1. DifferentiatedInstruction
incorporating ratio, whole numbers and fractions
Course Code: MAP114, MAP115 and MAP116
Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute
Slides are available at
www.banhar.blogspot.com

2. introduction |

3. | Hanusek, Jamison, Jamison & Woessmann
2008

4. | Hanusek, Jamison, Jamison & Woessmann
2008
Score 1960-1970s 1980s 1990s 2000s
500’s Japan Hong Kong
Japan
Korea
Hong Kong
Japan
Korea
Singapore
Hong Kong
Japan
Korea
Singapore
400’s Thailand Philippines
Singapore
Thailand
Malaysia
Thailand
Malaysia
Thailand
300’s Indonesia
Philippines
Indonesia
Philippines

5. Country
GDP per capita in
current USD
2012
Singapore 60,400
Malaysia 16,900
Thailand 10,100
Philippines 4,400
Upon separation from Malaysia in 1965, Singapore was
faced with … high levels of unemployment and
poverty. 70% of Singapore’s households lived in badly
overcrowded conditions, and a third of its people
squatted in slums on the city fringes. Unemployment
averaged 14%, GDP per capita was less than $2,700,
and half of the population was illiterate.

6. opening examples |

7. In the 1970’s, Singapore needed a way
to help students, most of whom were
not performing well in mathematics,
learn mathematics.
CPA Approach based on Bruner’s work
and a host of other learning theories
were applied. Today, many people refer
to this approach as Singapore Math.

11. 29 + 52 =

12. 29 + 52 =
1 51

13. 29 + 52 = 81
1 51

14. 29 + 52 = 30 + 51 = 81

15. Nanakuli Elementary School, Hawaii

16. Nanakuli Elementary School, Hawaii

17. Nanakuli Elementary School, Hawaii

18. case study |

24. differentiation |

26. “The idea of differentiating
instruction is an approach to
teaching that advocates active
planning for and attention to
student differences in
classrooms, in the context of high
quality curriculums.”
| www.caroltomlinson.com

27. Goh’s Report (1978)
recommended a
differentiated education
system for Singapore.
Grade 1 to 4
Mathematics
Foundation
Mathematics

28. Grade 1
Regular Program
Learning Support
Goh’s Report (1978)
recommended a
differentiated education

29. We want to make our education
system even more student-
centric, and sharpen our focus
in holistic education – centred on
values and character
development.
| Heng 2011

30. Differentiated instruction is
reflected in the Professional
Learning Communities (PLC) four
critical questions
| DuFour 2004
Educational Leadership
May 2004 | Volume 61 | Number 8
Schools as Learning Communities

31. what is it that the
teacher wants students
to learn

32. how does a teacher
know when students
have learnt it

33. what if students do not
learn it

34. what if they already
learnt it

35. model of
differentiation |

36. What to Differentiate
• Content
• Process
• Product

37. the content of instruction

38. Grade 1 to 4
Mathematics
Foundation
Mathematics
Example
Singapore Grade 5 and 6 Curriculum is
an example of content differentiation.

39. the processes and techniques
used to help make sense of a
given topic

40. the products produced by
students that demonstrate their
learning

41. Levels of Differentiation
• Student Level
• Class Level

42. differentiation for the entire class

43. differentiation for groups
within a class

44. Differentiation for Advanced
Learners
• Acceleration model
• Enrichment model

45. acceleration

46. enrichment

47. applying concepts|

50. concepts learning|

51. Cut into 4 equal parts.

54. practice|

59. Teaching of Ratio
incorporating multiplication and division
Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute
Slides are available at
www.banhar.blogspot.com

60. teaching of ratio |

73. word problem|

74. The number of boys to the number of
girls in a group was in the ratio 2 : 3.

75. The number of boys to the number of
girls in a group was in the ratio 2 : 3.
After ¼ of the boys and 69 girls left
the group, there were 51 more girls
than boys in the group.

76. multiplication |

82. Teaching of Rate & Speed
incorporating multiplication and division
Yeap Ban Har
yeapbanhar@gmail.com
Marshall Cavendish Institute
Slides are available at
www.banhar.blogspot.com

83. Rate Situations
Identify three rate situations in real-life applications.

85. Rate Situations
Constant Rate
Constant Speed
Graphical Approach
Calculus
3 apples for $2
35 cents per pound