Math Mammoth Fractions 1

73 pages
(includes answers)

Sample pages (PDF)
Contents and Introduction
Adding Mixed Numbers
Equivalent Fractions
Adding and Subtracting Unlike Fractions
Comparing Fractions

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Este libro en español

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

I have made a set of videos to match many of the lessons in this book. You can access them at https://www.mathmammoth.com/videos/fractions_1

Studying fractions involves lots of rules, and many students learn them only mechanically, not really understanding the underlying concepts and principles. Students then 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 fractions.

To avoid that, we use the visual model of a pie divided into slices all the way through the book. It is a natural model because a circle can be divided into any number of circle sectors (slices). When students work with this model from lesson to lesson, they will eventually start seeing 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 along with the book; however the visual pie model is probably sufficient for most students in the fifth grade level. I have also included (in the appendix) printable cut-outs for fractions from halves to twelfths.

The first lesson, Fraction Terminology, explains various fraction terminology such as proper and improper fractions, like and unlike fractions, and so on. The student can refer back to this information as needed.

The lesson Review: Mixed Numbers briefly goes over how to write fractions as mixed numbers and vice versa. The concepts in this lesson are prerequisites for the rest of the book.

The next lessons cover adding and subtracting mixed numbers when the fractional parts have the same denominator. The lessons are well illustrated with “pies” to help the student visualize how regrouping works in the context of fractions.

Then, it is time to study equivalent fractions, as a prerequisite for adding unlike fractions. Equivalent fractions are presented 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.

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

Finding the (Least) Common Denominator emphasizes the idea that we need to find a common denominator, and then convert the fractions to like fractions before adding.

Next, students add and subtract mixed numbers with unlike fractional parts and solve some word problems relating to the concept.

Then we cover the concept of comparing fractions. The lesson presents several strategies, many of which have been studied in earlier grades. New for this level is to convert the fractions to equivalent, like fractions, just like when adding fractions.

In the last two lessons of the book, students learn to measure items using 16th parts of an inch and to make line plots from measurement data.

The answers are appended.

This workbook is most suitable for 5th grade. However, it is not tied to any grade level and does not mention anything about grade levels (except in the introduction), and so it can be used in various settings. It is also very good for remedial teaching or for students with learning challenges because of its heavy usage of visual models.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

See also:

Free videos to match many of the lessons in this book.

Add and subtract fractions – online practice

Math Mammoth Fractions 2 – a sequel to this book, covering fraction simplification, multiplication, and division.

Customer reviews and testimonials

Review of Fractions 1 & 2 from Learning Legacy blog

Review of Math Mammoth Fractions books from Leaders in Learning blog