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Long Division

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Long Division with lots of subtraction

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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 Box Method, also referred to as the Area Model, is one of these strategies. It is a mental math based approach that will enhance number sense understanding. Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible.

If you plan on teaching the partial quotients strategy in your classroom (which I highly recommend) the Box Method is a great way to get started. It uses the same steps as partial quotients, but is organized a bit differently.
Let's learn how to perform the Box Method/Area Model 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 box. We write the dividend inside the box, and the divisor on the left side.

Step 2:
We want to figure out how many groups of 2 can be made from 324. We will do this in parts to make it easier. We could start by making 100 groups of 2, since we know that we have at least this many groups. So we multiply 100×2 to make 200, and then take that 200 away from 324. Now we have 124 left.

Step 3:
We make another box and carry the 124 over to it. Now let's take away another easy multiply of 2. How about 50 groups of 2? We know that we can take out another 50 groups of 2 from 124. 50×2=100, so we take 100 from 124. Now we have 24 left.

Step 4:
We make another box and carry the 24 over to it. We know that 12 groups of 2 makes 24, so let's write a 12 on top and take away 24 from the 24. Now we end up with 0, so we know that we are finished our equation.

Step 5:
Now we add the "parts" from the top of the boxes to find our quotient. 100+50+12=162, so we know that 324÷2=162.
ONE MORE EXAMPLE (WITH A REMAINDER)
Let's take a look at one more example. In this example, we will solve 453÷4.

1. First we wrote our dividend inside the box, and our divisor on the left side.

2. We took out 100 groups of 4 first. This made 400. We subtracted 400 from 453 and were left with 53.

3. We carried the 53 to the next box, and then took out another 10 groups of 4 to make 40. We took the 40 away from the 53 and were left with 13.

4. We carried the 13 over to the next box, and then took out 3 groups of 4 to make 12. We took the 12 away from the 13 and were left with 1.

5. We cannot take any more groups of 4 out, so our remainder is 1. To find our final quotient, we add 100+10+3+remainder 1 to make 113 R1.

HELPFUL RESOURCES FOR THE BOX STRATEGY/AREA MODEL FOR DIVISION
I would love to help you teach the box strategy for long division in your classroom. You may find the following resources helpful:
BOX STRATEGY/AREA MODEL TASK CARDS
These task cards give students the opportunity to practice the box method/area model 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 box method, and more. See the Box 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 box 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.

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The Box or Area Method: an alternative to traditional long division

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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 Box Method, also referred to as the Area Model, is one of these strategies.

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Long Division

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Long Division with a grid
Website #1

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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:
GRID METHOD TASK CARDS
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.

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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.

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Long Division with a grid
Website #2

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Homework Unlocked introduces you to the grid method of division and walks you through an example when there isn't a remainder.

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DMSB (Dad, Mother, Sister, Brother) METHOD

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DMSB (Dad, Mother, Sister, Brother) METHOD

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Long Division Step-by-Step

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K5 Learning teaches students a trick to use when learning long division.