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 whole number by a fraction, the product or answer is actually smaller not bigger. Children who learn only the algorithm, do not gain a concrete understanding of why multiplying a whole number by a fraction gives you a smaller product (answer) rather than making it bigger like in normal multiplication. 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.
This post is a free preview of my tutorial eBook entitled, Multiplying a Whole Number by a Fraction.
My eBook is unique, because – just like this post – it includes a video tutorial for each and every problem!
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.
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 one is easy. Click on the link below to watch how the pan of brownies should be cut and then colored. Pay close attention. Your next challenge will be very similar to this one.
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.
Long-Eared Carrot Eaters
Work with Me
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?
Gather the following materials:
- A blank piece of paper
- A pencil
- Crayons, or 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
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.
Pink Flamingo Research
On Your Own
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?
This one is the hardest.
Gather the following materials:
- A blank piece of paper
- A pencil
- Crayons, or a highlighter
- Write the question on your paper
- Create your mathematical model for this problem.
- Complete the algorithm for this problem
- 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!
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 firstname.lastname@example.org. I will put you on my email list and let you know as soon as it is available.
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 –
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.
One Last Thing
If you like this post and found it helpful, please leave me 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