__ESTIMATING WHEN YOU HAVE A THREE-DIGIT DIVISOR__

In today’s classroom, children must be able to read a word problem and then apply the concepts of division to their solution. In many cases children get flummoxed because they are asked to solve for the quotient, and they simply do not understand what is being asked of them. Here’s a great infographic by a fellow teacher that really helps, The Owl Teacher.

Once children figure out that they are being asked to divide two numbers, they are taught to round the divisor up or down before estimating how many time the divisor will go into the dividend. For example, with the problem 43,642 ÷ 739; Children are taught to round 739 down to 700. Next, since 739 x 6 = 4434, you would multiply by 6. But as you can see below, the 6 is too high and that would put you over, so you would have to erase and try again.

Is long division is the only way to solve for a problem like this?

With **Area Division**, children will never get frustrated, because they never guess too high and have to erase!

##### What if I told you that there was an easier way to divide large numbers?

# Area Division

Designed so that

ANYONE can succeed at Long Division!

Contents

Hello, my name is Brian McCoy, and I am a credentialed teacher in the state of California. I have been teaching elementary and middle school children for over a quarter of a century. After years of watching children struggle with the algorithm for long division, I set out to develop an easier method. I created Area Division, which is close enough to long division, that children can switch back once they understand the concepts.

Let me be clear, Area Division is NOT for children who already understand long division. The process does take a bit more time. However, Area Division is structure in such a way that absolutely anyone can successfully divide large numbers. I developed Area Division by incorporating skip counting, (I refer to it as “counting by the numbers” in my videos), and an area box for the division. By incorporating counting by the numbers, even students who do not know their multiplication facts can successfully divide large numbers. My goal is for children is to memorize their multiplication facts. However, until they know all their facts, they need a strategy. Counting by the numbers is the easiest strategy to learn. Therefore, I have added counting by the numbers to the end of each and every video. Children who do not know all their multiplication facts should watch and count with me at the end of each of these videos until they can count by all the number on their own. Repetition of this strategy will help in all areas of math that require multiplication. **Once a child knows all their multiplication facts, they can stop the videos after the problem is solved and before Counting by the Numbers begins.**

__WHEN CHILDREN DO NOT KNOW THEIR MULTIPLICATION FACTS…
__

__THEY NEED A STRATEGY!__

My goal is for children is to memorize their multiplication facts. However, until they know all their facts, they need a strategy. Counting by the numbers is the easiest strategy to learn. Therefore, I have added counting by the numbers to the end of each and every video. Children who do not know all their multiplication facts should watch and count with me at the end of each of these videos until they can count by all the number on their own. Repetition of this strategy will help in all areas of math that require multiplication. **Once a child knows all their multiplication facts, they can stop the videos after the problem is solved and before Counting by the Numbers begins.**

### 7-Steps to Understanding Area Division

I have incorporated a ** cyclical learning approach**, where each educational concept is first introduced, then reinforced, then revisited again and again – with each subsequent step rising to the next level of competency. There are 7-steps that take children for the basics of division to dividing decimals by decimals. Because Area Division is slightly different from the conventional Long Division, it is important that you begin the appropriate level of competency. If you fully understand the “Watch Me”, “Work with Me”, and “On Your Own” problems, you are ready for the next step in understanding Area Division. If not – You may want to spend a bit more time on this step.

I introduce each step of Area Division in a similar manner to how I teach my students within my class.

###### WATCH ME

For this first problem, I encourage you to simply watch how the problem is solved. I like to introduce any new concept in this manner, so you can relax and focus on the strategies for solving the problem.

###### WORK WITH ME

For this second problem, I encourage you to develop your skills by working side-by-side with me. I would like you to watch a bit of the video, then pause it, and copy what I do on your paper.

__ YOUR OWN__

For the remaining problems, I encourage you to solidify your skills by completing the problems on your own. Once you have completed the problem, watch the video, and correct your mistakes. Over the years, I have found that children make substantial jumps in understanding when they find their own mistakes and then fix them. That is why I have included this form of teaching into this post.

### 5.1- Watch Me

*Flying to the moon*

You recently joined the Junior NASA Club of America. As a member of the club, you get to board a rocket ship and fly to the moon. You will land on the moon and stay there fore 24 hours. Then you will return home. The moon is 239,145 miles from Earth. Your rocket ship will fly 321 miles per hour.

How long will it take you to reach the moon?

###### This is a “Watch Me” Challenge:

Simply watch the video below to see how this problem is solved. Pay close attention. Your next challenge will be very similar to this one.

### 5.2 – Work with Me

*Don’t Cry Over Spilt Sugar*

It’s your mother’s birthday, so you decide to bake her a cake. You reach for the sugar and carry it from the pantry towards the counter. Unfortunately, the bag rips. Sugar spills all over the floor. There are 56,566 granules of sugar on your kitchen floor. You begin to sweep the sugar up with a broom and dust pan. If each scoop of the dust pan picks up 768 granules of sugar, how many scoops will you need to complete before you have it all picked up?

__This is a Work with Me Video__

__This is a Work with Me Video__

- Gather the following materials:
- A blank piece of paper
- A pencil

- Play the video below.
- Pause the video when told.
- Copy the problem down on your own paper, and solve it with me.

Pay close attention. Your next challenge will be very similar to this one.

### 3.3 – On Your Own

*Colony of Ants*

The largest ant colony in the US is in California. This one ant colony runs for 560 miles along the coast. What if 246 ant eaters escaped from the zoo and started eating as fast as they could? What if they ate a total of 44,034 ants before they were caught and returned to the zoo? If they all eat the same amount of ants, how many ants would each ant eater have eaten?

###### Your Challenge:

__Gather the following materials__:

- A blank piece of paper
- A pencil

Solve this problem just as you did in the earlier one.

Don’t worry if you make a mistake – Some of our biggest leaps in learning come when we __make a mistake__ then __see what we did wrong__ and __fix it__.

Once you have completed this challenge, click the link below:

Keep your paper with you while you watch the video.

If you made a mistake, pause the video and fix your mistake.

That’s the fastest way to learn!

How did you do?

Were you able to complete all three problems successfully?

If you answered Yes – Then you are ready for the next level.

Area Division – Dividing When Your Quotient is a Decimal

**If you would like more time reviewing this concept, you can purchase my ebook by clicking on the link below.**

**Price**: $4.^{49
}**Available on Amazon**

After reading this book and completing the activities, you will be able to divide a 5-digit number by a 3-digit number (ie: 70,864 ÷ 824 = 86).

### Books within this Series

I have planned seven books for this series on Area Division. You can get a preview of each book by clicking on the links below and going to my blog. After reviewing the post, please leave a comment. I love hearing your thoughts.

Area Division – Book 1

An Introduction to Area Division

After reading this book and completing the activities, you will be able to divide a 3-digit number by a 1-digit number (ie: 524 ÷ 8 = 65 R 4). This book forms the building blocks of understanding for all books in this series.

Book 2

Area Division – Dividing 4-digits by 1

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 4,224 ÷ 8 = 528). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

Book 3

Area Division – Dividing 3-digits by 2

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 738 ÷ 82 = 9). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

Book 4

Area Division – Dividing 4-digits by 2

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 2,952 ÷ 82 = 36). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

Book 5

Area Division – Dividing 5-digits by 3

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 70,864 ÷ 824 = 86). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

Book 6

Area Division – Dividing When Your Quotient is a Decimal

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 533 ÷ 82 = 6.5). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

Book 7

Area Division – Dividing When your Divisor is a Decimal

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 1-digit number (ie: 35 ÷ 0.8 = 43.75) & (ie: 28.8 ÷ 0.8 = 36). If you do not already know all your multiplication facts, watch Counting by the Numbers and count along side me. In time you will no longer need to use this strategy, and you will know all your multiplication facts.

### Other Books & Creations by Brian D. McCoy

TeachersDungeon is an Educational Fantasy Game. **It is 100% FREE!** The game is set to the Common Core Educational Standards, and is web-based, so it can be played on any device. Many of the questions are accompanied by tutorials like the ones you saw here.

An Easy Way to Understand Fractions

Fractions tend to be very abstract. Because of this, children often have a very hard time understanding what in the world is happening with fractions. In this first book, I will demonstrate how to break a whole into parts. This may seem like a very basic concept, but it is essential to understanding fractions. For a FREE preview of this book, click here, __An Easy Way to Understand Fractions__.

MY ADVENTURES WITH CHICKENSPIKE – This is a chapter book that is perfect for children in 3rd and 4th grades. My Adventures with ChickenSpike is a Children’s Fantasy Book. The main character is a young boy who is being bullied. He travels to a distant planet and finds his inner strength. By the time he returns home not only is he no longer a victim, he is a hero!

RED – This is a young adult novel that is especially designed for children in 5th and 6th grades. Red is an action packed adventure with two main characters and a number of supporting characters that add humor and drama to this novel. Bruno Vic and Evelyn Rose attend Sir Francis Drake Middle School. Bruno is big, street-wise, and tough, but he also has high morals and undying loyalty to his friends. Evelyn Rose was born rich, but an unfortunate turn of events has landed her in the heart of the Tenderloin District of San Francisco. Bruno, Evelyn, and their friends are desperate to steer clear of the gangs, so the turn to a mysterious man that the gangs seem to fear. His name is Red.

### One Last Thing

If you like this post and found it helpful, please click one of the share buttons. My mission in life is to empower children academically, and to help them develop a strong self-esteem. You can help by sharing this post!

Thanks!

Hi and thank you for this post!

Area division is a really easy way to learn how to divide numbers.

It is so much easier to use than long division.

I personally recommend area division over long division.

Hello Owen –

I am very happy to hear that you like area division.

I agree – I think it is a lot easier than learning long division.

Thanks for sharing your thoughts.

Have a great day!