The document provides an overview of Singapore Math strategies that could be used in U.S. schools. It discusses the fundamentals of Singapore Math which include a focus on problem solving, thinking, managing information, visualization, generalization, and number sense. It also discusses how Singapore students have demonstrated high achievement in international math assessments like TIMSS. The pedagogical approach of Singapore Math focuses on understanding over procedural skills. Differentiated instruction and assessment are also emphasized.

1. Singapore Math
Strategies for U.S. Schools
White Plains NY  March 2012
yeap ban har  marshall cavendish institute
SESSION ONE
Overview & Fundamentals of
Singapore Mathematics
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore

3. Introduction
Anchor Green Primary School, Singapore

4. General Overview of Singapore and its
Education System
 Land
 700 sq km
 People
 4.7 million

5. General Overview of Singapore and its
Education System
 GDP per capita in current U.S. dollars
1965 $510 2010 $43 300

6. General Overview of Singapore and its
Education System
 Students
 500 000
 Teachers
 30 000
 Principals & Vice-Principals
 900
 Schools
 173 Primary Schools (Primary 1 – 6)
 155 Secondary Schools (Secondary 1 – 4)
 13 Junior Colleges (JC 1 – 2) Canossa Convent Primary School, Singapore
 15 Mixed-Level Schools
The data refers to 1-12 school system. Pre-school is not part of the formal education
system. The data excludes post-secondary education system which includes institutes
of technical education, polytechnics and universities.

7. 1992 Problem-Solving
Curriculum
1997 Thinking Schools,
Learning Nation
2004 Teach Less,
Singapore Mathematics: Background
Learn More
2010 Professional Learning
Communities
2011 21st Century
Competencies

9. Singapore Ministry of Education 1992, 2001, 2007, 2013

10. “Mathematics is an excellent
vehicle for the development
and improvement of a person’s
intellectual competencies”
Singapore Ministry of Education 2006

12. What to Teach?
Singapore Mathematics: What & How
How to Teach?

13. Singapore Examination & Assessment Board 2012
Case Study 1
As the instructor demonstrates the
lesson, study what is it that the teacher
wants students to learn. This is a Grade
6 problem involving fraction and ratio.

14. Case Study 1 16 units = $120
20 units =
04 units = $120  4
04 units = $30
20 units = $30 x 5
20 units = $150
John had $150 at first.

16. Case Study 1
what is it that the teacher
wants students to learn

17. SESSION ONE
Singapore Math Overview & Fundamentals of
Singapore Mathematics
Strategies for U.S. Schools
White Plains NY  March 2012
Fundamentals of
Singapore Mathematics
 Focus on Problem Solving
 Focus on Thinking
 Focus on Managing Information
 Focus on Visualization
 Focus on Generalization
 Focus on Number Sense
 Focus on Communication

18. Singapore Math
Strategies for U.S. Schools
White Plains NY  March 2012
yeap ban har  marshall cavendish institute
SESSION TWO
Mathematical Problem Solving
including Bar Models
Pathlight School, Singapore

20. Tom has some sweets.
Jerry has 5 sweets more than Tom.
Later, Tom gives Jerry 2 sweets.
Who has more sweets now?
2
Case Study 3
Primary 3 Lesson Study 2 5 2
Kong Hwa School
Tom Jerry Who has more sweets now?
Before x x+5 How many more?
After x–2 x+7

21. Tom has 9 sweets.
Jerry has 5 sweets more than Tom.
How many sweets does Jerry have?
Tom 9
Case Study 3
Jerry 5
9 + 5 = 14
Jerry has 14 sweets.

22. Tom has 9 sweets.
Jerry has 5 sweets more than Tom.
Later, Tom gives Jerry 2 sweets.
Who has more sweets now?
How many more?
Tom 9 2
Case Study 3
Jerry 5 2
9–2=7
9 + 5 + 2 =16
16 – 7 = 9
Jerry has 9 more sweets than Tom.

23. One day, 543 cars and 274 buses pass
through a toll booth. How many cars and
buses pass through the toll booth?
Math in Focus Grade 2
cars 543
Case Study 3
buses 274
543 + 274 = 
cars buses
543 274

24. 543 + 274 = 

25. 543 + 274 = 

26. 543 + 274 = 

27. 543 + 274 = 

28. 543 + 274 = 

29. 543 + 274 = 

30. Multiplication is taught with
a focus on meaning,
visualization, and making
connections.

31. Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Their total ages is 72 years.
Find their ages.
Sam
Case Study 6
Terry
72
Vanessa
60 12
72  6 = 12
Terry is 12 years old. Sam is 24 years old.
Vanessa is 36 years old.

32. Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Their total ages is 72 years.
Differentiation for Struggling
Find their ages. Learners
Sam is twice as old as Terry.
Case Study 6 Vanessa is 36 years old.
Their total ages is 72 years.
Find their ages.

33. Sam is twice as old as Terry.
Vanessa is three times as old as Terry Sam.
Their total ages is 72 years.
Find their ages.
Terry Sam
Case Study 6
Sam is twice as old as Terry.
Vanessa is three times as old as Terry.
Differentiation for Advanced Their total ages is 72 years.
Learners
Find their ages.

34. Primary Mathematics (Standards Edition) Grade 6
Case Study 2
As the instructor demonstrates the
lesson, study what is it that the teacher
wants students to learn. This is a task
from a Grade 6 textbook to motivate
the learning of algebra.

37. Singapore Math
Strategies for U.S. Schools
White Plains NY  March 2012
yeap ban har  marshall cavendish institute
REVIEW & CONSOLIDATE
Opening Lecture
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore

38. Average Learners
High Achievement
International Studies

39. Students in Singapore have demonstrated
high achievement and positive attitude
towards mathematics.
In Trends in Mathematics and Science Study,
about 40% of Singapore’s 4th and 8th
graders are in the Advanced International
International
1995
2003
2007
Benchmark (the international average is 5%
and 2% respectively).
Grade 4 Advanced 38 38 41 5
High 70 73 74 26
Intermediate 89 91 92 67
Low 96 97 98 90

40. Hong Kong
Singapore
S. Korea
Average
Taiwan
TIMSS
Trends in International Mathematics and Science Studies
Advanced 2 31 40 40 45
Grade 8
High 15 64 70 71 71
Intermediate 46 85 88 90 86
Low 75 94 97 98 95
Junyuan Secondary School, Singapore

41. TIMSS
Trends in International Mathematics and Science Studies
Grade 4 1995
Grade 8 1999
Advanced 38 42
High 70 77
Intermediate 89 94
Low 96 99
Fuchun Primary School, Singapore

42. TIMSS
Trends in International Mathematics and Science Studies
Grade 4 2003
Grade 8 2007
Grade 4 1995
Grade 8 1999
Advanced 38 42 38 40
High 70 77 73 70
Intermediate 89 94 91 88
Low 96 99 97 97
Fuchun Primary School, Singapore

43. The attitude index for Singapore students in
TIMSS is also relatively high compared to
other high-performing countries.
Also, the majority of students in Singapore
opt to study mathematics in Grades 11 and
12 when they are no longer required to.
Marsiling Secondary School, Singapore

44. Achievement
Attitude
Singapore 71 41
Hong Kong 67 40
Taiwan 50 24
Grade 4
Japan 62 23
Kazakhstan 89 19
England 62 16
Russia 80 16
International 72 5

45. Achievement
Attitude
Taiwan 37 45
S Korea 33 40
Singapore 60 40
Grade 8
Hong Kong 47 31
Japan 30 26
Hungary 30 10
England 40 8
International 54 2

46. High achievement was not a given. In 1960,
among 30 615 candidates who sat for the
first Primary School Leaving Examination,
45% of the candidates passed.
Keon Ming Public School, Singapore

47. All major international tests (literacy, science and mathematics) between 1964
and 2003 were placed on a common scale. Selected countries shown in the table.
Score 1960-1970s 1980s 1990s 2000s
500 Japan Japan Japan Japan
Korea Korea Korea
Hong Kong Singapore Hong Kong
Hong Kong Singapore
400 Thailand Singapore Malaysia Malaysia
Thailand Thailand Thailand
The Philippines
300 Indonesia Indonesia
The Philippines The Philippines
Reference: E. Hanusek, D. Jamison, E. Jamison & L. Woessmann (2008)

48. Average Learners
High Achievement
Pedagogy

49. Math in Focus

50. Pensar sin Limites (Spanish Edition)

51. Pensar sin Limites (Spanish Edition)

52. Maths Champion (Indonesian Edition)

53. Primary Mathematics (Standards Edition)

54. Primary Mathematics (Standards Edition)

55. Singapore Math
Strategies for U.S. Schools
White Plains NY  March 2012
yeap ban har  marshall cavendish institute
SESSION THREE
Differentiated Instruction
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore

61. “… over-emphasising procedural skills
without understanding the underlying
mathematical principles should be
avoided.”
Ministry of Education 2006

62. My Pals Are Here! Mathematics (Second Edition)

65. Singapore Math
Strategies for U.S. Schools
White Plains NY  March 2012
yeap ban har  marshall cavendish institute
SESSION FOUR
Assessment
Primary 3 Mathematics Lesson Study on Mass
CHIJ Our Lady of Good Counsel, Singapore

66. Grade Levels Assessment Notes
1–2 Basic Skills Emerging
Informal Familiar Applications Established
Assessment Novel Applications Independently
Scaffolding
With or without
materials
3–4 Basic Skills 40%
Informal Familiar Applications 40%
Assessment Novel Applications 20%
Standardized Test
5–6 Basic Skills 20%
Informal Familiar Applications 30%
Assessment Novel Applications 50%
Standardized Test

67. Jack and Kyla share $300.
Jack gets twice as much as Kyla.
How much does Kyla get?
Jack
Case Study 4
Kyla
$300  3 = $100
Kyla gets $100.

68. Natalia’s bag is 12 kg heavier than Peter’s.
The total mass of the two bags is 58 kg.
How heavy is Natalia’s bag?
How heavy is Peter’s bag?
Natalia 12
Case Study 5
Peter
58 – 12 = 46
46  2 = 23
23 + 12 = 35
Natalia’s bag is 35 kg. Peter’s bag is 23 kg.

69. Mrs. Lee used ¼ of the flour she bought to make cookies and a third
of the remainder to bake a cake. She then has 3.6 kg of flour left.
How much flour did she buy?
Case Study 7

70. Mrs. Lee used ¼ of the flour she bought to make cookies and ½ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Case Study 7

71. Mrs. Lee used ¼ of the flour she bought to make cookies and ¼ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Case Study 7

73. Mrs Lee used ¼ of the flour she bought to make cookies and ½ of
the remainder to bake a cake. She then has 3.6 kg of flour left. How
much flour did she buy?
Case Study 7

74. Jason, Edward and Sam had a total of $837. Jason had the least
amount of money. The ratio of Edward’s money to Sam’s money was
4 : 3 at first. Jason and Edward each spent a third of their money.
Given that the three boys had $648 left, how much did Jason have
at first?
An example of novel assessment task from
a Singapore school. This is for Grade 6.
$837 - $648 = $189
$189 x 3 = $567
This is Jason and Edward’s money at first.
$837 - $567 = $270
This is Sam’s money at first.
With this it is possible to find Edward’s hence
Jason’s amount easily. Did you get $360 for
Edward and $207 for Jason?

75. Homework for Bar Model 

76. Pablo is twice as tall as Wynn. Wynn is 20 cm taller than Zena.
Pablo is 100 cm taller than Zena.
Find their heights in meters.
Case Study 8
Pablo
Wynn
Zena

77. Rosa made paper cranes to fill a glass jar. She made 4 more cranes
each day than the day before. After 10 days, she has made 250
cranes. How many paper cranes did she make on the last day?
Case Study 9
Day 1
Day 2 4
Day 3 4 4
Day 4 4 4 4

78. Rosa made paper cranes to fill a glass jar. She made 4 more cranes
each day than the day before. After 4 days, she has made 52
cranes. How many paper cranes did she make on the last day?
Case Study 9
Day 1
Day 2 4
Day 3 4 4
Day 4 4 4 4