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

Double-Digit Multiplication Strategies

Have you ever wondered if your students will master double-digit multiplication? There are so many techniques, but which will be the best one for your learners? A few years back, I was struggling with these questions.

When we were in school, we were taught the standard algorithm. I can still remember standing nervously by the chalkboard completing long problems in front of my class. I was never really sure what I was supposed to do next. There were no tricks or shortcuts - just the basics of multiplication. And if the standard algorithm didn't work for you...well, you were up a creek. Thankfully, today, we have more than one way to teach multiplication.

3 "Out of the Box" Methods for Teaching Double-Digit Multiplication

TURTLEHEAD 

We know not every student learns quite the same way. So I ventured onto the web and wandered down the YouTube rabbit hole. However, it wasn’t a complete waste of time. I found one video that stood out from the rest in explaining double-digit multiplication -- the turtlehead method!

This video is very primary, but the kids will connect to the silly graphics and music. This method demonstrates all the important steps that kids usually forget to do in the standard algorithm. The turtle helps them remember where to start multiplying, to cross off the multiplier, and to put in that magic zero! After just one exposure to the video more students were suddenly becoming accurate as they follow the turtle’s cues. To help students remember the steps and give them a visual on the wall, you can create a poster.

LATTICE

For some kids, the steps of the standard algorithm or the turtlehead method are just too much for them.

A decade or so ago the trend in math was lattice multiplication. This technique can help you reach those students who struggle with algorithms that use a standard set-up.

Lattice multiplication creates a grid with double-digit numbers placed on the outside. There are diagonal lines that run through the grid to divide the grid boxes into halves. As each number is multiplied, the values are placed inside the grid. Once all the multiplying is done, the numbers are then added down from the right to left, moving downward.

When using this method, the student doesn’t have to remember about the magic zero. Most mix-ups may happen when students aren’t sure about where to multiply first. In the past, I have shown them how to draw a dot on the top right corner of the box. This will be their starting point for the lattice.

Please note: some standardized testing does not recognize lattice as a legitimate algorithm (or award points for correct answers) because it is not based on place value concepts; it is simply a "cool trick". 

AREA MODEL

One last way to reach students is multiplying using the area model. This organized method uses the concept of area: length x width. The numbers are broken down using expanded notation. Once the numbers are multiplied, the answers go inside the grid created in the area model. All of those answers are then added together to get the final answer.

From experience, I have learned to start with just one technique. As I saw some students struggling, I would introduce a new method to them. Some students were most comfortable with the standard algorithm because that is the technique they were taught by their parents- and that's great! But I would encourage them to at least give these others a try. I would even challenge them to solve using the method most comfortable and them check their answers using a different method.  

At the end of the day the most important thing was a student's ability to correctly solve the problem. And using one method or the next, soon enough, all my students were multiplying with ease!

Need some ideas for LONG DIVISION?
Click the link below to read about three strategies for success!

Long Division Strategies

Valentine Compliments Poster (Editable FREEBIE!)

Each February students exchange store-bought or even homemade valentines. This annual exchange can sometimes create angst and dread among your students. However, this year you could be the teacher that creates an experience that provides the warm and fuzzies as well as a keepsake. I am not saying ditch the cute cards, but this poster will make a bigger impact for sure! Do I have your attention yet?

Compliment posters will be something that your kids will be able to read over and over again, especially on those days that they might need a little extra boost. This is also a great tool to reinforce character education or the Positivity Project in your classroom.

You can find an editable freebie for this activity in my TeachersPayTeachers store here --> Valentine's Day Activity: Compliments Poster

The first thing you have to do is create a list with the name of each of your students on it. Each line should provide enough room for the name and a sentence to be written. Once your name list is complete, make a copy for each student and any teacher/adult who works in your room.

As I pass out the name list, I instruct the students to put an X by their name to ensure they don’t write one about themselves. After that we have a discussion about inside (character) traits and outside (physical) traits and which ones should be used for this task. For example, I might tell them that telling someone their shirt is nice, but doesn’t really tell them about the kind of person they are. Although the ultimate goal would be for each student to write a compliment regarding a character trait, I do allow for students to compliment a physical trait as long as it's appropriate and the student writing can't think of anything else. Giving evidence to support their compliments is also encouraged. I also post our character education traits and the Positivity Project principles for them to use as a resource.

After they have finished their compliments, I make sure I look over each of them. I make the students clean up their writing or make the compliments more complete. Once everyone is corrected and ready to go, the cutting begins. Soon each student will have a compliment strip for each kid and each adult in the room.

The posters will then be placed on the tables/desks around the room so each person can see where to place the compliments.The students voraciously pass out the paper strips to each poster; it's similar to the Valentine card exchange that happens at this time of the year. Everyone is eager to read what other people are complimenting. They take an interest in their posters and their classmates' posters as well.

As soon as the last compliment is passed out, the gluing begins. The strips are glued in a row under the name. Each student will soon have a poster full of compliments about themselves. Students are invited to either keep the poster at school or take it home; it's up to them. These posters will serve as confidence boosters and a keepsake for not only the current school year but for years to come.