 # The Grid Method for Long Division Long division is often considered one of the most challenging topics to teach. Luckily, there are strategies that we can teach to make multi-digit division easier to understand and perform.

The Grid method is one of these strategies.

The Grid Method is intended for those who plan to teach traditional long division. It follows the same steps as traditional long division, but uses a different method of organization. This makes traditional long division easier for some students.

The Grid Method is not a mental math based approach. If you are looking for a mental math approach to long division, be sure to check out my posts for the Box/Area Method and Partial Quotients.

Let’s learn how to perform the Grid Method for long division!

Below, I have included both a video tutorial and step-by-step instructions.

VIDEO TUTORIAL:

STEP-BY-STEP INSTRUCTIONS

Suppose that we want to solve the equation 324÷2.

STEP 1:
First we draw a grid. The number of sections in the grid depends on the number of digits in our dividend. For this equation, our grid will have 3 sections. We write the digits from 324 inside the grid, and we write our divisor (2) on the left side. STEP 2:
Now we ask ourselves, “How many times can 2 go into 3?” The answer is 1, so we write a 1 on top of the grid. We now multiply 1×2 to make 2, and take that 2 away from the 3. This leaves us with 1. STEP 3:
Now we bring that 1 over to the tens place of the next section on the grid. This gives us a 12 in the next section. Now we ask ourselves, “How many times does 2 go into 12?” The answer is 6, so we write a 6 on top of the grid. Now we multiply 6×2 to make 12, and take that 12 away from 12. This leaves us with 0. STEP 4:
We carry that 0 over to the tens place of the next section on the grid. This doesn’t affect that number, so we still have 4 in the next section. Now we ask ourselves, “How many times does 2 go into 4?” It goes 2 times, so we write a 2 on top of our grid. Now we multiply 2×2 to make 4, and take that 4 away from the 4. We are left with 0, which means that we have no remainder.

To find the final quotient, we simply list the digits from the top of the grid: 1, 6, 2. So 324÷2=162. LET’S TRY ANOTHER EXAMPLE

This time we will try an example that has a remainder. It also has more digits that our last example. Notice that when we have more digits in our dividend, we simply extend our grid. Let’s solve 6542÷5. Here are the steps that we followed to solve this equation:

• Section 1: First we knew that 5 goes into 6 one time, so we wrote a 1 on top. We multiplied 1×5 to make 5, and took that 5 away from the 6, leaving us with a 1. We carried that 1 over to the tens place of the next section. Now we have 15 in that section.
• Section 2: We know that 5 goes into 15 three times, so we wrote a 3 on top. We multiplied 3×5 to make 15 and took that 15 away from the 15, leaving us with 0. We carried that 0 over to the tens place of the next section.
• Section 3: 5 does not go into 4, so we write a 0 on top, multiply 0x5 to make 0, and take that 0 away from the 4. This leaves us with 4. We carry that 4 over to the tens place of the next section, giving us 42 in the final section.
• Section 4: 5 goes into 42 eight times, so we write an 8 on top of the grid. We multiply 8×5 to give us 40, and take that 40 away from the 42, leaving us with 2. This means that our remainder is 2.
• To find our final quotient, we list the numbers from the top of the grid: 1, 3, 0, 8, and then add our remainder of 2. So 6542÷5=1308 R2. NEXT STEPS:

I would love to help you teach the grid method and other division concepts in your classroom. You may find the following resources helpful:

FREE MINI COURSE

Register here for free Multi-Digit Multiplication and Division Mini Course. It will only take you about an hour to complete and you’ll leave with tons of new ideas, a strategic plan of action, free resources, a PD certificate, and more! These task cards give students the opportunity to practice the grid method for long division in a variety of different ways. Students will calculate quotients, solve division problems, figure out missing dividends and divisors, think about how to efficiently solve an equation using the grid method, and more. See the Grid Method Task Cards HERE or the Big Bundle of Long Division Task Cards HERE. THE LONG DIVISION STATION

The Long Division Station is a self-paced, student-centered math station for long division. Students gradually learn a variety of strategies for long division, the grid method being one of them. One of the greatest advantages to this Math Station is that is allows you to target every student and their unique abilities so that everyone is appropriately challenged. See The Long Division Station HERE. OR SEE ALL RESOURCES HERE.

• I was wondering if there is a way to do problems such as 409 divided by 12? I’m looking for an easier method to do harder problems. Thank you!

• I am concerned with teaching the grid method as a strategy for the division. Base ten place value and the ten to one relationship is an integral concept for whole number and decimal number computation. The grid method seems to be a trick or graphic organizer and does not bring out the place value or the relationship among the places, certainly, it does not conform with the “teaching for understanding” goal. Sadly, even though we encouraged preservice and in-service to carefully take advice or activities from the internet without investigating the research base they are busy and assume if it is on the web it must be OK. As a long time mathematics educator, I am concerned that the grid method is included in this posting.

• Hi Vickie! Yes, you are correct in saying that this method does not use place value understanding. In the beginning of the blog post, that’s why I mentioned that this is NOT a mental math based approach, but can be used for those who are planning on teaching traditional long division (which also does not rely on place value understanding). I also address this in the video, but I’ll try to edit this post to make it more clear. I absolutely agree with you that teaching for understanding is vitally important. In this blog post I also link to posts on the partial quotients and box methods, which are much more mental math focused.

• I love this method. I think it will really help my scholars who are having trouble with long division. I have tried many methods and I am excited about trying this one! I also purchased your resource on TpT. Thanks again!

• LOVE THIS!!! One of my students who struggles terribly with math was so excited to succeed with this today 🙂

One question: Does this method work with a divisor larger than one digit? The video only demo’d one-digit divisors.

• I am trying to learn this method to better learn how to help my daughter who is learning this method in school.
@J Riley i figured out a way to do this method with multi-digit divisors i will try to explain without the use of actual boxes. (lets assume each line is a new box each R will move into next box as normal)
12/6725=?
12 / 67 = 5 R7
12 / 72 = 6 R0
12 / 05 = 0 R5 (at this point we have a remainder of 5)
so our answer is 560 R5
lets try a 3 digit divisor
120 / 64925 = ?
120 /649 = 5 R49
120 / 492 = 4 R12
120 / 125 = 1 R5
so our answer is 541 R5
as you can see from the examples for 2 digit divisors, divide first into the first 2 digits (if it will go , if not read further).
For 3 digit divisors divide first into the first 3 digits ( if it will go , if not read further)
now lets try an example where you can’t follow these steps
34 /12465 = ?
34 / 124 = 3 R22
34 / 226 = 6 R22
34 / 225 = 6 R21
so our answer is 366 R21
all you do is divide first into the first 3 digits
remember each line is a different box in the box method so how i recommend teaching this with multi-digit divisors is instead of creating multiple boxes at the start create a new box each time you need one.
Maybe Shelley Gray could create an example on the website that reflects this? but in the meantime just use the above examples try on a piece of paper recreating my examples in boxes ( remember each line is a new box).
I know without a graphic “box” it maybe hard to visualize but try it out its the same principle just where you start whether you divide into the first digit or the first 2 digits etc.
I hope this helps 🙂