*RightStart*™ *Mathematics* is an intriguing program, comprised of *Levels A* through *G, *corresponding roughly to a program for kindergarten up into junior high.* Levels A* through *F* are considered the elementary grade program. *Level G* targets students in middle school and has its own set of manipulatives, so I review it separately below.

While first editions of *Levels A *through *E* are still available, *Levels A* through *F* are now available as *RightStart* second editions, referred to by the publisher as RS2. I recommend the second editions for most situations since they are more user-friendly than the first editions. The scope, sequence, and presentation have been adjusted to reflect new research and discoveries about how children learn and to better align with the more advanced scope and sequence of most newer math programs. This is particularly evident in *Level A *where the first edition has 77 lessons while the second edition has 132. The additional lessons address topics such as subtraction and fractions.

The scope and sequence of *RightStart Mathematics* is a bit different than other programs, and children should move through it at their own pace rather than treating each book as equivalent to a particular grade level. Because it covers so much and even teaches some concepts not typically taught before junior high or high school, you might take longer than one school year to complete a level. The scope and sequence is very advanced in some areas, so you might find that your child needs to work in what might be considered a lower level book. Remedial students should probably start at a lower level. A free placement test is available on the publisher's website. I think that a child completing *Level G *in junior high will be functioning at a level equivalent to or higher than that of most other programs.

The second edition courses build in review lessons at the beginning of each course that will familiarize those new to the program with its unique methodology. (*Math Set Bridges* remain available for those using a first edition course who are moving into an RS2 course. See the publisher's website for information if you need one of these.)

For each level you will need both the book bundle plus the set of manipulatives. Each book bundle has a lessons book and a separate worksheet book (print or digital). There is significantly less worksheet activity compared to most programs. Much of the practice and drill takes place through learning activities and games. Because of this, *RightStart* should work especially well for students who don’t like to do a lot of writing.

*Levels A* through *F* use the same set of manipulatives called the RightStart™ Math Set. The basic manipulative set includes the AL Abacus, place value cards, base 10 picture cards, six special card decks for math games, fraction charts, Drawing Board Geometry Set, geoboards, color cubes, colored tiles, calculator, geared clock, math balance, tangrams, centimeter cubes, 4-in-1 ruler, folding meter stick, goniometer (angle measurer), a set of wooden geometry solids, and a set of plastic coins. (Note that the calculator is used infrequently—not as a substitute for mastering computation skills.) All of these components are non-consumable. You can customize this set to reflect a different monetary system at the time you order the set, selecting from U.S., Euro, Canadian, New Zealand, and Australian versions.

You can save almost half the cost of the manipulatives by purchasing the RightStart Mathematics Super Saver Set. This includes only the hard-to-find items from the larger set, and leaves it to you to supply items such as a geared clock, a geoboard, and a meter stick. Downloadable files on the publisher's website provide substitutes for some items such as tangrams and abacus tiles.

Whether you use the complete RightStart Math Set or the RightStart Mathematics Super Saver Set, you will need to supply some household/school supply items in addition to the items from RightStart. These include such things as scissors, colored pencils, thermometer, digital clock, wide paper, and a measuring tape.

*RightStart* instructs parents to frequently use the math card games that come with the manipulatives set. Think of the card games as you think of phonics readers for a reading program, although card games are used up through *Level G* rather than just for beginners. The set includes the *Math Card Games* book with instructions for more than 300 games plus a DVD with videos demonstrating some of the games.

Periodic assessments are included, but these are often interactive using manipulatives as well as written responses, so they don’t seem at all like typical tests.

As you might have guessed, this program requires a great deal of one-on-one or group presentation. This is not a curriculum for independent study in the early grades. The parent or teacher must familiarize him or herself with the methodology and the concepts to be taught in each lesson beforehand. Because the methodology is unique, this will take more prep time when you start into the program, then less as you move along.

I’ve had discussions about the prep time with a few people who have used the program. One mom told me that she thought it unnecessary to really try to understand the methodology before starting. She thinks it works fine if you just prepare and present lesson by lesson. She’s comfortable with picking it up as she goes. Another parent felt the opposite. She wanted a grasp of the “big picture” before she was comfortable starting to teach. I’m in the latter camp. I think this “teaching style” preference is something to consider if you are concerned about prep time. If you can work with it, learning as you go, then your up-front prep time drops considerably.

You can purchase the book bundle for each level with either one coil-bound, printed workbook or a PDF file of downloadable worksheets. The workbook is consumable and cannot be reproduced, but the PDF worksheets may be reproduced for your family. While the initial cost might seem a little high, keep in mind that the investment in the manipulatives is spread out over six years. In addition, if you plan to use the course for more than one child and purchase the version with downloadable worksheets, there will be no additional costs in the future for that same course.

### Levels A through F

One of the hallmarks of this program for *Levels A* through *F* is the AL Abacus, a specially designed abacus used throughout their program. This particular abacus highlights a key feature of the program: its technique of teaching children to visualize numbers rather than counting. Children learn to quickly spot groups of five and think in terms of "five plus." This same sort of visualization (called *subitizing*) is used in other ways throughout the program.

But the abacus and visualizing are not the only things unique to this program. Designed by Dr. Joan A. Cotter, this program incorporates methods based upon research about how children learn. Like many other programs it is multisensory—using manipulatives, teacher-directed conversation, experiential learning, oral responses, constructed solutions (with manipulatives), games, and written work. However, the variety of manipulatives and the ways in which they are used, coupled with an unusual scope and sequence set this program apart from others.

*RightStart* uses a number of different approaches for teaching almost every concept. For example, in one lesson, children learn to solve simple equations like 3 + 4 with tally sticks, then with the abacus, then on the worksheet. They might use the math balance and the abacus in another lesson, then the balance, tiles, and a geared clock in another lesson. Simple card games are also incorporated into the curriculum.

*RightStart* covers the Common Core State Standards as a minimum but goes beyond the standards with advanced mathematical thinking and pacing such as we find in *Singapore Math*. Many concepts are introduced earlier than in other program and are taught in more depth at younger levels. It's an ambitious program!

For example, *Level A* (RS2) teaches addition and subtraction facts through 18, place value up to the thousands, mental addition, fractional units up to 1/10, telling time to the half hour, money (pennies, nickels, and dimes), measurement in both inches and centimeters, and geometry concepts such as cubes, cylinders, parallel, and perpendicular, This level includes an original song/book/CD, *Yellow is the Sun* to teach counting, visual number recognition (subitizing), and working with units of five. This ties in directly to instruction using the AL Abacus.

*Level B* (RS2) spends a significant amount of time on addition and subtraction, but it also introduces multiplication as arrays. As early as Lesson 27, students are adding numbers such as 40 + 10. They also learn about topics such as even and odd numbers, skip counting, the concepts of hundreds and thousands, parallel and diagonal lines, rectangles, right triangles, equilateral triangles, symmetry, addition with carrying, patterns, transformations, values of coins, perimeter, measurement, time telling, fractions (up through writing equations such as ½ of 12 = 6), and creating bar graphs.

*Level C* (RS2) begins with review then introduces an “Addition Table” as a tool for helping children understand relationships between addition facts. It continues with topics such as evens and odds, Roman numerals, “trading,” adding several two-digit numbers, adding four-digit numbers, arrays, multiplication, area and perimeter, subtraction with two-digit numbers, geometry related concepts (e.g., drawing horizontal lines and dividing equilateral triangles into fourths), telling time to the minute, money (including making change), measurement, line plots, area plots, working with tangrams, introductory division, fractions, negative numbers, and algebraic thinking.

*Level D* (RS2) spends a good deal of time on skills that will be needed as students move into more complex math. For example, they become very familiar with multiplication facts as well as patterns of multiples for each number. Then they begin work on factoring. Division with remainders is taught, but less time than I expected is devoted specifically to division. Other topics covered include fractions, measurement in both the metric and U.S. customary systems, geometry (including work with drawing tools), time, money, charts, graphs, and problem-solving skills.

*Level E* (RS2), works with multiplication of multi-digit numbers by two-digits, division of multi-digits by a single digit, and equivalent and mixed number fractions. It also works with prime numbers, factors, decimals to the hundredths, and percents. Algebraic concepts are introduced and problem solving is emphasized throughout. In geometry they study classification of triangles and polygons, symmetry, reflections, angle measurement, and work with 3-dimensional figures. Measurement, elapsed time, distance, money and capacity problems are explored. This level also teaches students how to use a calculator. However, the calculator is used strategically rather than as a crutch. For example, students learn the order of operations on a calculator, how to show dollars and cents, and how to calculate the cost of diesel fuel. Three lessons use the calculator as students get into some advanced work with prime numbers.

*Level F* (RS2) is the newest addition to the series. It continues to reinforce and then build upon earlier levels. Students work with the four basic operations with whole numbers as well as with fractions and decimals. The concept of percentages is taught in relation to both fractions and decimals. Early in the course, students learn about exponents and complex order of operations. For example, students evaluate the expression (5^{2} - 4^{2}) - [(5 - 4) • (5 + 4)] = on Worksheet 21-A. Student learn to convert units of measurement using both the U.S. and metric systems. Geometry concepts such as the area and volume of various geometric figures is taught, and students learn to make some geometric constructions. The Cartesian coordinate system is introduced,and students learn to construct lines based on a series of coordinate points. Even at this level, card games are continually used as key tools for practice and review.

### Level G

Children who have completed *Level F* can move directly into *Level G*, also titled *RightStart™ Mathematics: A Hands-on Geometric Approach*.

*Level G* teaches more geometry than is typically covered before high school level. While it addresses standards for the middle grades (grades six through eight), it also introduces some concepts generally taught in high school.

Among concepts covered are the construction of polygons, circles, tangents, bisectors, angles, arcs, etc.; finding perimeter and area of polygons and circles; determining the volume of three-dimensional figures; the Pythagorean theorem; right triangle properties; triangle congruency; Fibonacci sequences; and an introduction to trigonometry. Many basic postulates and theorems are presented although not named as such. There are no formal proofs, although solutions in the answer key are written out sequentially similar to the way you might do for a proof. With 165 lessons in the course, it appears that it should take about one and a half school years to complete. The publisher recommends introducing a pre-algebra program half way through *Level G,* and they particularly recommend* VideoText Interactive Algebra *which I discuss further below. This will slow the pace of the program if you use two courses simultaneously.

The publisher says: “This program incorporates other branches of mathematics, including arithmetic, algebra, and trigonometry. Some lessons have an art flavor, for example, constructing Gothic arches. Other lessons have a scientific background, sine waves, and angles of incidence and reflection; or a technological background, creating a design for car wheels. Still other lessons are purely mathematical, Napoleon’s theorem and Archimedes stomachion. The history of mathematics is woven throughout the lessons. Several recent discoveries are discussed to give the student the perspective that mathematics is a growing discipline.” (http://rightstartmath.com/wp-content/uploads/2015/05/RightStart-Geometric-Approach.pdf)

There are three books for this course: Lessons, Worksheets, and a Solutions book. *RightStart™ Mathematics: A Hands-on Geometric Approach* is a hands-on, discovery type course. Students make constructions (drawings), compare, and discover mathematical principles—an approach I consider very effective for learning geometry. Because of this, students also need the Geometry Set of tools for the course. It includes a small drawing board, T-square, two triangles, an arc compass, a 4-in-1 ruler, angle ruler, and removable tape. The Starter Kit Level G includes the three books, the tools, a set of Geometry Panels (geometric shape manipulatives), and a Casio calculator FX-300MS. The optional deluxe drawing board should be very helpful, but it is not essential. It is included in the deluxe kit.

Students should be able to work more independently through *A **Geometric Approach* than they can with the earlier levels. However, I did find a few explanations a bit complicated and confusing, even for older students. So students might need help from time to time. If need be, students may call RightStart for assistance with their lessons.

I have a minor concern about the overall progression of the program. Since this geometry course duplicates a significant amount of what will be covered in high school that means most students will end up repeating coverage of topics in their high school geometry course. Repetition will be helpful for some students but simply redundant for others. I can see where *A Geometric Approach* might work very well for a student who moves into a proofs-based course like *Geometry: Seeing, Doing, Understanding, third edition *(from W.H. Freeman). *RightStart* prepares them well for the more-rigorous approach of this type of geometry course. However, RightStart recommends *VideoText Interactive Algebra* as a more compatible program which is why they recommend that students start working in that course when they are about halfway through *Level G*.

While *RightStart: A Geometric Approach* requires students to use some of the arithmetic skills they have learned, it lacks any sort of systematic review. Since children coming out of the *RightStart* program for the earlier grades have covered so much material, it would seem prudent to continue with more practice and review of those concepts more than occurs within *A** Geometric Approach*. RightStart does recommend that students continue to use the card games while working through the geometry course, so this provide some of that review and practice.

### Summary

*RightStart Mathematics* second edition courses make a good program even better. It should work well for a wide range of students because of the variety of learning strategies. It is difficult to convey within this review the thoroughness with which concepts are taught using multi-sensory learning approaches. Dr. Cotter integrates concepts more than you find in most programs, and her development of conceptual understanding is outstanding. Her goal is to lay a much stronger foundation in mathematical thinking and understanding, and I think she accomplishes this very well.