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# Math Mammoth Ratios, Proportions & Problem Solving

131 pages

## Prices & ordering

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Printed copy \$11.80, b&w

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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 book suits best grade levels 6 and 7.

The book starts out with the basic concepts of ratio, rate, and unit rate. The lessons on unit rates not only show how to calculate them and gives practice at doing so, but also include practice with unit rates that involve complex fractions.

The two lessons on equivalent rates allow students to solve a variety of word problems involving ratios and rates. We also connect the concept of rates (specifically, tables of equivalent rates) with ordered pairs, use equations (such as y = 3x) to describe these tables, and plot the ordered pairs in the coordinate plane. Then, students encounter the concept of aspect ratio, which is simply the ratio of a rectangle's width to its height, and solve a variety of problems involving aspect ratio.

Next, students learn how rates can be used to convert measurement units. This method is in addition to the methods for converting measurement units that are explained in Math Mammoth books on decimals. It does not mean that students should "change over" and forget what they learned earlier — it is simply a different method for doing the conversions. Some students may choose one method over another; some may be able to master all of the methods. Most will probably choose one method they prefer for doing these conversions.

After this, we turn our attention to proportions (which is an equation of two ratios). The lessons show how to solve proportions using cross-multiplying and how to set up proportions the correct way. We also study briefly what cross-multiplying is based on (it's not a magic trick!).

The concept of direct variation is introduced in the lesson Proportional Relationships. Writing and graphing equations gives a visual understanding of proportionality. In two following lessons on proportions, students also practice solving rate problems in different ways, using the various methods that they have learned throughout the book.

The lessons Scaling Figures, Floor Plans, and Maps give useful applications and more practice to master the concepts of proportions. There is also an optional lesson, Significant Digits, that deals with the concept of the accuracy of a measurement and how it limits the accuracy of the solution.

Lastly, we study various kinds of word problems involving ratios and use a bar model to solve these problems. These lessons tie ratios in with the student's previous knowledge of bar models as a tool for problem solving.

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## How and where to order

You can buy Math Mammoth books at:

• Kagi store - all of the downloads and CDs. I maintain several order pages at Kagi:

Kagi accepts all major credit cards, Paypal (USD), checks, cash, money orders, purchase orders, wire transfers, TrialPay, and even cash. Read more about the payment methods here. Please see Kagi Shopper Help for any other questions about the ordering process.

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.

• 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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