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Secondary Mathematics and Additional Mathematics

Due to trademark issues, we will have to stop carrying Discovering Mathematics and Discovering Additional Mathematics after December 31, 2014. This will affect all the Discovering Mathematics titles that we now carry. We currently have no plan to replace these titles.

Please note that this will not affect the Dimensions Math CC series. This will continue to be available. Singapore Math Dimensions Math Common Core Series for Grades 7 and 8 is adapted from the best selling Discovering Mathematics used in Singapore schools.

  1. Why are the Discovering Mathematics books for grades 7-10 labeled 1-4?
    In Singapore, students attend Primary school for 6 years, then Secondary school usually for 4 years, and then can attend junior colleges for 2-3 years. Grades 7-11 in the U.S. are roughly equivalent to Secondary 1-4 in Singapore.

  2. Where does Discovering Additional Mathematics fit in?
    In Singapore, some students do a second math class in Secondary 3 and 4 called Additional Mathematics. The books we sell with Additional Mathematics in the title are used for these classes over a 2-year period. Since these books cover pre-calculus and calculus topics, they could be used after the Secondary 1-4 books.

  3. How do the Discovering Mathematics books correlate with the math sequence in the U.S.? Which is pre-algebra, algebra 1, geometry and so on?
    These books have an integrated approach. They progress sequentially through various topics in algebra, geometry, and some trigonometry, with minimal review of earlier levels. Please see the Scope and sequence. As a rough comparison:
    Secondary 1: pre-algebra, some algebra 1 and geometry
    Secondary 2: algebra 1 and geometry
    Secondary 3: some algebra 2, geometry, some trigonometry
    Secondary 4: some advanced topics and review
    Additional Mathematics: first half is mostly pre-calculus including trigonometry, second half is mostly calculus.

  4. What is the new Dimensions Mathematics Common Core Series? How does it compare?
    This series for 7th and 8th grade is a revision of the original Dimensions Math (Discovering Mathematics) series in order to include the Common Core Standards. A few topics were added to some chapters, and some topics were rearranged between the levels. There is some U.S. customary measurement, but metric measurement still predominates. Terms have been changed to reflect the common use in the U.S., such as gradient to slope and indices to exponents. American English spelling is used. Otherwise, it is the same as the original series. No topics were removed. It therefore follows the Singapore Mathematics Framework as well as covers the Common Core Standards.

  5. Will the new Dimensions Math Common Core Series be less advanced or rigorous than the original in order to accommodate the Common Core Standards?
    No, it will not. The two levels will together still include all the topics in the original. The 8th grade will in fact include a few topics from Discovering Mathematics 3 in order to cover all topics considered to be Algebra 1, such as the quadratic formula and fractional exponents (radicals). It will still include topics such as factorization of algebraic expressions and solving quadratic equations that are not part of the Common Core Standards for 8th grade but are part of the Singapore syllabus at that level.

  6. How does the format of the secondary level books compare to Primary Mathematics? How do the workbooks correlate with the textbooks? What is the structure of a lesson in the textbook and how long does it take?
    The textbooks contain both the lesson and the practice, instead of having the practice in a separate workbook. The workbook is now a supplementary, non-consumable book with additional problems that can be done after each chapter. The lessons include some activities that are similar to the learning tasks in Primary Mathematics, but there are also more worked examples with solutions provided and more written explanations. Some lessons are meant to take several days, with exercises only at the end of the lesson.

  7. Do you have placement tests?
    We have assessment tests for some levels. Please click here for Placement Tests. These tests cover the material in the level indicated on the test.

  8. Do you have a scope and sequence for these books?
    Yes. Please click here for Scope and Sequence.

  9. Do you have a list of contents? Sample pages?
    Yes. In the list of products, click on the picture of the product or on the words 'more info'. Then click on the tab that says Contents_Sample and scroll down. There are links to sample pages for each book.

  10. Are there teacher's guides available? Tests? Answer keys? Solutions?
    All secondary level textbooks and workbooks have answers to most, but not all, of the problems at the back. Depending on the series, there are various teaching resources available with additional answers or solutions. See the chart below for comparison between the series. However, none of the teacher guides have detailed, already prepared daily lesson plans.

  11. Which series should I use?
    It depends on your preference. New Elementary Mathematics is an older series and less modern in its format. Dimensions Mathematics Common Core has fully worked solutions for all levels including the workbook problems.

  12. Can I switch between series?
    You can switch between New Elementary Mathematics to Dimensions Mathematics Common Core between years.

  13. If my student is not able to easily answer all the problems or get most of the problems on reviews or tests correct, does that mean the program does not teach the material well?
    The problems have a range of difficulty level to allow all students to work to their maximum potential. If all the problems were easy, then the student is not working to his or her full potential. Some of the problems in the exercises are simply practice, but some are truly problems that allow a student to gain more depth of knowledge by reasoning through them and applying concepts in new ways. Also, in Singapore most students are expected to score between 50% and 75% on tests. Only better students will be able to score above 75%. If your student can answer all the problems easily, he or she would score well on such a test, but not being able to answer every problem easily does not necessarily indicate lack of understanding of the concepts. The grading scale in Singapore for the secondary level is:
    A1: 75% and above
    A2: 70% to 74%
    B3: 65% to 69%
    B4: 60% to 64%
    C5: 55% to 59%
    C6: 50% to 54% (passing grade)
    D7: 45% to 49%
    E8: 40% to 44%
    F9: Below 40%

  14. What if I have more questions or need more help with the content or choosing which books to get?
    Please visit our forums and post your questions or concerns. You can also email the curriculum advisor.

  15. It says in the chart below that some activities in Discovering Mathematics use Geometer's Sketchpad. What is that and where can I get it?
    Geometer's Sketchpad is a dynamic geometry software program produced and sold by Key Curriculum Press. (We are not associated with Key Curriculum Press and we are not responsible for any purchases made with this company.) You can use other dynamic software programs for the same activities, such as Geogebra but the steps will be different.

  16. New Elementary Mathematics (NEM)
    Discovering Mathematics original (DM)
    Dimensions Math (DMCC)
    First published 1991. New edition in 1996. This is based on the syllabus used prior to 2001 and is one of the texts used by students taking the TIMSS international test. This series is no longer used in Singapore
    First published in 2008.
    First published 2012. Based on the original Discovering Mathematics series.
    Textbook organization
    Textbook pages are black and white. Lessons in the textbook consist of explanations, worked examples, and occasional class activities which allow students to learn through discovery.

    At the end of each chapter there is a summary listing the concepts learned in the chapter, but not a review exercise. Each chapter is followed by an optional "Challenger" and a "Problem Solving" exercise.

    After 3-4 chapters there is a set of 5 short cumulative review exercises, and an optional Miscellaneous Exercise and Investigation for exploring some concepts in more depth. There are two practice cumulative assessments at the end of each textbook.
    Textbook pages are more visually attractive than NEM and in color. There are two textbooks for each level, A and B. Lessons in the textbook consist of explanations and worked examples. Each worked example is followed by a similar question (Try It!) that students can do to see if they understood the example.

    Many lessons include one or more class activities, which allow students to learn through discovery. Some of these use Geometers Sketchpad. Some lessons are meant to take several days. Each chapter is followed by a summary listing the major concepts, a review exercise, an open-ended Extend Your Learning Curve problem, and one or two questions for journal writing.

    At the end of each textbook is a list of problem solving heuristics with some examples corresponding to the topics for that level. There are no cumulative review exercises or assessments, but the chapter reviews tend to integrate concepts from earlier chapters.
    See the entry under DM.
    Exercise organization
    Exercises vary in length and tend to be long so it is possible to select problems rather than do all of them. The type of problems depends on the lesson; some exercises are all computation or skill problems and some are all word problems. More challenging problems are marked with an asterisk.
    The problems in each lesson's exercise are divided by difficulty level into Basic Practice, Further Practice, Maths@Work (application) and Brainworks (challenge). The chapter review exercises are not divided by difficulty level.
    See the entry under DM.
    Answers to the textbook problems.
    There are answers to the regular exercises, the periodic Miscellaneous and Review exercises and the Assessments in the back of the textbook.
    There are answers to the Try It! problems in the lesson, the lesson exercises except for Brainworks section, and the reviews at the back of the textbook.
    See the entry under DM.
    Teacher resources and fully worked solutions
    The Teachers Manual has a weekly schedule and fully worked solutions for the Challengers, Problem Solving, and Investigations. The solutions manual has fully worked solutions to the rest of the exercises. Teacher's Manual (NEMTM2) for grade 8 is no longer available.
    The Teachers Guide for each level has a weekly schedule, brief notes for the teacher, and fully worked solutions to all problems in the textbook, including class activities.
    The Teaching Notes and Solutions for each level has a weekly schedule, brief notes for the teacher, and fully worked solutions to all problems in the textbook, including class activities.
    The workbook is supplementary and contains additional problems for each chapter, practice test papers every 2 chapter and 2 mid-term and final term assessments. Only the test papers have room in the book to work the problems. Answers are in the back. There are no fully worked solutions.
    There is one supplementary workbook for each level. It has a set of problems for each chapter divided into Basic Practice, Further Practice, Challenging Practice, and Enrichment (even more challenging). Answers are in the back. There is a separate Teacher's Edition of the workbook with fully worked solutions.
    See the entry under DM. There is a separate Workbook Solutions with fully worked solutions.
    There are two sample tests at the end of each textbook and practice test papers for every 2 chapters, midterms, and semester test in the workbook. These are quite challenging, as the workbook is somewhat for enrichment.
    The workbook has mid-year and end-of year sample tests. There is a separate Question Bank book for each level with test questions arranged by difficulty level. Questions will have to be selected, copied, and transferred to a test paper, since answers are included on each page in the Question Bank.
    To be determined.

    Singapore Math is a registered trademark of Singapore Math Inc. and Marshall Cavendish Education Private Limited.