Students completing Singapore Math’s *Primary Mathematics* series are faced with an unusual problem when they complete the sixth level. Students at that point are generally beyond most seventh-grade math programs. The new series,* Dimensions Math, *should be a great “next step” for those completing *Primary Mathematics.*

*Dimensions Math* includes levels *6* through *8*, but level *7* would be the natural starting place for those who have completed *Primary Mathematics 6*. Most students transitioning from other math programs will need to complete a different seventh-grade level course or *Dimensions Math 6 *before moving on to *Dimensions Math 7*. The content of levels *7* and *8* is somewhat equivalent to content in other math courses for grades eight and nine even though students might take these courses while they are in grades seven and eight. Students who complete level *8* in *Dimensions Math* should be ready for algebra 2 or geometry. Over the two years of levels *7* and *8*, they will have completed the content of algebra 1. (That means that students completing *Dimensions Math 7* and *8* should be given credit for algebra 1.)

[Note: While levels *7* and* 8* are based in part on a Singapore series,* Discovering Mathematics*, level *6* is an entirely new course written specifically for the U.S.]

All courses are presented in two parts, A and B, and students should complete one part per semester in most situations.

These courses are unusual enough that I will list the contents fo each one so you have a better sense of what they cover.

*6A* teaches the order of operations, factors and multiples, multiplication, divisions, multiplication and divisions of fractions, decimals, negative numbers, ratios, rate, and percent. *6B* covers algebraic expressions, equations and inequalities, coordinates and graphs, area of plane figures, volume and surface area of solids, and displaying and comparing data.

*7A* cover factors and multiples; real numbers; introductory algebra, algebraic manipulation; equations in one variable; ratio, rate, and speed; percents; and angles, triangles, and quadrilaterals. *7B* continues with number patterns, coordinates and linear graphs, inequalities, perimeter and area of plane figures, volume and surface area of solids, proportions, data handling, and probability.

Book *8A* covers exponents and scientific notation, linear equations in two variables, expansion and factorization of algebraic expressions, quadratic factorization and equations, algebraic fractions, congruence and similarity, and parallel lines and angles in triangles and polygons. *8B* continues with coverage of graphs of linear and quadratic functions; the Pythagorean Theorem; coordinate geometry; different measurement of pyramids, cylinders, cones, and spheres; data analysis; and quadratic equations.

Some of these chapter headings do not clearly indicate the level of difficulty. For example, the very first chapter in *7A* on factors teaches students how to “represent the prime number factorization of a number in exponential notation.” In chapter 13 of *7B,* which teaches how to compute the volume of solid shapes, students use both algebra and geometry to compute the volumes of irregularly-shaped solids.

Both parts A and B are required for each course. For each part of a course, there are a textbook, a Teaching Notes and Solutions book, a workbook, and a Workbook Solutions. You absolutely need the first two items, and you will probably want to use the workbook as well. Textbooks are printed in full color. Illustrations and the attractive graphical layout of the pages make them visually interesting. Workbooks are printed in two colors, but there are no illustrations beyond those used to teach the math such as geometric figures and graphs. The teacher’s books are in black and white. None of the student books have sufficient space for writing answers, so you should consider these books to be non-consumable and have students write their solutions in a separate notebook.

The textbooks include both instruction and problems to solve. Students should be able to work independently through the lessons. Each chapter opens with a brief real-life situation that requires mathematical skills to give students an idea of why they might need to know what will be taught. Chapters are then broken down into two to seven lessons. For each lesson, a new concept is taught with an explanation and examples. Students are given the opportunity to “Try it!” with one or more sample problems so they can check whether or not they grasped the concept. “Remarks” in the sidebar highlight key points. “Discuss” questions show up occasionally in the sidebars. Discuss questions challenge students to think more deeply about concepts. These might be discussed with the teacher, pondered privately by the student, or ignored. Occasional “Class Activities” should be able to be done by a student working alone. “In A Nutshell” pages summarize rules and concepts in individual boxes within a single page for quick review.

Practice questions for each lesson are presented in four sets that become progressively more complex and challenging. Word problems show up mostly in the last two sets, so you don’t want to assign problems only from the first two sets. All practice questions address concepts taught only in that lesson. Occasional problems require the use of a calculator. Pages 59 and 60 in *7A* teach basic calculator operations using a TI-30Xa calculator. While you can use a different calculator, using this model will make things simpler.

One or more pages of review questions at the end of each chapter review topics taught in each entire chapter, but there are no questions from previous chapters. Chapters conclude with “Extend Your Learning Curve” and “Write in Your Journal” activities. The first requires research and writing, while the second requires reflection and writing. You might consider these optional. Answers for all problems are included at the back of each Textbook, but you might want to remove these pages to prevent cheating. The variety of problems—practical applications, word problems, and critical thinking problems in addition to basic problem-solving practice—should really help students learn the material well.

The student textbooks are available in either hardcover or paperback editions. The price of the hardcover books is not that much higher, so you might want to consider that option.

The Teaching Notes and Solutions books have brief notes on each chapter, but the bulk of each book consists of complete solutions for all problems in its companion textbook. While the simple answer keys at the back of the textbooks provide the answers, you will sometimes want to refer to the complete solutions. The Teaching Notes and Solutions books include answers for Class Activities and Discussion Questions as well.

Workbooks have additional problems presented in four groups: Basic Practice, Further Practice, Challenging Practice, and Enrichment. It might be possible to skip the workbooks, but I think they will be useful for additional practice on troublesome concepts. I also think they might be valuable for testing material. There are no cumulative exams in the course, so you could select problems from a workbook to assign for a test. You might also select problems from previous chapters to provide either cumulative review or cumulative testing. Separate Workbook Solutions books for each workbook have complete solutions for all workbook problems.

*Dimensions Math *is the result of collaboration between Star Publishing Pte Ltd of Singapore and Singapore Math, Inc. in the United States. The series for levels *7* and *8* follows the math framework for Singapore which is more advanced than in the U.S., but it also covers most of the Common Core State Standards for the U.S. This means that these two levels cover what is required for two different systems. That’s a lot to cover in a few short years. Consequently, you might want to slow down a bit, using the workbooks to solidify knowledge before moving on. Since this is a new series, it remains to be seen how well students are able to manage the workload.