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Teaching of Ratio, Rate and Differentiated Instruction
This document provides information on differentiated instruction for mathematics incorporating ratios, whole numbers, and fractions. It discusses Singapore's approach to math education in the 1970s which focused on differentiated instruction based on learning theories. It also outlines models of differentiation including differentiating by content, process, product, student level, and class level. Examples are provided on teaching ratios and rates incorporating multiplication and division.
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Teaching of Ratio, Rate and Differentiated Instruction
- 1. DifferentiatedInstruction incorporating ratio, wholenumbers 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
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- 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 capitain 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.
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- 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.
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- 12. 29 + 52= 1 51
- 13. 29 + 52= 81 1 51
- 14. 29 + 52= 30 + 51 = 81
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- 29. “The idea ofdifferentiating 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 LearningSupport Goh’s Report (1978) recommended a differentiated education system for Singapore.
- 32. We want tomake 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 isreflected 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 itthat the teacher wants students to learn
- 35. how does ateacher know when students have learnt it
- 36. what if studentsdo not learn it
- 37. what if theyalready learnt it
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- 39. What to Differentiate •Content • Process • Product
- 40. the content ofinstruction
- 41. Grade 1 to4 Mathematics Foundation Mathematics Example Singapore Grade 5 and 6 Curriculum is an example of content differentiation.
- 42. the processes andtechniques used to help make sense of a given topic
- 43. the products producedby students that demonstrate their learning
- 44. Levels of Differentiation •Student Level • Class Level
- 45. differentiation for theentire class
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- 47. Differentiation for AdvancedLearners • Acceleration model • Enrichment model
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- 56. Cut into 4equal parts.
- 57. Cut into 4equal parts.
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- 65. Teaching of Ratio incorporatingmultiplication and division Yeap Ban Har yeapbanhar@gmail.com Marshall Cavendish Institute Slides are available at www.banhar.blogspot.com
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- 80. The number ofboys to the number of girls in a group was in the ratio 2 : 3.
- 81. The number ofboys 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 ofboys 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.
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- 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 threerate situations in real-life applications.
- 93. Rate Situations Constant Rate ConstantSpeed Graphical Approach Calculus 3 apples for $2 35 cents per pound