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Math Mammoth Fractions 1
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Math Mammoth Fractions 1


The PDF file for this product 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 Acrobat Reader version 9 or greater.

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.

The book also has a lesson about measuring in inches and a review lesson.

Full answers are included.

Please check also the companion book Math Mammoth Fractions 2, which teaches simplifying, multiplication, and division of fractions and mixed numbers.

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Reviews (8)
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March 7th, 2014
This is a great Math Program. It has helped my kids find the confidence they need to be great at Math and has helped them to actually enjoy their Math lessons! So thankful for Math Mammoth. [...]
February 21st, 2013
This curriculum has helped my daughter understand fractions! :) [...]
May 11th, 2012
I love this curriculum because it allows my child to work on a specific topic until they get it down. It builds in easy steps. Sometimes the directions are a little confusing for the child (& for me) but we always figure it out. She just demonstrat [...]
May 8th, 2012
My son really enjoyed doing his first lesson and more, using colored pencils made it even more fun. Love the layout and the option to print out or fill answers in on computer. I am very please with my purchase. I really believe in the concept of being [...]
May 8th, 2012
When my 12-year old DS was having trouble with fractions using our regular math curriculum, I decided to try Math Mammoth Fractions 1 based on postiive reviews of it. I like how Math Mammoth explains concepts in several different ways. When one doesn't [...]
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File Last Updated:
March 03, 2018
This title was added to our catalog on January 19, 2007.