This document discusses differentiated instruction for teaching mathematical concepts like ratios, whole numbers, and fractions. It provides examples of how differentiated instruction can be implemented in areas like content, process, product, student level, and class level. Specific strategies are presented, such as using different models, acceleration and enrichment, to cater instruction to various student needs and abilities.

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. 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.

7. differentiated instruction in teaching basic concepts |

11. 29 + 52 =

12. 29 + 52 =
1 51

13. 29 + 52 = 81
1 51

14. 29 + 52 = 30 + 51 = 81

15. Charter Schools, Hawaii

16. Nanakuli Elementary School, Hawaii

17. Nanakuli Elementary School, Hawaii

18. multiplication |

23. differentiated instruction in teaching basic concepts:
another example |

25. Nanakuli Elementary School, Hawaii

26. Nanakuli Elementary School, Hawaii

27. Nanakuli Elementary School, Hawaii

28. differentiated instruction in application problems |

31. Charter Schools, Hawaii

32. Charter Schools, Hawaii

33. Charter Schools, Hawaii

34. Nanakuli Elementary School, Hawaii

35. Nanakuli Elementary School, Hawaii

36. case study |
Lesson Structure for DI
• Anchor Task
• Guided Practice
• Independent Practice

42. differentiation |

44. “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

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

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

47. 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

48. 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

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

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

51. what if students do not learn it

52. what if they already learnt it

53. model of
differentiation |

54. What to Differentiate
• Content
• Process
• Product

55. the content of instruction

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

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

58. the products produced by students that demonstrate
their learning

59. Levels of Differentiation
• Student Level
• Class Level

60. differentiation for the entire class

61. differentiation for groups
within a class

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

63. acceleration

64. enrichment

65. concepts learning|

66. Charter Schools, Hawaii

67. Charter Schools, Hawaii

68. practice|

69. Charter Schools, Hawaii

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

72. teaching of ratio |

76. word problem|

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

78. 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.

79. 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.