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  • Primary Mathematics

    1. Why are there three different editions of Primary Mathematics?

      The Primary Mathematics series was written in 1982 by the Primary Mathematics Project Team, appointed by the Curriculum Planning and Development Division of the Ministry of Education (MOE), Singapore. Over the past twenty years, this series has been identified with excellence and achievement in Singapore's primary school mathematics curriculum, culminating in Singapore students' success in the 1995, 1999 and 2003 TIMSS (Trends for International Mathematics and Science Study) studies.

      Primary Mathematics Third Edition is what was used in Singapore and used British spelling and other conventions used in Singapore. Some content from previous Editions (division of fractions) was added back into the U.S. Edition, and more was added back into the Standards Edition. Note: The Third Edition is no longer available for purchase.

      Primary Mathematics U.S. Edition is an adaptation of the Third Edition for use in the U.S. It is almost identical to the Third Edition but has a few added sections for U.S. customary measurement. It uses U.S. spelling and conventions. We will continue to carry the U.S. Edition indefinitely.

      Primary Mathematics Standards Edition is an adaptation of Primary Mathematics to meet the Mathematics Contents Standards for California Public Schools, adopted as an approved textbook by the California State Board of Education in 2007 for grades 1-5. It is similar to the U.S. Edition but has some rearrangement of topics and some added units, primarily in probability and data analysis, negative numbers, and coordinate graphing.

      Primary Mathematics Common Core Edition is the newest Edition of Primary Mathematics, written to align with Common Core State Standards, which includes materials for grades 1-5. A digital component, called Primary Digital, can be used as a supplement. Only minor changes were made to scope and sequence, however the Common Core Edition components are not interchangeable with earlier Editions. The format for the Teacher's Guides for the Common Core Edition have been updated to include student materials, making them wraparound guides.

    2. What are the differences between each Edition?
      The following table lists the major differences between the three editions, and the major features and components of each.

      Please note that components from one Edition are not interchangeable with components from other Editions.
    Common Core Edition Standards Edition U.S Edition
    First published 2014 2008 2003
    Format Differences All the textbooks are in color. Workbooks are black and white. The reviews at the end of each unit are not cumulative but cover only the unit. Practices are removed, and the questions from them integrated in the lessons instead.
    There is a glossary, index, and Common Core curriculum map at the back of each textbook.
    All the textbooks are in color. Workbooks are black and white. There is a cumulative review after each unit. There are practice pages in the textbook as well for more practice for several lessons or a chapter.
    There is a glossary and index at the back of each textbook.
    Textbooks for 4A-5B have a list of the California mathematics content standards.
    Workbook for 1A-2B have "Math at Home" pages at the back.
    Textbooks for 1A-2B are in full color, but for 3A and up are two-tone. Workbooks are black and white. There are cumulative reviews after some units, and sometimes more than one. There are practice pages in the textbook as well for more practice for several lessons or a chapter.
    There are no glossaries, indexes, Math at Home pages or list of standards in the textbook or workbook.
    Topic Differences Click to view a scope and sequence comparison of the three Editions of Primary Mathematics.
    Teacher Guides Teacher guides include small-scale pictures of textbooks and workbooks. Each lesson includes which of the Common Core standards are applicable to the lesson. Teacher guides do not include images of textbook and workbook pages. Each lesson includes which of the 2007 California Content Standard are applicable to the lesson. Only some levels have a revised edition of the guide with a table-like format for the lessons.
    Home Instructor Guides
    Forthcoming but not by the 2017-2018 school year.
    Home Instructor's Guides for Standards Edition 1A-5B are available. There are and will be none for 6A and 6B. Answer Keys 1A-3B and 4A-6B are available (answers are also in the guides). Home Instructor’s Guides for US edition 1A-6B are available. Answer Keys 1A-3B and 4A-6B are available (answers are also in the guides).
    Supplement Titles Extra Practice CC
    Challenging Word Problems CC
    Extra Practice
    Challenging Word Problems
    Extra Practice
    Singapore Math® Intensive Practice
    Challenging Word Problems
    Sample pages?
    See the Contents_Sample tab on the product detail information page of each item.
    Placement tests? Forthcoming. Use the placement tests for U.S. Edition in the meantime. Go to Placement Tests
    1. Are there answers in the textbooks or workbooks?
      No. Answers are in the guides or in separate answer keys.

    2. Do we need both the textbook and workbook? What is the difference between them?
      Yes, you need both. The textbook contains the learning tasks that are done as part of the lesson. It also has practices and reviews that are meant to be done in class. The workbook contains the independent work (which can be used for homework).

    3. What is the difference between the Teacher's Guide and the Home Instructor's Guide?
      The Teacher's Guide is geared towards class instruction, whereas the Home Instructor's Guide is geared towards teaching one or a few students. The Teacher's Guide has daily lesson plans, whereas the Home Instructor's Guide has lesson plans that are more flexible and can take one or more days depending on the needs of the individual student. Both have answers to all textbook and workbook problems, but the Home Instructor's Guides have more step-by-step solutions and some alternate solutions. For levels or Editions where there is not a Home Instructor's Guide, homeschoolers may use the Teacher's Guides. The format is different than the Home Instructor Guides since the Teacher’s Guides were designed for classroom use, but they are still applicable in homeschool settings.

    4. I am using Primary Mathematics to teach my children at home. Do I need a guide?
      A guide is highly recommended, but not obligatory. Primary Mathematics follows a concrete to pictorial to abstract sequence of instruction. The concrete introduction is not in the textbooks. Suggestions for introducing the concepts concretely are given in the guides. The guides provide background notes to the teacher explaining the concepts and how they fit in with the program as a whole, as well as information about what was previously taught. The guide also emphasizes places where concepts are taught differently from most U.S. texts, such as bar models to diagram word problems and the mental math techniques. From just looking at the textbooks, it has sometimes been assumed that learning math facts is not required, since the textbooks and workbooks do not include drills on the math facts. Learning math facts is, however, a necessary part of the curriculum and suggestions on how to help students memorize math facts, as well as some mental math sheets, are in the guides. Therefore, the guides round out the curriculum.

    5. Where can I find more practice exercises?
      Singapore Math Inc.® offers a variety of supplementary books for the elementary grades.

      Extra Practice is a series specific to each of the three Editions of Primary Mathematics: U.S., Standards, and Common Core. Challenging Word Problems comes in two Editions: U.S. Edition and Common Core Edition. Intensive Practice is a series that matches the scope and sequence of Primary Mathematics U.S. Edition, and can be used as additional practice for students using other Editions, keeping in mind there are some differences in scope and sequence.

      Other supplementary books are not components of the Primary Mathematics series - they are simply books from Singapore that provide additional practice. The other books are generic and often add to the content of Primary Mathematics. All of them can be used with any of the editions of Primary Mathematics with caution for the sequence of topics. Please see the FAQ on the supplements for more information.

    6. We plan to start using Primary Mathematics. Which Edition should we use?
      If you are a school and new to the program, we suggest the Common Core Edition. If you are a homeschooler, you may choose between any of the three Editions of Primary Mathematics. Factors for consideration include the added content in the Standards Edition and the alignment to Common Core State Standards in the Common Core Edition.

      The basic methodology for teaching foundational mathematics concepts is the same in all three Editions, and all three will equally prepare your student for pre-algebra regardless of any added or moved topics.

    7. Can we switch between Editions?
      You can switch between Editions but you should finish the B books of one level before switching to the A book of the next level in a different Edition. It is not advisable to switch from U.S. or Core Edition to Standards Edition between levels 5 and 6.

    8. I am not happy with the math being taught at my child's school and want to supplement at home. Which Edition should I get?
      If your school is following Common Core Standards, you should probably get the Common Core Edition if you want to be sure all the topics are covered. The Common Core Edition will still likely have different approaches and sequence of topics than what your child is learning in school. However, if you are supplementing your child's education and want to focus on foundational concepts, you should get the U.S. Edition.

    9. Is the Common Core Edition of Primary Mathematics "dumbed down" compared to the U.S. Edition?
      No, it is not. It meets the math requirements per grade level for the Common Core State Standards, and so some topics were added and rearranged, but it maintains the integrity of the Primary Mathematics curriculum. Most of the content is the same as in the U.S. Edition, and thus the third edition of Primary Mathematics, even if they are not part of the standards. This is one series that has not followed the trend of decreasing challenge with each new edition! Some topics were added, which could lead to concern that it is becoming "mile wide and inch deep" but the additions are fairly minimal. Some of the additions were simply made in order to be more explicit on material that was already in the curriculum, or to cover some of the same material at more grade levels, and some were added to meet the requirements of the Common Core Standards.

    10. How do I know where to place my child?
      Please use the Placement Tests. As a homeschool, you have the option to start your student at an appropriate level for that student and move at his or her pace, rather than being restricted to a particular level and perhaps missing some foundational concepts that are introduced better at an earlier level, or having to spend a specific amount of time on a topic your student already knows. We also have a forum where you can share similar concerns. Please note that placement tests for the Common Core Edition will be available soon, in the meantime we recommend you use U.S. Edition placements tests to place your student.

    11. What if I encounter problems when we have already started using these books?
      You are welcome to visit our forum for online help.

    12. Do we need to purchase additional products such as manipulatives for use with this curriculum?
      Teachers in Singapore use simple manipulatives such as flash cards, charts and 3-dimensional objects. Click here to view a chart listing the manipulatives used in the Home Instructor's Guides is available, and click here to see Manipulatives we carry.

    13. How teacher-intensive is the program?
      As with any program, effective supervision plays an important role. The more involved you are in your student's math education, the better the chances for addressing lack of comprehension in a timely manner. The curriculum was not designed to be self-taught.

    14. Is there any part of the Singapore Math® program which is independent learning?
      The student is expected to do all the work in the workbooks independently.

    15. Can we use Teacher's Guides, Home Instructor's Guides and Answer Key Booklets from one Edition with books from another Edition?
      No. The Primary Mathematics textbooks, workbooks, guides, and tests for one Edition cannot be used interchangeably with textbooks, workbooks, or guides for another Edition.

    16. Can you tell me more about the content differences between the U.S. Edition, the Standards Edition, and the Common Core Edition?
      Please see the Scope and Sequence information for each Edition and this Primary Mathematics Scope and Sequence Comparison table, which details when concepts are introduced and specifically addressed (this document is also linked on the Scope and Sequence page). The Scope and Sequence Comparison also includes the Common Core State Standards.

    Comparison with other math programs

    1. How do Singapore Math® programs compare with other math programs?
      Singapore Math® programs offer a balance between drill and creative problem solving. Customers who have used other programs think that the Singapore approach moves along to more abstract math concepts in a more rational way and, depending on the student's pace, more quickly. Other positive feedback indicates that the Singapore approach encourages greater problem solving skills and creative thinking.

    2. Do Singapore Math® programs use the incremental, spiral or unit-style approach?
      The Singapore Math® curriculum does not conform strictly to any of the above approaches. The strong point of Primary Mathematics is the way basic concepts are presented. There is always more than one approach, and the workbooks are instrumental in making sure the information is generalized in the way desired. There are 'Practice' and 'Reviews' at the ends of chapters and sections. There is an effective mix of drill, word problems and mental calculation instruction connected to all important concepts. (Note: some of the drill is provided in the guides). While typical U.S. curricula touch on a larger number of topics rather superficially, Primary Mathematics presents the core math curriculum in a way that better prepares students for higher math.

    3. How is math drilled in Singapore?
      Individual teachers approach the process of oral drill and use of manipulatives differently. There is, however, great emphasis on homework and practice.

    Model Drawing

    1. What is Model Drawing all about?

      Primary Mathematics teaches a problem solving technique in which students use pictorial models. This approach is often called the “model approach." In the model approach, students draw diagrams in which they represent the problem situations and relevant concepts using bars. Drawing the model permits students to visually relate various types of information given in the problem to an unknown amount and helps them to determine which mathematical expressions are useful in solving the problem. The purpose of drawing the models is not to have students follow specific rules, but rather to understand the concepts and work out a strategy for finding the answer. For complex problems, several strategies are possible, and drawing the model allows the student to visualize a good strategy. Drawing bar models is a valuable tool for solving non-routine problems. These problems might also be solved using algebra, but for children at the primary level a model approach can be preferable since it is less abstract.

      The model approach fits in with the program as a whole, and is not the only benefit to using Primary Mathematics. It can be taught in isolation from the rest of the program, at least to a certain extent, but is more effective when taught as a part of the whole. Model drawing is a problem solving method that can be used across different levels, and as a link to algebra in the secondary level. Students in Primary Mathematics 1 and 2 learn number bonds and part-whole concepts and use number bond diagrams to solve simple word problems before they are ready to draw proportional bars needed using the model approach.

      A commonly used strategy in using bar models is to draw units or divide the bar into units, equate the number of units to a quantity, which is either given or calculated from other quantities given in the problem, form a proportion statement, and finally to use a unitary or proportion method to get the answer. In Primary Mathematics, a unitary method is used in understanding and solving fraction, percentage, ratio, and rate problems, without necessarily drawing a bar model. These concepts are difficult for some students to grasp, and in Primary Mathematics are taught in the context of skills already mastered with the use of the model approach. A main feature of Primary Mathematics is a concrete to pictorial to abstract approach. Bar models are not the only place in the program where a pictorial approach is used to help students understand concepts.

      The model approach, while an integral part of Singapore mathematics, is not just what Singapore mathematics is all about, nor is it the total of the benefits that can be derived from using the Primary Mathematics program.

    Other series used in Singapore

    1. Who wrote the Primary Mathematics series?
      The Primary Mathematics Series was first published in 1982 and was the only series used in Singapore primary schools until 2001. Primary Mathematics was written by members of a project team put together by the Ministry of Education, Singapore.

    2. Who publishes the other series used in Singapore?
      The other series are published by various different publishers.

    3. How many other series were published in Singapore?
      There were about five series that were approved. Some of the series have already come and gone. Some have been revised.

    4. Why are you selling Primary Mathematics when there are so many other series used in Singapore?
      Primary Mathematics has been around for over thirty years and has a proven track record. Students from Singapore who scored well in the 1995 TIMSS, 1999 TIMSS and 2003 TIMSS were using the Primary Mathematics series. We have also consulted with several professors (who were advocating "back to basics" mathematics) in the U.S. and they have unanimously agreed that the newer texts lack the in-depth teaching of the original Primary Mathematics series. The original Primary Mathematics series were written by members of a team put together by the Ministry of Education (MOE) in Singapore. Teachers were also invited to test the material and to provide useful insights and suggestions.

      The newer series are written by authors hired by the publishers. It is our mission is to make available the best mathematics books from Singapore - and at this point in time, the Primary Mathematics Series, with its proven record, is still in the lead. We even got approval from the Singapore MOE to publish a U.S. Edition of the Primary Mathematics series so that we could add some material (U.S. measurement) requested by our U.S. customers, as well as include some material from an earlier edition (2nd Edition). Meanwhile, we are monitoring the results of the new series. After all, mathematics education is not about the latest 'new thing'. Please look at The Singapore Math® Story.
    5. What is the similarity between the other series and Primary Mathematics?
      The contents of the newer series used in Singapore changes over time. Both the Primary Mathematics series and the first wave of newer series are based on the 1999 reduced syllabus. (However, with the Primary Mathematics U.S. Edition, a chapter on division of fractions that was "reduced" was added back). Please look at The Singapore Math® Story.

    6. What are the differences between the newer series and Primary Mathematics?
      The newer series are written by different authors hired by the publishers. Hence the methodologies used for teaching the same concepts will vary between series (i.e. the differences are not limited to pictures, names and color schemes). Three initiatives were also introduced - National Education (to develop citizenship skills and values in the Singapore context), Information Technology (to bring hardware and software technology into schools. However, for the new series, the IT content is found only in the teacher's CD ROMs. It is not mentioned in the textbooks or workbooks, as the IT materials are not reviewed by MOE), and Critical and Creative Thinking (to infuse thinking skills). Newer textbooks first published in 2001 were revised in 2007. Changes in 2007 (for texts now used in Singapore) include use of calculators (starting in level 5), reduction in mental math, and removal of operations on compound units in measurement. Please look at The Singapore Math® Story.

    7. Why is Primary Mathematics no longer used in Singapore?
      The MOE decided to "open up" the textbook market in Singapore. Three initiatives were also introduced - National Education (to develop citizenship skills and values in the Singapore context), Information Technology (to bring hardware and software technology into schools. However, for newer series, the IT content is found only in the teacher's CD ROMs. It is not mentioned in the textbooks or workbooks, as the IT materials are not reviewed by MOE), and Critical and Creative Thinking (to infuse thinking skills).
    8. How can we make up for the three initiatives that are missing in the Primary Mathematics series?

      1. National Education - these are citizenship skills and values in the Singapore context. As such, they are not relevant to students outside of Singapore.
      2. Information Technology; - the IT content is not in the textbooks/workbooks of newer series. There is no difference between the Primary Mathematics series and newer series. Students in the U.S. and Canada are exposed to IT in many other aspects of their academic career and it is not essential that they learn it from a math book.
      3. Critical and Creative Thinking - these come in the form of harder problems at the end of the chapters in newer series (hence there are less "regular" practice problems in newer series). Primary Mathematics does contain some similar harder problems in the textbook practices, just not under a separate heading. More challenging problems are found in supplementary books such as Primary Mathematics Intensive Practice and Primary Mathematics Challenging Word Problems series. These are actually more challenging than those in newer series. The newer series also has some puzzles. Some of the creative thinking problems in the newer series are puzzles that involve math concepts that the students have not yet learned, and so must be solved more by guess and check. There are good critical thinking problems in the Intensive Practice supplementary books.

    9. Is Singapore Math Inc.® replacing Primary Mathematics with any new series?
      We have no intention of replacing Primary Mathematics. Primary Mathematics has been around for over thirty years and has a proven track record. We will continue to offer Primary Mathematics rather than promote any other series used in Singapore for the U.S./Canada markets.

    Singapore Math® is a registered trademark of Singapore Math Inc.® and Marshall Cavendish Education Pte. Ltd.