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Math Mammoth Fractions 2

98 pages
(of which 68 are lesson pages)

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Prices & ordering

Download: $5.00 at Kagi
Black & white printed copy: $10.20 at Lulu

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Sample pages (PDF)
Contents and Introduction
Multiplying Fractions by Whole Numbers 1
Multiplying Fractions by Fractions
Multiplication and Area
Divide Fractions by Whole Numbers
Fractions and Decimals in Measuring Units

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Math Mammoth Fractions 2 is a self-teaching worktext dealing with comparing, simplifying, multiplying and dividing fractions and mixed numbers.

The book not only shows 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 2 workbook is most suitable for 5th or 6th 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. In fact, the book is also very good for remedial teaching or for the learning disabled because it is so visual.

The book Math Mammoth Fractions 1 is a precursor to this book. It teaches the concepts of fractions, mixed numbers, equivalent fractions, addition and subtraction of like fractions and of unlike fractions, addition and subtraction of mixed numbers, and comparing fractions.

The two videos below show how division of fractions is taught in the Fractions 2 book:

Division of Fractions Conceptually, part 1

Division of Fractions Conceptually, part 2

Introduction

Math 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:

• simplifying; including simplifying before multiplying
• multiplication of fractions (and of mixed numbers);
• division of fractions (and of mixed numbers);
• converting fractions to decimals.

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 testimonials

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

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

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 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.

Jennifer Wheelock

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

Better Yet - Package Deals!
Blue Series package - $90 (download) or $95 (CD)
Blue Series for grades 1-3 - $38 (download)
Blue Series for grades 4-6 - $52 (download)
Golden/Green Series package - $65 (download) or $70 (CD)
Light Blue Series package - $118 (download) or $123 (CD)
All Inclusive package - $177 (download) or $182 (CD)
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*BONUS*: Buy any package listed above, and get the fully upgraded Soft-Pak software with more features and options for FREE (includes 4 math, 1 language arts, 2 testing programs).

*BONUS* - SOFT-PAK MATH SOFTWARE

I bet you'd have to agree: this is a steal! You can get Soft-Pak math programs (list price $24.95) for just a small $3.50 s&h fee - just by ordering ANY of my books at Kagi or CurrClick!

* Math Maker, for printable math activities with answer keys
* Math Master, for on screen practice of various math topics
* Math User, for answering the 900 multi-level word problems
* True/False Math Challenger for mastering facts 1-12


NOTE: if you purchase one of the package deals at Kagi store, you will get Soft-Pak in the download or included on the CD for FREE.

Soft-Pak may also be purchased at great 75% discount without a Math Mammoth purchase - click here for details.

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You can buy Math Mammoth books at:

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  In case of any problems with the download, you can always email me, and I can email the books to you directly. My contact info will be in the email you receive.

  
   
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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.