sample essay from Six-Way Paragraphs

What’s Rational About That?

Glance through the table of contents of a grammar school or high school mathematics textbook an you are likely to encounter the term rational number. While you are familiar with whole numbers, fractions, decimals, and percents, you may well wonder what a rational number is and how you passed through your school mathematics classes without encountering one.

In fact, you did learn definitions, computation, and applications for rational numbers, although they may not have been identified as such in your class. A rational number is any number that can be expressed as a ratio of two whole numbers, and so 4/5 (the ratio of 4 to 5), 2/3 (ratio of 2 to 3), and in fact all fractions are members of the set of rational numbers. Also included are all terminating decimals such as 0.25 (equal to 1/4 or 1 to 4) and repeating decimals like 0.333 ... (equal to 1/3 or 1 to 3). Percents are rational numbers, too, as any percent has an implied denominator of 100; for example, 35 percent equals the ratio 35 to 100, or 335 out of 100 parts. Even ordinary, everyday whole numbers are members of the set of rational numbers, since a whole number such as 4 can be written as 4/1 or the ratio 4 to 1. So your math classes have involved work with all these types of rational numbers as you learned to compute, estimate, and solve problems with them.

This brief description of the major subsets of the rational numbers may give you the impression that all numbers are rational, but that is not the case. For example, the square root of the number 9 is 3, a rational number. But the square roots of numbers such as 5 and 10 do not equal whole numbers and cannot be expressed as ratios. So the square roots of numbers that are not exactly divisible are not rational numbers.

source:
Six-Way Paragraphs in the Content Areas Advanced Level
Based on the work of Walter Pauk
p 124

I don't know how to teach reading comprehension, or whether the Six-Way books work. But I like them very much.

A side note: I bought this one because I was going to use it to give C. "precis-writing" assignments. The idea was for C. to read a Six-Way passage and then cut the word length by 100 words a pass.

That turned out to be impossible. The passages are so tightly written that neither of us could figure out what to cut.

(Not sure about that last sentence.... "not exactly divisible" - is that a correct way to describe a repeating decimal?)

The fun thing about all the Six-Way books is that the passages are chock-full of factoids.

I like factoids.

Here's the one on stunt people C. and I tried to cut.