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Math Mammoth Ratios & Proportions & Problem Solving

Math Mammoth Ratios & Proportions & Problem Solving math book cover
90 pages
(includes answers)

Sample pages (PDF)
Contents and Introduction
Solving Problems Using Equivalent Ratios
Scaling Figures 2
Problem Solving with Diagrams, part 1
Ratio Problems & Bar Models 2
Using Ratios to Convert Measuring Units


Prices & ordering

PDF download $5.00

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(credit cards, Paypal)


Printed copy $11.80, b&w

(credit cards, Paypal, PO)


small flag of SpainEste libro en español

Math Mammoth Ratios & Proportions & Problem Solving is a worktext that concentrates, first of all, on two important concepts: ratios and proportions, and then on problem solving.

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

My aim is to provide students with a thorough understanding of ratios and proportions, not only because that is the norm for 6th grade, but also because they are used so much in everyday-life applications, and because they are a natural extension to go to after the student understands the basics of fractions.

First, we study thoroughly the concept of ratio, including how it connects with fractions. Next, we turn our focus on equivalent ratios because those will lead us into proportions just a few lessons later. The lesson Ratios in Rectangles has applications about the aspect ratio.

Solving proportions is divided into three separate lessons. In the first one, we solve proportions by thinking through equivalent ratios. In the second one, the usual method of cross-multiplying is introduced.

Then follows a lesson that explains just why cross-multiplying is allowed. Then there is more practice with solving proportions and word problems. We also study scaling geometric figures and floor plans, which are simple applications of proportions.

After this, the last lessons concentrate on various kinds of word problems that can be solved with the help of bar or block diagrams (the same kind as in Singapore Math). These involve problems with fractional parts, and then problems involving ratios. The diagrams become a powerful tool to solve such problems without the use of algebra.

This book is suitable for 5th and 6th grades. It includes both the teaching material (lessons) as well as the exercises in the same book. The answer key is appended.


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    After completing the order at Kagi, you will see the download links on the receipt page. You will also 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.

    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.


  • CurrClick.com carries all Blue, Golden, and Light Blue series books as downloads. They accept credit cards and Paypal. You will be able to download the products immediately upon the purchase, and also return to your account at CurrClick to redownload.

  • Lulu offers printed copies for the Blue, Golden, and Light Blue series books.

  • Rainbow Resource carries printed copies for the Light Blue series books, plus Light Blue CDs. You can also find links to Rainbow Resource on the individual product pages on this site.

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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