit at a time until they can readily do problems with 4-digit dividends and a remainder. Then you can add one digit at a time to the divisor. To present the step-by-step instruction below, a 4-digit dividend with a 1-digit divisor and a remainder has been used.
Because of the difficulty of reproducing the division symbol that is the tool for working long division - the only division symbol without a name (a close parenthesis attached to a line at the top that is called a vinculum), it will be referred to only when you need to write the problem in that format.
To visually aid students' thinking, create two columns on the board - a Thinking Column and a Work Column. Have the students write out their thinking process on the left side and show their work on the right side.
The seven steps as presented here are in the 'bare-bone' words that you would speak to the class as you solve the problem on the board; you may need to expand the explanations for your class. The notes to you are italicized in parentheses. Begin by writing your mnemonic phrase at the top of the board and explain to the students that the words are going to help them remember what to do next.
1. Class, today we're going to learn how to do long division. It'll easy because we're going to write down our thinking so you can follow the same steps at home. We're going to use a Thinking Column on the left and a Work Column on the right.
2. We'll start by writing the problem in the Work Column: 1675 ÷ 7, where the dividend, 1675, is divided by the divisor, 7. (Use the close parenthesis and vinculum format.)
3. (Point to the D-word in your mnemonic phrase.) Our first step is to divide the first digit of the dividend (1) by the divisor (7). We'll write that division problem over here, in the Thinking Column: 1 ÷ 7 = 0. We'll write the 0 above the 1 of the dividend. The numbers on this line are the quotient.
4. (Point to the M-word in your mnemonic phrase.) Next, we multiply 7 x 0. (Point to the 7 in the divisor and the 0 in the quotient.) In the Thinking Column, just below the 1 ÷ 7 = 0, we'll write 7 x 0 = 0. (Put the 7 right under the 7 in the line above, and the 0 below the 0.) We will copy this answer, 0, right underneath the 1 in the dividend. (Draw an arrow from the 0 in the Thinking Column to the spot where you will copy it.)
5. (Point to the S-word in your phrase.) Next we subtract. Because 1 - 0 is 1, we draw the difference line and write 1 just below the 0.
6. (Point to the B-word in your phrase.) The next step is to bring down the next number in the dividend, 6. (Draw a down-arrow from the 6 to its new spot.)
7. Now we start all over again. (Point to the D-word in your phrase.) We'll divide 16 by the divisor, 7. We'll write that division problem over here in the Thinking Column: 16 ÷ 7 = 2. (Write it to the far left, as you did the first division sentence.) We'll write the 2 above the next digit of the dividend, the same number that we just brought down.
Repeat steps 4-7. You will have a remainder. Ask them what to do next, because you don't have any more numbers to bring down. If you have a mnemonic phrase that has a word for R (which stands for remainder), point to that here. Explain that the leftover number is called the remainder, so the answer to your problem is 239 Remainder 2.
Now that the kids have seen the problem done step-by-step, do another, but let them tell you what to do for each step. A few problems like that, and they should be ready to tackle some on their own. When they are ready, you can gradually eliminate using the Thinking Column and allow them to do that mentally.
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