Long Division Strategies

Long division can be such an exhausting unit. We oftentimes use colors and single-step instruction to break down this important skill. Yet, students continue to struggle with remembering all steps. I've had countless students remember the first step and become at a loss for how to move forward. Listed below are three proven methods to help all students divide successfully.

MNEMONIC DEVICES

To help student proceed past the first division I have used mnemonic devices. These little phrases will help students get past that first step hurdle.

A basic device will include the needed "Divide, Multiply, Subtract, Bring Down". The "Rs" represent "remainder" or "repeat". The "C" is for "Check".

To remember the steps for long division, there are countless choices:

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Depending on which steps you want to highlight in your mnemonic, you can choose one above or create your own!

Research shows that mnemonic devices help us remember important facts and principles. They can help with large pieces of information by organizing steps, parts, phrases, and the like.

Through repetitive guided practice, I reinforce the DMSCB until they remember the steps to complete a long division problem independently. Through the different practice problems, I provide opportunities for them to see how different outcomes can test their confidences. But as I have experienced myself, only practice will help students master this process.

But there are always those students who struggle with multi-step anything. Sometimes different safety nets must be put in place or new tools added to their toolboxes. Again as all good teachers do - we turn to others for suggestions!

BOX METHOD

I went searching for another way to reach those students who couldn’t remember past the Divide, Multiply, and Subtract steps. The box method became my new favorite way to teach long division!  

The box method is another way to get the job done with less thinking about which different step is coming next. This method uses a box that organizes the place values of the dividend. The divisor divides into each place one at a time. Instead of checking and bringing down, the difference from the subtracting step gets brought up into the next place value digit. Then the student divides, multiplies, and subtracts again.

This method takes a few steps out of the equation and allows long division to become less complicated. In my experience, this method allows most of the struggling students to be successful with long division.

PARTIAL QUOTIENT

Another way to teach long division is through partial quotient division. This method uses simple logic by allowing students to see the problem in a less abstract form. Partial quotient is also helpful for the students who haven’t mastered their facts.

When the student divides into the dividend they can use easy multiples of the divisor. The student is able to break up the problem into manageable parts so that it can be easier to divide. The student then records the partial quotient in a “work” column to the right of the problem. The problem is complete when the student can add no more to the work column because the remainder is less than the divisor. Lastly the partial quotients are added to find the quotient.

A teacher could search for hours trying to find new ways for every student to master a concept. But when it comes to long division - DMSCB and the box method are my top picks!

Need some ideas for MULTIPLICATION?

Click the link below to read about three successful strategies for teaching Double-digit Multiplication:

Double-digit Multiplication Strategies