New Elementary Math 1 Solution Manual
Don't let the title of this series fool you. “Elementary” refers to “the basics,” as in the basics of higher-level mathematics. New Elementary Math (NEM) 1 and 2 respectively cover introductory and intermediate algebra.
There’s quite a jump from Primary Math 6 to NEM 1 (7th grade). NEM 1 requires greater discipline on the part of the student because there is an intense amount of computational practice to be done. NEM course books are four times thicker than Primary Math textbooks. NEM takes a straightforward approach which emphasizes concepts, applications, and mathematical reasoning.
Each level requires one course book and one teacher’s guide (NEM 1, NEM 2). One supplementary workbook containing extra practice problems is available for each grade.
Course books have plain black and white pages with two-color diagrams and graphs. Although the texts are visually unexciting, they contain clear and simple explanations. As the student progresses to higher levels, course book explanations become more technical. Each lesson contains written explanations, worked examples, and an exercise set. Most lessons also include a class activity. Exercise sets are graded, with harder problems located towards the end of a set. Chapter reviews summarize main ideas and definitions but do not include review problems. For review problems, try the corresponding workbook problems for that chapter. Each chapter ends with a Challenger problem set and a Problem Solving section. The Problem Solving section describes and provides exercises for different problem solving techniques (guess & check, working backwards, using models, etc). After every few chapters, there are Revision, Miscellaneous, and Investigation exercises. Revision and Miscellaneous problems provide cumulative review, while Investigation exercises help build higher-order thinking skills. Each course book provides two sample final exams. Answers to both finals plus all lesson, revision, and miscellaneous exercises are located in the back of each book. Solution manuals are available. A Quick Revision Guide is included with the purchase of each course book. The guides are thin booklets consisting of study sheets on main ideas for each chapter.
Workbooks are more like non-consumable exercise banks. Students must show their work on a separate piece of paper. Problems provide specific instructions on when and when not to use calculators. Unlike Primary Math, workbook exercises are not directly correlated with the course book. In general, workbook exercises for each chapter should probably be completed before moving onto the next chapter. The workbook also contains sample tests and exams. Tests cover two chapters, and they usually consists of 6-8 multi-part, free-response questions. Midterms/final exams are longer.
Like the Singapore editions of Primary Math, NEM course books only cover metric units. Slightly different conventions and notation are also used in NEM. For example, spaces instead of commas are used to separate numbers with four digits or more. Repeating decimals are not designated by a bar, but by placing dots above the first and last digits in a repeating set. Time is expressed in military time, and a space is used to separate hours and minutes. For example, 2:30 pm would be written 14:30.
Compared to Saxon, NEM begins introducing algebraic concepts earlier, generally includes more complex geometry problems, and covers more trigonometry. However, Saxon’s Algebra 2 course covers a wider variety of topics, including polar coordinates, imaginary and complex numbers, and logarithms. In Algebra 2, students must solve 3 by 3 systems of linear equations, while NEM only covers 2 by 2 systems. Also, NEM is extremely weak in coordinate graphing. The slope-intercept method of graphing lines is also not covered. Instead, students graph equations by plotting points from an x-y chart. Systems of equations are primarily solved by algebraic manipulation; graphical interpretations are not emphasized. This approach to solving systems may be difficult for students who need visual representations in order to understand algebra.
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.