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You are here: Home → Blue Series → Fractions 1 & 2 Math Mammoth Fractions 1 & 2 workbooks![]() 102 pages (of which 66 are lesson pages) Prices & orderingDownload: $4.50 at KagiBlack & white printed copy: $9.20 at Lulu
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Contents and Introduction Understanding Fractions Part of a Whole Group Adding Mixed Numbers 1 Adding Unlike Fractions 1 Equivalent Fractions Subtracting Mixed Numbers 2: Renaming Comparing Fractions 1 ![]() 98 pages (of which 68 are lesson pages) Prices & orderingDownload: $5.00 at KagiBlack & white printed copy: $10.20 at Lulu
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Contents and Introduction Simplifying Fractions Multiplying Fractions by Whole Numbers 1 Multiplication and Area Divide Fractions by Whole Numbers How Many Times Does It Fit? Fractions to Decimals 1 Fractions and Decimals in Measuring Units Math Mammoth Fractions 1 and Math Mammoth Fractions 2 are self- teaching worktexts dealing with all fraction operations visually. Both books come as PDF ebooks that you download after completing the purchase, and then print as you need. 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. Fractions 2 teaches comparing, simplifying, multiplying and dividing fractions and mixed numbers. This book will be revised in February 2009. The books not only show fraction pictures one time at top of page but let the child work with pictures extensively, and to draw them herself 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 & 2 workbooks are most suitable for 4th, 5th, or 6th grade, and for remedial studies. However, they are not tied to any grade level and do not mention anything about grade levels, and so the books can be used in various settings. They are very good for remedial teaching or for the learning disabled because they are so visual. The video below explains the visual method used to explain equivalent fractions in the Fractions 1 book: Please read below some feedback I've received about the fraction books: 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! The students and myself liked the pictures and the step by step breakdown in all of the lessons. 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. I like the clear explanations. The fractions 2 book had the best explanation of why dividing by a fraction works like it does of any I found anywhere. 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. Introduction - Fractions 1 bookMath 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. Introduction - Fractions 2Math Mammoth Fractions 2 continues the study of fraction topics after Math Mammoth Fractions 1. The book at hand is meant for 5th or 6th grade, and deals in-depth with the following topics:
The topics of simplification, multiplication, and division of fractions are, again, first studied with the help of visual models. Students also complete various exercises using these visual models, before embarking on the more abstract exercises. This helps ensure that the student understands the underlying concepts, instead of merely following a rule. The study of fractions involves a lot of "rules" or shortcuts. Shortcuts in themselves are not bad; it certainly is easier and quicker to multiply or divide fractions using them. Therefore, it is needful to study and know the shortcuts, but students should not learn them only. With each topic, the students study the visual models and mental math problems first, before practicing the mechanical application of the shortcuts. The topic of simplifying fractions is presented as joining or merging slices together. This is the opposite process of splitting the pieces (equivalent fractions in Math Mammoth Fractions 1). Working with the visual model leads us to the "shortcut" of dividing the numerator and the denominator by some same number. Multiplication of fractions is studied in several steps. First, we study multiplying fractions by a whole number, which can be solved with repeated addition. The next lesson studies the connection between (fraction) × (whole number) and (whole number) × (fraction) (for example, 1/4 × 20 and 20 × 1/4), and explains how (a fraction) times (a whole number) means a fractional part of that number. This is all leading towards the full understanding of fraction multiplication being a fractional part of another fraction, and using the shortcut to solve such problems. The mental idea of finding 2/3 of 4/5, say, is developed through several steps. First, students learn to find a fractional part of another fraction that in the form 1/n (n being a whole number). For example, 1/3 of 1/5 is 1/15 (this is justified visually). Then they learn that 2/3 of 1/5 is just double the answer to 1/3 × 1/5, so it is 2/15. Then, the shortcut (the rule) for fraction multiplication is introduced, and it is justified by a "roundabout way" of solving fraction multiplications, which just means figuring it out in several steps. Students also study simplifying before multiplying, multiplication and area, multiplying mixed numbers, and compare fraction vs. decimal multiplication. After this, we turn our study to division. Again, there are several lessons that start out with easy, mental division problems, and gradually work towards the general case and the shortcut or rule for fraction division. The last major topic is converting fractions to decimals. Students learn to use first long division, and then the calculator for the conversion. They learn about repeating decimals. In this context, we also study converting measurements in the customary system into a decimal form, such as writing 2.34 miles as 2 miles 1,795 feet, or changing 4 ft 5 in to 5.42 ft. The last lesson in the book compares ratios and fractions, and shows how both concepts can be used in solving word problems. The answers are in the end of the book. After the answers, I have included printable fraction cutouts, with which you can make your own fraction manipulatives. Most children probably don't need the physical manipulatives anymore, if they have a solid foundation with the pie pictures from earlier fraction studies, but they are included here for the sake of completeness.
Customer reviews and testimonialsI 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 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. Better Yet - Package Deals! *BONUS* - SOFT-PAK MATH SOFTWARE
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The books listed below are from the Blue Series (worktexts by topic) and the Green Series (worksheet collections by topic). If you are looking for full curriculum by grade, or for workbooks/worksheets by grade level, please click on the "Navigate by grade" tab.
Addition & Subtraction
Addition 1 worktext (grade 1)Place Value
Place Value 1 worktext (grade 1)Multiplication & Division
Multiplication 1 worktext (grade 3)Clock and Money
Clock worktext (grades 1-3)Measuring
Measuring 1 worktext (grades 1-3)Fractions
Introduction to Fractions worktext (grades 2-4)Decimals
Decimals 1 worktext (grades 4-5)Geometry
Early Geometry worktext (grades 1-3)Problem Solving
The Four Operations (with a Touch of Algebra) worktext (grades 5-6)Other topics
Integers worksheets (grades 5-6)Make It Real Learning
States by the Numbers series (grades 3-6)This is a little "virtual" email course. You will receive:
A package of 300 free worksheets and sample pages; 7 math teaching articles on various topics ranging from coherent curriculum to fractions; 2 emails discussing the books; Homeschool Math newsletter (see archives).Note: You will FIRST get an email that asks you to confirm your email address. PLEASE check also your SPAM/JUNK folder for this confirmation email.
Confused about the different options? Take a 7-day virtual email tour around Math Mammoth! You'll receive:
A package of over 300 free worksheets and sample pages; 7 individual emails on 7 subsequent days that answer the most commonly asked questions, including "What is the difference between all these different-colored series?" Homeschool Math Newsletter (see archives).This way, you'll have time to digest the information over one week, plus an opportunity to ask me personally which book would be right for your child or students.
Note: You will FIRST get an email that asks you to confirm your email address. PLEASE check also your SPAM/JUNK folder for this confirmation email.