The various editions of Primary Mathematics have been among my Top Picks for years. The 2022 editions of Primary Mathematics (PM2022) are entirely updated from what is popularly known as the Singapore Math® line of products. This edition of the series has totally rewritten content, new digital components, and manipulative packages. It includes courses for kindergarten through fifth grade, and a sixth-grade course is due in the fall of 2022.
The required resources for each grade are configured differently than for the previous Primary Mathematics series. As with the courses for the previous editions, each grade is divided into two parts: A and B. For each part of a course, the required books are a Student Book, an Additional Practice book, and either a Teacher's Guide or a Home Instructor's Guide. (The Student Book and Additional Practice book function like the Textbook and Workbook in the previous Primary Mathematics series.) All books for students are 8.5” x 11” and the oversized guides are 10” x 12”—larger sizes than for the previous series. The PM2022 courses also require the use of manipulatives which I discuss under "Methodology" below.
Both parts of each year's course are covered by one Assessment Guide. In addition, there is an optional Mastery and Beyond book for each part of a course that provides even more practice and features reinforcement exercises that are cumulative, covering concepts from several lessons. (Mastery and Beyond books include their own answer keys at the back of each book.)
The Student Books, Mastery and Beyond books, and Teacher's Guides are all printed in full color, while the Home Instructor's Guides, Additional Practice books, and Assessment books are black and white. All of the books for students are consumable and include plenty of space for them to write and show their work.
The Scope and Sequence
Aside from the addition of a course for kindergarten, the scope and sequence is somewhat similar to that of the other Primary Mathematics series. All editions of Primary Mathematics move at a more advanced pace than most other math programs, but PM2022 moves at a slightly slower pace than the other editions. For instance, the concepts of ratio and percentage are introduced in fifth grade in the previous series, but PM2022's fifth-grade course has not yet introduced them.
At the beginning of the school year, students should be able to shift from any other Primary Mathematics series into PM2022 at the same grade level they would have used in the other series, but they will encounter a little repetition. Comparison charts online (scroll down the page a bit) show how chapters and topics in all of the series align by grades. Placement tests on SingaporeMath.com can help you determine the appropriate course for your child. Because of the advanced scope and sequence, your child might need to work at a lower level than you might expect, but this is less true of PM2022 than of the previous series.
Teacher's Guides and Home Instructor's Guides
The lessons in PM2022 require more teacher presentation using either the Teacher's Guide or the Home Instructor's Guide than previous editions. Both types of guides have complete lesson plans that coordinate all course components. They have lists of the required manipulatives to make it easy to identify what you need in advance. The guides also specify when to use pages in both the required and optional books. And they have answer keys and solutions for the questions in the Student Book.
Toward the back of each printed guide is a section titled Teacher Resources that shows reduced images of printable pages for number cards, grid paper, tangram shapes, a place-value chart, or other visual aids and manipulatives that will be used with the lessons. The full pages have to be printed from the online digital resources.
The Teacher's Guides, designed for classroom instruction, are printed in full color and cost quite a bit more than the Home Instructor's Guides. They include reduced images of Student Book pages, instructions for group activities, suggestions for differentiated activities to meet the needs of different learners, discussion suggestions for developing a "growth mindset," and other resources likely to be useful in classroom settings.
The Home Instructor's Guides were written in consultation with home educators, so they have instructions written for homeschool settings, and they include a few practical features not found in the Teacher's Guides, such as “Do More at Home” activity suggestions. These activities vary, but many of them are game-type activities or practical applications for using math around the home.
The Home Instructor's Guides have eliminated most of the classroom-oriented instruction to make them more efficient for home educators, but both types of guides still have more information than you can use. The biggest reason that I can see for a homeschooler to use a Teacher Guide would be if they want to see reduced images of student pages.
Purchase of either guide gives you one year of access to a large suite of digital resources. Many of these resources are viewed in a content player and are not downloadable, although some of them include embedded links to printable PDF pages. The digital resources include:
- Digital version of the guide you purchased
- Answer key for the Additional Practice books – These are printable and downloadable. They are also available through the publisher's website.
- Reteach – a book in printable PDF format for each grade with extra instruction and practice for students who are struggling. One book covers both parts of a course and includes answer keys.
- Transition Guide – This 205-page book is helpful for working with students who missed or haven’t mastered concepts that were taught in previous grades. If students miss problems in the review at the beginning of each chapter, the Transition Guide provides parents and teachers with links directly to lessons for those problems in a Reteach book (whichever level is needed) as well as to pertinent lessons in Additional Practice books.
- Extensions – a printable PDF workbook with activities that present more-challenging math problems and applications. One book covers both parts of a course and includes answer keys.
- Home Instructor’s Resources – these include printable files for the reduced-image pages at the back of the Home Instructor’s Guide—pages you need for teaching the lessons. (These are the pages I mentioned above for number cards, grid paper, tangram shapes, etc.)
I expect that some homeschoolers will very much appreciate the digital resources, perhaps using the digital Home Instructor's Guide rather than the printed guide. You receive free access for a year when you purchase a Teacher’s Guide or Home Instructor’s Guide, but you need to resubscribe for access each year in which you want to use a course.
Concrete methods of learning with manipulatives have always been important in Primary Mathematics, but a major difference in PM2022 is explicit instructions for teaching with manipulatives. Lessons are dependent upon the use of manipulatives. Like the previous Primary Mathematics series, these editions continue to teach in a sequence that takes students from a concrete math experience with manipulatives to pictures showing the same concept, then to the abstract use of numbers to represent the same concept. While the books in the previous Primary Mathematics series show images of manipulatives, the actual use of manipulatives is presented in the teacher’s guides, and their use is not essential. In contrast, PM2022 editions call for a number of manipulatives (e.g., dice, a balance, color tiles, and fraction tiles) in addition to household items, and they are used frequently throughout each course.
Pictures showing the concepts are used throughout all of the books, even for fifth grade. The continued use of manipulatives and many pictorial representations stands in contrast to most math programs for fourth grade and above which rely more on abstract presentations. Some students who are older still benefit from the use of manipulatives and pictorial representations, while others may be able to skip over them to the abstract presentations more quickly.
Packages of manipulatives are available from some distributors. Many of the same manipulatives are used for succeeding grades, so there are add-on packages with only the new manipulatives needed for the next grade.
All of the previous Primary Mathematics series have done an excellent job of helping students understand mathematical concepts, In PM2022, the methodology for presenting concepts has been updated to reflect the latest ideas about learning math, including the use of strategies such as ten frames and number bonds. Another minor change is the use of more gender-neutral and inclusive language.
The daily lessons follow a three-phase structure: readiness, engagement, and mastery. In the readiness phase, manipulatives or a practical application help students think about the new concept. Engagement is the body of the lesson with instruction and practice facilitated by the teacher. The engagement portion of the lesson concludes with a Lesson Debrief, an oral discussion that helps the child articulate what they have learned and what they might not yet understand. The mastery phase is where students practice on their own and apply what they have learned. Students will complete pages in both the Student Book and the Additional Practice book during the mastery phase. There are plenty of word problems in both books that require students to figure out which method of problem solving to apply. You might also use pages in Mastery and Beyond or from the digital Reteach or Extension books.
While a parent or teacher is to work with a student through the readiness and engagement phases, students should be able to work independently through the mastery phase. Both the Teacher's Guides and Home Instructor's Guides have tips about potential pitfalls, how to evaluate student responses, and how to help students who are struggling.
Lessons concentrate on one topic at a time. Chapter tests cover only concepts taught in that chapter. Both the Student Books and Additional Practice books have sets of practice problems at the end of each chapter that help prepare students for chapter tests.
It is important to note that review exercises at the beginning of each chapter ensure that students have already mastered prerequisite skills before tackling new material. Because lessons concentrate on only one topic at a time, students might have forgotten or never learned a skill they need for the upcoming lessons. You should use the Reteach or Transition Guide lessons if students need to work on a prerequisite skill.
The Assessment books have chapter tests and four or five cumulative assessments for each course. (The number and types of assessments vary for each course.) Mid-year and final cumulative exams are added for the Grade 3 course and above. When you purchase a physical Assessment book, you also have access to the digital PDF version of that book.
There are a number of activities toward the end of each chapter that might be considered optional. Every chapter has a Performance Task that gives students opportunities to apply what they have learned in extended, situation-based problems. These are useful!
“Solve! Heuristics” activities at the end of some chapters teach students detailed processes for problem solving in teacher-directed lessons. These are helpful for students who need assistance in this area.
At the end of each chapter is an optional self-reflection chart for students to check off yes, no, or not sure for key objectives they should have learned. Some chapters have a journal page for them to write out their thoughts under two headings: “I can show” and “I still wonder.”
STEAM (science, technology, engineering, art, and math) projects that might span one or more chapters involve cross-curricular math applications with activities as diverse as art, research, cooking, and creating games.
What’s Most Essential?
As you can see, these courses have many components, and you might not have the time or inclination to use all of them. If you want a minimalist approach, use the Home Instructor's Guides, the Student Books, Additional Practice books, and the manipulatives--and don’t try to utilize all of the activities. Also, these courses teach concepts from a number of different directions, so if your student has already grasped a concept well, you don’t need to belabor it with additional work with manipulatives and pictorial representations. That means you might be able to move through some parts of a lesson more quickly.
The other editions of Primary Mathematics remain available for homeschoolers who wish to use them. Previous editions were designed with an expectation that they would be taught with a high level of parental interaction. However, parents very familiar with math and who have children who catch on quickly have found that their children could complete much of the lesson material independently and skip instruction with manipulatives. I think it's harder to take such shortcuts with the 2022 editions of the Primary Mathematics series. But I expect that many homeschooling parents with children who need hands-on learning will find that PM2022's explicit instructional material and manipulative kits make their job much easier.