Dimensions Mathematics

Dimensions Math is the latest addition to Singapore Math's options for PreK-8th Grade students. The look and feel have changed, but the basic Singapore teaching methodology has not. Instructors will find much more detailed and easy-to-follow content in the Teacher's Guides and Home Instructor Guides, however, making this a good option for those new to Singapore Math.

If you aren't familiar with the Singapore method, we invite you to read our introduction here. In the primary grades, Singapore follows a "CPA" approach (Concrete→Pictorial→Abstract) designed to use a real-world foundation to get kids to think mathematically as opposed to just learning rote operations. If the STEM test scores of students in Singapore are any indication, it's an effective approach.

How Do These Work?

Grades PreK-5

Each grade level of Singapore Dimensions Math is divided into two semesters indicated by A and B designations. There is a pre-kindergarten level, a kindergarten level, and one level each for grades 1-8. The first two levels (grades PreK and K) provide several options to the instructor regarding how to approach each lesson, while Grades 1-8 generally offer fewer options.

For every semester, there is a student textbook, a student workbook, and the option of either a teacher's guide or a home instructor's guide; for grades K-8 there is also a test book for each semester. There are no extra practice guides at this time, but the intensive practice workbooks for Primary Mathematics can be used with Dimensions Math for students who need more challenge. And the answer to the age-old question is, Yes, you will need either the teacher's guide or the home instructor's guide. The teacher's guide is aimed at classroom use, while the home instructor's guide is for homeschool or tutoring situations.

The semester textbooks are divided into chapters, which are further divided into a chapter opener, a number of lessons, and a practice lesson to wrap up the chapter. Lessons average two pages in length and cover individual principles built around a main theme. Each lesson requires an instructor who leads the child through practice problems, discussion, manipulative use, and activities in order to present and solidify key concepts. For PreK-K, both textbooks and workbooks are in full color; for grades 1-8, textbooks are in color and workbooks are black and white.

For grades PreK-K, the chapter opener provides an interesting problem or situation to introduce a key idea. The lessons themselves are full of fun pictures to retain interest but also to illustrate the key concepts. Students work through scenarios, activities, and practice problems with help and guidance from the instructor. Once the textbook lesson is finished, students work through corresponding problem sets in the workbook, referenced in the "Exercise" section of each textbook lesson by a pencil icon that provides page and exercise numbers. Each chapter ends with one or more practice sets to reinforce what students have already learned and practiced.

For grades 1-8, the chapter opener presents a real-world situation to pique student interest in the new concept, followed by a "Think" section for teachers to guide students through a practice problem using a variety of approaches; in some cases, for instance, students are asked to solve the problem the long way, and then are provided a more efficient solution. The next section, "Learn," builds on the previous section with solutions to the "Think" problem, terms, and other relevant information. In "Do," students either work through practice sets alone or with the teacher, and complete activities as outlined in the teacher's books. Finally, in the "Exercise" section students are directed to more problems in the workbook. At intervals, there are also "Practice" and "Review" problem sets to further ingrain the material in students' minds.

Both the textbooks and the workbooks for grades PreK-5 feature a lineup of friendly characters to make learning a bit more fun and personable. Emma, Alex, Sofia, Dion, and Mei show up from time to time in pictures and in problems so that students aren't just constantly confronted with lifeless problems and concepts. The black and white K-5 test books are meant for periodic assessment of students' progress, and include complete answer keys in the back.

There are two options for teacher's materials for grades 1-5: Teacher's Guides for classroom use, and Home Instructor's Guides for home school or tutoring use. The Teacher's Guides begin each chapter with a scope and sequence for that chapter, along with a suggested number of class periods for completing it. A series of notes provide background for the chapter concepts along with important terminology. There are also lists of materials needed for the activities and/or snacks, blackline masters, a list of suggested storybooks, and the corresponding "Letter Home."

The manipulatives include both specialty items available from Singapore Math, as well as household items. Blackline masters and "Letters Home" can be downloaded from the Singapore Math website; blackline masters are for additional activities (including card games) and can be printed out for the number of students you're instructing. The "Letters Home" are chapter newsletters for teachers to send home with students to give to their parents—they outline for parents what the student is learning, and how the parent can reinforce those ideas and concepts at home. The storybooks are available for purchase separately, and are generally well-known or classic math-oriented picture books from authors like Sandra Boynton, Richard Scarry, and Jon Scieszka.

The Teacher's Guides are for use in a classroom setting. The activities require multiple students for success, and the discussions and teacher notes are oriented to teaching many students at one time. They can be modified for use in a home school setting, but not without some creativity, flexibility, and planning. Each student page (from both the textbook and the workbook) is included in reduced format, along with extensive teaching notes and answers to all problems. There are also pages for recording notes.

The Home Instructor's Guides (currently only available for grade 1, the rest are in production) are basically stripped-down versions of the Teacher's Guides, designed for use with one student at a time. They are lacking a lot of the content from the Teacher's Guides (such as lists of supplemental storybooks), but all the missing information is available for download free of charge on the Singapore Math website. The black and white Home Instructor's Guides follow the same basic format of the Teacher's Guides, but with much less teacher support material. They do offer answers to all problems, but they do not reproduce the pages from the student books.

Digital assessments are available for Grades 1-5 for classrooms only—they are explicitly not for sale to home schools, and must be included on a purchase order. Instructional videos are available for Grades 1-6, and can be purchased for home use. One year of videos is $85 (as of August 2021), available only from Singapore Math. Certified Singapore Math instructor Beth Curran leads students through each lesson of both semesters per year. We were not able to review these due to paywall protection.

Grades 6-8

Grades 6-8 were formerly known as Discovering Mathematics (a course that covered Grades 6-10); Discovering Mathematics is now out of print, and grades 6-8 have been renamed Dimensions Math but have not been otherwise revised. For each grade there are two student textbooks with accompanying teacher's guides, a workbook for each semester, and a workbook solutions and answers book for each grade (combined into a single volume for Grade 6). Teacher guides include a yearly lesson plan, brief teaching notes and full solutions to all exercises. While the teaching notes are helpful, they aren't enough to teach the course on, and are basically just supplemental information and suggestions for class activities and presentation.

Like the earlier grades in the series, exercises in the later grades are grouped according to purpose. After the chapter unit, students complete basic practice problems which serve as the practical introduction to the topic. Further practice problems are more complicated and nuanced, and the rest of the exercises are designed to show the practical application of the topic and help kids improve their logic and analytical skills. Students are also encouraged to keep a math journal where they record real-life contexts in which various topics might be useful. Textbooks are full color, while workbooks are black and white.

This is a fairly fast-moving course. Topics are taught for mastery, and thoroughly covered and practiced before moving on. Instruction is clear and there are many worked examples in the text, so most students who can pay attention and apply themselves should find getting through lessons fairly easy. Since the emphasis is on practical application of mathematical concepts, exercises are constructed to help students internalize information by following each step in the process carefully.

Dimensions Math for grades 6-8 is more or less student-directed. Of all the secondary Singapore math courses, this is the least teacher-reliant. As with any course, teacher involvement can never hurt, but you'll need to put together your own lesson plans and should probably have a pretty thorough knowledge of each topic you introduce.

How Does Dimensions Math Differ from Primary Mathematics Editions (US, Standards, & Common Core)?

There honestly aren't many differences between the US, StandardsCommon Core, and Dimensions editions of Singapore Math. All of them use the same basic approach both conceptually (mastery, C→P→A) and practically (chapters built around concepts and divided further into lessons and practice). All of them use a two-semester approach for each grade level, are teacher-directed, and use a student textbook and a student workbook as the main texts for each semester. All of them also use both English Standard and metric measurement, as well as US currency.

Dimensions Math is less cartoony than the other versions. It also seems to be a bit more advanced in scope and sequence than the others, though the topics covered are in the same order.

US Edition covers grades 1-6; Standards covers grades K-6; Common Core covers grades K-5; and Dimensions Math covers grades PreK-8.

There are more supplemental texts for students with the other editions, but there are a lot more supplements for download and use for Dimensions Math that the lack shouldn't be too noticeable. Also, as mentioned above, the US Edition Intensive Practice books can be used in conjunction with the corresponding semesters of Dimensions Math.

The biggest difference between Dimensions Math and the other Singapore Math options is definitely the amount and quality of teacher materials and support. PreK-5th grade require teacher involvement, but with the printed and downloadable content available, that should be no problem, even for inexperienced teachers.

Our Honest Opinion

Singapore Math has long been a staple at Exodus Books. The thoroughness of instruction, the well-researched approach, and the relative ease-of-use make it popular with both instructors and students. Dimensions Math has the distinction of being the most teacher-friendly of the US elementary grade offerings, with significantly more support both online and in book form. The student books are less cartoony and more straightforward, while remaining visually stimulating and engaging.

If you're looking for a student-led approach for PreK-5, this is definitely not it. Grades 6-8, by contrast, are intensively student-led, to the extent that there is not much by way of teacher support for those grades, either online or in book form. In order to get the most out of the PreK-5 books, instructors will need to spend time with the supplemental teacher or home instructor material prior to teaching, and will need to spend about half of each lesson with their student. Some have found the multiplicity of options for PreK-K to be too much, and have abandoned the series before first grade; we recommend pressing on.

All in all, this is a refreshing direction for Singapore Math. Previous iterations have skewed more and more to classroom instruction, as well as focusing more on Common Core metrics for gauging student progress. Dimensions Math is uncluttered and straightforward in terms of content and approach. The fact that it covers both the younger grades and the middle school grades makes it much more appealing than previous iterations. We've always recommended Singapore Math, and if you've already decided to go that route we highly recommend you consider Dimensions Math.

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Dimensions Math 1A - Home Instructor's Guide
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Dimensions Math 1A - Teacher's Guide
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Dimensions Math 1A - Tests
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$12.00
Dimensions Math 1A - Textbook
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$12.00
Dimensions Math 1A - Workbook
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in Dimensions Mathematics (Location: MAT-SMDM)
$12.00
Dimensions Math 1B - Home Instructor's Guide
from Singapore Math
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in Dimensions Mathematics (Location: MAT-SMDM)
$20.00
Dimensions Math 1B - Teacher's Guide
from Singapore Math
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in Dimensions Mathematics (Location: MAT-SMDM)
$25.00
Dimensions Math 1B - Tests
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$12.00
Dimensions Math 1B - Textbook
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$12.00
Dimensions Math 1B - Workbook
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Dimensions Math 2A - Teacher's Guide
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Dimensions Math 2A - Tests
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$12.00
Dimensions Math 2A - Textbook
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$12.00
Dimensions Math 2A - Workbook
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$12.00
Dimensions Math 2B - Teacher's Guide
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$25.00
Dimensions Math 2B - Tests
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$12.00
Dimensions Math 2B - Textbook
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Dimensions Math 2B - Workbook
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Dimensions Math 3A - Teacher's Guide
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Dimensions Math 3A - Tests
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Dimensions Math 3A - Textbook
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Dimensions Math 3A - Workbook
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$12.00
Dimensions Math 3B - Teacher's Guide
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$25.00
Dimensions Math 3B - Tests
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$12.00
Dimensions Math 3B - Textbook
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$12.00
Dimensions Math 3B - Workbook
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$12.00
Dimensions Math 4A - Teacher's Guide
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Dimensions Math 4A - Tests
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$12.00
Dimensions Math 4A - Textbook
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$12.00
Dimensions Math 4A - Workbook
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Dimensions Math 4B - Teacher's Guide
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Dimensions Math 4B - Tests
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Dimensions Math 4B - Textbook
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$12.00
Dimensions Math 4B - Workbook
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Dimensions Math 5A - Teacher's Guide
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Dimensions Math 5A - Tests
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$12.00
Dimensions Math 5A - Textbook
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$12.00
Dimensions Math 5A - Workbook
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$12.00
Dimensions Math 5B - Teacher's Guide
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Dimensions Math 5B - Tests
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Dimensions Math 5B - Textbook
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Dimensions Math 5B - Workbook
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Dimensions Math 6A & 6B - Workbook Solutions
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Dimensions Math 6A - Teacher's Guide
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Dimensions Math 6A - Workbook
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Dimensions Math 6B - Teacher's Guide
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$29.00
Dimensions Math 6B - Textbook
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