When I first looked at *Teaching Textbooks*, I knew right away that this series was going to be popular among homeschoolers. These fantastic courses were designed specifically for homeschoolers to solve some of the issues that make math challenging for them.

In the latest version, 3.0, online delivery of course material makes it easy to access lessons from computers, tablets, or phones--Mac, Windows, or Chromebook. The 2.0 versions presented on CD-ROMs or DVD-ROMs (to use on either Windows or Mac systems) and a physical textbook remain available, but the price is significantly lower for version 3.0. Content is identical in both versions 2.0 and 3.0 of each course. Printed textbooks for 2.0 remain available and can be used with 3.0 as well. However, 3.0 comes with an ebook textbook that you can print yourself.

With version 2.0, *Math 3* through *Math 7* courses each come with a set of four CD-ROMs. *Pre-Algebra* and *Algebra 1* each have ten. *Algebra 2* and *Geometry* each have 12, and *Pre-Calculus* has four DVD-ROMs. CDs or DVDs include lectures, problems, quizzes, and complete solutions. With version 3.0, all of this is available online.

Students begin each lesson by watching a lecture either online or on a CD-ROM of DVD-ROM. Lectures are audio presentations accompanied by step-by-step written explanations showing how to work each problem. Lectures are interactive, requiring students to answers questions from time to time, both to keep them engaged and to test their understanding. Then they might read the summary in the textbook. Next, they work the practice problems, mostly likely on the textbook pages, before entering their answers in the computer or other device. For incorrect answers, they should watch the solutions. Then they are ready to tackle the problem set, entering answers on the computer. They can still view solutions if they continue to make errors. Voice hints are available for the hardest problems. Parents should review progress before students go on to the next lesson. Each chapter concludes with a quiz. Note that courses also have an answer key for practice problems, lesson problems, and quizzes.

While it is possible to work only with the online lesson material or discs, most students prefer also having the companion textbook. As students encounter more difficult problems on the video presentations, such as with long division, they will then need to copy problems and work them on paper. The text saves the copying step, and it also provides an easy way for either student or parent to review a lesson. Even when students use the textbooks, they need to enter their answers on the computer or device since each course tracks and grades student work. Students can try again if they miss a problem, but the program will report this.

An automatic gradebook feature in both versions generates reports for practice problems (which are optional), assigned problems, and quizzes. The final score (expressed as a percentage) does not include the practice problems. The program also reports whether or not students view the step-by-step solutions to problems. The gradebook can be edited, so the parent or teacher can delete the record for a problem or an entire lesson if students need to redo them. In 3.0, some features have been added such as permanent grade storage and the ability to turn off hints and second chances. Parents can also manage students from any device.

Lessons and textbooks are both written directly to the student and do not assume the presence of a teacher. Explanations are clear and complete, with plenty of practical examples. A light-hearted touch gives the courses a user-friendly feeling while avoiding silliness. This is evident in all of the courses in everything from the layout of the books and the program's interface design and style of type through the occasional cartoon illustration and the wording of the text itself. The screen designs are colorful and nicely illustrated without being too busy.

Lessons are taught in a traditional fashion. The new concept is presented, followed by examples then practice problems. Next, students work through a set of problems on their own (about 18-25 problems per lesson). Problem sets include continual review of previously-learned concepts. In addition, key points are highlighted for quick student review. There are 95 to 142 lessons per course, with lessons grouped into chapters that concentrate on different topics. In all of these texts, students should aim to complete approximately one lesson per day. Adding in test days still should leave you at least 20 days in the school year for extra work on troublesome concepts, review, or “mathless” school days.

The textbooks range from 612 to 872 pages in length. Printed books are soft-cover with plastic-spiral bindings. The paper is a bit thin for textbooks, but the books are already more than an inch thick. (Pre-*Calculus* is two inches thick!) Durability might be a concern, and perhaps this is enough reason to go with version 3.0. Clearly, there are a lot of pages for each course, but there are two obvious reasons: each page is less crowded than pages in many other courses, and expanded explanations that make the material much more understandable take up extra space, particularly in high school level books.

Problem sets in each lesson are laid out so that students can actually do some of their work directly on the textbook pages. However, in high school level books it is not practical for students to solve lengthy problems on the textbook pages. You might skip the textbook entirely and have students solve and answer problems in separate notebooks. Whether or not you purchase the printed textbooks, I would encourage the use of a separate notebook because you really want to see the work showing how a student arrives at his or her answers.

Indices are include at the end of printed textbooks (2.0) as well as in the 3.0 ebooks. In 3.0 ebooks, clicking on a topic in an index will take you to the spot in the ebook where that topic is discussed.

In printed books (2.0) for Pre-Algebra and above, every exercise problem has a reference number telling the student in which lesson the relevant concept was first introduced. (These reference numbers will gradually be added to other print books as well.) In version 3.0, reference numbers are included in every course.

The *Teaching Textbooks* series is a college prep curriculum even though it is not as rigorous as some other courses. However, textbooks for the elementary grades move at a slower pace than other series such as *Horizons Math* and *Saxon Math*. Of course, you can always move ahead more quickly with a child who excels. You might even select a grade level higher than the student’s actual grade level. Placement tests on the publisher’s website will help you select the correct level. *Teaching Textbooks *should be a particularly good choice for the student who might have struggled with other math programs and needs a less-pressured pace and style of delivery.

With version 2.0, families are given permission to install the CD-ROMs of DVD-ROMs on as many computers as they like, which means that two or more students might be working in the same course at the same time. Even better, each time a student completes a course, you can simply reinstall for a new student. That means that all of your children can use the course over subsequent years. (Note: after two installations, you will have to contact the publisher for new activation codes.) You can access free demos and samples at the publisher’s website.

With version 3.0, you purchase a yearly (12-month) subscription for one child and one course. Large-family discounts (for families with four to eight students) are also available.

You can access a free demo at the publisher’s website: www.teachingtextbooks.com.

### Math 3

*Math 3* covers addition, subtraction, multiplication, division, fractions, money, time, geometry, and measurement, plus a final lesson that introduces percentages. Much of the addition and subtraction instruction reviews concepts that should have been learned at earlier levels since it begins with simple addition and very gradually builds toward carrying in lesson 47 and borrowing (regrouping) in lesson 87. Instruction on other topics also reteaches the basics before moving on to more advanced concepts. However, multiplication covers only through single-digit multipliers, and division covers only through single-digit divisors. Fractions are taught up through adding and subtracting fractions with common denominators. Numerous word problems help students with mathematical thinking and practical application. This level also includes plenty of pictorial representations in the textbook (e.g., number lines, fraction circles, multiplication arrays, clocks, coins, different types of graphs).

*Math 3* and *Math 4* have an extra bonus—a game that drills students on basic math facts. This pops up every five lessons. Parents can erase game scores if they wish to give students more practice time with the game.

### Math 4

*Math 4 *reviews and re-teaches concepts taught in *Math 3* then continues to build new concepts. Reflecting the slower pace of *Teaching Textbooks*, concepts that generally appear earlier in other courses don’t show up till near the end. Some examples would be multiplication by two-digit multipliers, long division, division with a remainder, and changing improper fractions to mixed numbers. Roman numerals are taught at this level. Note that *Math 4* includes a bonus math game for drill, just like *Math 3*.

### Math 5

*Math 5* again reviews the basics with the first 29 lessons heavily focused on addition, subtraction, and multiplication. It intro-

duces rounding and estimation. Significant time seems to be spent on decimals before complete coverage of fractions, but both topics are covered extensively at this level.

### Math 6

*Math 6* reviews the four basic arithmetic operations, place value, and time. It spends a great deal of time reviewing and teaching new concepts with fractions, decimals, and percents. It also covers geometry (points, lines, line segments, angles, both area and perimeter for polygons, circumference for circles, and introduction of geometric solids), units of measure (including the metric system), and graphing concepts (e.g., thermometers, bar graphs, circle graphs). A group of chapters at the end of the course called “Additional Topics” gives special attention to order of operations, decimal remainders, equations, and probability. A student with weak math skills might be able to pick up what he or she is missing since this course is fairly comprehensive on arithmetic basics. It might be too repetitive for a student who already has developed strong skills in the basic operations. (In my opinion, *Teaching Textbooks* *Math 6* is closer to *Horizon **Math 5* in concepts covered. It is easier than *Saxon **Math 7/6*.)

### Math 7

Topics taught in *Math 6* are revisited with brief review. Then each topic is tackled at a distinctly more challenging level. For example, fraction instruction moves on to ratios, percents include work with fractions and decimals plus real life applications like commissions and sales tax, and geometry gets into computing the volume of solids. Statistics, probability, graphing, equations, and inequalities are also taught this year. Additional Topics chapters delve into powers, exponents, square roots, the Pythagorean theorem, and negative numbers.

### Pre-Algebra

*Pre-Algebra* briefly reviews whole-number operations, fractions, decimals, percents, and measurement. Review has been greatly condensed from the first edition of this text, a commendable improvement. The rest of the book covers beginning algebra, negative numbers, exponents and roots—topics typical of all pre-algebra courses. *Pre-**Algebra 2.0* added 37 lessons that tackle plane and solid geometry, functions, relations, graphing, statistics, probability, and other more challenging concepts. Additional Topics covered at the end of the text include distance/time and other formulas, using the distributive property to solve equations, and absolute value. Extensive appendices with all important formulas, graphs, and other reference information are in the textbook. Backup chapter tests and supplemental exercises for each lesson are available upon request; however, these will not have step-by-step audio solutions to go with them.

NOTE: ** Pre-Algebra and above courses** have detailed appendices in the textbooks that contain important formulas and summaries of key concepts.

### Algebra 1

*Algebra 1* seems to have more review of basic operations and pre-algebra concepts at the beginning than do some other texts. *Algebra 1 *version 2.0 raised the bar a bit higher by adding sixteen new lessons covering functions, relations, statistics, probability, graphing with a calculator, the quadratic formula, absolute value, two-variable inequalities, and other more-challenging topics. These additions addressed concerns that version 1.0 was not challenging enough. Every exercise problem has a reference number telling the student in which lesson the relevant concept was first introduced. With version 2.0, overall, topic coverage is similar to that of many other first year algebra courses, but with more thorough explanation. While this course covers the essentials for Algebra 1, it is not as advanced as either the third or fourth editions of *Saxon **Algebra 1.*

### Algebra 2

As with *Algebra 1* version 2.0, *Algebra 2 *version 2.0 also addressed concerns that version 1.0 was not adequately challenging. Twenty lessons of new material, including logarithms, exponential functions, matrices, determinants, statistics, probability, and arithmetic and geometric sequences were added to make the content similar to other Algebra 2 courses.

While *Teaching Textbooks* algebra courses are still not as advanced as some courses, they do include practical applications in areas such as banking and physics plus word problems that help students understand how they might use algebra in the real world.

### Geometry

*Geometry* uses a traditional Euclidean approach, beginning with a chapter on logic and reasoning, then moving on to definitions, postulates and theorems. Formal proofs are introduced very early at the beginning of chapter three. However, constructions are not really incorporated into the text; they’re in the Additional Topics at the end. Analytical geometry using the coordinate plane is also reserved for the end of the book. As with the algebra courses, practical applications and occasional word problems help students understand how they might make use of geometry.

### Pre-Calculus

The *Pre-**Calculus* course includes problems modeled after those on the SAT II Math test and the CLEP Pre-Calculus test which should help students prepare for either exam. This is a challenging course that begins with functions and moves on from there. It covers various types of functions such as polynomial functions, radical functions, and trigonometric functions. It also teaches triangle trigonometry, trigonometric identities, vectors and polar coordinates, systems, matrices, determinants, advanced analytic geometry, sequences, probability, statistics, and introduction to calculus. Additional topics include Pascal’s triangle, the binomial theorem, synthetic division, more on sines and cosines, more on complex numbers, De Moivre’s theorem, and fitting a graph to data.