### Subtracting Fractions with Uncommon Denominators

As I have mentioned in prior posts, fractions are a difficult concept for children to understand. In this fifth Video-Post, I will demonstrate how to subtract fractions with different or uncommon denominators. I encourage you to take the time to do all the activities with your child before moving on to more advance Video-Posts. Each video tutorial will build upon what was taught in the last post.

*Mathematical Models*

After over a quarter of a century in the classroom, the most effective strategy I have ever found is having children draw mathematical models that illustrate what is happening with the math. When children draw mathematical models of multiplying a whole number by a fraction, it makes the abstract concepts of math concrete, and then they understand why the math works. When they understand why something works, they excel, and actually enjoy doing 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.

### My Analogy to Sports

Before I became a teacher, I coached gymnastics.

In order to be successful at gymnastics, or any sport for that matter, the athlete needs to have good technique. A strong basic technique, allows the athlete to excel in his or her sport. However, if the athlete has poor or improper technique, that athlete will struggle and not be able to compete at the higher caliber levels, like division-1 college sports.

The same is true with math.

In order to become proficient in math, children must have a strong understanding of the basics. My books on fractions are designed to develop a strong basic understanding, so children can excel throughout their educational career. Therefore, it is important that children train like an athlete and drill the basic concepts until they have a strong basic technique. Once they have a strong understanding, they are ready for the next book in this series.

Free Preview

This post is a free preview of my tutorial eBook.

My eBook is unique, because – just like this post – it includes a video tutorial for each and every problem!

__WATCH ME__

__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.

Geraldine the Day Dreaming Giraffe

5.1- Watch Me

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?

Your Challenge:

This one is easy. Watch the video below to see how to add these fractions. Pay close attention. Your next challenge will be very similar to this one.

__WORK WITH ME__

__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.

*Larry the Llama*

5.2 – Work with Me

Larry the Llama may look like a relaxed fella, but he is actually 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?

Your Challenge:

This one is a little harder.

__Gather the following materials__:

- A blank piece of paper
- A pencil
- A Sharpie marker
- Crayons
- A highlighter

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__

__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.

*Banana Gobbling Gorilla*

5.3 – On Your Own

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 hold 6/7 of the banana in his hand. He bends his head forward and gobbles 2/3 of a banana.

How much of the banana does this Gobbling Gorilla have left to eat?

Your Challenge:

__Gather the following materials__:

- A blank piece of paper
- A pencil
- A Sharpie marker
- Crayons
- A highlighter
- A blank piece of paper

Complete the __illustration__ and the __algorithm__ to find the answer to this problem.

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 play button on the video below:

Keep your paper with you while you watch the video.

If you make a mistake, pause the video and fix your mistake.

That’s the fastest way to learn!

*Doggie Shoe Thief*

5.4 – On Your Own

Your parents just bought you a puppy. He is tiny, fluffy, and adorable. Unfortunately, he is also a thief. Yes – your brand new puppy steals shoes. He rips them of of people’s feet as they walk past.

The lady in the photo above has shoes that slip partway off her feet each time she takes a step. She walks past your pup and her shoe slip a little. Now only 5/6 of her foot is covered by her shoe. Your puppy launched himself toward her shoe. He gripped it and pulls the shoe another 2/3 of the way off.

How much of the shoe is left on the lady’s foot?

__Gather the following materials__:

- A blank piece of paper
- A pencil
- A Sharpie marker
- Crayons
- A highlighter
- A blank piece of paper

Complete the __illustration__ and the __algorithm__ to find the answer to this problem.

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 play button on the video below:

Keep your paper with you while you watch the video.

If you make a mistake, pause the video and fix your mistake.

That’s the fastest way to learn!

Pay close attention. Your next challenge will be very similar to this one.

### Skateboard Sam

5.5 – On Your Own

Skateboard Sam is on a quest. He wants to the the first 6-year old to ride his skateboard the entire length of Gopher Road. Gopher Road got its name, because there are thousands of gophers on both sides to the road. Skateboard Sam loves riding his skateboard, while the gophers stand on their hind legs and watch him roll past.

Gopher Road is 4/5 of a mile long. Skateboard Sam has rolled for 3/4 of a mile.

How much further must Skateboard Sam ride his skateboard in order to accomplish his quest?

__Gather the following materials__:

- A blank piece of paper
- A pencil
- A Sharpie marker
- Crayons
- A highlighter
- A blank piece of paper

Complete the __illustration__ and the __algorithm__ to find the answer to this problem.

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 play button on the video below:

Keep your paper with you while you watch the video.

If you make a mistake, pause the video and fix your mistake.

That’s the fastest way to learn!

Pay close attention. Your next challenge will be in the Video-Post entitled, __Adding & Subtracting Mixed Numbers__. The concept builds from this one, so it is important that you understand how to illustrate fractions.

**Price**: $2.^{99}^{
}**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, shoot me an email at brian@teachersdungeon.com. I will put you on my email list and let you know as soon as it is available.

Subtracting Fractions with Different Denominators will help children in 3^{rd} through 6^{th} grades to understanding fractions at a deeper level. In this book, I will teach children how to create mathematical models that clearly show what is happening when you Subtract Fractions with Different Denominators.

# Books within this series

There are eleven books in this series on fractions. I have incorporated a ** cyclical learning approach**, where each educational concept is first introduced, then reinforced, then revisited again and again – with each subsequent book rising to the next level of competency.

For this reason, it is important that you begin the appropriate level of competency.

### Choosing the Right Book

**If you are a student who is struggling to understand concepts in this video**-post, I suggest you go back to my very first post (An Introduction to Illustrating Fractions). Do not worry if the concept seems too low for your grade. For example, if you are in 6^{th} grade, but you have never learned how to drawn a fraction box – don’t worry. There is nothing wrong with going back to the basic back for a moment to improve your technique. This will only make your math stronger as you increase in difficulty.

**If you**** are able to follow the concepts of this video-post**, but you can not complete the third problem on your own – Then this is the right book for you. You are ready to learn these concepts.

**If you**** can complete the third problem in this video-post on your own**, and you completely understand how it is done, then you are ready for the next concept in this series. Go to my next video-post.

All my books video tutorials linked to each and every problem. Below you will find links to blog-posts that give you a free preview of each book. By previewing my books, you can see exactly where your child’s level of understanding is, and which book you need.

Book 1

** An Easy Way to Understanding Fractions**

After reading this book and completing the activities, you will be able to draw mathematic models of fractions. This book forms the building blocks of understanding for all books in this series.

Book 2

Adding Fractions with Like Denominators

After reading this book and completing the activities, you will be able to add fractions with like denominators. You will be able to draw mathematic models that represent the addition of fractions, effectively proving why your answer is correct.

Book 3

Subtracting Fractions with Like Denominators

After reading this book and completing the activities, you will be able to subtract fractions with like denominators. You will be able to draw mathematic models that represent the subtraction of fractions, effectively proving your answer is correct.

Book 4

Adding Fractions with Different Denominators

After reading this book and completing the activities, you will be able to add fractions with different denominators. You will be able to draw mathematic models that represent the addition of fractions, effectively proving why your answer is correct.

Book 5

Subtracting Fractions with Different Denominators

After reading this book and completing the activities, you will be able to subtract fractions with different denominators. You will be able to draw mathematic models that represent the subtraction of fractions, effectively proving why your answer is correct.

Book 6

Adding Mixed Numbers

After reading this book and completing the activities, you will be able to add mixed number fractions with different denominators. You will be able to draw mathematic models that represent the addition of mixed number fractions, effectively proving why your answer is correct.

Book 7

Subtracting Mixed Numbers

After reading this book and completing the activities, you will be able to subtract mixed number fractions with different denominators. You will be able to draw mathematic models that represent the subtraction of mixed number fractions, effectively proving why your answer is correct.

Book 8

Multiplying a Whole Number by a Fraction

After reading this book and completing the activities, you will be able to multiply a whole number by a fraction (ie: 6 x ¼). You will be able to draw mathematic models that represent the multiplication of the whole number and the fraction, effectively proving why your answer is correct.

Book 9

Dividing a Whole Number by a Fraction – Coming Soon

After reading this book and completing the activities, you will be able to divide a whole number by a fraction (ie: 6 ÷ ¼). They will be able to draw mathematic models that represent the multiplication of the whole number and the fraction, effectively proving why your answer is correct.

Book 10

Multiplying Fractions – Coming Soon

After reading this book and completing the activities, you will be able to multiply a fraction by another fraction (ie: ½ x ¼). You will be able to draw mathematic models that represent the multiplication of fractions, effectively proving why your answer is correct.

Book 11

Dividing Fractions – Coming Soon

After reading this book and completing the activities, you will be able to divide a fraction by another fraction (ie: ½ ÷ ¼). You will be able to draw mathematic models that represent the division of fractions, effectively proving why your answer is correct.

### Special Note to Parents

Although my book can be used as a personal tutor for your child with problems for them to practice and instructions given through the video tutorials; I encourage you to complete this book side-by-side with your child. Here is why.

I’ve been teaching for over a quarter of a century, and have helped close to a thousand students. I have found that the **number-one** determining factor to any child’s educational success is the personal involvement of their parents. It’s more important than the school you choose. It’s more important than the teachers your child has from one year to the next.

Children naturally aspire to please their parents. It’s in their DNA. I know that this is not so evident through the adolescent years, when children are developing their independence and trying to establish who they are in the world as an individual. But trust me – even as they go through their adolescence, your child seeks your approval. Your child need your guidance, wisdom, and admiration. Your involvement in his or her life drives him or her to be the best person he or she can be. So if you are able to complete this book side-by-side with your child – please do so.

You may even find yourself loving math. I have had many parents come up to me after observing in my class. They say, “I wish I had learned math the way you teach it. I would have done much better.”

If you are not able to complete the entire book with your child, I encourage you to check in on your child periodically. Give him or her plenty of positive reinforcement for completing this book. Your praise will go a long way in helping your child develop positive self-esteem as well as self-confidence around mathematics.

### Why I Write

My mission in life it to pay it forward through education. When I was in first grade my parents divorced. Later I learned that I had a learning disability called dyslexia. When I should have been learning my basic math facts, I was thinking about my dad and the fact that I no longer lived with him. When I was trying desperately to read, my mind was flipping letters and words, which make decoding the English language next to impossible.

Needless to say, school did not come easy for me. I had a number of amazing teachers who were patient and helpful. I also had a few teachers who actually slowed my learning even more. As time went by, I knew that I wanted to go to college. I started developing some of my own strategies that helped me understand what was gong on with math.

When I decided to become a teacher, I wanted to help all children, not just the kids who were natural learners. My skills in educating students become so good that I was asked to teach the Gifted and Talented Class. My strategies not only helped kids who struggled, but also created a deeper understanding for the gifted student who needed depth & complexity in their learning plan.

Now, I am able to share my strategies with you through this book and the video tutorials that accompany it.

I wish you the best of luck!

### Want more Tutorials?

I’ve created an Educational Fantasy Game called, TeachersDungeon. It 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.

__Novels by McCoy__** –**

__Novels by McCoy__

I have written a number of books that are available on Amazon. I have nonfiction books on mathematics that link to video tutorials and are designed to help children gain a deeper understanding of the math. Here is a link to the first book in my series on fractions. I have also written a chapter book and a young adult novel. You can have a free preview by clicking on the links below.

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.

I hope you enjoyed this Video-Post. If you have any questions or want to share your thoughts, please leave a comment below. I do my best to respond to comments as quickly as possible.

Until next time…

Have a great day – Brian McCoy

In measurements, fractions appear whenever units are not small enough to express quantities in integers. For example, five quarter-dollars will buy you exactly as mush as a dollar and a quarter. One and a half dollar stands for exactly the same quantity as three half-dollars or six quarter-dollars.

Fractions are unavoidable and sooner or later we all have to learn to work with fractions. The mathematical usage of the word fraction has a very clear everyday connotation as a part of a bigger object. It would be unthinkable nowadays to just introduce fractions as a pair of numbers and postulate their basic properties. Still, to express fractions one needs a pair of numbers with a meaning and intuition attached to them.

When multiplying fractions, the numerators (top numbers) are multiplied together and the denominators (bottom numbers) are multiplied together. To divide fractions, rewrite the problem as multiplying by the reciprocal (multiplicative inverse) of the divisor. To add fractions that have the same, or a common, denominator, simply add the numerators, and use the common denominator. However, fractions cannot be added until they are written with a common denominator. The figure below shows why adding fractions with different denominators is incorrect.

Hi Mr. Calc –

Thanks for sharing. I checked out your website and you fraction calculator. It is very cool. I like the way your calculator breaks down the algorithm step-by-step, so children can see the solution for any given problem.

Thanks again & have a great day!