4-Simple Steps for Dividing!

There an Easier Way for Children to Learn Long Division!

For years I have watched children struggle with long division.  I have seen them get more and more frustrated as they rise through the grades.  Many times they have given up by the time they get to me in 6th grade.  I have looked for an easier strategy – one where all children would be successful dividing large numbers.  During a summer break, I dedicated all my free time to developing an alternative to long division.

Area Division
Designed so that
ANYONE can succeed at Long Division!

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.

WHEN CHILDREN DO NOT KNOW THEIR MULTIPLICATION FACTS…
THEY NEED A STRATEGY!

By simply writing the “counting by the numbers” above their problem, children who do NOT know their multiplication fact can succeed!  For example, with the problem 535 ÷ 7; Children can write “counting by the numbers” for 7’s.  The mathematical model below shows the results.

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 Books Teach Area Division
Each and every problem is link to a video tutorial!

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.

I scaffold the learning with the following process:

First, I have children complete a “Watch Me” problem, like the  one above.  Once they have completed the video, I have them copy down the entire problem into the notebook.

Next, I have students complete a “Work with Me” problem, where Children read the problem, and then watch a video.  While watching, children are instructed to pause the video and copy the problem along side me.

Finally, I have children complete a number of problems on their own in order to solidify their skills.  Once they complete each problem, they are instructed to watch the “On Your Own” video.  During these videos, I encourage children to correct their 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 all of my educational books.

The following offers a sample of each Book on Area Division

Book 1
An Introduction to Area Division

Problem Number 1
Cookies for sale

You love to bake.  Your favorite thing to bake is cookies, and everyone says your cookies are the best!  So, you decide to sell your cookies.  You have baked 524 cookies.  Each cookie box holds 8-cookies.

How many boxes do you need?
Will you have any cookies left over?

The video below shows how I teach children to to divide a 3-Digit Number by a 1-Digit Number.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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).

Book 2
Area Division – Dividing 4-digits by 1

Problem Number 1
Unicorns to the Rescue

You are traveling through a fantastic world of dwarves, giants, and trolls.  You are high on a bluff that overlooks a great lake when 4,389 trolls attack.  There is a thunderous sound of splashing hooves.  You look across the lake to see 7-Unicorns rushing to your rescue.

How many trolls does each unicorn have to defeat in order for you to escape?

The video below shows how I teach children to to divide a 4-Digit Number by a 1-Digit Number.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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).

Book 3
Area Division – Dividing 3-digits by 2

ESTIMATING WHEN YOU HAVE A TWO-DIGIT DIVISOR
Typically, children are taught to round the devisor before estimating how many time the divisor will go into the dividend.  For example, with the problem 433 ÷ 74; Children are taught to round 74 down to 70.  Next, since 7 x 6 = 42, 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.

ESTIMATING HIGH WITH AREA DIVISION
When children are struggling with the basic concept of division, you need to simplify the process, so they can feel successful.  This is why I teach children to estimate high.  With some problems, like 719 ÷ 83, it does add an extra step, but as you can see in the mathematical model below; there is NO erasing and it works every time.

With this strategy, children will never get frustrated, because they guess too high and have to erase!

Problem Number 1
Sleeping Lions

You are on a safari in the heart of Africa.  You look to the side of your jeep and see 17 sleeping lions.  As they sleep they are attacked by 816 buzzing flies that land on them and try to disturb their sleep.  If the flies are equally dispersed among the 17 lions, how many flies are on each lion?

The video below shows how I teach children to to divide a 3-Digit Number by a 2-Digit Number.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

After reading this book and completing the activities, you will be able to divide a 3-digit number by a 2-digit number (ie: 738 ÷ 82 = 9).

Book 4
Area Division – Dividing 4-digits by 2

 

Problem Number 1
Baby Llamas For Sales

You are raising baby llamas and sell them to llama farms around the world.  Your llamas are the cutest.  You made $3,431 by selling 73 llamas.  How much do each of your baby llamas cost?

The video below shows how I teach children to to divide a 4-Digit Number by a 2-Digit Number.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

After reading this book and completing the activities, you will be able to divide a 4-digit number by a 2-digit number (ie: 2,952 ÷ 82 = 36).

Book 5
Area Division – Dividing 5-digits by 3

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!

Problem Number 1
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?

The video below shows how I teach children to to divide a 5-Digit Number by a 3-Digit Number.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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).

Book 6
Area Division – Dividing When Your Quotient is a Decimal

Problem Number 1
Rock Climbing on a Sunny Day

You are an expert rock climber.  Your favorite thing to do on a sunny day is to climb a challenging escarpment.  This rock face is 533 feet high.  You climb to the top in just 82 minutes.  On an average, how many feet do you climb per minute?

The video below shows how I teach children to to divide when your quotient is a decimal.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

After reading this book and completing the activities, you will be able to divide when your answer is a decimal (ie: 533 ÷ 82 = 6.5).

Book 7
Area Division – Dividing When your Divisor is a Decimal

Problem Number 1
Skunk Juice

Sulky the Skunk has been chased by more dogs than any other skunk in the entire world.  Sulky is a sweet little fella, but when chased, he does spray, and the dogs do cry!  Whenever Sulky tries to eat some tasty garbage he is chased by a dog.  Sulky sprays 0.8 ounces of skunk juice each time he is chased.  In the past week, Sulky sprayed 55.2 ounces of skunk juice.  How many dogs did Sulky spray?

Hint: How many 0.8 ounces are in 55.2 ounces, or 55.2 ÷ 0.8 = n?

The video below shows how I teach children to to divide a decimal by a decimal.

For more information…
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

After reading this book and completing the activities, you will be able to divide decimals (ie: 35 ÷ 0.8 = 43.75) & (ie: 28.8 ÷ 0.8 = 36).

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.

 

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!

Have a fantastic day – Brian McCoy

18 Comments on “4-Simple Steps for Dividing!

    1. Hi there Evelyn –
      I am very glad to hear that this blog post has helped you.
      If you have another educational topic that you find difficult – let me know.
      I will see if I can help.
      Have a great day!

  1. I think area division is really cool.
    This video helped me understand area division, which is much easier than long division.
    Area division is super cool, and I didn’t even know that it existed until I read this post.

  2. Hello again Mr. McCoy, I like Area Division so much that I had to write another comment. I think it is so much easier that long division, and I think people can learn it faster. The part I like the best is when you make a mistake. You can just add an other box and keep on going. My math is much better with Area Division!

  3. Thanks, I just can’t stop watching the blogs Mr.Mccoy. This is really helping do my home work now and some times even on test. Thanks so much for taking all your time out to make these videos!

  4. Hi Mr. Mccoy, I like your “4 simple steps for dividing”. It is really an eye opener that there are always other ways, simple, precise, and easy in doing division. Thank you for sharing it.

    1. Hi Robert –
      First and foremost, I am really sorry for the delay in responding to you. I did not see your comment until just now.
      Thanks for you kind words. I strive to make the math accessible for all kids. My goal is to help them feel good about themselves and their educational abilities. Comments like yours make me want to keep working on this blog.
      Thanks again – Have a great day!

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