long divison helper


This is the long disvion helper. Here is a helper on partial quotients 

                

                                    

Step One: Setting Up the Problem

The first step in the partial quotient approach is to set up the problem. This looks much like a traditional long division problem except that a horizontal line gets drawn along the right side of the problem to create space for the student to track "partial quotients." 

           

Step Two: Picking Easy Multiples

The question in the mind of the student is simple: "How many groups of nine are there in 2,079?" The partial quotient method tries to get the student to the answer through basic logic. So the next question the student asks is, "Well, are there at least blank number of groups of nine in 2,079?" Fill in the blank with a number the student is comfortable with - let's say 100. So the question becomes "Well, are there at least 100 groups of nine in 2,079?" The student does the math and figures that 100 groups of nine (100 x 9) is 900. The student writes 100 in the partial quotient column and writes 900 under 2,079 in the problem template; then he does the subtraction to see how much is left.

 

Step Three: Can I Do That Again?

With 1,179 left in his dividend, the student should ask this basic question: "Can I take that many out

again?" If the answer is "yes" (like in this case), the student should do that. If the answer is "no," the student has to find a smaller easy multiple to take out. In this case the student writes 100 in the partial quotient column again and writes 900 under 1,179 in the problem template; then he does the subtraction again to see how much is left.

 

Step Four: Can I Do One More Time?

With 279 left in his dividend, the student should ask that basic, logical question again: "Can I take that many out one more time?" If the answer is "yes," the student should do that. But in this case the answer now is "no," so the student has to find a smaller easy multiple to take out. Let's assume this student is not very good with "nines" yet and decides to just take 10 "nines" out. The student writes 10 in the partial quotient column and writes 90 under 279 in the problem template; then he does the subtraction to see how much is left. Since the dividend left is still more than ninety, the student can repeat this step two more times

 

Step Five: Add up the Partial Quotients

When the student has taken this process as far as possible (the dividend left is less than the divisor) the final step is easy: add up the partial quotients to get the whole quotient. The student in this particular case will add 100+100+10+10+10+1 and get 231. There are 231 groups of nine in 2,079. Or, phrased more traditionally, 2,079 divided by 9 is 231