11-Steps to Understanding Fractions

In this post, I will teach you the basics to understanding fractions.  We will being with the first step of illustrating fractions, work through adding and subtracting fractions, and finally to multiplying and dividing fractions.  This post is intended for anyone who does not understand fractions.

Fractions are abstract and can be quite
difficult to understand

Contents

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.

  • 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 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.

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

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.

Step-1
An Easy Way to Understanding Fractions

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 one is a little harder.

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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:
  1. A blank piece of paper
  2. A pencil
  3. 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, click the link 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.

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

Price: $2.99
Available on Amazon

 

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.

A quick side note…
Special Note to Teachers

Hello Fellow Teachers –

If your classroom is anything like mine, you have a number of students that are right at grade level, and a handful of students that are either below or above grade level.  It can sometimes be a challenge to meet all the individual needs of your students.  Here’s what I do for my students that are blow grade level…

In the beginning of the year I do a quick assessment to see exactly where kids are at in their understanding number sense.  If children are below standards, I invite them to my “Math Ninja’s Class”.  This is a before school intervention class.

Here’s how I run my Math Ninja’s Class:

  1. At the beginning of class I compliment students on their dedication to their learning, and their commitment in coming to the Math Ninja Class.
  2. I direct each student to their individual level of understanding.  For example, I may have a student that is at the very beginning level of understanding.  I would put that student on the very first book, where he or she can learn to make mathematical models of fractions.  If another student is struggling with adding unlike denominators, I put him or her on the 4th book in my series.
  3. I give each student a set of headphones and have them go through the “Watch Me” problem, the  “Work with Me” problem, and all the “On Your Own” problems.
  4. As students complete each problem, I go for child to child reviewing their work.  This is actually pretty quick and easy for two reasons.  One, each child has already watched a video and corrected their work with the “video me”.  Two, while I am reviewing one students work, other children are either working on their problems or watching their videos and correcting their own work.
  5. When my students get a problem correct, I praise their work.  If they get the problem wrong, I check to make sure that they corrected their work as instructed during the video, and then I praise their efforts.

I run my Math Ninja’s Class 4-days per week, and it has been incredibly successful.  If you purchase any one of my books, feel free to put them on a devise that can be shared with all your students.  I put a PDF copy in my Google Drive and invite students to that folder.

Step-2
Adding Fractions
with Like Denominators

Mathematical Model

2.1- Watch Me

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?

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.

 

2.2 – Work with Me

Dog Food Stealing Raccoon

A raccoon has been seeking into your garage and eating your dog’s food for two nights.  He crawls through the doggy-door, opens the dog-food canister, tips it over, and start chowing down.  You hear the clamor of crashing containers and rush to the garage, but the raccoon scurries out the doggy-door and hides behind a tree in your back yard.

The first night your Dog-Food Stealing Raccoon hid 3/5 of his body behind the tree.  The second night he hid 4/5 of his body behind the tree.

How much of his body did your Dog-Food Stealing Raccoon hide behind the tree in all?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

2.3 – On Your Own

Trumpet Playing Dog

You have a very talented dog named Rex.  Not only can he sit, roll over, and fetch a ball, but Rex can also play the trumpet.  He is so good that he has been ask to give performances at local businesses.  The only problem is when Rex sees a cat.  It does not matter what he is doing, Rex will chase that cat.

Rex was giving a performance for the local fire department.  He was 2/9 of the way through the song when a black and white tabby-cat ran past.  Rex drop his trumpet and took off after the cat.  Another time, Rex was playing for the Local Librarians convention when a couple of Siamese cats ran up a tree next to the deck where Rex was performing.  Once again, Rex tossed his trumpet aside and took off after the cats.  That time he was 4/9 of the way through his song.

How many songs was Rex able to play in all, before he began chasing cats?

Your Challenge:
Gather the following materials:
  • A blank piece of paper
  • A pencil
  • Crayons, or a highlighter
  1. Complete the mathematical algorithm for this problem.
  2. Draw a mathematical model that shows the addition of fractions for this problem.
  3. Make sure your algorithm and your mathematical model agree with one another.

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 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.

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.

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

Price: $2.99
Available on  Amazon

 

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.

 

 

A quick side note…
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, you must have a strong understanding of the basics.  My books on fractions are designed to develop a strong basic understanding, so you can excel throughout your educational career.  Therefore, it is important that you train like an athlete and drill the basic concepts until you have a concrete understanding.  Once you have a strong understanding, you are ready for the next book in this series.

Step-3
Subtracting Fractions
with Like Denominators

Mathematical Model

3.1- Watch Me

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.

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.

 

3.2 – Work with Me

Kangaroo Feeding Time

You and your parents are visiting family friends who live in Australia.  They work at an animal habitat where they save injured animals.  There is a friendly kangaroo that needs to be fed, so they ask you to feed him.  You look at the bag of food and see that it is 5/7 full.  You feed the kangaroo 2/7 of the bag.  How much food is left in the bag?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

3.3 – On Your Own

Household Chore

Your parents give you a weekly chore that must be completed every Saturday before you can play with your friends.  This week you have to rake the leaves in the back yard.  Your back yard is 9/13 of an acer.  That’s pretty big, but you want to complete your chore, because your best friend invited you to go see a movie.  The movie starts in 1-hour and you have only finished 5/13 of an acer.  How much more must you rake in order to go see the movie with your friend?

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 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.

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.

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

Price: $2.99
Available on Amazon

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.

 

 

Another quick side note…
Special Note to Parents

Although these books 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 be involved in your child’s learning.  Here is why.

I’ve been teaching for over a quarter of a century, and have helped over 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 needs 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.

Here’s how I use these books in my class:

First, I introduce the book to my students.   I show them the first “Watch Me” problem along with the video.  Next, I show them the “Work with Me” problem and have the students put on headphones and complete the problem along side the video.  Finally, I have my students complete the book one problem at a time.  I have my students show me their work after they have watched the video that accompanies each problem.  If they got the problem correct, I praise their work.  If they got the problem wrong, I check to make sure that they corrected their work as instructed during the video, and then I praise their efforts.  I continue to check my students work after each problem, encouraging them to complete a minimum of 1-problem per day.

I have my students work with the books 4-days each week, because the repetition and repeated daily practice will ensure their understanding much better than if they only work with the book one or two days per week.  Once any student has completed a book, I introduce the next book in the series.  Just like the daily practice, I move students to the next book within the series as soon as they have completed the prior book, while the skills taught within that book are still fresh in their minds.

One last thought – I know that I have said it a number of times, but give your child plenty of positive reinforcement while completing this book.  Your praise will go a long way in helping your child develop a positive self-esteem as well as self-confidence around mathematics.

Step-4
Adding Fractions
with Different Denominators

Mathematical Model

4.1- Watch Me

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”?

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.

4.2 – Work with Me

Pull-Up Pete

You are in gym class attempting to do a pull-up.  Your best friend Pete is doing great.  On his first attempt he does 3/4 of a pull-up.  On his second attempt he does 5/6 of a pull-up.

How many pull-ups has “Pull-Up Pete” done in all?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

4.3 – 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?

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!

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.

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

Price: $2.99
Coming Soon to Amazon
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

5.1- Watch Me

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.

5.2 – Work with Me

Larry the Llama

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?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

5.3 – 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 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!


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.   Read on…

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

Price: $2.99
Coming Soon to Amazon
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.

6.2 – 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 scamper 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?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

6.3 – On Your Own

The 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?

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!

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.   Read on…

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

Price: $2.99
Coming Soon to Amazon
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

6.1- Watch Me

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.

6.2 – 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 hidden in the sand.  The octopus finds and eats 1 & 4/5 of the clams.

How many clams does the octopus have left to eat?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

6.3 – 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?

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!


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.   Read on…

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

Price: $2.99
Coming Soon to Amazon
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

7.1- Watch Me

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.

7.2 – Work with Me

Long-Eared Carrot Eaters

Ever since you were tiny-tiny 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 6-carrots.  They ate 4/7 of the carrots.

How much did your Long Eared Carrot Eaters eat?

This is a Work with Me Video
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Watch the video below. We will complete this change together.  I will take you through a step-by-step process.  You will pause the video and copy what I demonstrate.  Together, we will solve this problem.

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

7.3 – 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?

Your Challenge:
Gather the following materials:
  1. A blank piece of paper
  2. A pencil
  3. Crayons, or a highlighter

Now:

  1. Write the question on your paper
  2. Create your mathematical model for this problem.
  3. Complete the algorithm for this problem
  4. Make sure your mathematical model & your algorithm agree.

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 link 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!

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.   Read on…

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

Price: $2.99
Coming Soon to Amazon
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  Coming Soon

Price: $2.99
Coming Soon to Amazon
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  Coming Soon

Price: $2.99
Coming Soon to Amazon
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 Coming Soon

Price: $2.99
Coming Soon to Amazon
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.

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

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

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