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Secondary Mathematics

  1. Why do you only carry Singapore Math® material through 8th grade?
    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. In Secondary school, all students do one math class, but some students do an additional math class in Secondary 3 and 4 in which they cover pre-calculus and calculus topics. This makes it difficult to align their math material with the progression in the U.S. after 8th grade. At this time, we are focusing on K-8. For 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: The first half (done in Secondary 3) is mostly Pre-Calculus, and the second half (done in Secondary 4) is mostly Calculus.

  2. What is the Dimensions Math® Series? How does it compare to the math in Singapore?
    Dimensions Math® is a series for grades 7-8. The 7th and 8th grade books in the Dimensions Math® series are based on the original series from Singapore named Discovering Mathematics, revised to include the Common Core Standards. Compared to the Discovering Mathematics series, a few topics were added to some chapters in the 7th and 8th grade books, 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 for Secondary 1 and 2, but also covers the Common Core Standards.

  3. Are Dimensions Math® 7 and 8 less advanced or rigorous than the original Discovering Mathematics in order to accommodate the Common Core Standards?
    No, it is not. The two levels 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 still includes 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.

  4. What about New Elementary Mathematics?
    New Elementary Mathematics is an older series no longer in print or used in Singapore. We continue to sell it since it is still popular here in the U.S. and is also used in the Elementary Mathematics for Teachers text that we sell. It is more challenging than Dimensions Math®. It has not been adapted in any way for the U.S. The series meets the criteria for Singapore’s syllabus in 1990. If you have a student good in math, and do not have to worry about what specific topics are covered at a specific grade level, this series is an excellent preparation for higher math since it requires more problem solving abilities and have more challenging problems compared to Dimensions Math®.

  5. How does the format of Dimensions Math® or New Elementary Mathematics 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, and are longer than those in the Primary Mathematics workbook. They will therefore have to be assigned to be due after several days, rather than the next day.

  6. Do you have placement tests?
    We do not. A student going into 7th grade, or who can complete successfully Primary Mathematics Standards Edition 5A and 5B assessment tests, could start working with Dimensions Math® 7. They could possibly also take on New Elementary Mathematics 1 if they are good at math concepts. A student who has completed Pre-Algebra can do Dimensions Math® 8 or New Elementary Mathematics 2, but you should look at the table of contents to see if any of the previous level is needed.

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

  8. 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.

  9. 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 and they do not tell you exactly what to teach and when to assign exercises on a daily basis.

  10. Can I switch between series?
    It is not advisable to switch between New Elementary Mathematics to Dimensions Math® between years.

  11. 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.

  12. It says in the chart below that some activities in Dimensions Math® 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.

  13. After completing New Elementary Mathematics 2 or Dimensions Math® 8, what then?
    A student who has completed either of these should be able to do either a second year Algebra textbook (Algebra 2) or a Geometry textbook at the high school level. (A bright homeschooled student could potentially do a college level Intermediate Algebra or possibly a Pre-Calculus text, since there is so much repetition between different levels of college texts. However, not all geometry topics generally expected for high school and formal geometric proofs have not been covered.)

  14. New Elementary Mathematics (NEM)
    Dimensions Math ® (DMCC)
    First published 1991. New edition in 1996. These are 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 2012. Based on the original Discovering Mathematics series, which was first published in 2008.
    Textbook organization
    Lessons in the textbook consist of explanations, worked examples, and occasional class activities which allow students to learn through discovery. Each lesson is followed by an exercise, but the lesson and its exercise may take more than one day.

    At the end of each chapter there is a summary listing the concepts learned in the chapter, but no review exercise. Each chapter is followed by an optional "Challenger" and "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.

    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 labeled "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 Geometer’s Sketchpad. Each lesson is followed by an exercise, but the lesson and its exercise may take more than one day.

    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.
    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.
    Answers to the textbook problems
    There are answers to the regular exercises, the periodic Miscellaneous and Review exercises and the practice Assessments in the back of the textbook.
    There are answers all of the problems at the back, unless the answer involves a diagram or graph.
    Teacher resources and fully worked solutions
    The Teacher’s 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.
    The Teaching Notes and Solutions for each level has brief notes for the teacher, and fully worked solutions to all problems in the textbook, including class activities. It does not include lesson plans or a daily schedule.
    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 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, and should be graded accordingly.
    There are currently no tests, but you can use the workbook as a test bank.

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