One of the main reasons that traditional long division is so hard to learn is that a correct answer depends on a memorized series of steps – divide, multiply, subtract, bring down. If a student forgets which step to do and when to do it, there is a very high chance that he will end up with an incorrect answer.

This is why it is ESSENTIAL to teach strategies, rather than steps.

Strategies encourage REAL UNDERSTANDING. This is such an important part of math. We want our students to really understand what they are doing, and to know that there are different ways to come up with a correct answer.

In this article, I’ll discuss three different alternatives to traditional long division. I encourage you to focus on the first two, as they are very mental math focused.

Ready to get serious about teaching multi-digit division? Check out the Long Division Station HERE.

The Box/Area Method

The Box Method or Area Model is a mental math based approach that will enhance number sense understanding. If you plan on teaching the Partial Quotients strategy (which I will discuss next), this is an excellent way to introduce it.

Students solve the equation by subtracting multiples until they get down to 0, or as close to 0 as possible. For example, in the example below we took out 100 groups of 3, then 50 groups of 3, and then 1 more group of 3 to make a total of 151 groups of 3 taken out of the dividend. Please head over to THIS POST for a very detailed explanation of this strategy, complete with pictures.

Partial Quotients

Partial Quotients is a “must-teach” strategy for multi-digit division. If you teach the Box/Area Method first, this is a very natural progression.

When we use the partial quotients strategy, we set up the equation similarly to how a traditional long division equation is set up. The difference here is that we take out multiples of the divisor until we get down to 0, or as close to 0 as we can. Please see THIS POST for a very detailed explanation of this strategy, complete with lots of pictures.

The Grid Method

The Grid method is NOT a mental math based approach. This means that if you have students who are struggling with multi-digit division, you should focus on the previous two strategies that I described rather than moving on to this one. The Grid Method can be used for students who are ready for a challenge, or as an introduction if you plan on teaching traditional long division. Some students will find the grid very helpful in organizing their thinking.

When we use the grid method we just organize the digits from the equation into a grid. For a complete, detailed explanation of how to perform the grid method, along with lots of pictures, please see THIS BLOG POST.

NEXT STEPS:

• Use Long Division Task Cards in your classroom to reinforce the strategies in isolation. Find the bundle HERE.
• Incorporate the self-paced, student-centered Long Division Station into your classroom to ensure that every student is working to his/her full potential.
• Read more about The Box Method, the Partial Quotients Method, and the Grid Method to develop a teaching plan.

The post Effective Alternatives for Long Division appeared first on Shelley Gray.

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!

Wait! Are you looking for the Area Model for multiplication rather than division? Find it HERE.

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

VIDEO TUTORIAL

AREA MODEL/BOX METHOD FOR LONG DIVISION: 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.

The Area Model for Multiplication

The area model is fantastic for multiplication as well! If you’d like to read about how to teach this in a concrete way, here’s a post you may be interested in.

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 post Long Division Alternative: The Area or Box Method appeared first on Shelley Gray.