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

18. Nanakuli Elementary School, Hawaii

19. Nanakuli Elementary School, Hawaii

20. Nanakuli Elementary School, Hawaii

21. case study |

27. differentiation |

29. “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

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

31. Grade 1
Regular Program
Learning Support
Goh’s Report (1978) recommended a
differentiated education system for
Singapore.

32. 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

33. 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

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

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

36. what if students do not learn it

37. what if they already learnt it

38. model of
differentiation |

39. What to Differentiate
• Content
• Process
• Product

40. the content of instruction

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

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

43. the products produced by students that demonstrate
their learning

44. Levels of Differentiation
• Student Level
• Class Level

45. differentiation for the entire class

46. differentiation for groups
within a class

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

48. acceleration

49. enrichment

50. applying concepts|

53. Nanakuli Elementary School, Hawaii

54. Nanakuli Elementary School, Hawaii

55. concepts learning|

56. Cut into 4 equal parts.

57. Cut into 4 equal parts.

60. practice|

63. Nanakuli Elementary School, Hawaii

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

66. teaching of ratio |

79. word problem|

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

81. 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.

82. 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.

83. multiplication |

89. 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

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

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