*Dimensions Math*^{®} for pre-kindergarten through fifth grade is a new series based on the methods and advanced scope and sequence of the *Primary Mathematics* series (popularly known as *Singapore Math*.) Grades *PK, K, 1*, and* 2* are available as I write this review, and grade *3* should be available by the end of 2018. The publisher explains the rationale for creating this new version: “The *Dimensions Math*^{®} PK-5 series is designed to better serve U.S. teachers and students. We’ve updated aspects of Singapore math curriculum for clarity and relevance, while preserving the solid foundation that makes it unique” (http://dimensionsmath.com/overview/).

*Dimensions Math* applies Singapore Math’s methodology in a presentation that is fleshed out with explanations and activities. As with *Primary Mathematics*, the series teaches both skills and concepts, coming at them from a number of directions to ensure that students understand. Games and activities within the lessons give children opportunities to develop mental math skills and gain fluency with the math facts in interesting ways.

Differentiated activities in *Dimensions Math* make this series a little more adaptable to children of varying abilities, although it still seems primarily geared toward children of average to advanced ability.

Each course is taught in two parts (one part per semester): *A* and *B*. So for the entire course for each grade there are two student textbooks, two student workbooks, and two teacher’s guides in large, coil-bound books. Both student textbooks and workbooks for levels *PK* and *K* are in full color, but for levels *1* and *2*, textbooks are in color while workbooks are black and white.

In addition to course books, dimensionsmath.com has other necessary resource material available free online. There you will find resources under four categories: blackline masters, lesson materials, letters home, and videos.

Blackline masters are generally essential for lesson presentation and activities. The lesson materials section online lists hands-on materials needed for each chapter, specific blackline masters required, suggested storybooks that tie in with lessons, and a letter home to be used for class groups. The Letters Home inform parents about what children are learning, so these are obviously not needed for homeschooling. Under videos, you might find words to songs or short videos.

Lesson presentations in the teacher’s guides introduce and expand upon textbook lessons. Textbooks are not intended to be used on their own.

Instruction moves from concrete to pictorial to abstract to ensure that students understand concepts. To that end, each lesson begins with an interactive discussion, often using hands-on resources, based upon the first page of the lesson in the student textbook. This part of the lesson (labeled “Explore” or “Think”) lays the groundwork for new concepts or skills that will be taught and then practiced. All of this takes place using both the teacher’s guide and the student textbook.

Textbooks for *PK* and *K* have children write directly in them, but textbooks for grade *1* do not. The prefaces in both grade *1* textbooks say, “The colored boxes and blank lines in the textbook are used to facilitate student discussion. Rather than writing in the textbooks, students can use whiteboards or notebooks to record their ideas, methods, and solutions” (p. iii). In a homeschooling setting, students can answer orally or write in a notebook (or elsewhere), but if you don’t need to reuse the texts, you can have children write answers directly in them since there is sufficient space and this is the easiest way to work.

The teacher’s guides show reduced student pages with answers overprinted. Student textbook pages are shown within each lesson, but workbook pages with answers are grouped together at the end of each chapter. (It seems like they would be handier at the end of each lesson.)

Each course is presented in a number of chapters, and each chapter begins with an activity-based chapter opener, which is then followed by a number of lessons. Each lesson is designed to be completed within one day.

Lesson activities are labeled as foundational, on-level, or challenge (although foundational parts of lessons are not always marked). Generally, you will use both foundational and on-level activities, using challenge activities only for children who are ready for more. Many activities are presented with instructions for class groups. Some will be adaptable for one child and some will not. Since the courses teach concepts from a number of different directions, skipping occasional activities should not be a significant problem. Still, homeschoolers teaching one child have to be prepared to adapt lesson presentations throughout each course.

Lessons use quite a few hands-on and interactive activities. For example, Chapter 3: Lesson 4 in grade *1* teaches about number bonds and addition. Students are supposed to use linking cubes to mirror what is shown on the first page pictorially with birds, linking cubes, number bond diagrams, and addition equations. Students will continue with three more problems on the next page, all of which include a pictorial representation, a diagram, and an equation. Other lesson activity instructions have the teacher create both number cards and addition equation cards from blackline masters to be used for a game and more hands-on, interactive learning. Students then try to solve two problems that have only diagrams and equations. Six additional problems are provided for students who need more of a challenge.

After textbook lessons, children solve problems in their workbook, although *PK* and *K* lessons don’t always have a workbook activity. Problems that range in difficulty address some previously-taught concepts as well as the current concepts. You can assign some or all of the problems. The teacher’s guides indicate which pages to complete in the workbooks and when they are to be done.

You cannot just hand students one of these textbooks to work on their own. This is especially true for grades *PK* and *K*. Grades *1* and *2* put much more instruction within the textbooks, but they are still not intended for independent work. However, children in these levels who pick up math concepts easily should be able to complete more of the lesson activities on their own and might be able to skip some lesson elements presented from the teacher’s guide. Keep in mind that teacher’s guides sometimes include hands-on activities not mentioned in the student books. If your child needs hands-on work, you will want to rely more heavily on the teacher’s guides.

Levels *PK* and *K* are both quite advanced. For example, *PK* presents numbers and expects children to be able to recognize them (but not write them). At the end of part *B*, it introduces the concepts of addition and subtraction, including showing equations. Grade *K* teaches numbers to one hundred, counting by fives and tens, and both addition and subtraction (within ten). Both courses cover many other concepts, but these give you an idea of how advanced they are. (These courses do not correspond to the scope and sequence of *Early Bird Mathematics, *another program from Singapore Math for these grade levels.)

The sequence of lessons in grades *1* and *2* corresponds very closely to that of *Primary Mathematics* Common Core Editions for the same levels. So much so that it should be easy for children to shift from one program to another. (This should be the case for courses for grades three and above as well.) Because of the close correlation, parents who want to supplement levels 1 and above can use *Intensive Practice* workbooks that were created as supplements for *Primary Mathematics*.

The* Dimensions Math* PK-5 series seems especially good for group classes, but the adaptation required for teaching one student should be easy enough that I expect many homeschooling parents will find this new series very suitable for them as well. Another plus for *Dimensions Math* over *Primary Mathematics* is that it provides a younger starting point for introducing an advanced scope and sequence for pre-kindergarten or kindergarten. This means that there’s no need to switch programs between kindergarten and first grade. On top of that, *Dimensions Math* is priced significantly lower than *Primary Mathematics, *a fact likely to tip the scale in its direction for many homeschoolers.