If your memories of math in 4th grade are anything like mine, you might remember struggling to memorize the long division steps. Can you believe I never really understood long division until I became a teacher? Yep. That’s right! To unlock the secret to teaching long division and making it easy for my students (and for me), I had to remember a few simple concepts. I’ll share my essential concepts, a few of my favorite strategies, and a print-and-go resource with plenty of space for your students to work carefully through problems appropriate for their level. These are perfect for centers and independent work!
5 Essential Concepts for Teaching Long Division:
Teaching Long Division – Concept One
Numbers follow a pattern.
When students understand patterns, they can start to identify key relationships during long-division practice. They’ll be excited to notice how numbers are related. You can begin with basic concepts like teaching the patterns in multiples.
In these practice pages, I’ve given students lots of space on the side of each problem to record the multiples.
Teaching Long Division – Concept Two
Multiplication is putting equal groups together.
It’s essential for students to understand the concrete concept of multiplication. Students who are struggling with this concept would benefit from using number discs or beads to make copies of a number, keeping them in equal groups.
Teaching Long Division – Concept Three
Division is splitting apart equal groups.
Likewise, students need to understand the concrete concept of division. Using manipulatives to show how numbers can be split into equal groups will help any of your students who are struggling with the concept of division.
Teaching Long Division – Concept Four
Break numbers apart into smaller numbers (partial quotients) and think of friendly numbers.
For example, think MULTIPLES of 10 or 100. See the example below.
Teaching Long Division – Concept Five
Make a Ballpark Estimate before solving a math problem.
If students get into the habit of estimating before they divide, they’ll notice major mistakes before they’re through the entire problem.
Teaching Long Division – Concept Six
There are MANY ways to solve a math problem.
As teachers, we have the job of showing students several different ways to solve a problem, but in the end, the students use which way works best for them because everyone thinks differently. Encourage your students to share how they arrived at their answers! Getting students involved in discussions can lead to a deeper understanding of division.
Now that you understand the 6 key concepts to teaching your 4th graders long division, here are two of my favorite strategies.
The Unconventional Way: PARTIAL QUOTIENT STRATEGY
Using this strategy may seem strange at first, but many of my 4th grade students preferred using this division strategy. It’s a great strategy to introduce when teaching long division.
This strategy is all about breaking numbers into smaller numbers and thinking of friendly numbers as I mentioned above in Concept 4.
Here is an example using the number 520. This is just one way to break 520 into smaller friendlier numbers.
ONE: Rename the number and break it apart into friendlier numbers.
TWO: Rename 520 to 400 in this example.
THREE: Start a new division problem using the friendly number 100 instead of 120.
FOUR: Repeat and add your three quotients together to arrive at the final answer.
| To grab this Long Division Partial Quotients freebie, click here |
TRADITIONAL STRATEGY
I think the key to using this traditional Mom and Pop Strategy is to present it in a methodical and organized way.
This is the same ol’ strategy we’ve used since way back in the day! But the KEY to teaching students to use this traditional strategy is to present it in a methodical and organized way.
- Before beginning a problem, have students generate the first 9 multiples of the divisor. When I was a kid, I spent a lot of time trying to figure out what multiples were close to the dividend. Generating a list beforehand and referencing it throughout the problem will move things quicker.
- Draw lines between the place values of the dividend. This will help students see each place value and line up the numbers in the quotient correctly.
This is a simple shift in the way you teach your fourth graders, but it is the ONE THING that will change the game completely when it comes to long division… and multiplication! Each time they start a problem, they’re practicing multiples and recognizing patterns.
| Click here to grab this Long Division Practice freebie. (same as above) |
To Sum it All Up
Teaching long division can be simple for beginners when you use one of these two tried and true methods! Numbers are broken into smaller numbers (partial quotients) or using the traditional method with the habit of writing multiples to the side and BAM! Do you use one of these strategies? Or, something else? Comment with your favorite way to teach kids, long division!
Grab this FREEBIE!
Ready to try this strategy with your students? Because I know they’ll love learning this way, here’s a free worksheet using this strategy to help you get started. CLICK HERE to download this free printable worksheet.
If you found these long division strategies helpful, check out one of my most popular resources.
If you need some ready-to-print activities, you’ll love this bundle!
And, there’s even dedicated space for your students to keep track of the multiples off to the side. (Anyone who teaches grades 3, 4, and 5 knows how important it is to give students plenty of SPACE to work!)
Long Division Bundle
This Division Bundle contains 2 Division Practice PAPER Packets for Beginners (with no remainders). One packet is no remainders and the second packet is simple remainders.
Your students will gain division confidence and fact power with these packets.
Helping your 4th graders understand and master this skill can be challenging, but it’s an important skill they need to master with confidence!
If you’ve ever noticed your students struggling with long division, this packet is perfect practice. And, you can use it as quick check assessments, math centers, peer tutoring, morning work, homework, small group enrichment centers, or even partner work. Just print and go!
Fourth Grade teachers are loving this resource for tackling Long Division! One teacher said, “These are fantastic! My students are learning the steps to solve division problems. Even students who don’t usually want to try are trying and learning. Thank you for another wonderful resource.!!”
YES, I WANT THE LONG DIVISION RESOURCE
