# Primary Mathematics Curriculum – World’s #1 Ranked Program

## Did You Know? – Primary Mathematics Curriculum is Ranked #1 in the World

Singapore’s elementary students are the best in the world in mathematics. The international test rankings (TIMMS) have been supporting this fact continuously for more than a quarter of a century. Research points to the Singapore Primary Mathematics Curriculum as the major factor in this impressive and long-lasting success.

## What is Primary Mathematics?

The theory and practice of Primary Mathematics were developed in the early 1980s. A top Singapore researcher, Dr. Kho Tek Hong, headed a team of nine curriculum specialists who created the Primary Math Curriculum, model method, textbooks, and other resources. This curriculum, pedagogy and materials raised math standards in Singapore and propelled their students to the 1st place in the world in math.

The famous program is founded on the Constructivist's pedagogy and Concrete-Pictorial-Abstract (CPA) learning progression. Primary Mathematics teaching is an art that requires educators become skillful at using Constructivist pedagogy as well as specific teaching strategies for Primary Mathematics that include mental math and model method.

## Why Choose Primary Mathematics?

The Primary Math curriculum is the best because of its approach to teaching and learning mathematics. The instructional design of this curriculum is a delicate balance between understanding and practice. This skillful design is what makes math education accessible for kids who first learn for understanding and then engage in practice, which becomes meaningful and leads to long-lasting mastery of math facts.

Primary Mathematics learning is impressively rigorous by its way of taking young learners away from counting, early in Grade 1, to mastering a series of complex topic performances in upper elementary school.

## What is the Most Important Characteristic of the Primary Mathematics Curriculum?

Understanding this curriculum on a deeper level is the key to successful implementation of this powerful curriculum. The most important characteristic of this program is its focus on mastering the main key ideas that pervade mathematics of elementary school. The curriculum focuses on place value, unitary system, and model method with emphasis on mental math and problem-solving.

Emphasizing place value and units that help students develop flexibility with numbers and understanding of algorithms, fractions, and decimals. Bar modeling techniques provide students with effective strategies for solving real world problems.

## Primary Mathematics Curriculum Reduces a Need for Review

Singapore Primary Math curriculum is anchored on learning new concepts from already acquired knowledge in the previous units and years. After a topic is covered it then becomes a building block for learning a new topic and providing an informal review of the previously learned concept. Thus, each new concept also provides a feedback-loop for solidifying understanding of previously learned ideas and concepts that often make formal reviews unnecessary.

For example, Primary Math Grade 2 assumes that young students mastered decomposition of numbers to 10 and 20 using the number bonds tools acquired in Grade 1. This knowledge is used to teach addition and subtraction algorithms with high numbers in Grade 2.

Similarly, in Grades 3, the curriculum uses students’ knowledge of basic regrouping strategies within numbers to 20 learned in Grade 1 to teach algorithms of multiplication. This not only gives students a deeper understanding of multiplication but also provides a feedback-loop to solidify understanding of the addition algorithm thereby reducing or eliminating the need for a full review of addition algorithm.

## The "Singapore Math" term doesn't exist... in Singapore

It’s a common misconception that in Singapore, educators use Singapore Math in Grades 1-6. The “Singapore Math” term doesn't exist in Singapore! Teachers in Singapore exclusively use the Primary Mathematics syllabus and curriculum.

## Primary Mathematics is the Only Authentic Singapore Math

The authentic Primary Mathematics program, which became known as “Singapore Math”, refers specifically to the Primary Mathematics Third Edition and Primary Mathematics 2003 U.S. Edition textbooks and workbooks in Grades 1 through Grades 6. Researchers described this program as “coherent, focused and rigorous.”

All Singapore textbook programs, including Dimensions Math, Math in Focus, Eureka, and EngageNY were modeled after the authentic Primary Math Curriculum.

## All State Standards are Founded on the Primary Mathematics Curriculum.

After observing that Singapore students consistently take top places on TIMMS and PISA, US educators analyzed the Primary Math curriculum and textbooks to create many of the State Standards in K-5.

Similar to the Primary Mathematics Curriculum, the State and Next Generation Standards focus early learning of mathematics on numbers (place value system, regrouping calculations, solving word problems in four operations and fractions) and less on other topics (data, geometry and measurement). Also, US researchers embedded the Primary Mathematics problem-solving strategies that involve number bonds and bar models into the State and Next Generation Standards in K-5.

**What are the Major Differences between Primary Mathematics and Our Previous Program?**

When considering adoption of this curriculum many teachers ask the following question: what’s the difference between the Primary Mathematics Curriculum and our previous program? Singapore Math is the only curriculum that uses units to explain nearly everything. The program uses units to teach about whole numbers (composition and decomposition), four operations, mental math, standard algorithm, fractions, decimals, word problems, bar models, and measurement.

Over the elementary school years, students consistently use the “unit” strategies to solve problems in four operations, fractions, and decimals that make it easier to master these concepts, instead of using isolated and often “guess and check” strategies taught in other curricula.

## What’s the Difference between Primary Math Textbooks and Other Singapore-based Textbooks?

The authentic Primary Math textbooks are thin and focused, containing about 10 to 15 topics per grade totaling only about 200 pages in a textbook. Learning one to two pages per day helps students focus on the important concepts. Achieving mastery of the few concepts presented on fewer pages becomes achievable for most young learners.

To learn about the similarities and differences among Primary Math, Math in Focus and Dimensions Math read the article A Singapore Math Comparison Guide.

## Primary Mathematics Challenging Word Problems

Bar modeling techniques are the only fully developed heuristics in the world for solving a variety of challenging word problems. Many U.S. elementary curricula, including EngageNY, Eureka Math, Go Math, My Math, Common Core, and State Standards “borrowed” and re-named these Primary Mathematics problem solving strategies as tape diagrams, strip diagrams, and others.

Bar modeling is particularly powerful for solving a variety of non-routine problems. Fourth and fifth grade students who master bar modeling can solve 7^{th} grade Algebra problems and move well ahead of their peers who use non-Singapore curricula. Using bar modeling techniques helps students represent and solve most challenging multi-step word problems related to addition, subtraction, multiplication, division, fractions, decimals, ratios, rates, percent, and others.

## Primary Mathematics Curriculum for Teachers

The success of Singapore’s elementary students is attributed to both instructional materials and strong teacher training. That’s why it is strongly recommend for educators to get training prior to implementing the Primary Math curriculum. It is also recommended for schools to offer professional development to teachers after the adoption of the curriculum.

Many teacher training options are available, including onsite, online and blended PD.

### Who do I contact with more questions?

To learn more about teacher training options contact us at info@esingaporemath.com

## Primary Mathematics Curriculum for Parents

It’s a common misconception among educators and parents that Singapore Math is mostly about drilling, “Practice, Practice, and more Practice.” On the contrary, Primary Math is not exclusively about practice, drilling or memorization of facts. Research shows that while practice is important, focusing teaching exclusively on procedural fluency doesn’t help children make sense of math nor achieve long-lasting mastery.

Teaching this curriculum properly requires teaching for understanding using the CPA approach. Primary Mathematics practice is provided to children only after CPA. Maintaining a balance between understanding and practice is what makes learning math accessible and true mastery achievable.

For homeschooling parents who use Primary Math books, but find teaching from them to be challenging, we offer an Adaptive Learning edition of this outstanding curriculum. The program administers a placement test, which determines baseline knowledge and then adjusts to your child’s unique needs and provides the right lessons at the right time.

## Editions

The first edition of the Primary Mathematics Curriculum and textbooks were created in the early 1980s. Subsequently, the program and books have undergone several revisions to be more focused on solving real world problems and changes in technology.

Initially, the Primary Mathematics 3^{rd} Edition was introduced in the United States in 1999. After its success, the Primary Mathematics U.S. Edition was developed in 2003. Subsequently, Marshall Cavendish, the company, which publishes the Primary Mathematics curriculum, created the Standards edition to align the curriculum to California Standards in 2007. Later on, the company created the Common Core edition to align the curriculum Common Core Standards in 2013. The latest edition of Primary Mathematics was developed in 2022.

## Primary Mathematics 2022 Resources

The new Marshall Cavendish Primary Mathematics Curriculum and resources provide students with learning experiences to develop mathematical thinking, metacognition, and 21^{st} century competencies. The new resources in each grade include two Teacher Guides A and B, two consumable student books A and B, 2 additional practice workbooks A and B, 2 mastery and beyond workbooks A and B, assessment guide.

## Primary Mathematics 2022 by Grade Level

### Primary Mathematics Kindergarten

**Kindergarten A**

- Chapter 1 – Count and show numbers to 5
- Chapter 2 – Write numbers to 5
- Chapter 3 – Numbers to 10
- Chapter 4 – Shapes
- Chapter 5 – Compare numbers to 10

**Kindergarten B**

- Chapter 6 – Ways to make and break numbers to 10
- Chapter 7 – Numbers to 20
- Chapter 8 – Measurement
- Chapter 9 – Addition
- Chapter 10 – Subtraction
- Chapter 11 – Addition and Subtraction
- Chapter 12 – Numbers to 100

### Primary Mathematics Grade 1

**Grade 1A**

- Chapter 1 – Numbers to 10
- Chapter 2 – Addition within 10
- Chapter 3 – Subtraction within 10
- Chapter 4 – Numbers to 20
- Chapter 5 – Addition and subtraction within 20
- Chapter 6 – Addition and subtraction word problems
- Chapter 7 – Length

**Grade 1B**

- Chapter 8 – Numbers to 120
- Chapter 9 – Addition and subtraction within 100
- Chapter 10 – Data
- Chapter 11 – Shapes
- Chapter 12 – Time

### Primary Mathematics Grade 2

**Grade 2A**

- Chapter 1 – Numbers to 1,000
- Chapter 2 – Addition within 1,000
- Chapter 3 – Subtraction within 1,000
- Chapter 4 – Addition and subtraction using bar models

**Grade 2B**

- Chapter 5 – Length
- Chapter 6 – Multiplication
- Chapter 7 – Time
- Chapter 8 – Data
- Chapter 9 – Shapes

### Primary Mathematics Grade 3

**Grade 3A**

- Chapter 1 – Numbers to 10,000
- Chapter 2 – Addition and subtraction within 10,000
- Chapter 3 – Multiplication and division
- Chapter 4 – Multiplication and division of 6, 7, 8, and 9
- Chapter 5 – Time

**Grade 3B**

- Chapter 6 – Area and Perimeter
- Chapter 7 – Fractions
- Chapter 8 – Mass and liquid volume
- Chapter 9 – Data
- Chapter 10 – Shapes

### Primary Mathematics Grade 4

**Grade 4A**

- Chapter 1 – Multi-digit whole numbers
- Chapter 2 – Addition and subtraction
- Chapter 3 – Multiplication and division
- Chapter 4 – The four operations using bar models
- Chapter 5 – Fractions
- Chapter 6 – Mixed numbers, improper fractions, and operations on fractions

**Grade 4B**

- Chapter 7 – Decimals
- Chapter 8 – Area and perimeter
- Chapter 9 – Geometry
- Chapter 10 – Measurement, time, and conversion

### Primary Mathematics Grade 5

**Grade 5A**

- Chapter 1 – Multi-digit whole numbers
- Chapter 2 – The four operations with whole numbers
- Chapter 3 – Addition and subtraction of fractions
- Chapter 4 – Multiplication and division of fractions
- Chapter 5 – Word problems: the four operations of fractions
- Chapter 6 – Decimals

**Grade 5B**

- Chapter 7 – The four operations of decimals
- Chapter 8 – Word problems: the four operations of decimals
- Chapter 9 – Volume
- Chapter 10 – Properties and classification of 2-D shapes
- Chapter 11 – Line plots and the coordinate plane
- Chapter 12 – Number patterns and relationships