###### 3-Steps to Understanding Fractions!

Fractions can be very confusing. Unless children are taught to illustrate 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 introduction video-post begins my **cyclical learning approach** to fully understand fractions:

**An Easy Way to Understand Fractions!**

**Step 1** – Create a fractions box and cut the box into the same number of parts as the denominator. In this case (4/6), the denominator is six, so the fraction box gets cut into 6-parts.

**Step 2** – Color in the number of fractions parts indicated by the numerator. In this case (4/6), the numerator is four, so you would color in 4-parts.

**Step 3** – Make sure that your fraction agrees with your mathematical model. In this case you have 4 out of 6-parts, which is equal to 4/6, so your fractions agrees with your mathematical model.

###### The “1.1 Watch Me” video below shows a

detailed explanation of this problem!

*Mathematical Models*

*Make Abstract Concepts Concrete!*

Contents

By drawing Mathematical Models, you 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.

### 11-Video Posts

to

Fully Understanding 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 step rising to the next level of competency. There are 11-Video-Posts (like this one) that take children for the beginning basics of fractions all the way through multiplying and dividing fractions.

I introduce each step of Understanding Fractions in a similar manner to how I teach my students within my class.

###### WATCH ME

For this first problem, I encourage you to simply watch how the problem is solved. I like to introduce any new concept in this manner, so you can relax and focus on the strategies for solving the problem.

###### WORK WITH ME

For this second problem, I encourage you to develop your skills by working side-by-side with me. I would like you to watch a bit of the video, then pause it, and copy what I do on your paper.

__ YOUR OWN__

For the remaining problems, I encourage you to solidify your skills by completing the problems on your own. Once you have completed the problem, watch the video, and correct your mistakes. Over the years, I have found that children make substantial jumps in understanding when they find their own mistakes and then fix them. That is why I have included this form of teaching into this post.

### 1.1- Watch Me

*Puppy in a Seatbelt*

You and your mother bake a pan of brownies. You to cut the pan of brownies into 1/6 parts, because they will to 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?

###### This is a “Watch Me” Challenge:

Simply watch the video below to see how this problem is solved. Pay close attention. Your next challenge will be very similar to this one.

### 1.2 – Work with Me

*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 clip-clop on the kitchen floor. Your whole family runs into the kitchen and sees a full-grown ram eating part of your pizza.

There is only 2/3 of the pan of pizza left. Can you illustrate how much is left?

__This is a Work with Me Video__

__This is a Work with Me Video__

**Gather the following materials:
**A blank piece of paper

A pencil

A Sharpie marker

Crayons or a highlighter

- Play the video below.
- Pause the video when told.
- Copy the problem down on your own paper, and solve it with me.

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

### 1.3 – On Your Own

*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?

###### Your Challenge:

__Gather the following materials__:

- A blank piece of paper
- A pencil & a pen or sharpie
- Crayons or a highlighter

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, play 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!

How did you do?

Were you able to complete all three problems successfully?

If you answered Yes – Then you are ready for the next level.

Adding Fractions with Like Denominators

**If you would like more time reviewing this concept, you can purchase my ebook by clicking on the link below.**

**Price**: $4.^{49
}**Available through Amazon**

This eBook is designed to help children in 3^{rd} through 6^{th} grades to understanding fractions at a deeper level. This is an introduction to creating mathematical models that illustrate fractions. I teach children how to use rectangles as models for fractions. I use rectangles rather than circles, because rectangles can easily be converted into equivalent fractions when children advance to add or subtract fractions with unlike denominators. The rectangles are also used when children illustrate multiplication and division of fractions. Therefore, the more children become familiar with illustrating rectangular fractions, the more proficient they will be in adding, subtracting, multiplying, and dividing fractions.

When children illustrate fractions, they are able to see the abstract concepts of fractions. Once children become familiar with drawing these mathematical models, they develop a concrete understanding and will excel in their education.

# 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

**Fractions are abstract and can be very confusing, therefore, it is important that you begin the appropriate level of understanding. **

**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 like: 3/7, 4/5, and 8/9. 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 (ie: 3/7 + 2/7 = 5/7). 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

(ie: 3/7 – 2/7 = 1/7). 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

(ie: 3/4 + 2/3 = 1 & 5/12). 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

(ie: 2/3 – 1/4 = 5/12). 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

(ie: 2 & 3/4 + 3 & 5/6 = 6 & 7/12). 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

(ie: 3 & 3/4 – 2 & 5/6 = 11/12). 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.

### 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 Introduction to Area Division

Area Division is structure in such a way that absolutely anyone can successfully divide large numbers. I developed Area Division by incorporating skip counting, and an area box for the division. By incorporating skip counting, even students who do not know their multiplication facts can successfully divide large numbers.

MY ADVENTURES WITH CHICKENSPIKE – This is a chapter book that is perfect for children in 3rd and 4th grades. My Adventures with ChickenSpike is a Children’s Fantasy Book. The main character is a young boy who is being bullied. He travels to a distant planet and finds his inner strength. By the time he returns home not only is he no longer a victim, he is a hero!

RED – This is a young adult novel that is especially designed for children in 5th and 6th grades. Red is an action packed adventure with two main characters and a number of supporting characters that add humor and drama to this novel. Bruno Vic and Evelyn Rose attend Sir Francis Drake Middle School. Bruno is big, street-wise, and tough, but he also has high morals and undying loyalty to his friends. Evelyn Rose was born rich, but an unfortunate turn of events has landed her in the heart of the Tenderloin District of San Francisco. Bruno, Evelyn, and their friends are desperate to steer clear of the gangs, so the turn to a mysterious man that the gangs seem to fear. His name is Red.

### One Last Thing

If you like this post and found it helpful, please click one of the share buttons. My mission in life is to empower children academically, and to help them develop a strong self-esteem. You can help by sharing this post!

Thanks!

Thank You for this.

Hey Simple 3-D

Thanks for your support!

Have a great day!

Hi Mr. McCoy –

This is Great!

It really helped me understand fractions better.

You have amazing strategies. That is why I am glad that you are my teacher.

Hi Andrew –

Thanks so much. I think you are an awesome student.

I’m glad you found this post on Fractions helpful.

Have a great day!

Hi Andrew –

Right back at you – I think you are awesome!

Thank you for you kind words.

Have a great day!