Essentially, Dimensions Math PK-5 is the new and improved Singapore math program, while Primary Mathematics is the original curriculum that put Singapore math on the map. Please read this Dimensions or Primary page for more!
To compare the content of the books, take a look at samples of both programs.
In typical U.S. math programs, students get a worked example, then solve problems that very closely follow that example, repeating all the same steps with different numbers. In Singapore math, students must think through concepts and apply them in new ways from the very start. Since they can’t rely on simple replication, students are pushed to greater engagement and broader thinking. In U.S. math programs, concepts and skills are more compartmentalized within and across grade levels than in Singapore math, where a strong sense of connectivity to past learning is woven throughout. Unique Singapore math methods, such as number bonds and bar modeling, also set Singapore math apart from typical U.S. math pedagogical styles.
Placement tests for Dimensions Math and Primary Mathematics are here.
Dimensions Math includes expanded teaching materials, here on our Resources page, such as videos, Blackline Masters, letters home, and more.
The Concrete, Pictorial, Abstract (CPA) approach develops a deep understanding of math through building on existing knowledge. This highly effective framework introduces concepts in a tangible way and progresses to increasing levels of abstraction. In the concrete phase, students interact with physical objects to model problems. In the pictorial phase, they make a mental connection between the objects they just handled and visual representations of those objects. For example, real oranges (or counters standing in for oranges) are now represented as drawings of oranges. In the abstract phase, students use symbolic modeling of problems using numbers and math symbols (+, −, ×, ÷).
By varying the methods and phases of CPA fluidly, educators help reinforce important connections. Students work towards math mastery when they view concepts with increasing levels of abstraction over time. Not all lessons include all three CPA stages as application of this approach varies by topic. Instead, CPA principles are woven throughout the curriculum, and support other important strategies such as number bonds, bar modeling, and mental math.
We started Singapore Math Inc. over 25 years ago because we thought everyone should have access to this incredibly effective teaching method. Please read Our Story for more.
Singapore math programs do not continue beyond Grade 8. Students may move onto Geometry and Algebra 2. If you’re looking for online teaching, you might check out High School Math Live or Thinkwell. Art of Problem Solving is good for students who excel at math. We also recommend geometry books by Jurgensen and algebra books by Dolciani.
Yes, with fully worked solutions for many of the problems. The Home Instructor's Guides and Teacher's Guides have answers for both the Textbooks and Workbooks. They also include lesson notes and suggestions. If you only want answers to the Workbook and Textbook problems, you can get the Answer Key Booklets (there's one for Grades 1–3 and one for Grades 4–5).
We don’t recommend using the Workbooks by themselves as you and your student will miss most of the core material, explanations, exercises, and teaching notes.
Primary Mathematics has four editions: U.S. Edition, Standards Edition, Common Core Edition, and the 2022 Edition.
Primary Mathematics U.S. Edition
Almost identical to the original program from Singapore, but uses U.S. measurements and currency.
Primary Mathematics Standards Edition
Written to meet the California Public School standards prior to Common Core, this edition includes probability, data analysis, negative numbers, and coordinate graphing.
Primary Mathematics Common Core Edition
Aligns with Common Core. This edition has changes to the scope and sequence.
Primary Mathematics (2022 Edition)
Content and lesson structure is entirely new. More differentiation and more aligned with U.S. school standards.
Letters Home and other Dimensions resources are on the Dimensions Math PK-5 Resources page. They're organized by grade level.
The content was created by our team of teachers and experts with over 100 combined years of Singapore math classroom experience. The series was designed and published in-house by Singapore Math Inc.
Lessons begin with a class activity to encourage discovery. Worked examples of new concepts are followed by similar questions for students to solidify their understanding.
- Basic Practice: Simple questions that drill comprehension of concepts
- Further Practice: More challenging questions that involve direct application
- Challenging Practice: Questions that require synthesis
- Maths@Work: Questions that apply mathematical concepts to real world situations
- Brainworks and Enrichment: Questions involving higher order thinking or an open-ended approach to problems
Each chapter in Grades 7-8 is followed by a review exercise. The Extend Your Learning Curve activity encourages students to consider math outside the classroom with questions requiring sentence or paragraph reflections on their learning experiences.
As in all our programs, the school year is divided into two semesters: A and B. A books cover the first half of the year, and B books cover the second half of the year.
Grade 6 includes (A and B) Textbooks, Workbooks, Teacher’s Guides, and Workbook Solutions.
Grades 7-8 include (A and B) Textbooks, Workbooks, Teaching Notes and Solutions, and Workbook Solutions.
The Dimensions Math 6-8 program brings the Singapore math approach to middle school, emphasizing problem solving and empowering students to think mathematically. This rigorous series integrates pre-algebra, algebra, geometry, some trigonometry, and advanced math topics. Learn more here.
Dimensions Math 7 and 8 together cover Pre-algebra and Algebra 1 topics, with some geometry. Dimensions Math 6 is aligned with Common Core Standards, and so while it does include some Pre-algebra topics, it is not a Pre-algebra text in the traditional sense. It is a Grade 6 text.
Dimensions Math 7 assumes students are new to Pre-algebra topics, such as integers and simple algebraic equations, but goes farther into Algebra topics than would a traditional Pre-algebra text. Therefore, Dimensions Math 8 has greater expectations for what students have covered previously (particularly with regard to linear equations) than a traditional Algebra 1 text. The two grades, 6 and 7, are meant to be done as a set.
After grade 8, students may move onto Geometry and Algebra 2 programs.
Both are highly effective Singapore math programs. They are more similar than they are different.
They both follow the Singapore math approach, which emphasizes the CPA (Concrete, Pictorial, Abstract) progression, centers the use of number bonds and bar models to solve word problems, and encourages mastery of mental math to gain number sense, computational fluency, and logical thinking.
If you're trying to decide between the two programs, you may find this helpful: Dimensions or Primary?
Lessons in Grades 1-5 are well-defined and follow a consistent sequence. They begin with a problem for discussion, move to an explanation of the concepts, introduce vocabulary, and provide various approaches to solving the problem. This is followed by a set of learning tasks that extend the concept, ending with a set of problems to assess understanding.
Textbooks and Workbooks include additional problems. Workbooks offer independent practice while maintaining the careful progression of exercise variation. They are where students hone their skills, and are a necessary component of the series. Workbook exercises are differentiated and include basic problems, practice problems, and challenging problems.
Teacher’s Guides are in full color and include reduced-size copies of Textbook and Workbook pages for easy reference to every lesson. The Teacher’s Guides give more ideas for differentiation and include math literature suggestions.
Yes, you need both Textbooks and Workbooks to successfully use the Dimensions Math curriculum. They are designed to be used together and the program is incomplete if one is left out. Textbooks introduce concepts and are central to learning and understanding new topics. Workbooks provide practice and independent work, which is essential for solidifying new knowledge.
The school year is divided into two semesters: A and B. There are A and B Textbooks, Workbooks, Teacher’s Guides, and Tests for each grade. Textbooks, Workbooks, and Teacher's Guides are necessary to successfully use this program. Tests are optional. Note that there is only one Tests book for Grade K, and none for Grade PK. There's also a Dimensions Math video subscription. Free Dimensions Math resources, such as Blackline Masters, can be found here.
We offer free placement tests. If you're new to Singapore math, we highly recommend giving your student a placement test to be sure they start at the appropriate level.
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Here's a great introduction (PDF). We created Dimensions Math to better serve teachers and students. We preserved all the methods and content that make Singapore math so effective, while making improvements to educator resources, design, and more. Concepts are presented in a new format with vibrant imagery, while the progression and scope that define Singapore math remain intact. This is our most substantial program yet. Take a look inside each book of the program here.
Primary Mathematics 2022 Edition is a K-5 program written to align with U.S. standards while reflecting current practices of math instruction in Singapore. The content and lesson structure are completely new and do not resemble those of previous Primary Mathematics editions.
Like previous editions of Primary Mathematics, the program builds strong problem solving, critical thinking, and computational skills through classic Singapore math methods, such as the concrete-pictorial-abstract approach and bar modeling.
Singapore has consistently ranked at the top in international math testing for decades.
Two international tests, the TIMSS (Trends in International Mathematics and Science Study) and the PISA (Programme for International Student Assessment), assess math and science competency in countries around the world. Singapore students consistently rank among the top on both tests.
You can view samples of our major programs here. You may also click the Look Inside tab on each product page for samples.
Earlybird Kindergarten provides a systematic introduction to essential math concepts and basic reasoning skills. Through engaging graphics, hands-on tasks, and active participation, students build a strong foundation that prepares them for elementary math.
Earlybird Kindergarten Common Core Edition aligns with the Common Core State Standards. Earlybird Kindergarten Standards Edition aligns with the Mathematics Framework for California Public Schools.
Earlybird Kindergarten Components:
Textbooks develop concepts in a focused and fun way. Each unit includes several lessons with a specific learning objective. Exercises that focus on repetition ensure the reinforcement of facts. Math at Home activities in tear-out sheets provide opportunities for family involvement in the learning process. Detailed instructions for parents are provided in the teaching notes.
Activity Books follow the sequence of textbooks and provide opportunities for consolidation, remediation, and enrichment.
Teacher’s Guides offer useful and detailed suggestions to facilitate meaningful engagement. They include step-by-step lesson plans and ideas to develop concepts in a compelling way.
Essential Math is a Kindergarten series that encourages students to explore and understand the world around them through math. This series does not align specifically with an elementary program, but makes a good early math education on its own or as a supplement.
New Elementary Mathematics covers Grades 7-8. It emphasizes the development of mathematical concepts and their applications, proficiency in problem solving, reasoning, and higher order thinking. It lays a solid foundation for high school level math. The series includes a textbook, a workbook, and solution manual for each grade.
New Elementary Components:
Textbooks include differentiated exercises for students at various levels, class activities, and chapter reviews. Many opportunities for revision reinforce skill mastery.
Workbooks include questions for more practice and tests to assess students at various stages. They make an excellent supplement, and are not an integral part of the program.
Solution Manuals are a great resource and guide for instructors when working through difficult problems with students. They provide step-by-step solutions to the main textbook exercises.
Earlybird Science (Grades 1-2) opens the door to the challenging and engrossing world of scientific discovery. Simple explanations of concepts are illustrated and reinforced in the activities and experiments that follow. The series is filled with interesting topics ranging from satellites and dinosaurs to the care of pets in everyday life.
My Pals Are Here Science (Grades 1-6) offers an experiential entry into scientific processes and concepts. This colorful series sparks student curiosity and encourages inquisitiveness. Relatable examples from everyday life make science accessible.
Blackline Masters are on the Dimensions Math PK-5 Resources page.
In Dimensions Math 6-8 Textbooks, lessons engage students with different levels of problem solving and real world application of math topics. Lessons progress as follows:
Chapter Opener: Introduces a topic through a real world example and identifies learning objectives.
Example: Helps students understand and master a concept through a worked example.
Try It!: Gives students an opportunity to answer a similar question to check how well they have grasped the concept.
Class Activity: Introduces new concepts through cooperative learning methods.
Basic Practice: Provides simple questions that involve the direct application of concepts.
Further Practice: Provides more challenging questions that involve the direct application of concepts.
Math@Work: Provides questions that involve the application of integrated concepts to practical situations.
Brainworks: Provides higher-order thinking questions that involve an open-ended approach to problem solving.
In A Nutshell: Consolidates important rules and concepts for quick and easy review.
Extend Your Learning Curve: Extends and applies concepts to problems that are investigative in nature and engages students in independent research.
The core student components are the Student Book (textbook), Additional Practice (workbook), and Mastery & Beyond (distributed practice workbook). Educators need to have either a Home Instructor's Guide or Teacher's Guide. The Assessment Guides are optional.
Student Book answer key: Home Instructor's Guide and Teacher's Guide
Additional Practice answer key: Additional Practice Answer Keys
Mastery & Beyond answer key: In back of book
Assessment Guides: Included in the book
Please reach out to our School Support Team at email@example.com to request information regarding digital access for Primary Mathematics (2022 Edition).
We are considering developing lessons for Grades 7-8 in the future, but they are not currently in production.
Dimensions Math PK–5 is not aligned with the Common Core State Standards, but covers the standards in its own unique progression. The few standards not included in the Textbooks (for example, line plots of measurements to fractions of an inch in Grade 3) are covered in the Teacher’s Guides. Dimensions Math 6-8 meets and exceeds Common Core State Standards.
Yes, Primary Mathematics U.S., Common Core, and Standards Editions will all still be available. Primary Mathematics (2022 Edition) is not replacing earlier editions.