# Math High School

## Jacobs' Geometry

*Saxon* is a tried and true mathematics choice for many homeschoolers, but one complaint about the high school level texts *Algebra I* and *Algebra II* is that geometry is included piecemeal in the algebra courses rather than being taught separately in a systematic fashion. Jacobs' *Geometry* is one alternative for those who find this to be a problem. It is a friendly, thorough approach to high school geometry that starts with an introduction to deductive reasoning and takes the student through to non-Euclidean and coordinate geometry.

The format is very appealing, at least to my high-school age son and myself. The book is divided into chapters covering broad topics like Rays and Angles, Congruent Triangles, and Quadrilaterals. These are subdivided into lessons. Each lesson opens with a cartoon or thought puzzle which draws the student into the topic being discussed. There are three sets of problems in each lesson: the first one usually checks comprehension of concepts and knowledge of theorems, the second set is an application of the lesson to proofs, and the third set, usually a single question, presents a brain-teaser which allows the student to think and ponder creatively.

A Letter to the Student at the beginning tells the story of Pythagoras, the Greek geometer, who taught a reluctant student by paying him for each theorem he learned. By the end of the course, the student was paying Pythagoras. The anecdote sets the tone for the whole book, the assumption being that geometry is a noble, worthwhile endeavor and that a student will realize this and be willing to apply himself to mastery.

Though I haven't used the *Jacobs' Algebra*, the format looks similar to Geometry. My high-schooler is using it now in short sections as a review. With my next high schooler, I am planning to go from *Saxon Algebra ½* to *Jacobs' Algebra*. There is no book in the *Jacobs*' series after Geometry; the author Harold Jacobs recommends Algebra II and Trigonometry by Paul A Foerster as the next step before Calculus.

## Math Talk

I have long been a fan of the poems for two voices books by Paul Fleischman. This book puts a twist on the idea by covering math topics in poems. It's a really unique and engaging way to memorize a math concept, reciting it as a poem. A poem for two voices is a poem recited by two people where sometimes the same words are said in tandem, sometimes alternately, and sometimes, the speakers speak at the same time saying different things.

Here is a sample of part of a poem from the book: (The first column is the first speaker and the second column, the second - shown smaller than actual size)

Some of the math concepts in the poems are fairly simple ideas that would pertain to a grammar school student, however most of the ideas are for middle schoolers or high schoolers. There were a few math concepts I had never heard of, such as fractals, (the geometry of nature), Fibonacci numbers (adding the last two numbers in a series to give the next number), and Mobius strips (circular strip with a twist in it).

While you don't learn everything you need to know about the math concepts in the poems, you get an introduction to the idea and the basic or interesting facts. For tessellations, the reader learns that not all figures tessellate; for triangles, the reader learns that the angles in the figure must equal 180 degrees. Some of the accompanying illustrations are also instructive. I could not have visualized the Mobius strip without the drawing of it.

This is a fun way to talk about these concepts. Trying to say the poems as a team takes a lot of concentration and brings a lot of laughs along the way. The book would make a great addition to a living math program or be a nice break from a formal textbook program.

Recommended for grades 4-12