Food for Thought: Two different ways to approach Division

Many parents are scratching their heads as schools are teaching different methods to do math problems.  Take, for example traditional long division.  There is traditional division and common core partial quotient division.  In order to simplify the approach we will take a look at both methods.

The approach that most parents are familiar with is traditional division as modeled here:

Often teachers will teach a mnemonic: daddy, mommy, sister, brother to help students remember the steps.  This stands for divide, multiply, subtract and bring down.  The approach is fairly formulaic and once memorized fairly easy to implement.  The trick is always remembering the steps.

Common core partial quotient division is entirely different from traditional division.  Below is an example of it:

Partial quotient involves a lot of estimating.  In this problem the student would begin by estimating how many times 8 goes into 136.  The student chose 10 so the 10 goes to the right.  The student then multiplies 8×10 and gets 80.  The next step would be to subtract 80 from 136 and the answer is 56.  Now the student estimates how many times 8 goes into 56.  The exact answer is 7 and the 7 goes to the right.  The answer is achieved by adding 10+7=17.

Some of my students that are homeschooled naturally gravitate towards one method or another.  In some cases schools might prefer one method over another.  Both can be learned with patience and repeated practice.