Long Division Gets Crazy Hard for kids!
When children move into division of a 3-digit number by a 2-digit number like 769 ÷ 89, things get crazy hard. Even if kids understand how to do long division, they have to estimate how many times 89 will go into 769. When the estimate is wrong, they have to erase and try again. Many times, I find children’s papers looking like this with eraser smudges. Sometimes the papers are even ripped from so much erasing. The photo shows a student who estimated 5 first. Then he tried 7, but that was too small also. Finally, he tried 8. The actual answer is 8 with a remainder of 57. This student did get the correct answer, but many do not. All the erasing can quickly make a child feel frustrated and insecure about math.
Papers like the one shown above are typical of students would are learning to divide with long division.
If a child estimates incorrectly with Area Division, they simply make another area box and continue to solve the problem. It is much more simple, and makes children feel successful rather than frustrated! The photo below shows the same step-by-step process used on the paper above. When you watch the videos below, you will see me demonstrate both estimating correctly and incorrectly. This will show your child what to do if they make a mistake.
Area Division is 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. 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.
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!
I have developed these posts in a similar manner to how I teach in the classroom.
First, I introduce a concept and just have children watch how to complete the strategy.
Next, I have children complete the strategy step-by-step along side me.
Finally, I have children attempt the strategy on their own, and then I go over the strategy with them.
Without further ado, here is the Watch Me Problem:
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.
1 – Watch Me
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?
This one is easy. 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.
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.
2 – Work with Me
You are a scientist studying the mighty tiger on the Asian Continent. You find a streak of 37 tigers? Your team of scientists add all their stirpes and find that they have 967 stripes in all. If each tiger has the same amount of stripes, then how many stripes does each tiger have?
This one is a little harder.
Gather the following materials:
- A blank piece of paper
- A pencil
Watch and complete this challenge with me. I will take you through a step-by-step process. Together, we will solve this problem.
Pay close attention. Your next challenge will be very similar to this one.
ON YOUR OWN
For the remaining problem, I encourage you to solidify their 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 my ebooks.
3 – On Your Own
You are an animal dentist. You clean teeth on the most dangerous of felons. You have cleaned 946 lion’s teeth. If each lion had 43 teeth, then how many lions did you work your dentistry miracle on?
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 video 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!
This post is an introduction to my Tutorial eBook
All My Books Include Video Tutorials
for each and every problem!
Coming Soon to Amazon
I have completed the planning and outline stages of this book, and will be publishing it soon.
If you would like to be notified as soon as it is published, leave a comment below, and I will let you know as soon as it is available.
There are seven levels in this series on Area Division. I have incorporated a cyclical learning approach, where each educational concept is first introduced, then reinforced, then revisited again and again. Each subsequent level rises to the next level of difficulty.
For this reason, it is important that children begin the appropriate level of competency.
CHOOSING THE RIGHT LEVEL
I have created seven blog-posts that introduce Area Division. Each blog-post corresponds to a complete book, which teaches that level of competency. The blog-posts offer a free sample for each book within this series. Because Area Division is a new way of doing long division, I suggest you start on my very first lesson, which you can review for free by clicking here, (http://teachersdungeon.com/blog/long-division-answers-there-is-an-easier-way/ ). Each blog-post contains three problems that are accompanied by a video tutorial.
Work through the blog-post with me.
- If you are able to do all three problems, and you fully understand the lesson, move onto the next level.
- If you are not able complete the third problem on your own, then you are at your level of learning. I suggest that stop and purchase that book.
Do not worry if the concept seems too basic. For example, if you are in 6th, 7th, or 8th grade, but you are still struggling with long division, and you need to start on the very first book in this series – don’t worry!
I make many analogies to training in sports. After college, I coached gymnastics. Often a gymnast would come to our gymnastics club after learning poor techniques at a recreational sport facility. In order to be a high level gymnast, you must have proper basic techniques otherwise, you will never be able to achieve the incredible skills that are performed at the Olympics and by our collegiate gymnasts.
When any gymnast came into our club with poor technique, I would retrain the basics. Sometimes this would take months. But, in the end, these gymnasts would win medals and perform high-level skills with excellent technique. The same is true with mathematics. If you understand the basics of mathematics, you will excel as you rise through the grades and into college.
Therefore, do no despair if you need to start at the very first lesson. Once you perfect your basic understanding of Area Division, you will excel and begin winning high grades in mathematics!
Books within this Series
I have planned seven books for this series on Area Division. At this point, I have not completed the entire series, but I have blog-posts that introduce each level. You can get a preview of each book by clicking on the links below and going to my blog. After reading 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.
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.
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.
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.
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.
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.
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.
If you need more help, please leave a comment below. I am happy to help and will reply as quickly as possible.
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.
Have a great day – Brian McCoy