Division Tutoring Tips: How To Help Students Succeed

How to Tutor Division Successfully

Multiple Methods

When students struggle with the multiple steps of long division (divide, multiply, subtract and bring down), they may do better with an alternative approach. Students that can approach long division with several methods have the option of choosing one method that may work better in a particular situation than others. It must be remembered, however, that they will ultimately need to understand the traditional approach, especially when dividing polynomials. Some alternative methods include:

Factoring

In this method, the problem is written as a fraction. The fraction is then reduced by factoring. When the fraction is in its simplest form, divide. Example: 168 ÷ 24 is written as 168/24. For many students, it will be easiest to divide the numerator and denominator each by 2, giving 84/12. Divide again by 2, with the result 42/6; repeat again, resulting in 21/3. Divide both by 3, and you have 7/1. The answer to 168 ÷ 24 is 7.

Repeated subtraction ('chunking')

For this method, the division problem is set up in the traditional way. The simplest, but longest, way to do repeated subtraction is to subtract the divisor from the dividend over and over. Example: 386 ÷ 16 becomes 386 - 16 = 370 - 16 = 354 - 16, etc. Then, count the number of times 16 has been subtracted (24), and whatever is left over (2) is the remainder.

Chunking may be used to shorten the process. First, try to use multiplication facts. For example, in the problem 386 ÷ 16 you might easily see that the result of 16 x 10 is smaller than 386, so you can write 160 under the 386 and x 10 to the right of that. Then subtract, just as in traditional division (386 - 160), with the difference being 226.

You could again multiply 16 x 10, writing 160 under the 226 and x 10 to the right and subtracting; the difference is 66. The next simplest calculation is 16 x 2, or 32; write 32 under the 66 and x 2 to the right. Subtract: 66 - 32 = 34.

Add 16 x 2 again. Following the same procedure as before, subtract 32 from 34, write x 2 at the right and solve (difference of 2). Since there are no more digits to the right and 2 is smaller than 16, it is the remainder.

Next, add the numbers that have been written to the right (10 + 10 + 2 + 2), giving the sum of 24. The answer to 386 ÷ 16 is 24, remainder 2.

Double division

Double division is similar to chunking. Instead of deciding what multiplication fact can be used, a few multiplication facts are written to the left of the problem. In the problem, 3867 ÷ 16, the facts written might be 1 x 16 = 16, 2 x 16 = 32 and 4 x 16 = 64. Because 16 goes into 38 two times, write the 32 under the 38, and put a zero under the remaining digits of the dividend (3200). To the right, write the 2 from 2 times followed by the number of zeros added (two zeros, so write 200). Then subtract with the difference being 667. Since 16 goes into 667 four times, write 64 under the 66 and add one 0 under the 7. To the right, 40 is written; in the problem, subtract 667 - 640 with the difference of 47. 47 ÷ 16 = 2. Write 2 at the right, subtract 47 - 32 = 5. You now add the numbers that were written on the right side of the problem: 200 + 40 + 2 = 242, remainder 5.

Practice

All of the above methods require students to know subtraction and multiplication math facts. Review these facts at the beginning of each session with quick worksheets, flashcards, songs or games. Similarly, give your student a lot of opportunities to practice division. Most students need repetition in order to master the steps.

Compare

You will want to compare the method or methods that the student finds the easiest with the traditional process. Chunking and double division may be easier to correlate with the traditional method because they use the same problem format. Once the student understands that the process is basically the same for these different methods, you can teach them the traditional method with few or no problems.