Math Mammoth Fractions 1 & 2 workbooks

Introduction - Fractions 1 book

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 doing lots of mistakes while they confuse the different rules and apply the wrong one. That can even make them to fear fractions or at least not like them too well.

To avoid that, the student needs to UNDERSTAND these things, not just learn mechanical rules. Fractions don't have to become enemies - they can be our friends! Really, we use them all the time in everyday life and they are very needful.

To achieve this goal, we use visual models all the way through this book. I encourage you use some fraction MANIPULATIVES. The basic model in the book is a 'pie' divided into equal parts.

In the first lesson, Understanding fractions (see sample) the student also learns to draw pie models of certain often used fractions.

Encourage your student to draw the fractions for the problems in the following lessons, too! That will help her to VISUALIZE the fractions, and then she won't make the stupid mistakes of blindly applying a rule and getting silly results because of making a mistake. She will be able to spot her mistakes.

The second lesson Part of a Whole Group (see sample) talks about part of a certain number of objects, and taking a part of that. It ties fraction concept in with division of whole numbers. For example, to find 1/4 of a number of objects, you would divide by four. To find 2/5 of a number, first find 1/5 by dividing by 5, then take double that.

This subject is 'revisited' in the end of the ebook, as it may be a little hard for some kids to grasp quickly. Don't worry if that is the case with yours - this topic is not crucial in the development of the next subjects, so you can always come back to the topic later.

The lesson about Mixed numbers (see sample) teaches the concept of mixed numbers with pictures. The child also writes the mixed numbers as fractions.

Next lesson, Mixed Numbers to Fractions (see sample), starts out without mentioning the rule. Instead the child first gets to practice the conversion with drawing pictures. It is almost always BETTER if the child learns to do this conversion picturing the fractions in his mind. That assures understanding.

The rule is good too but is so easily forgotten.

And the other lesson Fractions to Mixed Numbers - and Fraction/Division Connection (see sample) talks about an important point: the connection between a fraction and division (7/3 is the answer to 7 ÷ 3). This also gives us a way to convert fractions to mixed numbers.

Adding and Subtracting Like Fractions (see sample) is the easy topic. Do some problems with the manipulatives first to let the student see the concept. The student needs to fix in her mind how easy it is to add like fractions so that she doesn't later 'apply a rule' of adding the numerators AND the denominators.

Equivalent Fractions (see sample) are presented here as parts that have been split further. The rule is of course 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 the understanding of the concept instead of a memorization of a mechanical rule.

Adding and Subtracting Unlike Fractions (see sample) requires that the fractions are first converted into like fractions, and for that one needs to find a common denominator.

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 also to be only memorized and poorly understood, so the lesson here first lets the student to add unlike fractions without discussing the LCD. This is done to emphasize the main idea, which is that you need to convert the fractions so they become like fractions, and then add.

Some students can intuitively see what kind of parts will work, and in that case you can omit the discussion on how to find the common denominator for now. Your student will encounter that concept in 6th or 7th grade math.

The lesson gives in the end the rule for a common denominator that it has to be in both multiplication tables of the denominators. That is the same as saying it has to be a common multiple, but you can choose which terminology you use at this point. Also, ANY common multiple works - it doesn't have to be the least!

The lesson on Adding Mixed Numbers lets the student first develop 'a rule' on her own. You as the teacher should discuss that rule and correct it if there are any mistakes. The real 'rules' are found in the end of the lesson.

The same applies to Subtracting Mixed Numbers (see sample). The student can first try to do the subtractions on her own. There are a couple of different cases: the fractional parts can be like fractions or unlike fractions, and one may be able to subtract the fractional parts separately or not (in which case you need to rename one whole into a fraction or subtract in parts). This topic is divided into three lessons in the book.

Part of a Whole Group Revisited ( see sample) goes back to taking a part of a certain number of objects, or taking a fractional part of a whole number.

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

Introduction - Fractions 2

See complete contents here.

Comparing Fractions (see sample) starts with a visual model to prompt the student to think about converting the fractions to have the same denominator.  Also included comparing fractions with number lines.

Simplifying fractions (see sample) is presented as joining or merging slices together, in other words as the opposite process of splitting the pieces.  Visual models are studied extensively to ensure understanding instead of mere memorization.

Multiplying Fractions by a Whole Number (sample) discusses multiplying by whole number as repeated addition.  Another topic is how fraction times a whole number means fraction of that number.  For example,  1/4 of 20  is expressed mathematically as  1/4 x 20.  The lesson shows the interesting connection between (fraction) x (whole number)  and  (whole number) x (fraction).

Multiplying Fractions by Fractions (sample page) really is not nearly so difficult a concept as many people think; it is based on the simple notion that for example 1/2 x 1/4 means half OF one fourth.  So if you have one fourth of a pie left, and you take half OF it, you end up with one-eighth part.  We will present this notion and try to work towards finding the actual easy rule.  Also included a discussion why the rule works.

Multiplication and area (see sample) interprets the process (fraction) x (fraction) as an area calculation.  Pictures are at the core of understanding this.

Multiplying Mixed Numbers lesson contains lots of word problems.

Simplify Before Multiplying (see sample) The lesson justifies the rule in a couple of different ways, starting from the notion that if you first multiply and then divide by the same number, you have in essence done nothing.

Dividing Fractions by a Whole Number (see sample) is thought of as dividing part of pie between certain number of people.  Then is presented the connection to multiplying by the reciprocal number.

Dividing Fractions by Fractions (sample page) first discusses mental math problems where you think "how many times does this go into this?"  The student is then led to notice how the first easy divisions in the lesson are the same again as multiplying by the reciprocal number.  The rule for dividing fractions by fractions is presented.

Dividing Mixed Numbers (sample page) practices fraction division further, and includes a discussion why the division rule works.

There are three Review lessons (see sample).

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

Better Yet - Package Deals!
Blue Series package - $60 (download) or $65 (CD)
Blue Series for grades 1-3 - $34 (download)
Golden/Green Series package - $50 (download) or $55 (CD)
Blue/Golden/Green Series Inclusive package - $95 (download) or $100 (CD)
LightBlue Series package - $81 (download) or $86 (CD)

Learn more about the package deals!

*BONUS*: Buy any package listed above, and get the all new, 2008 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... but you need to order at Kagi store!

* 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

See screenshots

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.

All the books on this website are available for *nearly instant download.
*Order processing at Kagi takes 1-2 hours; I do not know how quick it is at the other stores.

Most of them are also available as printed copies.

---

How and where to order?

You can buy Math Mammoth books at

• Kagi store - all of the ebooks and CDs. Kagi accepts all major credit cards, Paypal, check, cash, money order, purchase order, and a wire transfer. I maintain four different order pages at Kagi:
  • One for the Blue series,
  • another for the Golden and Green Series, and
  • third for the LightBlue complete curriculum products, and
  • one more for the Packages (CDs or downloads).
  
   
• CurrClick.com - all Blue, Golden, and Lightblue series books (downloads). Credit cards, Paypal.
• The Old Schoolhouse Store - the Blue Series ebooks. Credit cards, Paypal.
• Lulu - printed copies for the Blue and Golden series books.
• Winterpromise - printed copies and CDs for the LightBlue series.

---

Kagi - my main reseller

Kagi handles all my downloadable products and the CDs, and accepts all major credit cards, checks, Paypal (USD), money orders, and even cash. Please see Kagi FAQ for any questions about the payment methods.

After completing the order at Kagi, you will receive an email with download links for each book you bought, or for a zip file for the packages. You click on the links and download the books to your computer's hard drive. That's it!

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.

Buy Blue Series at Kagi

Buy Golden/Green Series

Buy Lightblue Series

Buy package downloads or CDs

---

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.