This plenary session was for all teachers teaching mathematics in Grades 1 through 8. It is based on MAP101 Fundamentals of Singapore Mathematics.

1. Professional Development
Singapore Mathematics
Seoul  9 – 11 July 2012
Dr Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com
MAP101
www.mcinstitute.com.sg
www.facebook.com/MCISingapore

2. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

3. Introduction
This course is an overview of Singapore
Math. It includes the what and how of
teaching mathematics.

5. Curriculum document is available at http://www.moe.gov.sg/

6. THINKING SCHOOLS
LEARNING NATION
Singapore Ministry of Education 1997

7. what
is singapore
mathematics

8. key focus
of singapore
mathematics

9. problem
solving

10. thinking

11. an
excellent
vehicle
for the development
&improvement of
a person’s intellectual
competencies
Ministry of Education Singapore 2006

12. conceptual
understanding

13. FUNDAMENTALS
of singapore
math
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

14. Singapore Math
Visualization

16. 110 g
180 g 110 g
Bella puts 180 g brown sugar on the dish.
290 g

17. on an identical dish
110 g
2 units = 180 g
1 unit = 90 g
180 g 110 g
3 units = 270 g
Bella puts 270 g brown sugar on the dish.
290 g

19. Singapore Math is based on the CPA Apporach.
Pictorial representations can be more concrete
(pictures) or more abstract (diagrams such as bar
model).
An alternate way to solve the brown sugar
problem:

20. Singapore Mathematics
focuses on the ability to
visualize. For example,
bar models are used
extensively.
Bar models were introduced to overcome the
pervasive problems students had with word problems
– even the basic ones.

21. Such word problems are used to help
students
 Deal with information
 Handle and clarify ambiguity – one
dish or two
 Develop visualization – bar models
are used extensively
 Practice mental strategies – numbers
used are not difficult to compute

22. Singapore Math
Visualization

23. Procedural & Conceptual
Understanding
Singapore Math places an emphasis on
both. Procedures are explained in a
conceptual way. For example, long
division is seen simply as breaking
large numbers into smaller ones before
dividing.

30. Using number
bonds to make
sense of long
division
Differentiated Instruction for advanced
Over-
learners – how does one get the result
emphasizing
of 51  3 from 60  3.
procedural Balancing
knowledge procedural
knowledge
with
conceptual
understanding

31. Singapore Math
Patterns & Generalization

33. Task Extension for
Advanced Learners

34. C H E R Y L

35. C H E R Y L
1

36. C H E R Y L
2

37. C H E R Y L
3

38. C H E R Y L
4

39. C H E R Y L
5

40. C H E R Y L
6

41. C H E R Y L
7

42. C H E R Y L
8

43. C H E R Y L
9

44. C H E R Y L

45. C H E R Y L

46. C H E R Y L

47. C H E R Y L

48. C H E R Y L

49. C H E R Y L
Which letter is 99?

51. Method 1
The positions of 11, 22, 33 are at C, H, E respectively.
Positions of multiples of 11 can be located.
Method 4
The position
for 99 can be
found by
writing out all
the numbers
Method 3 but this is not
Numbers ending with 9 efficient
are at E. So, 99 is at E method.
Method 2 too.
The positions of numbers ending with 1 and 6 can
be located ta either ends. Thus 91 or 96 can be
located. Subsequently, 99 can be located.

52. D A V I D

54. Method 1
The letters under A and I are
even. So 99 cannot be there.
Method 2
The positions of numbers ending
with 9 form a diagonal pattern.
Method 3
The numbers under first D
increases by 8. Thus 17 + 80 = 97
is under first D. The position for
99 can be worked out.
Method 4
The positions of multiples of 8 I is
definitely under A. 8 x 12 = 96 is
under A. The position of 99 can
be worked out.
Method 5
Numbers under V is 1 less than
multiples of 4. So, 2011 (1 less
than 2012) is under V. 99 is less
than 100.

55. Method 2
The positions of numbers ending with 9
form a diagonal pattern.
The methods were the ones that
participants in Chile came up with.

56. Another Method
In a course done in December 2010 with a group of
Chilean teachers, there was a method that involves
division. For Cheryl, it was 99  10.
For David, it was 99  8. Are you able to figure out that
method?

57. Singapore Math
Patterns & Generalization

58. Singapore Mathematics: Focus on Problem Solving

64. CPA Approach based on
Jerome Bruner was used
to learn division of
fractions – using paper
folding and subsequent
drawing.

66. Singapore Mathematics: Focus on Conceptual Understanding

67. Singapore Math
Learn New Concept Through
Problem Solving

68. Textbook Study
Observe the various meanings of
multiplication from Grade 1 to Grade
3.

69. Multiplication Facts
We do a case study on multiplication
facts. We will see the use of an anchor
task to engage students for an
extended period of time.

74. Strategy 1
Get 3 x 4 from 2 x 4
Strategy 2
Doubling
Strategy 3
Get 7 x 4 from 2 x 4 and 5 x 4
Strategy 4
Get 9 x 4 from 10 x 4

75. Strategy 1
Get 3 x 4 from 2 x 4

76. Strategy 3
Get 9 x 4 from 4 x 4 and 5 x 4
This is essentially the distributive
property. Do we introduce the
phrase at this point?

77. Strategy 2
Doubling

78. Strategy 4
Get 9 x 4 from 10 x 4

79. Unusual Response
Get 4 x 8 from 4 x 2. Can it be done? Does the number
of cups change? Does the number of counters per cup
change?

80. Differentiated Instruction
These are examples of how the lesson can be
differentiated for advanced learners.

82. Prior to learning multiplication, students
learn to make equal groups using concrete
materials. Marbles is the suggested
materials.

83. After that they represent these concrete
situations using, first, drawings ..

84. Open Lesson in Chile

85. … and, later, diagrams. Students also
write multiplication sentences in
conventional symbols.

86. First, equal groups –
three groups of four. Third, four multiplied three
times ….
Second, array –
Three rows of four

87. Textbook Study
Observe how equal group
representation evolves into array and
area models. Also observe how the
multiplication tables of 3 and 6 are
related on the flights of stairs.

88. They begin with equal group representation.

89. 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

90. In Primary 2, students learn
multiplication facts of 2, 5, 10 and 3
and 4. In Primary 3, they learn the
multiplication facts of 6, 7, 8 and 9.

91. Later, the array meaning of
multiplication is introduced.

92. Square tiles are subsequently used to lead to
the area representation of multiplication.

97. Open Lesson at Broomfield, Colorado

98. Students who were already good in the skill of multiplying two-digit number
with a single-digit number were asked to make observations. They were
asked “What do you notice? Are there some digits that cannot be used ta
all?”

99. Singapore Math
Drill-and-Practice Through
Problem Solving

100. Singapore Math
Three-Part Lesson

101. Singapore Math
Three-Part Lesson

103. Singapore Math
Three-Part Lesson

105. FUNDAMENTALS
of singapore
math The following slides are for additional
tasks that are discussed on the second
day for Grades 5 – 8
Mayflower Primary School, Singapore
Slides are available at
www.banhar.blogspot.com

114. Marcus gave ¼ of his coin collection to his sister
and ½ of the remainder to his brother.
As a result, Marcus had 18 coins.
Find the number of coins in his collection at first.
3 units = 18
8 units = ???
Marcus had 48 coins at first.