div2

Long division need not be the traumatic learning experience for 4th and 5th graders. This app (div2) does all the tedious multiplications and subtractions, leaving the student to learn and practice the basic long division skills of correctly guessing each digit of the quotient (answer) and testing whether it is correct. An additional benefit is the feedback that is provided after each quotient digit.

The long division exercises in this app are carried to 2 decimal places (hence the name div2). The user can specify the number of digits in the dividend (the number divided into) and the divisor. The divisor and dividend are randomly generated integers, so the user will never see any problem more than once. The random numbers of divisor and dividend may sometimes be such that the divisor goes evenly into the dividend, in which case the quotient may end in one, or more zeros.

If long division is done the old fashioned way (with pencil and paper) the student must struggle for each digit of the quotient, multiplying his guess by the divisor and then subtracting the product to test whether his/her guess is correct and to get the difference for determining the next quotient digit. If the student has guessed wrong, the whole step of multiplication and subtraction must be repeated over again. Worse still, the student may fail to detect the error of an incorrect guess, and the error will propagate through the rest of the solution. When the answer is scored (by the teacher, or someone) the hapless student must go back through the entire process to determine what went wrong.

This app will develop proficiency in the key long division skill of guessing the correct quotient digit. When the student is faced with a long division exam problem that must be done with pencil and paper, this proficiency will enable him/her to avoid wasting time multiplying incorrect quotient digits by the divisor, when the correct digit could be guessed to begin with. The instructions in this div2 app provide a set of rules that will guarantee that the user never requires more than 2 guesses for any quotient digit; half the time these rules will even give the correct guess on the first try. If you have a 4th or 5th grader struggling with long division, you will find this app to be a life-saver. Of course, the student who is having trouble with multiplication and subtraction should master these fundamental skills first (see my apps “multables” and “sub3”). Once multiplication and subtraction are mastered, this app will avoid the boring exercise of these skills while trying to master long division.