The *Ray’s Arithmetic* series by Joseph Ray was probably the most popular math series in the U.S. in the 1800s. Mott Media has published slightly updated editions of these books for many years. Even the updated editions of *Ray’s Arithmetic* present math concepts in a sequence and manner very different from what we find in other math programs. Those books assume that teachers are presenting lessons based on their own prior familiarity with the subject matter, so they do not include lesson presentation instructions. This approach is very problematic for many homeschooling parents. Consequently, the current *Ray's Arithmetic* books serve best as a source for practice problems for both written and mental math rather than as your main program for math.

*Ray’s for Today* is not just an update of the old books. Instead, the series' authors, Lori Horton Coeman and Joyce Bohn, have created what is almost an entirely new curriculum, with courses for each grade. They have retained many of the problems found in the original books, problems such as “If eggs are worth 1 cent each, what will 10 eggs cost?” (p. 59 of *Ray's for Today **Level 2: Student Text*). The word problems sometimes use examples from rural life and monetary values from long ago, although, as the *Ray's for Today* courses progress beyond third grade, more of the problems have been updated or changed for modern audiences. Even though the problems from *Ray’s Arithmetic* (or adapted versions of those problems) are a major part of the new courses, the authors have added so much more that there’s really no comparison between *Ray’s Arithmetic* and *Ray’s for Today. *Within the new format, some of the old problems seem a little odd, but this probably won’t matter much to students.

The *Ray’s Arithmetic *series consists of four books that cover concepts that are generally taught in grades one through eight. In contrast, *Ray’s for Today* has complete courses for grades one through six with courses for grades seven and eight due in 2020 and 2021, respectively. The scope and sequence of *Ray’s for Today* is closer to those used by other publishers than to that of *Ray’s Arithmetic*, so it should be relatively easy to shift into or out of this program if need be.

One thing that sets this series apart is that *Ray’s for Today* concentrates on core skills and spends less time on peripheral topics that can easily be taught later. It strives to teach for mastery and conceptual understanding so that children become fluent with foundational arithmetic skills. To that end,* Ray’s for Today* also features more word problems and mental math exercises than are found in most other programs.

For each level, there are an instructor’s manual and a student text. Each book comes as pre-punched pages for you to insert into your own binder, or you can purchase binders from Mott Media.

Instructor’s manuals include brief lesson notes, answer keys, the Scope and Sequence for that level, a Benchmarks Checklist that lists detailed skills and concepts for you to check off as they are mastered, and a Summer Skills Review page with suggestions for keeping math skills current over the summer. In addition, each instructor’s manual has many teaching aid pages at the back, such as a calendar page, the multiplication table, clock faces, geometric shapes, coordinate grids, bank checks to complete, and pages from which you will create games to be used with lessons. These pages can be reproduced as needed, and you might want to copy some onto cardstock.

All of the instructor’s manuals also include “Cement Mixers,” oral math drills to be used to help “cement” math skills. Cement Mixers and other oral work are vital components of the lessons. In the younger levels, a large part of each lesson is done orally. With *Level 4* and above, students work much more independently, but those levels continue mental math drills and oral word problems to help students develop fluency with mental math and thinking skills. In fact, there are about 60 pages of Cement Mixers in the instructor’s manual for *Level 6*! Cement Mixers can be used whenever parents wish to use them within each unit. (Some courses provide Cement Mixers at the beginning of each unit, while others provide them all together in one section.)

Units generally focus on one topic at a time. Typically, a unit might consist of 10 lessons on fraction concepts or 15 lessons on division, or a handful of lessons on another topic. The first unit in all of the courses is an exception since this unit is a cumulative review of all that students should have learned up through the previous year. In another exception, *Level 4* adds 29 lessons of cumulative review mid-year. Cumulative tests help students stay current on previously learned concepts, but there are relatively few of those tests. The Cement Mixers also help with review since they draw on a wide range of math skills beyond what’s covered in any one unit.

### Levels 1 through 3

*Ray’s for Today* for the first three levels requires a great deal of parent-child interaction. Much of the work is done orally and with hands-on resources. Children learn through concrete discovery activities, gradually moving to the abstract stage where they use numbers and symbols to represent what they have learned. While you don’t need expensive manipulatives, you will need to collect a number of objects to be used for each unit. A “packing list” for each unit lists required items such as counters, jumbo-sized wood craft sticks, rubber bands, coins, crayons, a teaching clock, play money, and index cards.

Parents can read from the student text as they work with their child. Lessons sometimes begin with a story to set the scene for the upcoming lesson.

The use of stories and number problems so far exceeds what I have seen in any other program that it is difficult to convey how different this approach is. While the approach takes more time, it is probably more effective.

Here's one example of how *Ray’s for Today* teaches division in *Level 2*. Students learn the concept of division through hands-on activity, using counters along with visual aids such as a multiplication chart and a picture of "number bonds" to illustrate numeric relationships. Students practice using counters and visual aids along with word problems and games. Most of this is done with the parent through interaction and discussion. Eventually, students learn to write problems in the standard linear form. There are rarely pages of problems for students to solve on their own in a traditional fashion, although such pages do show up for review and cumulative practice.

The *Level 1* student text is 427 pages, *Level 2* is 481 pages, and *Level 3* is 436 pages. Even with all of those pages, the amount of writing is still relatively low compared to many other programs because the student books include instructional material, visual representations of math concepts, and word problems. Pages in the student texts are printed in black and white. There are relatively few images, so text takes up with most of the space on each page.

There are no tests until *Level 3*, but parents can use the unit reviews as cumulative tests if they want to test at younger levels.

While the program for *Level*s *1* through *3* requires teacher involvement most of the time, it is not difficult to teach since everything is laid out for parents to just follow along. Time for preparing the manipulatives, visual aids, and games is also required before you start teaching.

The publisher summarizes the essential objectives of *Level 1* for each student as: “learn how to read, write, count and conceptually understand the numbers through 100.” However, this simplified statement doesn’t tell you that *Level 1* also teaches addition up through 10 + 10 = 20; the corresponding subtraction facts; skip counting; telling time; identifying shapes; working with money; recognizing fractional parts; and reading tallies, charts, and graphs.

*Level 2* continues to teach numbers up through 1,000 along with introducing multiplication of numbers with products up to 100 and division of numbers up through 100 divided by 10. Students are not expected to master all of these concepts this year, although they should start to exhibit proficiency. Parents should read the brief lesson material in the instructor’s manual then work through the lessons, primarily using only the student book. Sometimes parents will use visual aids, games, or other resource pages from the back of the instructor’s manuals.

*Level 3* reinforces what was taught in *Level 2*. Students work on multiplication and division with multipliers and divisors up to 10, addition and subtraction with regrouping, place value up to the hundred thousands, and fractions (including common denominators and changing improper fractions into mixed numbers). They learn other topics such as Roman numerals (up to 100), telling time, measurement (including an introduction to the metric system), money, recognition of geometric figures, graphing, and rounding numbers.

### Levels 4 through 6

*Level*s *4* through *6* are much less teacher-intensive than the first three levels. The teaching material is included in the student text, and the authors expect that students will generally be able to read the material on their own. Occasionally, parents will need to work through a lesson with the student, and when this is the case, it is indicated clearly in the instructor’s manuals. Some lessons need to be taught because they will use resources from a “packing list” that lists required items or resource pages from the back of the instructor’s manual; other lessons need to be taught because they require students to do mental math as they respond to oral questions. Overall, the preparation time is much less since the lessons for older students shift away from hands-on learning activities and toward more pictorial and abstract methods for presenting new concepts.

Students at these levels maintain a separate binder for all of their work. They are to copy problems onto blank paper (plain, lined, or graph) and show their work as well as their answers.

Student texts for these levels have more text and fewer images. Consequently, the student texts for *Level 4* and *Level 5* have only 360 pages and 405 pages, respectively—a little less than the three lower levels. *Level 6* expands to 487 pages, but some of that is taken up with a glossary that is not included in the other student texts.

Unit reviews, unit tests, and three or four cumulative tests in each course are to be used for assessment. Students will need to copy and solve problems on paper just as they do with their daily lessons. Reviews and tests are printed on the backs of lesson pages or the backs of other cumulative tests. Consequently, you might want to copy those pages so that students can take a test without having access to other information or previews of upcoming tests.

*Level 4* helps students learn to work with numbers through the millions, addition and subtraction of fractions, equivalent fractions, reducing fractions, multiplication with a two-digit multiplier, long division with a two-digit divisor, sets, common multiples, money, time, measurement (both U.S. and metric systems), decimals (at an introductory level), and advanced word problems (e.g., problems that require calculating time, rate, and distance). Geometry concepts taught this year include types of triangles, perimeter, area, circles (i.e., radius, diameter, and chord), and the use of a protractor.

*Level 5* teaches place value up to hundred billions, long division with remainders, rounding, estimating prime and composite numbers, fractions (all four functions of addition, subtraction, multiplication, and division), decimals (all four functions), percents, ratios, the coordinate plane and ordered pairs, measurement using both U.S. and metric systems, graphing, and advanced word problems. Extensive geometry lessons cover topics such as perimeter, area, volume, types of angles, types of triangles, symmetry, congruence, corresponding parts, transformations, and surface area.

*Level 6* teaches greatest common divisors, lowest common multiples, the order of operations, use of a calculator, money (e.g., computing transactions with discounts), time (e.g., time zones, converting units of time), measurement (e.g., unit conversions), reciprocal fractions, decimals, percents, ratios, proportions, function tables, graphs, and advanced problem solving. It introduces the use of letters in equations to represent unknown values as well as number concepts such as exponents, square roots, and powers of ten.

### Summary

Authors Coeman and Bohn have drawn from some of the best modern instructional methods while using the original *Ray’s Arithmetic* as the source for many of the problems. *Ray’s for Today* is a huge improvement over the original series, and I can guarantee that homeschoolers will find it much easier to work with.