1. Bina Bangsa School, Jakarta
y e a p b a n h a r @ g m a i l . c o m
w w w . b a n h a r . b l o g s p o t . c o m
Teaching of
Measurements

2. Course Content
• Some Data on Student Achievement
• Review – Problem-Solving Approach
• Review – Learning Theories
• Case Study – Area & Volume
• Challenging Problem Solving
The slides shown during the course are included here. Photographs of the board
are on TEACH Facebook.East Coast Primary School, Singapore

3. The focus on problem solving and
thinking rather than on content is one
of the key features of mathematics
teaching and learning in various
education systems.
East Coast Primary School, Singapore

4. Mathematics is “an excellent vehicle for the
development and improvement of a person’s
intellectual competence”.
Ministry of Education, Singapore (2006)
thinkingschools
learningnation

5. Ministry of Education, Singapore (1991, 2000, 2006, 2012)

8. The twin goals of mathematics in the basic
education levels, K-10 are Critical Thinking and
Problem Solving.
Mathematical problem solving is finding a way
around a difficulty, around an obstacle, and
finding a solution to a problem that is unknown.
Department of Education, The Philippines (2012)

10. Singapore Math allows average
learners perform at a high level. The
following are some data from some
international research on math
achievement and attitude.
East Coast Primary School, Singapore

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

12. mathematics

13. gradefourmathematics
Singapore
South Korea
Hong Kong
Taiwan
Japan
Northern Ireland
Belgium
Finland
England
Russia
International
43
39
37
34
30
24
10
12
18
13
4
78
80
80
74
70
59
50
49
49
47
28
94
97
96
93
93
86
89
85
78
82
69
99
100
99
99
99
96
99
98
93
97
90
606
605
602
591
585
562
549
545
542
542
500
advanced
high
intermediate
low
average

14. gradeeightmathematics
South Korea
Singapore
Taiwan
Hong Kong
Japan
Russia
Israel
Finland
United States
England
International
47
48
49
34
27
14
12
4
7
8
3
77
78
73
71
61
47
40
30
30
32
17
93
92
88
89
87
78
68
73
68
65
46
99
99
96
97
97
95
87
96
92
88
75
613
611
609
586
570
539
516
514
509
507
500
advanced
high
intermediate
low
average

15. gradeeightmathematics
Singapore
Malaysia
Thailand
Indonesia
International
48
2
2
0
3
78
12
8
2
17
92
36
26
15
46
99
65
55
43
75
611
440
427
386
500
advanced
high
intermediate
low
average

20. Case Study - Area
East Coast Primary School, Singapore

21. Case Study - Volume
East Coast Primary School, Singapore

22. 40 cm x 30 cm x 60 cm = 72 000 cm3
72 000 cm3 ÷ 5 x 3 = 43 200 cm3
43 200 cm3 ÷ 1800 cm2 = 24 cm

23. 40 cm x 30 cm x 60 cm = 72 000 cm3
72 000 cm3 ÷ 5 x 2 = 28 800 cm3
28 800 cm3 ÷ 1200 cm2 = 24 cm

24. Challenging Problems – Money and
Other Measurement Topics
East Coast Primary School, Singapore

25. Weiyang started a savings plan by putting 2
coins in a money box every day. Each coin was
either a 20-cent or 50-cent coin. His mother
also puts in a $1 coin in the box every 7 days.
The total value of the coins after 182 days was
$133.90.
(a) How many coins were there altogether?
(b) How many of the coins were 50-cent coins?

26. Weiyang started a savings plan by putting 2
coins in a money box every day. Each coin was
either a 20-cent or 50-cent coin. His mother
also puts in a $1 coin in the box every 7 days.
The total value of the coins after 182 days was
$133.90.
(a) How many coins were there altogether?
(b) How many of the coins were 50-cent coins?
182  7 = 20 + 6 = 26
182 x 2 + 26 = 364 + 26 = 390
There were 390 coins altogether.

27. Weiyang started a savings plan by putting 2
coins in a money box every day. Each coin was
either a 20-cent or 50-cent coin. His mother
also puts in a $1 coin in the box every 7 days.
The total value of the coins after 182 days was
$133.90.
(a) How many coins were there altogether?
(b) How many of the coins were 50-cent coins?
$133.90 - $26 = $107.90
There were  50-cent coins.
50-cent 20-cent
 