There are many milestones on the road through grade school math, but one in particular marks an especially significant destination. It’s the motherlode of arithmetic, a recipe with so many of the previous numerical ingredients from so many previous grades, a mountain of math skill awaiting its ascent, a task requiring the flexing of a mixed metaphor of mental muscles like no other.
And also, the one thing that strikes terror into a math-phobic 4th grader’s heart like no other.
But does long division really need this huge build up? Is it really that much more difficult than, say, multiple-digit multiplication? Yes and no.
Long division is certainly a test of many different skills, but they are all ones that have been should be largely rote by the time long division is introduced. I believe the main issue that brings tears and seizures when long division pops up is essentially a lack of confidence in basic math facts. Learning the long division algorithm is a little daunting, but it’s a small step if the prerequisites are truly mastered. And to that, let me just say it again… Drill, baby, drill.
That said, why is long division such an important rite of passage?
The four basic steps in long division (partial division, multiplying, subtracting, bringing down) all incorporate concepts ranging from basic operations and place value to simple numerical algorithms. These skills mimic a lot of what later, more abstract, math looks like. I’m staring at you algebra, hiding there around the corner.
Long division is the arithmetic skill that most closely resembles the mechanics of tasks in algebra, trigonometry, calculus and more. It requires doing several basic operations in a particular sequence, thinking about their results, trying intermediate solutions (especially with multiple digit divisors), backtracking and hopefully making sense of the process along the way.
This makes long division not just another skill to learn on the journey… It’s the first step down a completely different road.
Of course I wouldn’t be a good dad if I didn’t offer directions! I’ve had a collection long division worksheets with detailed answer keys on the site for quite some time, and they’re actually some of the top ranked math worksheets on the web.
I’ve also just created a long division calculator, and it’s one of the best teacher resources I’ve built on the site in a long time. Enter a divisor and a dividend, and it will work the problem in front of you, with remainders, in real time, and it provides guides that show where all the numbers come from. Trying to get across where that intermediate product comes from in that jumble below the problem? Watch the calculator run its course, then put your mouse over the digit in the quotient to highlight it and the product. It really is useful and it was a lot of fun to build….
I hope you’ll give it a try yourself and share it with anyone you know that’s learning or teaching long division… It’ll go a long way towards paving that road towards future success in math.