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
PDF download $5.00
Printed copy $11.80, b&w
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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