Primary Mathematics Common Core Edition Answer Key Booklet 4A-5B

Countries around the world first became interested in Singapore's math curriculum when results of the Third International Math and Science Study (TIMSS) were published in 1995. Conducted by the International Study Center at Boston College, achievement tests in both math and science were administered to students in over 40 countries. Students from Singapore ranked highly in mathematics achievement: 1st in the fourth, seventh, and eighth grade levels and 2nd at the third grade level. Results for the U.S. were disappointing: 10th in the third grade, 11th in the fourth grade, 23rd in the seventh grade, and 27th at the eighth grade level. In a follow-up study in 1999, Singapore again ranked 1st in eighth grade math achievement while U.S. eighth graders ranked 19th. Although a first place ranking does not necessarily imply the best program, something about Singapore's math program was working.

"Singapore Approach Math" is a general term referring to a type of mathematical instruction (i.e. curriculum) developed from a syllabus designed by Singapore's Ministry of Education in the 1980s. There were a number of revisions and the 3rd edition was the last edition used in Singapore. The good test scores were associated with this material and all of our Singapore Approach Math programs are based primarily on the 3rd edition although it is no longer available for sale. Components from different editions are not interchangeable but a student can move between the editions in-between levels.

Primary Math US (1-6) is an adaptation of the 3rd edition for use in the U.S. Although a small amount of content (division of fractions) from the 2nd edition was added back into the US edition, it is almost identical to the 3rd edition. The US edition adds sections for U.S. customary measurements and uses U.S. spelling and conventions. We expect this edition to be available indefinitely. ©2003

Primary Math S/E (Standards Edition) (K-6) was adapted to meet the pre-Common Core CA math standards. An additional amount of content (probability, data analysis, negative numbers, coordinate graphing) from the 2nd edition was added back in and topics were rearranged but it is similar to the US edition. Cumulative Reviews at the end of each Unit and practice sets within each unit were added. Textbooks are in color. ©2008 This edition includes Earlybird Kindergarten Math.

Primary Math CC (Common Core) (K-5) is aligned to the Common Core State Standards and is another adaptation of the 3rd edition. Only minor changes were made to the scope and sequence. Unit Reviews are no longer cumulative and Practices were removed although some of the content was incorporated into the lessons. ©2014 Includes Earlybird Kindergarten Math CC. This edition will be available for the foreseeable future.

Primary Math 2022 Edition (K-5) is a completely new revision retaining all the excellent teaching methods of the earlier Primary Math programs. Incorporating both cumulative assessments and challenging problem solving, mastery learning is emphasized. The scope and sequence is similar to previous editions and topics are aligned to state and national standards. ©2021-2022

New Elementary Math (7-8) is a no-frills program based on an older Singaporian program and covering integrated algebra and geometry. It's considered a sequel to the Primary Math programs.

Math in Focus (K-8) was developed by Great Source (a division of Houghton Mifflin Harcourt) in conjunction with Marshall Cavendish (the original publisher in Singapore). Although the basic instructional sequences are similar and the content is very close to the SE, material added to the most recent editions brings it into alignment with CC. Math in Focus has a more American look and "feel." ©2010, 2014

View the Singapore Approach Math Comparison Chart.

The teaching methodology utilized by ALL the Singapore Approach math programs is an exceptionally effective progression from concrete to pictorial to abstract reasoning. Not exactly incremental (like Saxon) or spiral (again, like Saxon) or unit-style (like Horizons), basic concepts are presented using more than one approach and with an emphasis on mastery. Textbooks and workbooks and Teacher Guides cohesively and effectively mix drill, word problems, and mental calculation with instruction and apply to all important concepts. There is a program-wide emphasis on basic computational skills (i.e. number operations, fractions, decimals, and percents) coupled with critical thinking and problem solving. Creative problem solving is centered in the bar model drawing methodology. To visually represent problems students are taught to translate them into bar models which help to both understand the concepts and to develop a good solution strategy, as well as serving as a bridge to algebraic thinking. In comparing the various editions of Primary Math (US, SE, and CC), it's important to remember that in all of the basic characteristics they are much more alike than they are different. We can get bogged down trying to determine the actual differences between the editions when, in reality, they are extremely minor in relation to the solidarity and consistency of the teaching methodology.

The CC edition is aligned to the Common Core State Standards which have been adopted by many states but which are still controversial. In relation to Primary Math, this alignment has not impacted in any significant way the general methodology of the program. In fact, it still has the same basic structure, content, and format of its original predecessor developed over thirty years ago. However, there has been a small amount of content (data analysis, probability, negative numbers, and coordinate graphing) added, and topics have been rearranged. If you want to carefully compare the three American editions (US, SE, and CC) from Singapore Math, Inc, we have a scope and sequence chart on our website that includes all three.

There are some format changes in the CC edition. As in the SE (but not the US) all textbooks are in color. Workbooks are still black and white (as in all editions). Instead of being cumulative, reviews at the end of each unit cover only the unit material. Practices (frequent in the SE texts) have been removed but some of that content has been incorporated into the lessons. Most significantly, the Teacher Guides now include reduced-size copies of both textbook and workbook pages. As would be expected, the Teacher Guide specifies which CC standards are applicable to each lesson.

It is NOT possible to mix basic components (i.e. workbooks, textbooks, TGs, or HIGs) from one edition with those from another edition although the supplementary material can be used across editions. It IS possible to change from one edition to another but changes should be made after completing the B books of one level and before the A books of another level.

There are two full-color Textbooks (A and B) for each level. Although the texts are written to the student, it is assumed that instruction is being facilitated and supervised by the teacher. For instance, much of the concrete aspect of the lesson presentation is conducted by the teacher using manipulatives and supplies outlined in the Teacher Guide before progressing to the pictorial representation found in the textbooks. Also, the mental math activities (an important component of the program) are based in the Teacher Guide. The Textbooks could be used either as consumable (working and writing answers to problems as the student progresses through the lesson) or as non-consumable - answering orally in dialog with the teacher or writing answers on separate pieces of paper.

Workbooks (black and white) correlate directly with the textbooks and the student is expected to do all the work in them independently. The workbooks provide focused practice on the mathematical concepts presented in the textbook lessons. It's important to note that the workbooks are just that - practice and reinforcement - with the bulk of the mathematical instruction presented through the textbooks. Although many people feel that there is an appropriate amount of practice/reinforcement in the workbook when coupled with the textbook, some students will need or want more and that's where the supplementary books - Extra Practice and Challenging Word Problems come in.

Teacher Guides are exceedingly useful - if not necessary - for these courses. They help the teacher understand the course material, particularly key concepts such as the bar modeling method which the parent might not be familiar with. They provide detailed lesson plans (not quite scripted but thorough) which coordinate the textbook presentations with the workbook practice. Lessons often include references to Mental Math, Reinforcement, or Enrichment activities as well as suggestions for memorizing math facts. There are reproducible worksheets for Mental Math and Reinforcement as well as descriptions for activities and games found in the back of the TG. Answers to those worksheets as well as the workbook exercises and the textbook examples are all found in the TG. Now with this CC edition, reduced copies of the student pages (with answers) are included, as well. (8.5" x 11," 260 pgs, spiral-bound)

The Singapore approach math programs remain a strong option. All three editions will equally prepare your student for pre-algebra. Their pacing is slightly more advanced than some (most notably Saxon) which works well for some students. Because of these pacing differences, it is a good idea to take a placement test prior to moving from another program into any of the Singapore approach programs. We have tests specific to the US and SE editions but not yet for the CC. If considering the CC, it's recommended that students take the US placement test. Due to the reduced practice exercises and cumulative reviews, some students are more likely to need the supplemental Extra Practice workbooks when using the CC edition.

Suggested manipulatives include: base ten blocks, linking cubes, measuring tools, number cubes, number discs (or place value disks), place value chart, solid blocks, and miscellaneous items such as fraction squares, geometric shapes, play money, and graph paper.