## FAQ

### Top Questions

The Dimensions Math program is a cohesive PK-8 series (Primary Mathematics is Grades 1-6). It is an updated version of the Singapore math approach that includes much more material to support educators.

Grades PK-K include specific visualization activities and provide suggestions for small group and center work. 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. 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 the textbook and workbook pages for easy reference to every lesson. The Teacher’s Guides give more ideas for differentiation and include math literature suggestions.

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.

View the Dimensions Math® PK–5 series overview (PDF). Dimensions Math 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. The series follows the principles outlined in the Singapore mathematics framework, including the Concrete, Pictorial, Abstract (CPA) approach, mental math strategies, and bar modeling.

In the Dimensions Math program, concepts are introduced and explained in a new format with vibrant imagery, while the progression and scope that define Singapore math remain intact.

### Dimensions Math Program

Yes. Textbooks contain learning tasks that are central to lessons, as well as practices and reviews to be done in class. Workbooks contain additional practice and independent work, which can be assigned as homework or completed in the classroom.

The first year of use, the cost is $48 per student including all necessary Textbooks and Workbooks. In the second year and beyond, the cost is $24 per student (because Textbooks are reusable). This does not include Teacher’s Guides or Tests.

Each lesson opens with a problem to encourage student curiosity and introduce new concepts. Lessons include discussion and exploration, strategic use of manipulatives, and exercises that progress systematically.

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.

Dimensions Math 1–5 follows the same Singapore math approach as Primary Mathematics 1–6. It emphasizes the CPA (Concrete, Pictorial, Abstract) progression. It centers on the use of number bonds and bar models to solve word problems, and encourages the mastery of mental math to gain number sense, computational fluency, and logical thinking.

The problem solving processes of the learning tasks deepen and broaden student understanding of concepts (in contrast to the method of simply following an example to solve a similar problem). There is minimal vocabulary and textual information. Concepts are conveyed primarily through images and careful sequencing.

Dimensions Math PK–5 is not precisely 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.

The school year is divided into two semesters. There are A and B Textbooks, Workbooks, Teacher’s Guides, and Tests corresponding to the two halves of the school year. There are also online resources.

As an example, this is the complete set for Grade 1:

Dimensions Math Textbook 1A

Dimensions Math Textbook 1B

Dimensions Math Workbook 1A

Dimensions Math Workbook 1B

Dimensions Math Teacher’s Guide 1A

Dimensions Math Teacher’s Guide 1B

Dimensions Math Tests 1A

Dimensions Math Tests 1B

The Dimensions Math program is a cohesive PK-8 series (Primary Mathematics is Grades 1-6). It is an updated version of the Singapore math approach that includes much more material to support educators.

Grades PK-K include specific visualization activities and provide suggestions for small group and center work. 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. 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 the textbook and workbook pages for easy reference to every lesson. The Teacher’s Guides give more ideas for differentiation and include math literature suggestions.

The Dimensions Math 6-8 series 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 PK–5 is not precisely 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.

The school year is divided into two semesters. Grade 6 includes A and B Textbooks, Workbooks, Teacher’s Guides, and Workbook Solutions corresponding to the two halves of the school year. Grades 7-8 include Textbooks, Workbooks, Teaching Notes and Solutions, and Workbook Solutions for the two halves of the school year.

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.

Exercises include:

- 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.

Dimensions Math PK–5 was designed and published in-house by Singapore Math Inc. The series content was created our team of teachers and experts with over 100 combined years of Singapore math classroom experience.

Dimensions Math includes expanded teaching materials, here on our Resources page, such as videos, Blackline Masters, letters home, eBooks, and more.

Textbooks provide a systematic, well-rounded approach to math that facilitates the internalization of concepts and instills curiosity. Lessons engage students with different levels of problem solving and real world application of math topics. Textbooks A and B for each grade correspond to the two halves of the school year.

**Follow along using the slider below. **

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.

Placement tests for our programs are located at https://www.singaporemath.com/placement-tests

Blackline Masters, along with other resources can be found here. https://www.singaporemath.com/programs/dimensions-pk-5/resources/

Letters Home and other resources are organized by grade level. Once you are on the resource page click on the grade levels below to jump to the resources for that grade.

https://www.singaporemath.com/programs/dimensions-pk-5/resources/

Our new Dimensions Math At Home™ video lessons are now live! A complete video program covering all lessons in the Textbooks and Workbooks. Currently available for grades 3-5, with 1-2 and 6 upcoming. Watch free chapters here.

For Dimensions grades 7-8 as well as Primary Mathematics lessons, visit Singapore Math Live, which provides tools and information for teaching those program levels at home.

View the Dimensions Math® PK–5 series overview (PDF). Dimensions Math 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. The series follows the principles outlined in the Singapore mathematics framework, including the Concrete, Pictorial, Abstract (CPA) approach, mental math strategies, and bar modeling.

In the Dimensions Math program, concepts are introduced and explained in a new format with vibrant imagery, while the progression and scope that define Singapore math remain intact.

### Singapore Math Method

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.

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.

Singapore consistently ranks at the top in international math testing. The intentional progression of concepts in the Singapore math approach instills a deep understanding of mathematics.

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.

Our Singapore math programs raise U.S. student performance internationally and at home on standardized and state assessments. With the use of our programs, more students rank “At or Above NAEP Proficient” on U.S. national math assessments.*

### Homeschooling

**Welcome to the start of your Singapore math journey!**

**This is the place to:**

- Learn about our world-renowned Singapore Math® programs
- Find the right grade level for your kids
- Figure out what materials you need
- Join our large community of Singapore Math curriculum users

**Step 1. Learn about our Singapore Math® programs**

Our two most popular programs are **Dimensions Math®** PK–8 and **Primary Mathematics** 1–6. Please note that Primary Mathematics is only available to customers in the USA and Canada.

Start by learning about what each has to offer to decide on a good fit for your family.

**Step 2. Give a placement test**

Not sure which level is right for your child? We offer free placement tests to determine the appropriate starting point.

**Step 3. Find the books and materials you need**

Once you’ve decided on a program and a suitable grade, head to the shop to gather the essential textbooks, workbooks, and educator resources that make up a complete school year.

After collecting the essential material, you can add optional items like tests books and manipulatives to enhance the core program.

Our programs divide the school year into two halves, or semesters: A and B.

As an example, the complete year of Dimensions Math Grade 1 core materials includes 6 books: Dimensions Math Textbook 1A, Dimensions Math Workbook 1A, Dimensions Math Teacher’s Guide 1A, Dimensions Math Textbook 1B, Dimensions Math Workbook 1B, and Dimensions Math Teacher’s Guide 1B.

Core and optional materials for Dimensions Math PK–8 (PDF)

Dimensions Math at Home™ complete guided lessons for Dimensions Math 3–5

**Step 4. Connect to free resources, news, and our online community**

There are so many ways to stay in the loop and continue learning with Singapore math!

Browse Dimensions Math resources

Connect with other parents and teachers in the Singapore Math user community Facebook group to get the most out of your curriculum. It’s a great place for sharing tips and asking questions.

Stay up to date on product releases and more by following us on Instagram, and subscribing to our newsletter.

Our new Dimensions Math At Home™ video lessons are now live! A complete video program covering all lessons in the Textbooks and Workbooks. Currently available for grades 3-5, with 1-2 and 6 upcoming. Watch free chapters here.

For Dimensions grades 7-8 as well as Primary Mathematics lessons, visit Singapore Math Live, which provides tools and information for teaching those program levels at home.

### Dimensions Math At Home Video Lessons

**Buy your books and manipulatives**

Which books do I need? (PDF)

Which manipulatives are recommended? (PDF)

Not sure which grade to buy? A placement test can help. Looking for more help and resources? Our FAQ has more details on how the program works. Our resources page for Dimensions Math PK–5 includes Blackline Masters and suggested materials. We also hope you’ll join our large and growing Facebook user community for support from fellow Singapore math users.

**Bookmarks for viewing and purchasing your grade:**Do not access the videos directly from vimeo.com or vimeo.com/purchases unless you are willing to view thumbnails of suggested content from Vimeo, some of which may not be suitable for children. Please use our dedicated pages below:

dmathome1.singaporemath.com

dmathome2.singaporemath.com

dmathome3.singaporemath.com

dmathome4.singaporemath.com

dmathome5.singaporemath.com

dmathome6.singaporemath.com

Please email school@singaporemath.com to discuss options, including school discounts, with us directly.

You cannot purchase these through a purchase order. If you are with a school, please email school@singaporemath.com and we will walk you through the process of getting multiple subscriptions.

We are reviewing developing lessons for Grades 7-8, but are currently focusing solely on creating videos for Grades 1-6, of which grades 3-5 are now complete, and Grades 1,2, and 6 are going to be released later this year.

All sales are final, but you may contact Vimeo directly about the possibility of an exchange.

Our new Dimensions Math At Home™ video lessons are now live! A complete video program covering all lessons in the Textbooks and Workbooks. Currently available for grades 3-5, with 1-2 and 6 upcoming. Watch free chapters here.

For Dimensions grades 7-8 as well as Primary Mathematics lessons, visit Singapore Math Live, which provides tools and information for teaching those program levels at home.

### Other Math and Science

## Earlybird Kindergarten

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.

**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

Essential Math is a kindergarten series that encourages students to explore and understand the world around them through math. It teaches the fundamental concepts that students need to be successful in the future. This series does not align specifically with an elementary program, but makes a great early math education on its own or as a supplement.

## New Elementary

New Elementary Mathematics covers (G7-8) 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.

**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.

## Science

Earlybird Science (G1-2) 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 (G1-6) 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.

Lower Secondary Science (G7-8) helps students discover scientific knowledge in real life contexts. Purposeful visuals, experiments, problems, and projects communicate the basics of biology, chemistry, and physics. Critical thinking is encouraged.

Science Matters (G9-10) covers biology, chemistry, and physics at the high school level. The series promotes learning through engaging activities, and prepares students for practical competencies needed in today’s world.

They can do Geometry, and then Algebra 2. If you’d like video or online teaching, you could do HighSchoolMathLive or Thinkwell. For students who excel at math, you could use The Art of Problem Solving. If you want to teach them yourself, the Geometry books by Jurgenson et al and Algebra Structure and Methods books by Dolciani et al are good.

### Primary Math Program

Dimensions Math 1–5 follows the same Singapore math approach as Primary Mathematics 1–6. It emphasizes the CPA (Concrete, Pictorial, Abstract) progression. It centers on the use of number bonds and bar models to solve word problems, and encourages the mastery of mental math to gain number sense, computational fluency, and logical thinking.

The problem solving processes of the learning tasks deepen and broaden student understanding of concepts (in contrast to the method of simply following an example to solve a similar problem). There is minimal vocabulary and textual information. Concepts are conveyed primarily through images and careful sequencing.

The Dimensions Math program is a cohesive PK-8 series (Primary Mathematics is Grades 1-6). It is an updated version of the Singapore math approach that includes much more material to support educators.

Grades PK-K include specific visualization activities and provide suggestions for small group and center work. 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. 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 the textbook and workbook pages for easy reference to every lesson. The Teacher’s Guides give more ideas for differentiation and include math literature suggestions.

Placement tests for our programs are located at https://www.singaporemath.com/placement-tests

Primary Mathematics offers U.S. Edition, Common Core Edition, and Standards 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*More closely aligns with Common Core. This edition has changes to the scope and sequence.

Please note that Primary Mathematics is not for sale to customers outside of the USA and Canada.

Yes, with worked out solutions for many of them as well. The HIGs and TGs have answers for both the Textbooks and Workbooks. They also include lesson suggestions. If all you want is answers to the Workbooks you could get the Answer Keys. There is one for Grades 1–3 and one for Grades 5–6. It does have answers to Textbook as well, but since it is only answers, it’s cheaper and may be all you need.

However, we don’t recommend using just the Workbooks, as it means missing out on most of the core material, explanations, exercises, and teaching notes.

### Program Comparisons

Dimensions Math 1–5 follows the same Singapore math approach as Primary Mathematics 1–6. It emphasizes the CPA (Concrete, Pictorial, Abstract) progression. It centers on the use of number bonds and bar models to solve word problems, and encourages the mastery of mental math to gain number sense, computational fluency, and logical thinking.

The problem solving processes of the learning tasks deepen and broaden student understanding of concepts (in contrast to the method of simply following an example to solve a similar problem). There is minimal vocabulary and textual information. Concepts are conveyed primarily through images and careful sequencing.

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.

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.

Placement tests for our programs are located at https://www.singaporemath.com/placement-tests

### Schools

While we don’t offer professional development directly, we recommend the following trainers and training companies with experience teaching Singapore math.

Our upcoming School Training Workshops and Webinars might also be helpful.

Dimensions Math includes expanded teaching materials, here on our Resources page, such as videos, Blackline Masters, letters home, eBooks, and more.

### Singapore Math Inc.

We started Singapore Math Inc. because we thought everyone should have access to this effective teaching approach. All of our programs preserve the techniques, sequencing, and rigor that define Singapore math. We continue to provide the original curriculum that put Singapore math on the map, while evolving the Singapore math approach through other series to better serve today’s students and educators.

**We believe the highest quality math education should be accessible to all. Our commitment to this mission began over twenty years ago when we introduced the world to Singapore math, and it remains our guiding principle as we develop new and affordable Singapore Math® programs.**

When we moved from Singapore to the U.S., we found our daughter’s public school math program lacking. We began to supplement her education with the math curriculum used at her previous school in Singapore. Through this process, we realized that the Singapore math method was uniquely effective and that it would be useful to other parents and teachers in our community. We started selling the original Singapore Math program, Primary Mathematics, from our home in 1998 to share this powerful approach.

Since those early years, Singapore math has become an established part of national and international conversations about math education. We’ve continually improved and expanded our programs to suit the diverse and ever-evolving needs of U.S. students and educators. Our latest series, Dimensions Math® PK-5, takes what we love about the Singapore math approach and makes it more accessible, affordable, and engaging to today’s students and educators.

One thing that will never change is our core belief that everyone deserves an excellent math education, regardless of their situation. We know that a foundation in Singapore math creates the conditions for future success, and our goal is to make the finest math education in the world available to as many students as possible. We intentionally develop and price all our offerings with this in mind.

Thank you for growing with us as we raise math standards for all!

Sincerely,

Jeffery and Dawn Thomas

Singapore consistently ranks at the top in international math testing. The intentional progression of concepts in the Singapore math approach instills a deep understanding of mathematics.

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.

Our Singapore math programs raise U.S. student performance internationally and at home on standardized and state assessments. With the use of our programs, more students rank “At or Above NAEP Proficient” on U.S. national math assessments.*

### Using Our Store

We offer free shipping on orders of $50 or more within the continental U.S. Please see our Shipping and Returns page for more information.