Primary Mathematics
Comparison with other Math Programs
Model Drawing
New series
 Why are there three different editions of Primary Mathematics?
The Primary Mathematics series was written in 1982 by the Primary Mathematics Project Team, appointed by the Curriculum Planning and Development Division of the Ministry of Education (MOE), Singapore. Over the past twenty years, this series has been identified with excellence and achievement in Singapore's primary school mathematics curriculum, culminating in Singapore students' success in the 1995, 1999 and 2003 TIMSS (Trends for International Mathematics and Science Study) studies.
Primary Mathematics Third Edition is what was used in Singapore and uses British spelling and other conventions used in Singapore. It is based on a second edition, which is no longer in print. Some content was removed in going from the second to the third editions. Some of this (division of fractions) was added back into the U.S. Edition, and more was added back into the Standards Edition. We no longer offer the Third Edition.
Primary Mathematics US Edition is an adaptation of the Third Edition for use in the US. It is almost identical to the Third Edition but has a few added sections for U.S. customary measurement. It uses U.S. spelling and conventions. The same guide is used for both, and it is possible with minor adjustments to use the U.S. Edition workbook with the Third Edition textbook, except for 6B, if desired. We will continue to carry the U.S. Edition indefinitely.
Primary Mathematics Standards Edition is an adaptation of Primary Mathematics to meet the Mathematics Contents Standards for California Public Schools, adopted by the California State Board of Education in 1997 for grades 15 as one of the approved textbooks. It is similar to the U.S. Edition but has some rearrangement of topics and some added units, primarily in probability and data analysis, negative numbers, and coordinate graphing. The Standards Edition components are not interchangeable with the US or Third Edition components.
 What components are available for each edition?
The following table lists the major differences between the three editions, and the major features and components of each.

Standards Edition

U.S Edition

Third Edition

First published

2008

2003

1998

Changes from earlier editions

Same as U.S. Edition, but different sequence of some topics both between semesters and between levels. All the textbooks are now in color, not just 1A2B. (Workbooks are still printed in black and white.)

Uses U.S. currency, American spelling (e.g. color), terms (e.g. gas) and conventions (e.g. commas for thousands). Same sequence of topics as Third edition.

Uses Singapore currency, British spelling (e.g. colour), terms (e.g. petrol) and conventions (e.g. spaces for thousands)

Additions to earlier editions

Same additions as in U.S. Edition.
New chapters or sections added on data analysis and probability, plane and solid figures, negative numbers, and coordinate graphing. Additional review problems. Glossary and index at the back of each textbook. Textbooks for 4A5B have a list of the California mathematics content standards. Workbook for 1A2B have "Math at Home" pages at the back.

New chapters in 2A, 2B, and 3B, and some changes to other levels covering U.S. standard measurements (chapters on metric measurement are still there).


Material from second edition of Primary Mathematics

Additional sections on mental math, additional review problems, reteaching pages in 4A5B.

Unit in 6B "Division of Fractions"


Books/sets.
Each textbook (for one half of a year) has an accompanying workbook.

Textbooks 1A, 1B, 2A, 2B, 2A 2B, 4A, 4B, 5A, 5B, 6A, 6B
Workbooks 1A, 1B, 2A, 2B, 2A 2B, 4A, 4B, 5A, 5B, 6A, 6B.

Textbooks 1A, 1B, 2A, 2B, 2A 2B, 4A, 4B, 5A, 5B, 6A, 6B
Workbooks 1A, 1B, 2A, 2B, 2A 2B, 4A, 4B, 5A, 5B, 6A, 6B.

Textbooks 1A, 1B, 2A, 2B, 2A 2B, 4A, 4B, 5A, 5B, 6A, 6B
Workbooks 1A part 1 and part 2, 1B part 1 and part 2, 2A part 1 and part 2, 2B part 1 and part 2, 3A part 1 and part 2, 3B part 1 and part 2, 4A part 1 and part 2, 4B part 1 and part 2, 5A, 5B, 6A, 6B.

Teacher resources

Teacher's Guides, Standards Edition (answers are in the teacher's guides).
Home Instructor's Guides are currently being developed. Guides 1A through 5B are now available. Answers Keys (answers are also in the guides).

Teacher's Guides, U.S. and 3rd Editions.
Home Instructor's Guides, U.S. and 3rd Editions. Answer Keys, U.S. and 3rd Editions (answers are also in the guides).

Additional Books

Extra Practice 1, 2, 3, 4, 5.
Tests 1A, 1B, 2A, 2B, 3A, 3B, 4A, 4B, 5A, 5B.



Contents?
Sample pages?

See the Contents_Sample tab on the product detail information page of each item.

Scope and Sequence?

Go to
Scope and Sequence

Go to
Scope and Sequence

Go to
Scope and Sequence

Placement tests?

Go to
Placement Tests


Are there answers in the textbooks or workbooks?
No. The textbook does have answers to some of the examples, but it also includes learning tasks, practices, and reviews where answers are not supplied within the textbook since the tasks and practices in the textbook are used to guide a student's learning or assess understanding. The workbooks do not have an answer key at the back. Answers are only in the Teacher's Guide or Home Instructor's Guide. Both the U.S. Edition and Standards Edition have a separate answer key you can get instead of a guide.

Do we need both the textbook and workbook? What is the difference between them?
Yes, you need both. The textbook contains the learning tasks that are done as part of the lesson. It also has practices and reviews that are meant to be done in class. The workbook contains the independent work (can be used for homework).

What is the difference between the Teacher's Guide and the Home Instructor's Guide?
The Teacher's Guide is geared towards class instruction, whereas the Home Instructor's Guide is geared towards teaching one or a few students. The Teacher's Guide has daily lesson plans, whereas the Home Instructor's Guide has lesson plans that are more flexible and can take one or more days depending on the needs of the individual student. Both have answers to all textbook and workbook problems, but the Home Instructor's Guides has stepbystep solutions and some alternate solutions to all the word problems. The Teacher's Guide has solutions to only selected word problems.

I am using Primary Mathematics to teach my children at home. Do I need a guide?
A guide is recommended, but not obligatory. Primary Mathematics follows a concrete to pictorial to abstract sequence of instruction. The concrete introduction is not in the textbooks. Suggestions for introducing the concepts concretely are given in the guides. The guides also provide background notes to the teacher explaining the concepts and how they fit in with the program as a whole, as well as information about what was previously taught. The guide also emphasizes places where concepts are taught differently from most U.S. texts, such as bar models to diagram word problems and the mental math techniques. From just looking at the textbooks, it has sometimes been assumed that learning math facts is not required, since the textbooks and workbooks do not include drills on the math facts. Learning math facts is, however, a necessary part of the curriculum and suggestions on how to help students memorize math facts, as well as some mental math sheets, are in the guides. Therefore, the guides round out the curriculum.

Where can I find more practice exercises?We have supplementary books for Primary 16 that provide ample practice exercises (answers provided). The supplementary books are not components of the Primary Mathematics series  they are simply books from Singapore that provide additional practice. The U.S. Editions of supplementary books follow the same sequence as the units in the Primary Mathematics U.S. edition. The other books are generic and often add to the content of Primary Mathematics. All of them can be used with any of the editions of Primary Mathematics with caution for the sequence of topics. The U.S. Editions have additional content on U.S. standard measurement. Please see the FAQ on the supplements for more information.

We plan to start using Primary Mathematics. Which edition should we use?
If you are a school and new to the program, we suggest the Standards Edition. If you are a homeschooler, the edition you use depends on how important the added content of the Standards Edition is to you.

Can we switch from the U.S. Edition to the Standards Edition?
For 1A2B it is possible to switch from the A book in the U.S. Edition to the B book in the Standards Edition. For levels 35, you will need to finish the B books of one level before switching to A book of the next level and not switch mid year. Between levels 5 and 6, it is not advisable to switch editions at all.

I am not happy with the math being taught at my child's school and want to supplement at home. Which edition should I get?
You can use either the U.S. Edition or the Standards Edition. The material added to the Standards Edition is taught later in the Singapore math syllabus, after the students have foundational knowledge. Your child is probably receiving adequate instruction in these additional topics and may just need a better founding in foundational concepts in which case the US Edition would be sufficient.

Is the Standards Edition of Primary Math "dumbed down" compared to the U.S. or Third Edition?
No, it is not. It meets the math requirements per grade level for California, and so some topics were added and rearranged, but it maintains the integrity of the Primary Mathematics curriculum. Most of the content is the same as in the U.S. Edition, and thus the third edition of Primary Mathematics, and some content was added in from the second edition of Primary Mathematics. In fact, it is probably in places a bit more challenging than the U.S. edition because of the addition of material from the second edition of Primary Mathematics. This is one series that has not followed the trend of decreasing challenge with each new edition! Some topics were added, which could lead to concern that it is becoming "mile wide and inch deep" but the additions are fairly minimal. Some of the additions were simply made in order to be more explicit on material that was already in the curriculum, or to cover some of the same material at more grade levels. For example, some content that was repeated between grade levels was removed in going from the second edition to the third edition to create a "reduced content" edition. It is now back in the Standards edition, such as a review of equivalent fractions now in 4A, or the connection between division and fractions now in both 4A and 5A.

How do I know where to place my child?
Please use the Placement Tests. We also have a forum where you can share similar concerns.

What if I encounter problems when we have already started using these books?
You are welcome to visit our forum for online help.

Do we need to purchase additional products such as manipulatives for use with this curriculum?
Teachers in Singapore use simple manipulatives such as flash cards, charts and 3dimensional objects. We carry some manipulatives. A chart listing the manipulatives used in the Home Instructor's Guides is available.

How teacherintensive is the program?
As with any program, effective supervision plays an important role. The more involved you are in your student's math education, the better the chances for addressing lack of comprehension in a timely manner. The curriculum was not designed to be selftaught.<

Is there any part of Singapore Math which is independent learning?
The student is expected to do all the work in the workbooks independently.

Can we use U.S. Edition Teacher's Guides, Home Instructor's Guides and Answer Key Booklets with the Standards Edition books?
No. The Primary Mathematics U.S. Edition textbooks, workbooks, guides, and tests cannot be used interchangeably with the Primary Mathematics Standards Edition textbooks, workbooks, and guides.
 I have been using the U.S. Edition. I would like more specific information on the content differences between the U.S. Edition and the Standards Edition.
Please see the Scope and Sequence and following table, which lists additions or changes in the Standards Edition with respect to the U.S. edition.
1A

Number Sense: Use > and < symbols (moved down from 2A). Some pages specifically for learning math facts added (addition and subtraction within 20).
Measurement and Geometry: Arrange and describe objects by proximity, position, and direction. Classify plane and solid figures by common attributes (e.g., curved or flat surfaces, number of corners and sides).Compare and measure capacity.

1B

Statistics, Data Analysis and Probability: Represent and compare data using tally charts and bar graphs as well as picture graphs.
Measurement and Geometry: Estimate time. (e.g. It is a little after 11 o’clock.) Number Sense: Make reasonable estimates of quantities of objects within 100. Count by twos and fives (explicit pages, already present implicitly in US edition).Write addition and subtraction problems vertically.

2B

Number Sense: Use repeated subtraction for division, form groups with remainders. Find the fraction of a set (e.g. 2/3 of 15) using objects and diagrams.
Measurement and Geometry: Estimate time (about how long will it take to…). Identify and name common 3dimensional objects. Statistics, Data Analysis and Probability: Use tally charts and bar graphs (bar graphs moved down from 3B). Find range and mode of data.

3A

Number Sense: Round numbers to the nearest 10, 100, or 1000 (moved down from 4A). Mental math moved from 3B to 3A. Estimate to verify the reasonableness of calculated results. Multiply and divide thousands by a 1digit number (US edition multiplies and divides hundreds).
Algebra and Functions: Recognize and use the commutative and associative properties of multiplication (e.g. 5 x 7 x 3 = 15 x ?). Statistics, Data Analysis and Probability: Present data in tables and graphs (moved down from 4A). Use tally charts and line plots in presenting and analyzing data. Identify whether events are certain, likely, unlikely, or impossible, record possible outcomes of simple events, summarize and display the results of simple probability experiments, predict future events.

3B

Number Sense: Multiply and divide money amounts in decimal notation by converting to whole numbers (US edition has add and subtract money amounts, but not multiply and divide). Add and subtract fractions with the same denominator (moved down from 4A). Find the fraction of a set, only whole number answers. Represent money amounts as fractions of a dollar.
Measurement and Geometry: Identify and classify polygons, quadrilaterals, triangles, and common solids. Find the volume of solid figures by counting the number of cubes that would fill them (moved down from 4B).

4A

Number Sense: Use place value concepts for numbers within 1,000,000,000 (US edition: within 10,000,000). Round numbers to the nearest ten thousand, hundred thousand, and million (as well as tens, hundreds, and thousands). Understand the definition of prime numbers. Use concepts of negative numbers (e.g. number line, owing); compare and order integers. Mental math: subtract from 1000, add/subtract numbers close to a multiple of 100, add/subtract some 3digit numbers, multiply by a number close to a multiple of 10 or 100 (e.g. 19, 99), multiply by 25. Relate fractions to division. (Finding the fraction of a set where the answer is not a whole number has been moved up to 5A.)
Algebra and Functions: Use letters to stand for unknowns in equations and inequalities. Use order of operations to solve expressions with or without parentheses (moved down from 5A). Understand and use formulas containing letters to solve problems involving area, perimeter, and volume (e.g. P = 2 x (l + w)). Measurement and Geometry: Find the radius and diameter of a circle. Visualize and make 2dimensional drawings of common solid figures; identify nets of solids (moved down from 6A).

4B

Measurement and Geometry: Identify congruent figures. Use congruent figures to make tiling patterns (moved down from 5).
Identify figures that have rotational symmetry. Locate and name points on a coordinate graph, draw points corresponding to a linear relationship on a coordinate graph, find the length of vertical or horizontal line segments by subtracting appropriate coordinates (first quadrant). Algebra and Functions: Understand and derive simple linear functions. Statistics, Data Analysis and Probability: Represent data with line graphs (moved down from 5). Represent data on a line plot. Identify mode for categorical data, and mode and median for numerical data. Represent all possible outcomes of probability experiments; express the outcomes as a fraction of total outcomes.

5A

Number sense: Use place value concepts for numbers in the billions. Find the greatest common factor and lowest common multiple.
Determine the prime factors of numbers to 100 and write the number as the product of their prime factors using exponents. Understand and compute positive integer powers of nonnegative integers (e.g,. 43). Mental math: review and extend strategies taught earlier, multiply 2digit numbers. Find the fraction of a whole number even when the answer is not a whole number (moved up from 4A). Additional material on multiplying a whole number by a fraction. Divide a whole number or a fraction by a fraction (moved down from 6B). Measurement and Geometry: Derive and use the formula for area of a parallelogram. Find the surface area of rectangular prisms.

5B

Number Sense: Multiply a decimal number by a decimal number; divide by a decimal number. Add negative integers; subtract positive integers from negative integers.
Measurement and Geometry: Use the sum of angles of a quadrilateral to find unknown angles. Statistics, Data Analysis and Probability: Find the mean, median, and mode of data. Display data in a histogram. Display data in a circle graph (moved down from 6A). Algebra and Functions: Identify ordered pairs of data from a graph. Use the distributive property in equations and expressions with variables. Identify and graph ordered pairs in the four quadrants of a coordinate grid. Solve problems involving linear functions with integer values, write the equation, and graph the ordered pairs.


How does Singapore Math compare with other math programs?
Singapore Math is a balance between drill and creative problem solving. Customers who have used other programs think that the Singapore approach moves along to more abstract math concepts in a more rational way and, depending on the student's pace, more quickly. Other positive feedback indicates that the Singapore approach encourages greater problem solving skills and creative thinking.

Does Singapore Math use the incremental, spiral or unitstyle approach?
The Singapore Math curriculum does not conform strictly to any of the above approaches. The strong point of Primary Math is the way basic concepts are presented. There is always more than one approach, and the workbooks are instrumental in making sure the information is generalized in the way desired. There are 'Practice' and 'Reviews' at the ends of chapters and sections. There is an effective mix of drill, word problems and mental calculation instruction connected to all important concepts. (Note: some of the drill is provided in the guides). While typical U.S. curricula touch on a larger number of topics rather superficially, PM nails the core math curriculum in a way that better prepares students for higher math.

How is Math drilled in Singapore?
Individual teachers approach the process of oral drill and use of manipulatives differently. There is, however, great emphasis on homework and practice.

What is the grading scale used in Singapore?
A* to U Grade System
A*: 91% and above
A: 75% to 90% B: 60% to 74% C: 50% to 59% (passing grade) D: 35% to 49% E: 20% to 34% U: 0% to 19% (Ungraded)
50% is the minimum passing mark for primary school math.
A*distinction (91% and above).
Note: some schools adopt the Band System from Primary 1 to Primary 3 (or Primary 5). By Primary 6, most schools would have switched to A* to U Grade System.

Should we use this grading scale with the tests for Standards Edition? Probably not. The tests for the Standards Edition should be graded according to typical US grading scales. Tests in Singapore, and sample tests in supplementary books we import, will have a greater percentage of challenging problems.

What is Model Drawing all about?
Primary Mathematics teaches a problem solving technique in which students use pictorial models. This approach is often called the “model approach”. In the model approach, students draw diagrams in which they represent the problem situations and relevant concepts using bars. Drawing the model permits students to visually relate various types of information given in the problem to an unknown amount and helps them to determine which mathematical expressions are useful in solving the problem. The purpose of drawing the models is not to have students follow specific rules, but rather to understand the concepts and work out a strategy for finding the answer. For complex problems, several strategies are possible, and drawing the model allows the student to visualize a good strategy. Drawing bar models is a valuable tool for solving nonroutine problems. These problems might also be solved using algebra, but for children at the primary level a model approach can be preferable since it is less abstract.
The model approach fits in with the program as a whole, and is not the only benefit to using Primary Mathematics. It can be taught in isolation from the rest of the program, at least to a certain extent, but is more effective when taught as a part of the whole. Model drawing is a problem solving method that can be used across different levels, and as a link to algebra in the secondary level. Students in Primary Mathematics 1 and 2 learn number bonds and partwhole concepts and use number bond diagrams to solve simple word problems before they are ready to draw proportional bars needed using the model approach. A commonly used strategy in using bar models is to draw units or divide the bar into units, equate the number of units to a quantity, which is either given or calculated from other quantities given in the problem, form a proportion statement, and finally to use a unitary or proportion method to get the answer. In Primary Mathematics, a unitary method is used in understanding and solving fraction, percentage, ratio, and rate problems, without necessarily drawing a bar model. These concepts are difficult for some students to grasp, and in Primary Mathematics are taught in the context of skills already mastered with the use of the model approach. A main feature of Primary Mathematics is a concrete to pictorial to abstract approach. Bar models are not the only place in the program where a pictorial approach is used to help students understand concepts.
The model approach, while an integral part of Singapore mathematics, is not just what Singapore mathematics is all about, nor is it the total of the benefits that can be derived from using the Primary Mathematics program.
 Who wrote the Primary Mathematics series?
The Primary Mathematics Series was first published in 1982 and was the only series used in Singapore primary schools until 2001. Primary Mathematics was written by members of a project team put together by the Ministry of Education, Singapore.

Who publishes these new series?
The new series are published by different publishers.

How many new series were published in Singapore?
There were about five series that were approved. Some of the series have already come and gone. Some have been revised.

Why are you selling Primary Mathematics when there are so many new series used in Singapore?
Primary Mathematics has been around for over twenty years and has a proven track record. Students from Singapore who scored well in the 1995 TIMSS, 1999 TIMSS and 2003 TIMSS were using the Primary Mathematics series. We have also consulted with several professors (who were advocating "back to basics" mathematics) in the US and they have unanimously agreed that the new texts lack the indepth teaching of the original Primary Mathematics series. The original Primary Mathematics series were written by members of a team put together by the Ministry of Education (MOE) in Singapore. Teachers were also invited to test the material and to provide useful insights and suggestions. The new series are written by authors hired by the publishers. It is our mission is to make available the best mathematics books from Singapore  and at this point in time, the Primary Mathematics Series, with its proven record, is still in the lead. We even got approval from the Singapore MOE to publish a U.S. Edition of the Primary Mathematics series so that we could add some material (U.S. measurement) requested by our U.S. customers, as well as include some material from an earlier edition (2nd Edition). Meanwhile, we are monitoring the results of the new series. After all, mathematics education is not about the latest 'new thing'. Please look at The Singapore Math^{®} Story.

Which series is the most popular with schools and homeschoolers in the U.S. and Canada?
The Primary Mathematics Series is the most popular series used in both schools and homes. Schools usually start using this series after reviewing the books, and after talking to other school users. Some school users attend Singapore mathematics conferences. Many of these conferences are held by academics who are driven by their confidence in the Primary Mathematics Series. Homeschoolers in the US and Canada are a discriminating group, and although the new series were available at our store, most of them inevitably end up using the Primary Mathematics Series. Many of them have come back with very positive feedback about the program. At this point in time, we no longer carry any of the new series.

What is the similarity between the new series and Primary Mathematics?
The contents of the new series changes over time. Both the Primary Mathematics series and the first wave of new series are based on the 1999 reduced syllabus. (However, with the Primary Mathematics U.S. Edition, a chapter on division of fractions that was "reduced" was added back). Please look at The Singapore Math^{®} Story.

What are the differences between the new series and Primary Mathematics?
The new series are written by different authors hired by the publishers. Hence the methodologies used for teaching the same concepts will vary between series (i.e. the differences are not limited to pictures, names and color schemes). Three initiatives were also introduced  National Education (to develop citizenship skills and values in the Singapore context), Information Technology (to bring hardware and software technology into schools. However, for the new series, the IT content is found only in the teacher's CD ROMs. It is not mentioned in the textbooks or workbooks, as the IT materials are not reviewed by MOE), and Critical and Creative Thinking (to infuse thinking skills). New textbooks first published in 2001 have been revised in 2007. Changes in 2007 (for texts now used in Singapore) include use of calculators (starting in level 5), reduction in mental math, and removal of operations on compound units in measurement. Please look at The Singapore Math^{®} Story.

Why is Primary Mathematics no longer used in Singapore?
The MOE decided to "open up" the textbook market in Singapore. Three initiatives were also introduced  National Education (to develop citizenship skills and values in the Singapore context), Information Technology (to bring hardware and software technology into schools. However, for the new series, the IT content is found only in the teacher's CD ROMs. It is not mentioned in the textbooks or workbooks, as the IT materials are not reviewed by MOE), and Critical and Creative Thinking (to infuse thinking skills).

How can we make up for the three initiatives that are missing in the Primary Mathematics series?
 National Education  these are citizenship skills and values in the Singapore context. As such, they are not relevant to students outside of Singapore.
 Information Technology;  the IT content is not in the textbooks/workbooks of the new series. There is no difference between the Primary Mathematics series and the new series. Students in the US and Canada are exposed to IT in many other aspects of their academic career and it is not essential that they learn it from a math book.
 Critical and Creative Thinking  these come in the form of harder problems at the end of the chapters in the new series (hence there are less "regular" practice problems in the new series). Primary Mathematics does contain some similar harder problems in the textbook practices, just not under a separate heading. More challenging problems are found in supplementary bookssuch as Primary Mathematics Intensive Practice, Primary Mathematics Challenging Word Problems and the Brain Maths series. These are actually more challenging than those in the new series. The new series also has some puzzles. Some of the creative thinking problems in the new series are puzzles that involve math concepts that the students have not yet learned, and so must be solved more by guess and check. There are good critical thinking problems in the supplements Intensive Practice and Brain Maths.

Is Singapore Math Inc.® replacing Primary Mathematics with any new series?
We have no intention of replacing Primary Mathematics. Primary Mathematics has been around for over thirty years and has a proven track record. We will continue to offer Primary Mathematics rather than promote the new series in the U.S./Canada markets.
Singapore Math^{®} is a registered trademark of Singapore Math Inc.



