Math Mammoth Fractions 1

111 pages
(includes answers)

Sample pages (PDF)
Contents and Introduction
Understanding Fractions
Part of a Whole Group
Adding Mixed Numbers 1
Adding Unlike Fractions 1
Comparing Fractions 1

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Este libro en español

Math Mammoth Fractions 1 is a self-teaching worktext dealing with fraction operations visually. Fractions 1 teaches the concepts of fraction and mixed number, the concept of "part of a whole", addition and subtraction of like fractions, addition and subtraction of mixed numbers, equivalent fractions, addition and subtraction of unlike fractions, and comparing fractions.

The PDF version of this book is enabled for annotation. This means that if you prefer, your student can fill it in on the computer, using the typewriter and drawing tools in Adobe Reader version 9 or greater.

I have created a set of videos to go with this book. Please access them on this web page: Fraction videos, part 1.

The book not only shows fraction pictures one time at top of page but lets the child work with pictures extensively, and to draw them himself in the various exercises. This helps ensure that different concepts are not just rules without the understanding!

Also, in some lessons the child is asked to try to discover the rule or concept studied, encouraging independent thinking, experimenting, and discovery. This way fraction studies will not be just one meaningless rule after another but a bunch of interconnected principles that the student understands.

Fractions 1 workbook is most suitable for 4th and 5th grade, and for remedial studies. However, this book is not tied to any grade level and does not mention anything about grade levels, and so it can be used in various settings. It is also very good for remedial teaching or for the learning disabled because of being so visual.

The book Math Mammoth Fractions 2 continues the study of fraction topics and is a sequel to this book.

The video below explains the visual method used to explain equivalent fractions in the Fractions 1 book:

Introduction - Fractions 1 book

Math Mammoth Fractions 1 is the first book of two that cover all aspects of fraction arithmetic. This book at hand covers the concepts of fraction and mixed numbers, equivalent fractions, adding and subtracting like and unlike fractions, adding and subtracting mixed numbers, and comparing fractions. The book Fractions 2 covers simplifying fractions and multiplication and division of fractions.

Studying fractions involves lots of rules, and many students learn them only mechanically, not really understanding the underlying concepts and principles. Then they end up making lots of mistakes because they confuse the different rules and either apply the wrong one or apply the right rule but don't remember it quite right. All this can make students even fear fraction math.

To avoid that, this book uses the visual model of a pie divided into slices all the way through the book. It is a very natural model, because it uses a circle that can be divided into any number of circle sectors (slices). When students work with this model from lesson to lesson, they will eventually be able to "see" these pies in their mind. This, in turn, gives them the ability to do many of the easier fraction calculations mentally. It also enables students to really UNDERSTAND these concepts, and not just learn mechanical rules.

You are welcome to use manipulatives alongside the book; however the visual pie model is probably sufficient for most students in 5th grade level. I have also included (in the appendix) printable cutouts for fractions from halves to twelfths. You can use them to make your own fraction manipulatives. To make the manipulatives sturdier, glue the printed pages on cardboard, and cut the parts only after gluing. The whole circle is there to illustrate "one whole" - needed when studying mixed numbers. You will probably need to print at least two copies of each cutout page. You can use the white cutout fractions if you need to save on ink and let children color them. Just use consistent colors so that thirds are always the same color, fourths are the same color, etc.

In the first lesson, Understanding Fractions, the student learns to draw pie models of certain common fractions. This skill is needed later on in various exercises through the book.

The lesson Mixed Numbers teaches the concept with pictures. The child also writes mixed numbers as fractions.

The next lessons, titled Part of a Whole Group 1, 2, and 3 have to do with finding a part of a certain number of objects, and of course has lots of practical applications. It ties the concept of a fraction with division of whole numbers.

Next we study adding and subtracting like fractions, which is an easy topic. Next lesson reviews mixed numbers and further practices changing mixed numbers to fractions and vice versa. Next we add and subtract mixed numbers with like fractional parts.

Then it is time to study equivalent fractions, as a prerequisite for adding unlike fractions. Presented equivalent fractions as parts that have been split further. The rule is to multiply both the numerator and the denominator by the same number, but try to emphasize the terminology of "splitting the existing parts into so-and-so many pieces" or something similar. That should help students to understand the concept instead of memorizing a mechanical rule.

Add Unlike Fractions 1 is an introductory lesson in the sense that the student is not yet introduced to the rule for finding the common denominator. In this lesson, the common denominator is either given, or the student figures it out using pictures.

Add Unlike Fractions 2 emphasizes the idea that we need to find a common denominator, and then convert the fractions to like fractions before adding. Many textbooks introduce here the concept of Least Common Denominator, LCD, which is the best common denominator to use since it is the smallest. That concept tends to be only memorized and poorly understood, so the lesson here does not overtly emphasize that one always needs to find the LCD. Your student will encounter the concept of LCD again in 6th and 7th grade.

Finally we also add and subtract mixed numbers with unlike fractional parts, and add & subtract several unlike fractions.

The last new concept in this book is that of comparing fractions. Once the student has mastered converting two fractions to equivalent, like fractions, this should be fairly easy.

Answers are in the end of the book.

Customer reviews and testimonials

Review of Fractions 1 & 2 from Learning Legacy blog

Review of Math Mammoth Fractions books from Leaders in Learning blog

Hi Maria,
We have used Mammoth Math in the past when my child was "getting stuck" when it came to long division. And we purchased fractions from you about three weeks ago and I have to say fractions is coming easy. We tried various other curriculums for our homeschooling math and only yours has given my child both the visual, and hands on, in ways that he needed. In fact your method of teaching fractions is exactly how I learned when was in school in Australia. Thank you so much for a program that is easy to teach, easy to understand and easy to learn. My child actually enjoys math for the first time. We look forward to the next level of Mammoth math.
Frances Castelli
October 2010

Your [Fractions 1, Fractions 2] books have been such a help to us! My son has attended a private school since kindergarten, but we recently found out the school hasn't been teaching to grade-level standards in math. So, while he has wonderful grades, he is behind his peers from public school. He will be attending public school this fall, so we are using your worktexts to get him caught up this summer. I am not much of a "math person", so we are both benefiting from your series!

Thanks so much,
Robbie
July 2010

The workbooks are WONDERFUL and I love how fractions are explained so simply and attractively, my 13 yo daughter is sure to understand fractions now. Thank you for a great teaching product!

SHannon

The students and myself liked the pictures and the step by step breakdown in all of the lessons.

Tia Kline

These books fill the gap between using manipulatives (concrete level) and abstract (symbolic) level. Too often students are expected to make that leap from the concrete level without spending time at the representational level.

Paula Listzwan

I am amazed at how effective these lessons are. I think what makes them interesting to my student is that the problems are often interesting to solve, with an interesting word problem or just the mathematical reasoning interests her in a way that I've never seen with her.

Cyndi Kane

I began homeschooling my daughters back in May of 2008. Math Mammoth was one of the first websites that I came across on the internet. I had looked over Maria's site. I began targeting my math homeschool after what she provided as far as course knowledge. I began throwing long division and fractions at my oldest daughter. She totally freaked out. She kept telling me that she was not taught many of these subjects. I began teaching her what I knew about these particular subjects. As time moved forward, I realized that I need to check and see where she was at in her math.

I emailed Maria on this. She suggested many websites that I could test my daughter. I found out that she was a year and half behind. I thank God that I found Maria Miller's website because I have purchased the fraction book to help my daughter. She now has fractions down pat. She also has the long division down as well.

Maria takes these problems down to the basics and explains in excellent detail how to solve a fraction or long division math problem. Without the tools that she has given me, I would not have been able to bring my daughter forward and current on her math skills. Maria teaches it as I was taught many many years ago. She provides the tools to help our children succeed in mathematics. I just wish that there were more websites like hers in the other subjects.

I am currently using the Geometry module for my youngest daughter. She is enjoying that module immensely. It explains it perfectly for her.

Thank Maria for having an incredibly useful website and books. I thank the heavens above for someone like you.

Sincerely,
Amy K. Burt
November 30, 2008

I recently bought two of your books [Fractions 1 and 2]. I am a public school 8th grade math teacher. I use your materials to go back and fill in the "gaps" for children who have missed important concepts in their past education. Your products have worked wonders!!!!! I can't get over how complete and rigorous they are.

I plan to homeschool my daughter when she is old enough and I can't wait to use these materials with her...

thanks!!!!!
Jill Gaspard

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