11-Steps to FULLY Understand Fractions

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

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-Steps to 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.

Step-1
An Easy Way to Understanding Fractions

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?

The video below shows how I teach children to illustrate Fractions.

I teach the 11-Steps to FULLY Understand Fractions in a similar manner to how I teach students within my class.

First, I have children complete a “Watch Me” problem, like the  one above.  Once they have completed the video, I have them copy down the entire problem into the notebook.

Next, I have students complete a “Work with Me” problem, where Children read the problem, and then watch a video.  While watching, children are instructed to pause the video and copy the problem along side me.

Finally, I have children complete a number of problems on their own in order to solidify their skills.  Once they complete each problem, they are instructed to watch the “On Your Own” video.  During these videos, I encourage children to correct their 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 all of my educational books.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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.

Step-2
Adding Fractions
with Like Denominators

Mathematical Model

Math Ninja Celebration

You just won the “Math Ninja” award at your school for solving problems about fractions.  It’s Celebration time!  Your mother made you two special pies to celebrate your awesomeness.  One pie is chocolate and the other is lemon.  She asked you to cut both pies into 1/7 parts.  After cutting the pies you are overwhelmed with temptation.  You decide to eat a few slices from each pie.  Now there is only 3/7 parts of the chocolate pie and 4/7 parts of the lemon pie.

How much pie do you have in all?

The video below shows how I teach children to add like Fractions.
 

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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.

Step-3
Subtracting Fractions
with Like Denominators

Mathematical Model

Go-Kart Race

You and your three very best friends are invited to the National Go-Kart Race.  The race course is 8/9 of a mile long.  It twists this way and that; curving around tight corners and then shooting up one hill and down another.  You are driving like a pro.  You are in the lead.  You have completed 4/9 of the course.  How much further must you go in order to win the race.

The video below shows how I teach children to Subtract like Fractions.

 

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers

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.

.

Step-4
Adding Fractions
with Different Denominators

Mathematical Model

Little Pat’s Race

You are teaching little kids how to ride mini-motorcycles.  Your best rider is Little Pat and he is only 6-years old.  Little Pat has entered a race.  He has ridden his mini-motorcycle 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”?

The video below shows how I teach children to Add Un-Like Fractions.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it soon.

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.

Step-5
Subtracting Fractions
with Different Denominators

Mathematical Model

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?

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.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it soon.

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.

Step-6
Adding Mixed Numbers

Mathematical Model

6.1- Watch Me

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 figure-8 shape in the sky?

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.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it soon.

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.

Step-7
Subtracting Mixed Numbers

Mathematical Model

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?

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.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it soon.

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.

Step-8
Multiplying a Whole Number
By a Fraction

Mathematical Model

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?

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.

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.
I have completed the planning and outline stages of this book, and will be publishing it soon.

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.

Step-9
Dividing a Whole Number
By a Fraction

Mathematical Model

Book 9
Dividing a Whole Number by a Fraction 

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it 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.

Step-10
Multiplying Fractions

Mathematical Model

Book 10
Multiplying Fractions 

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it 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.

Step-11
Dividing Fractions
Mathematical Model

Book 11
Dividing Fractions

Would like more information on this concept?
Check out my interactive ebook!

Price: $12.50
Available at Teachers Pay Teachers
Coming Soon – I am currently working to complete this series on fractions.

I have completed the planning and outline stages of this book, and will be publishing it 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.

Thanks for reading this article.
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

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 my series on Division.  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.

One Last Thing

If you like this post and found it helpful, please click one of the share buttons for FaceBook, InstaGram, or LinkedIn at the top of this post.  You can also leave a comment.  I would love to hear how this this post and/or my books have helped.  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!

Thanks & have a fantastic day – Brian McCoy

2 Comments on “11-Steps to FULLY Understand Fractions

    1. 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/long-division-answers-there-is-an-easier-way/
      Have a great day!

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