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-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.

1.1- Watch Me

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?

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.

1.2 – Work with Me

Mountain Bike Tour

You and your family love mountain biking.  You decide to go on a family mountain biking tour across a 230-mile trail of the Rocky Mountains.  Your plan is to ride 7 miles each day.

How many days will it take you to complete your mountain biking tour?

This is a Work with Me Video
  1. Gather the following materials:
    1. A blank piece of paper
    2. A pencil
  2. Play the video below.
    1. Pause the video when told.
    2. 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.

1.3 – On Your Own

Junior NASA Club

You have joined the Junior NASA Club of America.  It is a very cool club that teaches you about being an astronaut.  Today you get to put on a space suit and fly in a super fast jet.  Your jet will fly super fast for 9 seconds.  You will travel 345 miles in that time.

How far will you travel each second?

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 4-digits by 1

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 3-digit number by a 1-digit number (ie: 524 ÷ 8 = 65 R 4).

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!

Have a fantastic day – Brian McCoy

16 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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