3-Steps to Fully Understand Multiplying a Whole Number by a Fraction!

Multiplying a whole number by a fraction, like 2/3 x 5 can be very confusing.
If you are multiplying, why is the answer smaller than 5?

Unless children are taught to illustrate the addition of the fractions, they often never fully understand what is happening with the fractions.  This leaves children with a limited understanding, which can be frustrating and confusing as they enter higher levels of mathematics.
This 8th video-post continues my cyclical learning approach to the next level of understanding:

3-Steps to Fully Understand Multiplying a Whole Number by a Fraction!

Step 1 – Create your fractions boxes.  In this case you would create 5 whole boxes.  Then cut each box into 3-parts.  If you’re new to illustrating fractions, you might want to review my first video-post in this series, An Easy Way to Understanding Fractions.
Step 2 – count your fraction parts.  In this case you would have 10/3.  If you move the shaded parts, you can make 3-wholes and have an extra 1/3.  Therefore you answer is 10/3 or 3 & 1/3.
Step 3 – Now, move to your algorithm.  Convert your whole number into a fractions, and then multiply your numerators and denominators.  In this case you would get 10/3 or 3 & 1/3, which agrees with your mathematical model.

The “8.1 Watch Me” video below shows a
detailed explanation of this problem!

Mathematical Models
Make Abstract Concepts Concrete!

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 like the one above, they begin to understand what is actually happening with fractions.  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.

 

8.1- 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:
A blank piece of paper
A pencil
A Sharpie marker
Crayons or a highlighter

  1. Play the video below.
    • Pause the video when told.
    • Copy the problem down on your own paper, and solve it with me.
  2. 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:
  • 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 mistakeSome 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.
Dividing a Whole Number by a Fraction

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

Price: $4.49
Coming Soon to Amazon

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

Multiplying a Whole Number by a Fractions will help children in 3rd through 6th 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 multiply a whole number by a fraction.

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 6th 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!

Have a fantastic day – Brian McCoy

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