The document announces an international education seminar on January 4th 2012 in Singapore to introduce the Singapore method for teaching mathematics. The seminar will be led by Dr. Yeap Ban Har and will include presentations and workshops on the basic theories and models used in the Singapore approach, such as the bar model for problem solving. A schedule and contact information is provided for those interested in learning more about the Singapore math teaching method.

1. Seminario Internacional de Educación
Conocer el método Singapur
para la enseñanza de matemáticas
4 January 2012
Dr Yeap Ban Har
banhar@sg.marshallcavendish.com
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com

2. Seminario Internacional de Educación
Conocer el método Singapur
para la enseñanza de matemáticas
8:30 a 9:00 Acreditación
9:00 a 9:15 Inauguración: Presentación Dr. Ban Har
9:15 a 10:30 Plenaria 1:
Teorías básicas en la enseñanza de matemáticas
10:45 Preguntas
11:00 a 11:30 Café
11:30 a 13:00 Continuación Plenaria 1
13:00 a 14:00 Almuerzo
14:00 a 16:00 Plenaria 2:
El modelo de las barras
en la enseñanza de resolución de problemas
16:00 Café
16:30 a 18:00 Continuación Plenaria 2
18:00 Cierre MAP101 & MAP111

3. What to teach in
mathematics so
that it is useful
to students. How to teach it
so that all
children can
learn it well.

4. what
is singapore
mathematics

5. Singapore Mathematics: Focus on Thinking
an
excellent
vehicle
for the development
&improvement of
a person’s intellectual
competencies
Ministry of Education Singapore 2006

6. See Page 4

7. 110 g
180 g 110 g
Bella puts 180 g brown sugar on the dish.
290 g

9. 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.
See also Page 70 290 g

10. There was a discussion
about the fact that the
total weight is
ambiguous. In the case
where we take the total
weight to be the total of
the dish and Bella’s
sugar, the solution is a
shown in .

11. Fundamental of Singapore Method
Singapore Mathematics
focuses on the ability to
visualize. For
example, bar models are
Singapore Mathematics used extensively.
focuses on the ability to
handle information.
Hence the emphasis on
word problems.

12. Singapore Math
Visualization

13. See Page 5

14. C H E R Y L

15. C H E R Y L
1

16. C H E R Y L
2

17. C H E R Y L
3

18. C H E R Y L
4

19. C H E R Y L
5

20. C H E R Y L
6

21. C H E R Y L
7

22. C H E R Y L
8

23. C H E R Y L
9

24. C H E R Y L

25. C H E R Y L

26. C H E R Y L

27. C H E R Y L

28. C H E R Y L

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

31. D A V I D

33. Methods
Method 1: Look at the ones digit. 99 has 9
as the ones digit. So it is at E.
Method 2: Use division. One method
divides 99 by 6 but this was found to be a
coincidence. Later, it was found that
dividing by 10 works.
Another method subtracts 6 before
dividing by 10.
Method 3: Look at the first column – 1, 11, 21, 31, 41 – hence 101 is at C. 99 can then be
found by working backwards.

34. Can the three methods
be used for DAVID?
Two new methods were
given for DAVID
Method 4
See the pattern as
DAVIDIVA. This is confirm
by difference of 8
between 1 and 9, 9 and
17 etc.
Method 5
Notice 4n – 1 (1 less than
multiple of 4) under the
letter V.

35. Fundamental of Singapore Method
Singapore Mathematics
focuses on the ability to
see patterns and make
generalizations.

36. Singapore Math
Patterns & Generalization

37. Singapore Mathematics: Focus on Problem Solving
See Page 6

38. See Page 7

43. CPA Approach based on
Jerome Bruner was
used to learn division of
fractions – using paper
folding and subsequent
drawing.
See Page 10

44. Singapore Math
Learn New Concept Through
Problem Solving

45. How many 4s are there in 12? 12 ÷ 4 = 3

46. Seminario Internacional de Educación
Conocer el método Singapur
para la enseñanza de matemáticas
4 January 2012
Dr Yeap Ban Har
banhar@sg.marshallcavendish.com
Marshall Cavendish Institute Singapore
Presentation slides are available at
www.banhar.blogspot.com

47. Fundamental of Singapore Method
Singapore Mathematics
focuses on the ability to
visualize. For
example, bar models are
used extensively.

48. What is the Bar Model Method?

49. 5 units = 60
1 units = 60 : 5 = 12
8 units = 8 x 12 = 80 + 16 = 96
Number of women There are 96 people at the party.
Number of men
Number of children
Correction: In the Spanish course
book, it should be “1/6 del resto son
hombres.”

51. Bar Model Method
In Early Grades

55. Correction: In the Spanish course
Jack book, it should be “el doble de Kyla”.
Kyla
3 units = $300
1 units = $300 : 3 = $100
Kyla gets $100.

57. Larry
Maria
4 units = $300
1 units = $300 : 4 = $75
3 units = 3 x $75 = $300 - $75 = $225
Maria gets $225.

59. What if the larger number is 58?
1st Number
Then the smaller number is 58 – 12 = 46.
2nd Number 12
What if the sum of the numbers is 58?
58 + 12 = 70 58 – 12 = 46
The larger number is 70. 46 : 2 = 23
Then the smaller number is 23 and the
larger number is 23 + 12 = 35.

61. 58 – 12 = 46
Peter
46 : 2 = 23
Natalia 12 Peter’s bag weighs 23 kg.
Natalia’s bag weighs 23 kg + 12 kg = 35 kg.

62. Basic Models include Part-Whole Model
and Comparison Model

63. Mathematics to develop visualization
through bar models, number sense
through mental calculation, and ability to
manage information through word
problems.

64. 1st Day
2nd Day 4
3rd Day 4 4
4th Day 4 4 4
250
5th Day 4 4 4 4
6th Day 4 4 4 4 4
7th Day 4 4 4 4 4 4
8th Day 4 4 4 4 4 4 4

65. 1+2+3+4+5+6+7+8+9=?
1st Day
There are 45 fours.
2nd Day 4 45 x 4 = 180
10 units = 250 – 180 = 70
3rd Day 4 4 01 units = 70 : 10 = 7
4th Day 4 4 4 She made (7 + 9 x 4) = 43 paper
cranes on the last day. 250
5th Day 4 4 4 4
6th Day 4 4 4 4 4
7th Day 4 4 4 4 4 4
8th Day 4 4 4 4 4 4 4

67. Sam
Terry 72
Vanessa

68. Pablo
Wynn
?
Zena
100

69. Advanced Techniques

70. 270
110

71. 2 units = 160 g
1 units = 160 g : 2 = 80 g
The container weighs
270 110 g – 80 g = 30 g
Using algebra
x+ 3y = 270
x + y = 110
110 So, 2y = 160
y = 160 : 2 = 80
x + y = 110
So, x = 30
The container weighs 30 g.

72. x y y y
270
x y
110

73. boys
34
girls

74. boys
68
girls

75. boys
88 – 68 = 20
girls

76. boys
88 – 68 = 20
girls

77. boys
girls

78. boys
girls

79. boys 2 girls units = 14
34 1 girls unit = 7
girls 3 girls units = 21
21 girls wear spectacles.
34 – 20

80. Homework

81. cookies cake 3,6 kg

82. cookies

83. cookies
cookies

84. basketball
soccer Answer: 60
basketball
soccer
Answer: 100

85. basketball
soccer
Answer: 84

86. 210