These are the slides for Day 1 of the institute, taught by Yeap Ban Har.

1. Experiencing
Singapore Math
Experiencing Singapore Math
M AT H I N F O C U S : S I N G A P O R E M AT H C O M M U N I T Y
INSTITUTE
July 24, 2012  Chicago, IL
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

2. Experiencing
Singapore Math
 Land
 270 sq miles
 People
introduction  4.7 million
 GDP per capita
 1965 USD510
 2010 USD43,300
in current USD
Junyuan Secondary
School, Singapore

3. General Overview of Singapore and
its Education System

4. 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
 15 Mixed-Level Schools School, Singapore
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.

5. 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

6. Experiencing
Singapore Math
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)

8. "Solving problems is central to mathematical proficiency
and is articulated to a varying degree across the
international curricula. Singapore applies the highest
degree of specificity to it, placing it at the centre of all
mathematical learning.“
Review of the National Curriculum in England Research Report
UK Department for Education

9. Experiencing
Singapore Math
1982
Introduction of Singapore mathematics
textbooks as they are known today.
Mathematics is “an excellent
vehicle for the development
1992 and improvement of a person’s
Introduction of Problem- intellectual competence”.
Solving Curriculum Ministry of Education Singapore 2006
1997 2001
Thinking Schools Introduction of textbooks published by
Learning Nation private publishers and approved by
Ministry of Education.
2007
New editions of textbooks are
published with the introduction of the
revised curriculum.
2013
Fourth version of the problem-solving
curriculum will be implemented.
Page 1

10. Experiencing
Page 4
Singapore Math

11. Experiencing
Singapore Math
 on Visualization
Fundamentals of Singapore Math
Focus
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

12. 110 g
290 g Page 2

13. 2 units = 290 g – 110 g = 180 g
1 units = 180 g 2 = 90 g
110 g
3 x 90 g = 270 g
Bella puts 270 g sugar on the
dish.
? ?

14. Experiencing
Singapore Math
Escuela de Guetamala, Chile

15. x + 2x = 12
Experiencing
Singapore Math

16. Experiencing
Singapore Math
60% of Jon’s money is $12.
Find the amount of Jon’s money.
King Solomon Academy, London

17. Box A has 20 more Edgewood Elementary School, New York
books than Box B. Box
C has twice as many
books as Box B. The
three boxes has 340
books. How many
books are there in Box
A.

18. Experiencing
Singapore Math
Solve 3x – 2 =
8
Globe Academy, London

19. Experiencing
Singapore Math
3x – 2 = 8
Globe Academy, London

20. Experiencing
Singapore Math
Share 3 fourths equally among 3.
3 fourths 3 = 1 fourth
Page 5

21. Experiencing
Singapore Math
Share 3 fourths equally between 2.
3 fourths 2
= 6 eighths 2 Share 3 fourths equally among 4.
= 3 eighths
3 fourths 4
= 12 sixteenths 4
= 3 sixteenths

22. Experiencing
Singapore Math
12 cookies 4
12 pieces 4
12 sixteenths 4
12 tenths 4 12 cookies 4 cookies
12 x 4 12 pieces 4 pieces
12 x 4x
Page 13

23. Share 3 fourths equally between 2.

24. =

25. Experiencing
Singapore Math

26. Experiencing
Singapore Math

27. Experiencing
Singapore Math

28. Experiencing
Singapore Math

29. Experiencing
Singapore Math

30. Experiencing
Singapore Math
Junyuan Secondary School, Singapore
 Concrete to
Visual
visualization  J Bruner
 Human
Intelligences
 H Gardner
Page 11

31. King Solomon Academy, London

32. Experiencing
Singapore Math
King Solomon Academy, London

33. Singapore Math
Experiencing
King Solomon Academy, London

34. Experiencing
Singapore Math
Globe Academy, London

35. Experiencing
Singapore Math
Globe Academy, London

36. Experiencing
Singapore Math
Globe Academy, London

38. Experiencing
Singapore Math
 on Patterns
Fundamentals of Singapore Math
Focus
Yeap Ban Har
Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

39. Experiencing
Singapore Math
Da Qiao Primary School, Singapore

40. Experiencing
Singapore Math
Junyuan Secondary School, Singapore
Mathematical
patterns and Practices
“Mathematically
generalization
proficient students
look closely to discern
a pattern or structure.”

41. Experiencing
Singapore Math
Fundamentals of Singapore Math
Case Study on
Multiplication
Yeap Ban Har
Marshall Cavendish Institute
Singapore

yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

42. Desde los primeros años, los estudiantes
aprenden a hacer conjuntos o grupos iguales
utilizando materiales concretos.
From the early grades, students learn to make equal
groups using concrete materials.

43. Luego, representan estas situaciones
concretas utilizando, en primer lugar, los
dibujos y, …
After that they represent these concrete
situations using, first, drawings ..

44. … más tarde, diagramas (modelos de
barras). Después de eso, escriben
multiplicaciones. Por supuesto, los
profesores volverán a las representaciones
concretas y pictóricas una y otra vez en
aprendizajes posteriores.
… and, later, diagrams. After that they write
multiplication sentences.

45. Multiplication involving whole numbers is
taught over five years, starting in Primary 1.
The focus is on one of the meanings of
multiplication – equal sets or equal groups.
La multiplicación con números enteros se
imparte en cinco años, a partir de 1º básico.
La atención se centra en uno de los
significados de la multiplicación; conjuntos
iguales o grupos iguales. Los estudiantes
aprenden a representar 3 platos de frutas
como de 3 x 6, cuando hay 6 frutas en cada
plato. No se espera que recuerden las tablas
de multiplicar.

46. conjuntos iguales o grupos
iguales

48. There is a progression from equal groups to
skip-counting.
Hay una progresión de los grupos de iguales
para saltar de conteo.

49. 1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30

50. In Primary 2, students learn multiplication
facts of 2, 3, 4, 5 and 10. In Primary 3, they
learn the multiplication facts of 6, 7, 8 and 9.
En 2º básico, los
alumnos aprenden
las tablas de
multiplicación del
2, 3, 4, 5 y 10. En
3º
básico, aprenden
las tablas de
multiplicación, de
6, 7, 8 y 9.

51. Later, the array meaning
of multiplication is
introduced.
Más tarde, se introduce el
significado del producto
vectorial.

55. Students apply their Los estudiantes
understanding of aplican sus
multiplication to conocimientos de la
solve word problems multiplicación para
including those that resolver problemas
include multiplicative que incluyen la
comparison, and at comparación
the same time, multiplicativa, y al
deepen their mismo
understanding of tiempo, profundizan
multiplication. su comprensión de la
multiplicación.

57. Multiplication is also
applied to find the area
of rectangles and
square when Primary 3
students learn the
concept of area.
La multiplicación se
aplica también para
encontrar el área de
rectángulos y cuadrados
cuando los estudiantes
de 3º básico aprenden
el concepto de
área, contando
unidades cuadradas al
final de 3º básico.

58. In Grade 3 they Después de completar las
learn tablas de multiplicar, los
multiplication of estudiantes aprenden
2-digit with 1- multiplicaciones que van
digit numbers as más allá de la tabla de
well as multiplicar. Ellos aprenden a
multiplication of multiplicar números de dos
3-digit and 1-digit dígitos con números de 1
numbers. dígito, así como la
multiplicación de números
de tres dígitos y números de
un dígito.

59. 42
In Primary 4, the learn
multiplication of 4-digit 4
and 1-digit numbers as
well as multiplication of 3- 34
digit and 2-digit numbers.
The focus is on partial
products.
En 4º básico, aprenden a multiplicar números
de cuatro dígitos y un dígito, así como
multiplicar números de tres dígitos y dos
dígitos. La atención se centra en productos
parciales.

60. Finally in Primary 5,
students learn to use
calculator to multiply
larger numbers. 5º básico los estudiantes
Por último, en
aprenden a utilizar la calculadora para
multiplicar grandes cantidades.

61. Pedagogical Principles of Singapore Method
Concrete  Pictorial  Abstract Approach
10 5 = 2
Principios pedagógicos del Método Singapur
Concreto  Pictórico  Abstracto

64. Pedagogical Principles of Singapore Method
Spiral Approach
10 : 5 = 2
12 : 5 = 2
restante 2
Principios pedagógicos del Método Singapur
Enfoque en Espiral

65. “Un plan de estudios de la manera que se
desarrolla debe revisar estas ideas básicas
en varias ocasiones, construyéndose sobre
ellos hasta que el estudiante ha comprendido
todo el aparato formal que conllevan”.
(Bruner 1960 en El Proceso de la
Educación). as it develops should revisit this
“A curriculum
basic ideas repeatedly, building upon them
until the student has grasped the full formal
.
apparatus that goes with them.” (Bruner 1960
in The Process of Education).

66. En los cursos de 1º a 4º básico, se utilizan
cantidades discretas, por ejemplo piedrecillas
y los niños. En 5º básico se utilizan
cantidades continuas como las medidas
estándar de 13 kg y 13 cm.
In Grades 1 to 4, quantities used are discrete
ones e.g. pebbles and children. In Grade
5, continuous quantities like standard
measures 13 kg and 13 cm are used.

67. En 1º básico no se utiliza el símbolo ÷ o :
para la división. El símbolo se introduce en 2º
básico. La idea de resto se introduce en 3º
básico. 1, the symbol ÷ or : is not used. The
In Grade
symbol is introduced in Grade 2. The idea of
.
remainder is introduced in Grade 3.

68. The idea of
regrouping
before
dividing is
introduced
later in Grade
3 and is
taught in
La idea 4 as
Grade de reagrupar antes de dividirse se
introduce al finalizar 3º básico y también se
well.
enseña en 4 º básico.

69. Experiencing
Singapore Math
Fundamentals of Singapore Math
Challenging Word
Problems using Bar
Models
Yeap Ban Har

Marshall Cavendish Institute
Singapore
yeapbanhar@gmail.com
Slides are available at
www.banhar.blogspot.com

70. 2 units = 290 g – 110 g = 180 g
1 units = 180 g 2 = 90 g
110 g
3 x 90 g = 270 g
Bella puts 270 g sugar on the dish.
? ?

71. Experiencing
Page 15
Singapore Math

72. Experiencing
Page 15
Singapore Math

73. Math in Focus
Grade 1
Experiencing
Singapore Math

74. Experiencing
Singapore Math
Math in Focus
Grade 2
Escuela de Guetamala, Chile

76. 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
buses 274
543 + 274 = 
cars buses
543 274

77. Lesson  July 23, 2012
Carl
$4686
Ben

79. Differentiated instruction
for students who have
difficulty with standard
algorithms. Use number
bonds.

80. 2x + x = 4686
3x = 4686
Students in Grade 7 may use algebra to deal with such situations. Bar
model is actual linear equations in pictorial form.

81. Lesson  June 18, 2012
Jack $3
Jack
Kyla $2
Kyla
gave
more
had
than

82. Lesson  June 18, 2012
Open Lesson at Hawaii, USA

87. Lesson  June 18, 2012
What if Kyla
Story 1 had this
Jack had $3. amount
before?
Jack gave Kyla $2
more.
Jack Kyla
Before $3 $1 $5 $19
After $1 $3 $7 ?

89. Lesson  June 18, 2012
Story 2
Kyla had $3 more than Jack. Who had
more money
Jack $2 afterwards?
How much
Kyla $3 more?
Jack gave Kyla $2.

90. Kyla had $3 more than Jack.
Jack gave Kyla $2.
How much more did Kyla have than Jack?
Students in Grade 6 may use algebra to deal with Story 2.
Kyla had $(x + 3)
Jack had $x
Then, Jack had $(x – 2)
And Kyla had $(x + 5)
Kyla had $(x + 5) – $(x – 2) or $7 more than Jack.

91. Lesson  July 23, 2012
In the end ... At first …
Alice 20
Betty 10
Charmaine
Dolly

92. Lesson  July 23, 2012

93. Experiencing
Singapore Math
Junyuan Secondary School, Singapore
 Concrete to
visualization Visual
and managing
 J Bruner
 Human
information Intelligences
 H Gardner

95. can learn.
Our students must
too.
Google learns from typos and spelling mistakes we all make when searching to help give you
quicker and more accurate search results. So if you type ‘grizzly pears’, we can guess that you
probably meant ‘grizzly bears’.
Goggle does not have a degree in English. We can do this because over the years we’ve
studied how people search and learned what the most common errors are. So it’s good to
know that all those little mistakes aren’t made in vain.