Dimensions Math® is a series for pre-kindergarten through fifth grade that is based on the methods and advanced scope and sequence of the Primary Mathematics series (popularly known as Singapore Math.) The Dimensions Math PK-5 series retains the key features of Primary Mathematics, but it has been designed to be more suitable for U.S. teachers and students. In addition, the lesson presentations have been fleshed out with better explanations and activities. Many parents will appreciate having more direction for teaching lessons and more optional activities, while other parents might prefer the sparser instructional information in Primary Mathematics.
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.
Each course is taught in two semester-long parts (A and B). The book titles, starting with PKA and PKB for pre-kindergarten, reflect the grade and semester. The complete course for each grade has two student textbooks and two student workbooks. There are also two teacher’s guides in large, coil-bound books. Both student textbooks and workbooks for pre-kindergarten and kindergarten are in full color, but for grades one through five, textbooks are in color and workbooks are black and white.
In addition to the course books, you need to access the publisher’s page where it lists the materials and resources needed for each course and provides many printable pages that are essential for both teaching and activities. The materials section on the website lists the hands-on resources needed for each chapter, such as base ten blocks, play money, and straws. There are suggestions for storybooks that tie in with the lessons; many are suggested up through second grade but only a few beyond that level. For prekindergarten and kindergarten, you will also find quite a few brief videos for songs such as “The Ants Go Marching” and “Five Little Monkeys.”
How It Works
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.
The textbooks are not intended to be used on their own. Lesson presentations begin from the teacher’s guides because they introduce and expand upon what is in the textbooks.
To ensure that students understand concepts, instruction moves from concrete to pictorial to abstract. To that end, each lesson begins with an interactive discussion, often using hands-on resources along with 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 then practiced. All of this takes place using both the teacher’s guide and the student textbook.
Lessons use quite a few hands-on and interactive activities. For example, Chapter 3: Lesson 4 in textbook 1A it teaches about number bonds and addition. Students are to use linking cubes to mirror what is shown on the first page of the lesson—a page with illustrations that show addition facts 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 activity instructions for this same lesson have the teacher create number cards and addition-equation cards from printable pages. These cards will 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-challenging work.
After the textbook lessons, children solve problems in their workbooks. (The pre-kindergarten and kindergarten lessons don’t always have a workbook activity.) Problems range in difficulty and 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 with on their own. This is especially true for pre-kindergarten and kindergarten. Beginning with the first grade, the courses put much more instruction within the textbooks, even though they are still not intended for independent work. With that being said, children in these grades 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. Fourth and fifth graders are expected to do some independent work.
The 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.
The textbooks for pre-kindergarten and kindergarten have children write directly in them, but textbooks for first grade and up do not. The publisher says, “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” (Dimensions Math: 1A, p. iii). In a homeschooling setting, students can answer orally or write in a notebook (or elsewhere). 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 have been handier at the end of each lesson rather than at the end of each chapter.)
Optional test books are available for each course for first through fifth grades—two test books (A and B) per course. These books include both chapter and cumulative tests plus answer keys.
Adapting and Differentiating
Differentiated activities in Dimensions Math make this series somewhat adaptable to children of varying abilities, although it still seems primarily geared toward children of average to advanced ability. Workbook activities for first grade and above often include optional “challenge” problems for children who are ready for more-challenging work.
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.
Scope and Sequence
The courses for pre-kindergarten and kindergarten are both quite advanced. For example, the pre-kindergarten course presents numbers and expects children to be able to recognize them but not write them. At the end of PKB, the course introduces the concepts of addition and subtraction, including showing equations. The kindergarten course 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. (Note: Dimensions Math is more advanced for these levels than Early Bird Mathematics, another program from Singapore Math. You cannot start with Early Bird Mathematics and shift directly into the next grade level of Dimensions Math.)
The sequence of lessons for grades one through five roughly corresponds to that of Primary Mathematics Common Core editions for the same levels—enough so that it should be easy for children to shift from one program to another. Because of the close correlation, parents who want to supplement for first grade and above can use the 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. More importantly, Dimensions Math provides a starting point for introducing a math program with an advanced scope and sequence beginning in pre-kindergarten or kindergarten that can be continued through fifth grade.