**I. From the beginning of the "Special Rules" chapter (Chapter VI) of Wentworth's New School Algebra** (published in 1898) [click to enlarge]:

**II. The two problem sets within the entire Year 4**[click to enlarge]:

*Interactive Mathematics Program*that come closest to providing practice applying the Distribute Law to algebraic expressions(Oops, the first two of these can be simplified without applying the Distributive Law. The other two, by the way, among just a handle of problems throughout the entire book that require factoring)

(Oops, these problems, like the majority in the IMP book, don't involve any algebraic manipulation at all; just plugging in numbers.).

**III. Extra Credit:**

There are no problems in the Year 4

*Interactive Mathematics Program*that involve demonstration or application of "Special Rules" in polynomial multiplication--Square of Sums, Square of Differences, Product of Sum and Difference. Is application of these "Special Rules" a 21st Century Skill?

## 1 comment:

Can I say none of the above?

Obviously Interactive Math is a joke, reminds me of one about making a gin martini: waft the opened vermouth bottle over shaker, but I don't consider the late 19th century algebra book is an improvement.

Wentworth's isn't illustrating any underlying concepts. They are giving the student a long, very long, list of rules to be applied depending on the problem trying to be solved. It's like pre-Copernician astronomy. Who can remember all that crap. Who'd want to?

I humbly suggest for binomials you use FOIL -- Firsts, Outers, Inner's, Lasts. One thing to remember and it always works. Once they show facility with it, you can back up to show the underlying principle at work and then take a swing at applying the underlying principle on a trinomial or two, but only to show, yeah this is really hard, in fact, there's a better way (matrices & linear algebra) so let's move on.

Post a Comment