Contents
 Welcome to Illustrating Fractions This Article is an Introduction to Fractions
 Mathematical Models Make Abstract Concepts Concrete!
 Lesson 1 Illustrating Basic Fractions
 Lesson 2 Adding Fractions with Common Denominators
 Lesson 3 Subtracting Fractions with Common Denominators
 Lesson 4 Adding Fractions with Different Denominators
 Book 5 Subtracting Fractions with Different Denominators
 Lesson 6 Adding Mixed Numbers with Unlike Denominators
 Lesson 7 Subtracting Mixed Numbers with Unlike Denominators
 Lesson 8 Multiplying a Whole Number by a Fraction
 Lesson 9 Dividing a Whole Number by a Fraction
 Lesson 10 Multiplying Fractions
 Lesson 11 Dividing Fractions
 Mathematical Model
Welcome to Illustrating Fractions
This Article is an Introduction to
Fractions
This lesson is designed to offer math help online for children who are learning fractions. There are 2 simple strategies that I teachthroughout all 11 steps in understanding fractions. The 1st step is to draw a box and cut it into the number of parts represented by the denominator. The 2nd step is to color the number of parts represented by the numerator. This is a simple, yet very effective means of developing a concrete understanding of fraction. It is also forms the building blocks to understanding fractions how to add, subtract, multiply and divide fractions.
This Math Help Website is Designed to build a concrete understanding of fractions!
All Problems have Math Video Tutorials!
What happens when you add two fractions with different denominators?
 3/4 + 2/3 = 9/12 + 8/12 = 17/12 = 1 & 5/12
How do you borrow when subtracting fractions?
 3 & 1/3 – 2 & 2/3 = 2 & 4/3 – 2 & 2/3 = 1/3
Why do fractions get bigger when you divide and smaller when you multiply?
 1/2 ÷ 1/4 = 2
 1/2 x 1/4 = 1/8
Mathematical Models
Make Abstract Concepts Concrete!
By drawing Mathematical Models, your child will understand…
 That fractions are simply parts of a whole!
 Why you must have common denominators when adding or subtracting!
 Why an improper fractions is more than a whole, and how to write it as a mixed number!
 How to borrow from a whole number, to make an improper fraction, so you can subtract a smaller fraction from a bigger one!
 Why your answer is smaller when you multiply fractions, and bigger when you divide fractions!
 But Most importantly – you will gain a concrete understanding of fractions, that will help you to excel, and actually enjoy doing the math!
Abstract Concepts Become Concrete
When you multiply a fraction by a whole number, the product or answer is actually smaller not bigger. Children who learn only the algorithm, do not gain a concrete understanding of why multiplication is shrinking a number rather than making it bigger. As a matter of fact, I have spoken with many adults who have only memorized the algorithm and didn’t even realize that the answer was smaller. In today’s classroom, memorizing the algorithm is no longer enough – children need to understand why the the math works.
Fractions are abstract and can be quite
difficult to understand
Most people have a difficult time understanding fractions, because they never took the time to illustrate what is happening when you are working with fractions.
Mathematical Models are the most effective strategy I have ever found for developing a concrete understanding of fractions. When you draw mathematical models, it makes the abstract concepts of math concrete, and then you can understand fractions at a deeper level. One you understand why something works, you will begin to excel, and actually enjoy doing the math.
Mathematical Models
Make Abstract Concepts Concrete!
11 Lessons Teach a Deeper Understanding of Fractions
Cyclical Learning Approach
I have incorporated a cyclical learning approach with math tutorial videos. Each educational concept is introduced, then reinforced, then revisited again and again to ensure success. I have broken this series on fractions into 11 steps or lesson. You will find each lesson in the table of content below.
How to use this Article:
 Grab a sheet of blank paper, and complete each problem.
Use Colored pencils or a highlighter to shade the fractions boxes. Bright colors not only make the learning more fun, it makes learning fractions much easier to understand.  Correct your work, while watching the math tutorial videos.
 After correcting your work, take your paper to your parent or teacher for a final check, and to make sure you understand the concepts taught within this article.
I have scaffold these problems:
 The first problem is a WORK WITH ME.
Read the problem then gather all your materials, so you con do the problem with me.
Play the math tutorial video and pause it when told.
Copy the problem down on your own paper, and solve it with me.
When the math tutorial video is complete, review the problem with your parent or your teacher.  All the following problems are ON YOUR OWN.
Solve the problems just as you did in the first two.
Once you have completed the problem, watch the math tutorial video.
Keep your paper with you while you watch the video.
If you made a mistake, pause the math tutorial video and fix your mistake.
That’s the fastest way to learn!
Don’t forget to take your paper to your parent or your teacher for a final review.
Lesson 1
Illustrating Basic Fractions
Challenge 1 – Watch Me
Puppy in a Seat Belt
You and your mother bake a pan of brownies. You cut the pan of brownies into 1/6 parts, because there will be six people at your grandmother’s birthday party. You load the brownies into the car. Then, you buckle your puppy next to the brownies. You think your puppy is buckled tight, but you are wrong! When you look back, you see that your puppy has escaped. He is eating some of the brownies.
There is only 4/6 of the pan of brownies left.
Can you illustrate how much is left?
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
Pizza Stealing Ram
You live in a mountain cabin. Once a month, your dad drives into town and buys a pizza for you and your mom. He cuts the pan of pizza into 1/3 parts, because there are three of you eating the pizza. You all go to the bathroom to wash up for dinner when you hear the front door burst open. The sound of hooves clipclop on the kitchen floor. Your whole family runs into the kitchen and sees a fullgrown ram eating part of your pizza.
There is only 2/3 of the pan of pizza left.
Can you illustrate how much is left?
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
Party Crashing Cow
You are celebrating a birthday, so your parents buy a beautiful cake for your party. All together there are nine people at the party, so your parents cut the cake into 1/9 parts. You and your friends are climbing the big oak tree in your back yard. You see the neighbor’s cow leading her baby toward the picnic table. Your cake is sitting on the picnic table. It’s far too tempting for the cows. Before anyone can stop them, the mother cow eats a mouthful, and the baby cow eats a nibble or two.
There is only 5/9 of the cake left. Can you illustrate how much is left?
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 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
Problem 1 Can you illustrate 3/5? 
Problem 2
Can you illustrate 7/9?

Problem 3
Can you illustrate 1/4?

Problem 4 Can you illustrate 4/7?

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
Adding Fractions with Different Denominators
Adding fractions, like 2/3 + 3/4 can be very confusing. Unless children are taught to illustrate the addition of the fractions, they often never fully understand what is happening with the fractions. This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 4th videopost continues my cyclical learning approach to the next level of understanding:
4Steps to Adding Fractions with Unlike Denominators!
Step 1 – Illustrate the two fractions (2/3 and 3/4). Then use your LCM (Least Common Multiple) to convert your fractions, so that they have common denominators.
Step 2 – Count up the total number of fraction parts, in this case you would get 17/12. If you move the parts around you can change this improper fraction into the mixed number of 1 & 5/12.
Step 3 – Now move to your algorithm. Multiply both 2/3 and 3/4 by the Giant1, as shown above. This will convert your fractions, so that they have common denominators. Now you can add the numerators.
Step 4 – Make sure that your algorithm agree with your mathematical model. In this case, you have 17/12. If you change 17/12 into a mixed number you have 1 & 5/12, which agrees with your mathematical model.
Mathematical Model
Book 4 – Problem Number 1
Little Pat’s Race
You are teaching little kids how to ride minimotorcycles. Your best rider is Little Pat and he is only 6years old. Little Pat has entered a race. He has ridden his minimotorcycle 2/3 of a mile. He only needs to stay in front of the pack for another 3/4 of a mile to win.
What is the total length of “Little Pat’s Race”?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
PullUp Pete
You are in gym class attempting to do a pullup. Your best friend Pete is doing great. On his first attempt he does 3/4 of a pullup. On his second attempt he does 5/6 of a pullup.
How many pullups has “PullUp Pete” done in all?
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
Pumping Iron Ant
It’s Saturday. You go outside for a day of relaxation. You look on the ground and see an ant pumping iron. Well, he is actually pumping branches. You are amazed. The first branch he pumps is 5/7 of a pound. He throws that one away and grabs another branch. This one is 2/3 of a pound.
How many pounds has your “Pumping Iron Ant” lifted?
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
Problem 14/5 + 1/4? 
Problem 27/8 + 2/3? 
Problem 34/7 + 11/14? 
Problem 48/9 + 1/2? 
Video HereOnce 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.
Book 5
Subtracting Fractions with Different Denominators
Subtracting fractions, like 2/3 + 1/4 can be very confusing. Unless children are taught to illustrate the subtraction of the fractions, they often never fully understand what is happening with the fractions. This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 5th videopost continues my cyclical learning approach to the next level of understanding:
4Steps to Subtracting Fractions with Unlike Denominators!
Step 1 – Illustrate the two fractions (2/3 and 1/4). Then use your LCM (Least Common Multiple) to convert your fractions, so that they have common denominators. If you’re new to illustrating fractions, you might want to review my first videopost in this series, An Easy Way to Understanding Fractions.
Step 2 – Once you have converted your fraction boxes according to your LCM, you’re ready to erase some of your fraction parts. In this case you would erase 3parts, which leaves you with an answer of 5/12.
Step 3 – Now move to your algorithm. Multiply both 2/3 and 1/4 by the Giant1, as shown above. This will convert your fractions, so that they have common denominators. Now you can subtract the numerators.
Step 4 – Make sure that your algorithm agree with your mathematical model. In this case, you have 5/12, which agrees with your mathematical model.
Mathematical Model
Book 5 Problem Number 1
Geraldine the Day Dreaming Giraffe
Geraldine the Giraffe is a day dreamer. She day dreams most of the day away, while other giraffes are busy stretching the necks to the high branches for food. Geraldine walks around day dreaming about her boyfriend Gary. By the end of the day, she will be very hungry and will have to scramble to get enough food.
There is only 2/3 of the day remaining. If Geraldine day dreams for another 1/4 of a day, how much of the day will be left for her to eat?
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Challenge 2 – Work with Me
Larry the Llama
Larry the Llama may look like a relaxed fella, but he is actually a top ranked runner in the llama community. He races around his yard faster than any other llama in his herd. Today is the annual llama race. The course is 5/6 of a mile long. Larry races as fast as he can for 3/4 of a mile.
How much further does Larry have to run and stay ahead of the herd in order to win the race?
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
Banana Gobbling Gorilla
You are on safari in Africa. As the jeep drives past a group of gorillas, you notice that one of them is gobbling a bunch of bananas. He rips one from the stalk, but part of the banana stays on the stalk and part is in the gorilla’s hand. The gorilla is holding 6/7 of the banana in his hand. He bends his head forward and gobbles 2/3 of the banana.
How much of the banana does this Gobbling Gorilla have left to eat?
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
Problem 12/3 – 5/8? 
Problem 23/4 – 2/7? 
Problem 34/5 – 3/6? 
Problem 45/6 – 4/9?

Video HereOnce 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.
Lesson 6
Adding Mixed Numbers with Unlike Denominators
Adding mixed numbers, like 2 & 3/4 + 3 & 5/6 can be very confusing. Unless children are taught to illustrate the addition of the fractions, they often never fully understand what is happening with the fractions. This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 6th videopost continues my cyclical learning approach to the next level of understanding:
4Steps to Fully Understand Adding Mixed Numbers with Unlike Denominators!
Step 1 – Illustrate the two fractions (2 & 3/4 and 3 & 5/6) and use your LCM to change the fractions so that they have common denominators.
Step 2 – Add the fractions boxes to solve the problem.
Step 3 – Now, move to your algorithm. Use the Giant1 to convert your fractions, so they have common denominators.
Step 4 – Add your whole numbers and your fractions to solve the problem. Make sure that your algorithm agrees with your illustration.
Mathematical Model
Book 6 – Problem Number 1
Red Tailed Hawk
You are on a hike when you see a Red Tailed Hawk souring across the sky. It is absolutely beautiful! The hawk is circling round and round in two circles that form an 8. The upper portion of the Eight is 2 & 3/4 miles around. The lower portion of the Eight is 3 & 5/6 miles around.
How far does the Red Tailed Hawk fly each time he completes his figure8 shape in the sky?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Hungry Chipmunk
You are camping in Yellowstone National Park. You are sitting on the picnic table at your campsite eating chips when a cute, little chipmunk scampers up to you. You feed him 2 & 2/3 bags of chips. The next day you are eating more chips when the friendly chipmunk reappears. This time you feed him 2 & 3/5 bags.
How many bags of chips did you feed your Hungry Chipmunk?
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
Mural Project
Your class was asked to create two murals for your school. The murals will be painted on a number of walls near your school’s gymnasium. Your teacher has chosen two art projects for the murals. One is a drawing of Native Americans. The other is a drawing of the people from your community. You get to use 1 & 4/9 walls for one mural and 1 & 2/3 walls for the other drawing.
How many walls will be covered by these two drawings?
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
Problem 11 & 2/3 + 2 & 5/8? 
Problem 23 & 3/4 + 4 & 2/7? 
Problem 32 & 4/5 + 4 & 3/6? 
Problem 45 & 1/6 + 1 & 1/9? 
Once you complete the problem – Hit PLAY on the math tutorial video below. This problem is broke into 2 videos. The first one covers the first two problems and the second one covers the 3rd & 4th problem. Good Luck!
Please read on!
The 7th Lesson in this series will begin after this brief message.
Lesson 7
Subtracting Mixed Numbers with Unlike Denominators
Subtracting mixed numbers, like 3 & 3/4 – 2 & 5/6 can be very confusing. Unless children are taught to illustrate the addition of the fractions, they often never fully understand what is happening with the fractions. This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 7th videopost continues my cyclical learning approach to the next level of understanding:
4Steps to Fully Understand Subtracting Mixed Numbers with Unlike Denominators!
Step 1 – Illustrate the two fractions (3 & 3/4 – 2 & 5/6 ) and use your LCM to change the fractions so that they have common denominators.
Step 2 Once you have converted your fraction boxes according to your LCM, you’re ready to erase some of your fraction parts. In this case you need to convert one of your wholefractions boxes into 12/12 as shown above. Then erase 10boxes, which leaves you with an answer of 11/12.
Step 3 – Now, move to your algorithm. Use the Giant1 to convert your fractions, so they have common denominators.
Step 4 – Subtract your whole numbers and your fractions to solve the problem. Make sure that your algorithm agrees with your illustration.
Mathematical Model
Book 7 – Problem Number 1
Sloth
You are on vacation in the rain forest of South America. You discover a slow sloth clawing across the ground. He is headed for a large tree 3 & 3/4 yards away. You watch his slow progress as he moves one foot in front of the other. After a full minute the slow sloth has only traveled 2 & 5/6 yards.
How much further does your slow moving sloth have to travel before he reaches his tree?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Hungry Octopus
You are part of the Junior Marine Biology Club of America. Your Club is scuba diving off the coast of Monterey California. You observe an octopus eating clams. There are 2 & 2/3 clams hidden in the sand. The octopus finds and eats 1 & 4/5 of the clams.
How many clams does the Hungry Octopus have left to eat?
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
Carrot Chomping Horse
You have wanted a horse of your own for as long as you can remember. You have saved and saved. Finally, you have enough money for your horse. She is a beautiful mare and she loves chomping on carrots. You buy 2 & 7/9 carrots for her. She chomps away 1 & 2/3 of the carrots.
How many carrots are left?
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
Problem 12 & 2/3 – 1 & 5/8? 
Problem 24 & 3/4 – 1 & 2/7? 
Problem 34 & 4/5 – 3 & 5/6? 
Problem 45 & 1/6 – 1 & 1/9?

Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 8th Lesson in this series will begin after this brief message.
Lesson 8
Multiplying a Whole Number by a Fraction
Multiplying a whole number by a fraction, like 2/3 x 5 can be very confusing.
If you are multiplying, why is the answer smaller than 5?
Unless children are taught to illustrate the addition of the fractions, they often never fully understand what is happening with the fractions. This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 8th videopost continues my cyclical learning approach to the next level of understanding:
3Steps to Fully Understand Multiplying a Whole Number by a Fraction!
Step 1 – Create your fractions boxes. In this case you would create 5 whole boxes. Then cut each box into 3parts.
Step 2 – count your fraction parts. In this case you would have 10/3. If you move the shaded parts, you can make 3wholes and have an extra 1/3. Therefore you answer is 10/3 or 3 & 1/3.
Step 3 – Now, move to your algorithm. Convert your whole number into a fractions, and then multiply your numerators and denominators. In this case you would get 10/3 or 3 & 1/3, which agrees with your mathematical model.
Mathematical Model
Book 8 – Problem Number 1
Evian Drinking Kangaroo
You are a scientist studying the strange occurrence of a kangaroo that drinks nothing but Evian water. You are tasked with the job of making sure that the kangaroo drinks the correct amount of water.
You have 5 bottles of Evian water. You must feed the kangaroo exactly 2/3 of the Evian water. How much water will you give the kangaroo?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Long Eared Carrot Eaters
Ever since you were tinytiny you loved bunnies. For your last birthday, your parents bought you two baby bunnies. You love petting their long ears as they nibble away at their food. Last night you gave them 6carrots. They ate 4/7 of the carrots.
How much did your Long Eared Carrot Eaters eat?
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
Pink Flamingo Research
You are a biologist researching pink flamingos and their diet. You are tasked with the job of discovering how much they eat. You watch as a pink flamingo eats 11 shrimp. However, you notice that the flamingo only eats 3/4 of each shrimp. The flamingo spits the rest of the shrimp into the water, where tiny fish nibble at the remains.
How much shrimp have you observed the pink flamingoes eat?
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
Problem 12/3 x 5 = ? 
Problem 24 x 2/7 = ? 
Problem 33 x 4/6 = ? 
Problem 41/6 x 8 = ?

Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 9th Lesson in this series will begin after this brief message.
Lesson 9
Dividing a Whole Number by a Fraction
Mathematical Model
Book 9 – Problem Number 1
Lazy Lion Pride
Meet the laziest pride of lions in the entire continent of Africa. This pride of cats has found 6 trees that overlap with thick branches intertwining from one tree to the next. The Lazy Lions divide each tree into 3/4 parts. Each lion gets 3/4 of a tree for napping. How many of these Lazy Lions are sleeping in the trees?
* Hint: How many 3/4’s are in 6?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Mathematical Meerkats
These Meerkats are confused. They just found three tasty scorpions, which they love to eat. Now, they are leaning back and trying to do the math.
Each meerkat wants to eat 2/3 of a scorpion, because that is the perfect sized meal for a growing meerkat.
Is there enough scorpions for each of these four meerkats to have 2/3’s of a scorpion?
How many 2/3’s are in 3?
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
Wet Willy
Wet Willy is an adorable pup who went for a swim in his owner’s pool. He jumped out, ran into the living room, and shook himself dry. Water flew all over the place. It slashed onto 3 paintings, one of which was an irreplaceable painting of President Washington. Wet Willy knew that he did something wrong. He started licking all the water off the paintings, but he can only lick 3/5 of a painting at a time.
How many 3/5 portions of the paintings will Wet Willy have to lick before he’s done?
Hint: How many 3/5’s are in 3?
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
Problem 12/3 ÷ 5 = ? 
Problem 24 ÷ 2/7 = ? 
Problem 33 ÷ 4/6 = ? 
Problem 41/6 ÷ 8 = ? 
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 10th Lesson in this series will begin after this brief message.
Lesson 10
Multiplying Fractions
Mathematical Model
Book 10 – Problem Number 1
Ferlon the HighFiving Tortoise
Ferlon may be slow, but he is friendliest critter this side of the Mississippi River. He is constantly highfiving all his friends as he walks through his neighborhood. Today, he walked 5/7 kilometers. If Ferlon highfives his friends for 3/8 of the time he is walking, what portion of the kilometers is Ferlon the HighFiving Tortoise exhibiting
his friendly nature to all his friends?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Pinky Tuskadaro the Calculating Orangutan
Meet Pinky Tuskadaro. He’s a mathematical genius! Pinky has to use his fingers and toes, but he can add, subtract, multiply, and divide. As a mater of fact, Pinky spends 6/7 of his waking hours calculating mathematical facts.
If Pinky is awake 3/5 of the day, how much of the day does Pinky Tuskadaro the Calculating Orangutan spend calculating mathematical problems?
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
Wrong Way John
Wrong Way John is a wandering giraffe. He is constantly turning the wrong way, getting stuck in the brambles, and loosing his way. Last week he traveled 3/4 miles.
If he gets lost 3/8 of the time he is traveling, what portion of the miles is Wrong Way John lost?
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
Problem 12/3 x 5/8? 
Problem 23/4 x 2/7? 
Problem 34/5 x 3/6? 
Problem 45/6 x 4/9? 
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
The 11th Lesson in this series will begin after this brief message.
Lesson 11
Dividing Fractions
Mathematical Model
Book 11 – Problem Number 1
Terrance the Ticklish Mule
Terrance loves his alfalfa, but his owner keeps tickling his nose. His owner loves Terrance, but he can’t help tickling his favorite mule. Each day, Terrance eats 2/3 pounds of alfalfa. His owner divides the alfalfa into portions that are 2/7 pounds, how many portions will Terrance get to eat?
Hint: How many 2/7’s are in 2/3?
Now – Press PLAY and watch the math tutorial video below. Then copy these strategies into your notes.
Challenge 2 – Work with Me
Singing Camels
Kami & Connie Camel love to sing. They walk around their paddock and sing to all the on lookers. Kami & Connie’s paddock is 8/9 miles long.
If Kami& Connie break the paddock into portions that are 3/4 miles, how many portions will our “Singing Camels” walk and sing?
Hint: How many 3/4’s are in 8/9?
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
Honovi the Honey Lov’n Grizzley Bear
Honovi is always on the lookout for bees. She follows them back to the hive and collects as much honey as possible. Yesterday, Hovoni found a hive. While the bees crawled under her fur and stung again and again, Honovi stole 4/5 pounds of honey. If Hovoni divides the honey into portions that are each 1/8 pound, how many portions can she make?
Hint: How many 1/8’s are in 4/5?
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
Problem 12/3 ÷ 5/8? 
Problem 23/4 ÷ 2/7? 
Problem 34/5 ÷ 3/6? 
Problem 45/6 ÷ 4/9? 
Once you complete the problem – Hit PLAY on the math tutorial video below. Good Luck!
Please read on!
Need Help with Division?
I have a series on division that is specifically designed for children who do not have all of their multiplication facts memorized. The series is designed in a similar manner to this series on multiplication, where each and every problem is linked to a video tutorial. Here is a link to my series on Division.
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 webbased, 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, selfassured, 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!
Is there any updates coming soon from this site?
Hi Selo –
I am sorry for the delay. At the end of the school year (last year), I was asked to create a series on my method of teaching division. We have a number of students at my school who struggle with long division, and I have created an alternative called area division. I created the series, but it took me all summer to complete it.
Now school is back in session, and I am teaching full time, but I will do my best to complete this series on fraction.
Thanks for reminder that I need to get back to work on fractions.
In the meantime – if you need help with division, check out Area Division
http://teachersdungeon.com/blog/longdivisionanswersthereisaneasierway/
Have a great day!
Hi Brian, your “11Steps to FULLY Understand Fractions” is so brilliant. You have a very profound knowledge on fractions. You have presented a lot of ideas on how to deal with fractions. This is very helpful to all kind of students and also to all teachers. Regarding adding and subtracting fractions, let me also share my idea on how to deal with fractions.
Adding and Subtracting fractions maybe difficult at first but keeping on practicing will make it easier in the long run. To add and subtract fractions successfully is to make the rules stick to your memory. So I have to mention again the rules here.
Rules are:
Same denominator:
Add both numerators then reduce. The result would be the final answer.
Different denominator (4 steps):
1. Multiply the numerator of first fraction to the denominator of second fraction. The result is the new numerator of first fraction.
2. Multiply the numerator of the second fraction to the denominator of first fraction. The result is the new numerator of second fraction.
3. Multiply both denominators. The result is the common denominator for two fractions.
4. Add the two new numerators. The result is the answer.
To make it stick to your memory:
Rules for subtraction:
Same denominator:
Subtract second numerator from first then reduce. The result would be the final answer.
Different denominator (4 steps):
1. Multiply the numerator of first fraction to the denominator of second fraction. The result is the new numerator of first fraction.
2. Multiply the numerator of the second fraction to the denominator of first fraction. The result is the new numerator of second fraction.
3. Multiply both denominators. The result is the common denominator for two fractions.
4. Subtract new second numerator from first new numerator. The result is now the answer.
To make it stick to your memory:
Same numerator:
Add two fractions 50 times.
Subtract two fractions 50 times.
Different denominator:
Add two fractions 100 times.
Subtract two fractions 100 times.
To check if your answer is right and your step by step solution is correct:
Use fraction calculator with button from http://www.fractioncalc.com to be sure that your fraction solution is correct.
The key here is to make the rules implanted into the minds of the students so that they will never forget.
Hello Anne –
Thank you for your kind words and great advice.
I really like your suggestion to practice working with fractions until it become easy. I also like your suggestion to solve problems and then check your work with the the fractions calculator website.
Have a fantastic day – Brian