Primary Mathematics Mastery and Beyond 3B (2022 Edition)
Mastery & Beyond is a distributed practice workbook. It provides practice of essential math concepts at select points to help students make connections. While the Additional Practice is for daily use, Mastery and Beyond is intended to be used at key points in a chapter after multiple lessons.
Note: Two books (A and B) for each grade correspond to the two halves of the school year. Answer key in back of book.
Concepts covered include: Numbers to 10,000 (create sets; group into thousands, hundreds, tens, and ones; compare and order whole numbers; write multi-digit numbers in expanded form; and use place-value models; add/subtract whole numbers). Fractions (understand concepts, compare and order; recognize equivalents; write whole numbers as fractions). Add and subtract money. Solve real-world problems involving addition and subtraction of money. Solve addition and subtraction problems with greater numbers by using a bar model. Multiply and divide up to 2-digit numbers by any number from 2 to 10. Use x, ?, and = symbols to represent multiplication and division equations. Multiply 2-digit numbers by a 1-digit number, with and without renaming. Use bar models to represent multiplication and division situations. Express a fraction as the sum of repeated unit fractions. Add and subtract money amounts. Use mental math strategies to add, subtract, multiply, and divide. Use rounding to estimate sums and differences. Understand that multiplication and division are related. Understand the relationships between the numbers in multiplication-division fact families. Use a variety of concrete, pictorial, and symbolic models for multi-digit addition, subtraction, multiplication, and division. Write addition, subtraction, multiplication, and division equations. Use and create models that demonstrate equality or inequality. Identify right angles and compare angles to right angles. Classify and sort polygons and quadrilaterals. Solve real-world problems in measurement. Solve addition, subtraction, multiplication, or division word problems involving mass in kilograms or grams and volume or capacity in liters. Tell time to the minute. Convert between hours and minutes. Add and subtract units of time. Compare angles to right angles. Measure perimeter of plane figures. Find and compare the area of plane figures in different square units. Find the area of rectangles and composite figures. Use bar graphs, picture graphs, and line plots to solve real-world problems. Build skills in addition, subtraction, multiplication, division, and measurement through problem solving. Apply the inverse relationship between multiplication and division. Solve real-world problems involving addition, subtraction, multiplication, division, measurement, and money. Consult or download the complete Scope and Sequence for a full report of covered topics and concepts.
Packed with all the features we have come to love about Singapore Math in general, and Primary Math in particular, this 2022 edition is completely NEW! You’ll recognize the basic components – semester student books and home instructor guides – and the wonderful Singapore educational methodology, but it’s the user-friendliness of these components and their bright, breezy appearance that you will LOVE. Differentiated practice options and digital resources round out the advantages of this new edition. This first-in-twenty-years revision of the iconic Primary Math is “the same. . . but BETTER!”
Placement tests for Primary Math 2022 is available on our website – at the listings for the grade-level components and on the Rainbow Resource math placement tests page. These tests can be particularly helpful if you are coming in from a different math program. The scope and sequence of the older Singapore math programs is quite similar to the new edition, so it should be a smooth transition to move from one to another in-between grade levels.
The Primary Math 2022 core components for Grades K through 5 include a Student Book, Mastery & Beyond workbook, Additional Practice workbook, Assessment Guide, Home Instructor Guide (HIG), and Teacher Guide (TG). The Home Instructor and Teacher Guides come with an access code for Digital Resources. Once activated, this code provides a one-year subscription to McEduHub – the publisher’s resource website. After expiration, subscription renewals are available to purchase via your McEduHub account. The HIG and the TG each provide digital eBooks, with additional digital resources including access to the answer key PDF for the Additional Practice book. The HIG and TG also provide an online Transition Guide, useful if the student (or parent) is new to the Singapore math methodology. Other digital resources available to purchasers of the HIG or TG include concept interactives and animations, games, and digital manipulatives.
Singapore students consistently rank at the top of international benchmark assessments. The Singapore Math approach with its proven effectiveness has a foundation of Concrete to Pictorial to Abstract teaching. This means, simply, that each concept is introduced using manipulatives and items the student can feel and touch and see. The Additional Practice workbook (K-6) provides concept practice on level with the Student Book. The colorful Mastery and Beyond (K-5) provides sectional practice exercises, answers included. Assessment Guides provide both chapter and cumulative tests (answers included). Manipulative Kits are available for K-6. Digital Resources (with HIG purchase – 1-year renewable subscription) include e-Book versions of the Student Book, Home Instructor Guide, pdf Teacher Resources, Mastery and Beyond (K-5), Reteach (K-5) and Extension (K-6) books, and solutions for the Additional Practice (K-6) workbooks. Digital manipulatives and key concept interactives (animations) are also included. The attractive student materials, user-friendly teaching materials and practical digital resources make Primary Math 2022 a terrific choice. Then, that same concept is presented in pictorial form – drawings of the manipulative items. Lastly, the concept is transferred into abstract form – numerical representations. Building on this foundation is a problem-solving methodology that uses visual models that promote mastery, as well as creative and critical thinking. The learning progression is incremental, with one concept building on another supported by reinforcement and review, as well as differentiated activities and practices.
With the goal of progression from Readiness (recall) to Engagement (learn) to Mastery (practice), book chapters have a consistent and distinctive organizational pattern. The Chapter Opener sets the stage with a real-world mathematical situation that invites curiosity and interest. A Recall lesson reviews concepts learned in the past that will be expanded in the upcoming chapter. “Learning” is divided into Sections, each with multiple Lessons that focus on specific skills and provide instruction as well as practice exercises. Following the instructional sections, the chapter concludes with a Performance Task (tasks set in real-world contexts), a STEAM project, (inter-disciplinary tasks), and a Chapter Practice (reviews and reinforces skills across the chapter) to be followed by a chapter test/assessment.
Students and teachers (parents) form a learning team and the instruction is based on this teacher-student interaction. Within the Primary Math 2022 components, the Home Instructor Guide (HIG) or Teacher Guide (TG) show how to use the manipulatives (household items as well as special materials) with both instructions and illustrations. The Student Book introduces the pictorial instruction which morphs into the abstract by the time the student reaches the practice exercises. Lessons have specific parts which reflect this process: Learn, Learn Together, and Practice on Your Own.
The colorful and engaging Student Books are consumable. The Practice on Your Own pages in the Student Book provide practice at the end of each lesson, but these are just the tip of the iceberg in terms of practice and homework options available. Mastery and Beyond pages provide practice exercises cumulative over several lessons. Additional Practice has exercises correlated to each lesson (these double the amount of practice for each lesson). For students who need additional instructional support, there is a Reteach Workbook and for those students who need additional challenge, there is the Extensions Workbook. The Reteach and Extensions books are only available as digital versions.
It’s the Home Instructor Guide or Teacher Guide that pulls all these elements together and outlines the role of each component. You will need one OR the other of these. Both provide course overview information, manipulatives and materials needed, detailed daily lessons, answers/solutions to the Student Book exercises, and countless helps toward effective teaching. Both also reference digital teacher resources, some of which are downloadable and/or printable from the website.
Teacher Guides are classroom oriented (large, oversized 10”x12”) while the Home Instructor Guides are designed for one-on-one instruction. One example of this difference is the number of lesson activities in the TG that encourage students to work in pairs or groups. This is absent from the HIG for obvious reasons. Another example is the page in each lesson in the TG that is devoted to differentiated instruction where suggestions are made for Additional Support, On-Level Practice, and Extension activities. These suggestions include homework assignments from the Reteach, Additional Practice, and Extension workbooks that correlate with the lesson. On the other hand, the HIG has these same assignments, but devotes less time to teaching suggestions and wraps everything into a single paragraph.
In addition to the general page orientation, there are three other differences between the TG and the HIG. The Teacher Guide is in color and includes reduced copies of the Student Book pages. The Home Instructor Guide is grayscale with answers/solutions in the sidebars. Another difference is the price point. We appreciate the publishers providing such a user-friendly resource geared to home-teaching situations for less than half the cost. However, if having reduced color copies of student pages is important –consider using the TG. Currently, Level 6 has only two TG options: a color edition or a Black & White Exclusive Home Instructor’s Copy TG (available only for home educators). The content and layout of the color and B&W TEs are identical except for colored printing and cost. A Level 6 HIG is planned for potentially 2024.
A Transition Guide, mentioned in both the Teacher Guide and Home Instructor Guide, is a detailed guide for teachers that enables them to transition students into the Singapore math program. The guide provides teachers with background information on important concepts and highlights potential challenges that students might face. It is also a help to teachers who are unfamiliar with the math approach. This Transition Guide is available digitally for purchasers of the Teacher Guide and Home Instructor Guide. Please note that when the Transition Guide references page numbers it is for the TG and not for the HIG.
The Assessment Guide provides tests for each chapter and cumulative tests after every 2-3 chapters, plus mid-year- and end-of-year cumulative assessments. There are a variety of test formats utilized – multiple-choice, short answer, and constructed response. There are four types of test items: recalling fundamentals; grasping of concepts, skills, and procedures; demonstrating mathematical reasoning; and solving problems in real-world contexts. Answers are in the back of the book. Included with the purchase is a one-year access to the book’s digital version of this, which provides answers and tests that can be printed. A Level 6 Assessment Guide is projected to be available at the end of 2023.
With its combination of attractive student materials, user-friendly home instructor materials, and practical digital resources, Primary Math 2022 should be a great option for many students.
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.