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Math Mammoth Introduction to Fractions

Math Mammoth Introduction to Fractions book cover
100 pages
(answers included)

Sample pages (PDF)
Contents and Introduction
Halves and Quarters
Understanding Fractions
Comparing Fractions
Equivalent Fractions
Adding Fractions and Mixed Numbers 1


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small flag of SpainEste libro en español

Math Mammoth Introduction to Fractions contains lessons for fraction arithmetic for grades 1-4. This material does not include division or multiplication of fractions, nor adding unlike fractions, which are topics for 5th and 6th grades. Also, most of the material here is for 3rd and 4th grades, and only a few lessons are meant for grades 1-2.

The topics covered are on a simple level, constantly illustrated with visual models, and with small denominators. The presentation avoids spelling out specific rules for manipulating fractions, but instead relies on the usage of pictures on a very concrete level. Children easily confuse the various rules for fraction arithmetic, because there are so many. There is a place for the rules, as shortcuts for ideas that are already understood, but we do not start with them. The goal is to let the big ideas sink in conceptually first, followed by some shortcuts.

The topics covered are

  • one half and one fourth
  • concept of a fraction
  • concept of a mixed number
  • comparing fractions
  • equivalent fractions
  • adding and subtracting like fractions
  • adding and subtracting mixed numbers with like fractional parts
  • adding one fraction that has tenths and another that has hundredths (such as 3/10 + 7/100)
  • multiplying a fraction by a whole number

The lessons are organized by topic, not by increasing difficulty. For reference, 1st grade students study only the concept of one half and one fourth. In 2nd grade, they study the concept of a fraction and optionally the easiest (first) lesson on comparing fractions. In 3rd grade, students study the concept of a fraction, fractions on a number line, comparing fractions, and equivalent fractions. Then in 4th, they study mixed numbers, comparing fractions, equivalent fractions, adding and subtracting fractions and mixed numbers, and multiplying fractions by whole numbers.

The answers are at the end of the book.

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

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By purchasing any of the books, permission IS granted for the teacher (or parent) to reproduce this material to be used with his/her students in a teaching situation; not for commercial resale. However, you are not permitted to share the material with another teacher.

In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.


Math Mammoth books are PDF files. You will need Adobe Reader to view them, including if you use a Mac or Linux. You can try other PDF viewers, but they seem to either omit or mess up some of the images.

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