Teaching of Ratio, Rate and Differentiated Instruction

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  • 1. DifferentiatedInstructionincorporating ratio, whole numbers and fractionsCourse Code: MAP114, MAP115 and MAP116Yeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available atwww.banhar.blogspot.com
  • 2. introduction |
  • 3. | Hanusek, Jamison, Jamison & Woessmann 2008
  • 4. | Hanusek, Jamison, Jamison & Woessmann 2008Score 1960-1970s 1980s 1990s 2000s500’s Japan Hong KongJapanKoreaHong KongJapanKoreaSingaporeHong KongJapanKoreaSingapore400’s Thailand PhilippinesSingaporeThailandMalaysiaThailandMalaysiaThailand300’s IndonesiaPhilippinesIndonesiaPhilippines
  • 5. CountryGDP per capita incurrent USD2012Singapore 60,400Malaysia 16,900Thailand 10,100Philippines 4,400Upon separation from Malaysia in 1965, Singapore wasfaced with … high levels of unemployment andpoverty. 70% of Singapore’s households lived in badlyovercrowded conditions, and a third of its peoplesquatted in slums on the city fringes. Unemploymentaveraged 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, mostof whom were not performing well in mathematics, learnmathematics.CPA Approach based on Bruner’s work and a host of otherlearning theories were applied. Today, many people refer tothis approach as Singapore Math.
  • 8. 29 + 52 =
  • 9. 29 + 52 =1 51
  • 10. 29 + 52 = 811 51
  • 11. 29 + 52 = 30 + 51 = 81
  • 12. Nanakuli Elementary School, Hawaii
  • 13. Nanakuli Elementary School, Hawaii
  • 14. Nanakuli Elementary School, Hawaii
  • 15. Nanakuli Elementary School, Hawaii
  • 16. Nanakuli Elementary School, Hawaii
  • 17. case study |
  • 18. differentiation |
  • 19. “The idea of differentiating instruction is an approach toteaching that advocates active planning for andattention to student differences in classrooms,in the context of high quality curriculums.”| www.caroltomlinson.com
  • 20. Goh’s Report (1978) recommended adifferentiated education system forSingapore.Grade 1 to 4MathematicsFoundationMathematics
  • 21. Grade 1Regular ProgramLearning SupportGoh’s Report (1978) recommended adifferentiated education system forSingapore.
  • 22. We want to make our education system evenmore student-centric, and sharpen our focusin holistic education – centred on values andcharacter development.| Heng 2011
  • 23. Differentiated instruction is reflected in the ProfessionalLearning Communities (PLC) four criticalquestions| DuFour 2004Educational LeadershipMay 2004 | Volume 61 | Number 8Schools as Learning Communities
  • 24. what is it that the teacher wantsstudents to learn
  • 25. how does a teacher know whenstudents have learnt it
  • 26. what if students do not learn it
  • 27. what if they already learnt it
  • 28. model ofdifferentiation |
  • 29. What to Differentiate• Content• Process• Product
  • 30. the content of instruction
  • 31. Grade 1 to 4MathematicsFoundationMathematicsExampleSingapore Grade 5 and 6 Curriculum isan example of content differentiation.
  • 32. the processes and techniques used to help makesense of a given topic
  • 33. the products produced by students that demonstratetheir learning
  • 34. Levels of Differentiation• Student Level• Class Level
  • 35. differentiation for the entire class
  • 36. differentiation for groupswithin a class
  • 37. Differentiation for Advanced Learners• Acceleration model• Enrichment model
  • 38. acceleration
  • 39. enrichment
  • 40. applying concepts|
  • 41. Nanakuli Elementary School, Hawaii
  • 42. Nanakuli Elementary School, Hawaii
  • 43. concepts learning|
  • 44. Cut into 4 equal parts.
  • 45. Cut into 4 equal parts.
  • 46. practice|
  • 47. Nanakuli Elementary School, Hawaii
  • 48. Teaching of Ratioincorporating multiplication and divisionYeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available atwww.banhar.blogspot.com
  • 49. teaching of ratio |
  • 50. word problem|
  • 51. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.
  • 52. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.After ¼ of the boys and 69 girls leftthe group, there were 51 more girlsthan boys in the group.
  • 53. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.After ¼ of the boys and 69 girls leftthe group, there were 51 more girlsthan boys in the group.
  • 54. multiplication |
  • 55. Teaching of Rate & Speedincorporating multiplication and divisionYeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available atwww.banhar.blogspot.com
  • 56. Rate SituationsIdentify three rate situations in real-life applications.
  • 57. Rate SituationsConstant RateConstant SpeedGraphical ApproachCalculus3 apples for $235 cents per pound