Dimensions Math® for pre-kindergarten through fifth grade is a relatively new series 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.
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 parts (one part per semester): A and B. So for the complete course for each grade there are two student textbooks and two student workbooks (softcover books), plus 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 through 5, textbooks are in color while workbooks are black and white.
In addition to the course books, you need to access the publisher’s page where it lists the resources needed for each course and provides many printable pages. The printable pages, which are used for both teaching and activities, are generally essential. A “materials” section online lists the hands-on materials needed for each chapter such as base ten blocks, play money, and straws. There are suggestions for storybooks that tie in with lessons, although many are suggested up through second grade and few beyond that level. For prekindergarten and kindergarten, you will also find quite a few brief videos. The videos are 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.
Textbooks are not intended to be used on their own. Lesson presentations begin from the teacher’s guides as they introduce and expand upon what's in the textbooks.
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 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 and 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 grade 1 teaches about number bonds and addition. Students are to use linking cubes to mirror what is shown on the first page where it is illustrated 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 both number cards and addition equation cards from printable pages 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 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 on their own. This is especially true for grades PK and K. The first-grade course and above all 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. Fourth and fifth graders, especially, should be doing much more independent work.
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.
The textbooks for PK and K have children write directly in them, but textbooks for grade 1 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), 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.)
An optional test book is available for each course for first through fifth grade. These include both chapter tests and cumulative tests. Answer keys are at the back of each book.
Adapting and Differentiating
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. Workbook activities for first grade and above often include optional “challenge” problems for children who are ready for them.
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.
Scope and Sequence
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. Dimensions Math is more advanced for these levels.)
The sequence of lessons in 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 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. More importantly, Dimensions Math provides a younger starting point for introducing an advanced scope and sequence for pre-kindergarten or kindergarten, and 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.