Teaching Area Model Division to 4th Graders

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Learning long-division can be challenging for fourth graders. Luckily, there’s the area model division (4th grade) to the rescue! Also referred to as the Box Method, this is a great method for children to become fluent in long division.

So if you’re wondering how to teach area model division to your 4th-grade students, we’ve complied several tips that will get you through!

What Is Area Model Division (4th Grade)?

You can start your lesson by explaining that the area model division is simply a model that looks like a rectangular diagram that we use in mathematics to divide numbers.

More specifically, by applying this model, we break the rectangle into smaller boxes with the help of number bonds to make the division easier. In the end, to find out what the quotient is, we’ll simply add up the smaller boxes.

How to Teach Area Model Division (4th Grade)

Review Place Value

Students need to have a solid understanding of place value to be able to use the area model for division. So make sure to review their place value understanding and identify any students that are still struggling with it.

You can introduce a brief activity by asking students to find the place value of each digit in a given number, such as finding the place value of 2, 3, 5, and 9 in 2,359. You may also want to check out our article on place value.

How to Perform Area Model Division (4th Grade)

After the brief review of place value concepts, you can proceed with teaching the steps of doing area model division to fourth graders. Start by saying that you want to find the quotient or the answer to a particular division problem, such as:

268 ÷ 2 = ?

You can explain to students that using the area model to solve this division problem requires drawing a rectangular area. Point out that we’ll divide the rectangular area into smaller parts and break up the dividend based on its place values. We’ll also keep the divisor at the very beginning to the left.

Since we know that 268 = 200 + 60 + 8, we can present it in the following way in the rectangle:

200

Explain that we’re doing this so that we end up with smaller areas that are easier to divide by two. That is, it’s easier to do the mental math of dividing 200 by 2 or 8 by 2 than dividing 268 by two.

Next, perform the division of each of these numbers by two:

200 ÷ 2 = 100

60 ÷ 2 = 30

8 ÷ 2 = 4

Finally, point out that the only thing left to do is simply add up all of these partial quotients so as to get the quotient of 268 2. In other words:

100 + 30 + 4 = 134

By applying these simple steps of breaking up the dividend, we found out that 268 ÷ 2 = 134.

Why We Don’t Always Break Up Dividends This Much…

Make sure to point out to students that the way we break up a dividend varies from case to case. Highlight that the general rule to remember is that we try to break it up to pieces that would be easy to divide by the divisor.

Provide an example of this. For instance, let’s say we want to find the quotient of 972 ÷ 9. Ask students if it would be wise to break 972 into 900 + 70 + 2? If the students get the gist of the main principle of how the area model works, they should be able to reply ‘no’.

Why? Because while 900 may not be difficult to divide by the divisor, 70 is not easily divided by 9. So we’ll try to look for a number that we can easily divide by 9, which in this case is 72, as most students already know that 9 x 8 = 72 by heart.

Point out to students that this is why we’ll break up the dividend in the following way (again keeping the divisor at the beginning):

900

Explain that afterward, we’ll simply perform the steps we already implemented above, that is, we’ll divide each of these numbers by the divisor and add up the partial quotients in order to get the final quotient. In other words:

900 ÷ 9 = 100

72 ÷ 9 = 8

100 + 8 = 108

So the quotient of 972 ÷ 9 is 108. Since students are already fluent in multiplication from previous lessons, you can encourage them to even check whether the answer is correct by multiplying 108 by 9.

Solving Word Problems With Area Model

Once children are comfortable with using the area model to solve division problems, you can introduce word problems that require division where the area model can also be applied. First, remind students that we need to identify the key question that is being asked in the problem.

It’s crucial to identify what information is important in the word problem and what isn’t. To do this, you can also encourage students to use a highlighter. Normally, this is something that students are familiar with from lessons on multiplication word problems.

You may also benefit from checking out our article on multiplication word problems.

You can then present a word problem requiring division to your class. For instance, take the following word problem:

“Ms. James bought 315 stickers for her classroom. She wants to give them out equally amongst her 5 students. How many stickers will each of them get?”

Point out that the main question that we’re trying to find out is the number of stickers students will get if Ms. James divides 315 stickers into 5 equal groups of stickers. By highlighting the number of stickers that Ms.James bought and the way she divided them to her 5 students we get an idea of what information we already have.

Thus, we can create the following equation:

315 ÷ 5 = ?

Now you can move on to using the area model to show students how to solve the division problem. Point out that we know that 15 is divisible by 5 and 300 is divisible by 5 as well (since we know that 30 can be divided by 5). So we can break up the dividend as follows:

300

300 ÷ 5 = 60

15 ÷ 5 = 3

Then, we’ll simply add the partial quotients:

60 + 3 = 63

So the final quotient is 63.

Activities to Practice Area Model Division

Pair Work

This is a simple activity that will help children reinforce their knowledge of area model division. To implement this activity, you’ll need to bring large construction paper and division cards (i.e. cards with division problems) in class. You’ll also need a number of markers.

Divide students into pairs. Make sure that students are adequately paired up so that those that have stronger math skills are paired with students whose math skills may not be so strong. Provide students with the instructions for the activity.

Each pair gets one division card, construction paper, and markers. Explain to your students that they’re supposed to work together with their partners to present and solve the division problem on the construction paper with markers, using the area model.

For example, if students got a division card with the following division problem: 455 ÷ 5, they’re supposed to create an area model on the construction paper, and break the dividend based on its place values in order to find the quotient.

At the end of the activity, each pair presents their construction paper in front of the class. Encourage students to actively explain each step of the way and why they solved the division problem the way they did.

Area Model Division Task Cards

This is a fun game that you can use in your class to practice division using area models. To play this game, you’ll need to prepare task cards with division word problems on them. Make sure you have one word problem per group, depending on the number of students.

Divide students into groups of 3, 4. Hand out one task card to each group. Explain that they have to work together with the other members of the group in order to solve the word problem. Point out that they must use the are model to solve the problem.

The first group that manages to solve the problem on their task card wins the game. In case of a tie, you can also introduce two additional task cards to the given groups. The first one that manages to solve the word problem is declared the winner.

Before You Leave…

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This article is based on:

Unit 4 – Multi-Digit Whole Number Division