There’s an Easier Way for Children to Learn Long Division!
For years I have watched children struggle with long division. One major reason that is that memorizing all the multiplication facts can be difficult for some kids. 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 6^{th} 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. The end product is this series of lessons with math video tutorials.
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.
This Math Help Website is Designed to Build a Concrete Understanding of Division!
7 Lessons Teach Area Division
Each and every problem is link to a math video tutorial!
I have incorporated a cyclical learning approach with math tutorial videos. Each educational concept is introduced, then reinforced, then revisited again and again – with each subsequent step rising to the next level of competency. There are 7-lesson that take children from 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 have scaffold these problems:
- The first problem is a Watch ME.
Students should read the problem and then click on the video to watch how the problem is solved.
Students should copy the entire problem into their notebook. - The second problem is a WORK WITH ME.
Students should read the problem then gather all their materials, so that they can do the problem with me.
Students should play the math tutorial video and pause it when told.
Finally, Students should copy the problem down on their own paper, and solve it with me.
When the math tutorial video is complete, students should review the problem with their teacher or parent. - All the following problems are ON YOUR OWN.
Students should solve the problems just as they did in the first two.
Once you they completed the problem, they should watch the math tutorial video.
Students should keep their paper with them while they watch the video.
If they made a mistake, they should pause the math tutorial video and fix their mistake.
That’s the fastest way to learn!
Lesson 1
Dividing three digits by one (548 ÷ 6 )
Challenge 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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
If you found this first problem helpful – please read on!
I have more problems and video after this brief message.
I’ve created this lesson as well as my game, TeachersDungeon, because I want to give back to the profession that I love so very much. If you would like to become a patron and help support this website, you can do so in purchasing one of my educational books.
If you are a teacher or the parent of a child that could benefit from one of my eBooks please visit my store at TeachersPayTeacher. I use the name, McCoy’s Math Link at Teachers Pay Teachers.
Challenge 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?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Junior NASA Club of America
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?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 1389 ÷ 7 = |
Chalenge 2486 ÷ 6 = |
Challenge 3947 ÷ 8 = |
Challenge 4762 ÷ 9 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 2nd Lesson in this series will begin after this brief message.
Each of my books includes 10 word problems and another 16 Drill & Kill problems. Each and every problem is linked to a video tutorial like the ones in this post. If you would like to purchase this book, click the Photo.
Lesson 2
Dividing Four digits by One (7,898 ÷ 8 )
Challenge 1 – Watch Me
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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 2 – Work With Me
Lost Polar Bears
You are traveling through Alaska. There are 6,391 polar bears that are lost in the tundra. You decide to help them find their way by leading them to the nearest glacier. However, you can only lead 8 polar bears per trip.
How many trips must you lead before all of the lost polar bears find a new home?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Eyes in a Peacock Muster
You own a Peacock farm. Your favorite thing to do each morning is to look across the farm and see the muster of peacocks. Muster is the noun we use to describe a group of peacocks. As you know, Peacocks have the image of eyes on their tail feathers. If a predator wants to eat them the peacocks will flash their tail feathers, and the predator will think that there are a lot of animals looking at him, so he will get scared and run away.
With their tail feathers flashing the eyes, you see 4,568 eyes. If each tail feather has 3 eyes on it, how many tail feathers do your birds have?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 13,189 ÷ 7 = |
Chalenge 24,286 ÷ 6 = |
Challenge 37,947 ÷ 8 = |
Challenge 42,762 ÷ 9 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 3rd Lesson in this series will begin after this brief message.
Lesson 3
Dividing Three digits by Two (798 ÷ 84 )
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!
Challenge 1 – Watch Me
17 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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 2 – Work With Me
Tiger Streak
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 stripes 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?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Lion Dentistry
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?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 1389 ÷ 74 = |
Chalenge 2426 ÷ 69 = |
Challenge 3947 ÷ 18 = |
Challenge 4762 ÷ 93 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 4th Lesson in this series will begin after this brief message.
Lesson 4
Dividing Four digits by Two (6,781 ÷ 84 )
Challenge 1 – Watch Me
Baby Llamas for Sale
You are raising baby llamas and selling 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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 2 – Work With Me
Road Trip
Your parents just bought a travel-home. Now it’s time to hit the road. You’re heading across the states. It’s 2,924 miles from California to New York. If you go from California to New York in 43-hours, how fast do you drive?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Grand Prix Motorcycle Race
You and your family go to the Grand Prix Motorcycle Race every year. Each competitor must ride his or her bike 9,732 mile in just 12-days. How many miles must the racers ride their motorcycles each day?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 13,189 ÷ 47 = |
Chalenge 24,286 ÷ 36 = |
Challenge 37,947 ÷ 38 = |
Challenge 42,762 ÷ 93 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 5th Lesson in this series will begin after this brief message.
Each of my books includes 10 word problems and another 16 Drill & Kill problems. Each and every problem is linked to a video tutorial like the ones in this post. If you would like to purchase this book, click the Photo.
Lesson 5
Dividing Five digits by Three (64,781 ÷ 874 )
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!
Challenge 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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 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?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Australian Ant Eater
The largest ant colony in the US is in California. This one ant colony runs for 560 miles along the coast. What if 246 Australian 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?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 193,189 ÷ 678 = |
Chalenge 274,286 ÷ 646 = |
Challenge 337,947 ÷ 568 = |
Challenge 412,762 ÷ 439 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 6th Lesson in this series will begin after this brief message.
Each of my books includes 10 word problems and another 16 Drill & Kill problems. Each and every problem is linked to a video tutorial like the ones in this post. If you would like to purchase this book, click the Photo.
Lesson 6
Dividing When Your Quotient is a Decimal (533 ÷ 82 = 6.5 )
Challenge 1 – Watch Me
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 559 feet high. You climb to the top in just 86 minutes. On an average, how many feet do you climb per minute?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 2 – Work With Me
Cloud Eating Camel
You are a scientist studying the strange occurrence of camels eating clouds. This camel has eaten 108 clouds in just 48 hours. On average, how many clouds did this camel eat per hour?
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Nectar Guzzling Humming Bird
You are an ornithologist. That’s a scientist who studies every aspect of birds, including their songs, their flight patterns, their physical appearances, and their migration patterns. Today, you are studying the beautiful humming bird. This bird has drunk 703 milligrams of nectar in just 76 hours. On average, how many milligrams of nectar has this bird drank per hour?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 1324 ÷ 45 = |
Chalenge 2Convert 4/6 into a decimal |
Challenge 3611 ÷ 65 = |
Challenge 4Convert 5/9 into a decimal |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 7th Lesson in this series will begin after this brief message.
Book 7
Area Division – Dividing When your Divisor is a Decimal
Lesson 7
Dividing When Your Devisor is a Decimal (1.026 ÷ .38 = 2.7 )
Challenge 1 – Watch Me
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?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes!
Challenge 2 – Work With Me
Surfer King
You are the king of surfing. You surf the big waves, and you love the challenge. Last year, you surfed a total of 17.1 miles. You need to go from where the wave first starts to break all the way to the beach in order to count your ride as a Surf Run. Each Surf Ride is 0.6 of a mile. How many Surf Runs did you have last year?
Hint: how many 0.6 miles are in 17.1 miles, or 17.1 ÷ 0.6 = n.
Now – Gather your materials and press PLAY. We’ll solve this problem together while you watch the math tutorial video below
Challenge 3 – On Your Own
Waterfall Hike
You love hiking. You came across majestic view on one of your hikes. The waterfall is 28.8 miles from the trail head where your parents parked. You walked 0.8 miles every hour. How many hours did it take you to get to the falls?
Hint: How many 0.8’s are in 28.8, or 28.8 ÷ 0.8?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems like the three above. The books also include another 16 Drill & Kill problems like the 4 in challenge 11.
Drill & Kill
This is where we Drill until we Kill all our mistakes!
I call this section of the book, Drill & Kill, because we will drill this concept until we are perfect, and we kill any mistakes!
The following problems can all be solved with the same strategies we used to solve the first ten problems.
- Solve all four problems on each page.
- Watch the math tutorial video & correct your work.
- Review your work with your parent or teacher.
If you get all 4 problems correct, your parent or teacher may tell you that you’re ready to move to the next book/article within this series.
Good Luck!
Drill & Kill
Challenge – 11
Challenge 1116.25 ÷ 3.75 = |
Chalenge 2158.4 ÷ 4.8 = |
Challenge 372.96 ÷ 0.76 = |
Challenge 435.04 ÷ 4.8 = |
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Each of my books includes 10 word problems and another 16 Drill & Kill problems. Each and every problem is linked to a video tutorial like the ones in this post. If you would like to purchase this book, click the Photo.
Are you interested in saving some big money?
Purchase this series in bulk and SAVE BIG!
Want More Tutorials?
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.
One Last Thing
If you like this post and found it helpful, please leave a brief comment. As a teacher, perhaps the greatest reward I receive is from parents, children, and fellow teachers who use my strategies of education and succeed.
My mission in life and as an educator is to make people feel empowered, self-assured, and happy about who they are in this world! We all have gifts to bestow upon our world. Go forth and do so, and know that you are awesome!
Hi Mr. McCoy, I wanted to thank you for showing me how to do area division. It is a lot easier than doing long division.
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!
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.
Hi there Franccesca –
I am glad to hear that you like using Area Division to solve your math problems.
Good luck to you.
Have a great day!
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!
Hi Evelyn,
I sure appreciate your comments.
Keep up the great work & have a fantastic day!
I like, will read more. Cheers!
Hi Alane –
I am glad to hear that you enjoyed this post.
Thank you for your comment.
Have a great day!
Still loving all of the videos.
Your blogs are helping!
Thanks!
Hi there Malik –
That’s Great! Thanks so much for sharing your success.
Have a fantastic day!
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!
Hi Malik –
Thank you for your kind words. It is great to hear that my blog is helping you.
Best wishes to you my friend and have a great day!
You to have a fantastic day
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.
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!
At first it was really hard but ounce I did more problems it got eaiser.
This does interest me
Thanks!
If you would like more information, please visit my TeachersPayTeachers store.
https://www.teacherspayteachers.com/Store/Mccoys-Math-Link
You can find helpful math problems & video like the samples in this post.
Have a great day!