Teaching of Ratio and Rates & DI

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Teaching of Ratio and Rates & DI

  1. 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. 2. introduction |
  3. 3. | Hanusek, Jamison, Jamison & Woessmann2008
  4. 4. | Hanusek, Jamison, Jamison & Woessmann2008Score 1960-1970s 1980s 1990s 2000s500’s Japan Hong KongJapanKoreaHong KongJapanKoreaSingaporeHong KongJapanKoreaSingapore400’s Thailand PhilippinesSingaporeThailandMalaysiaThailandMalaysiaThailand300’s IndonesiaPhilippinesIndonesiaPhilippines
  5. 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. 6. opening examples |
  7. 7. In the 1970’s, Singapore needed a wayto help students, most of whom werenot performing well in mathematics,learn mathematics.CPA Approach based on Bruner’s workand a host of other learning theorieswere applied. Today, many people referto this approach as Singapore Math.
  8. 8. 29 + 52 =
  9. 9. 29 + 52 =1 51
  10. 10. 29 + 52 = 811 51
  11. 11. 29 + 52 = 30 + 51 = 81
  12. 12. Nanakuli Elementary School, Hawaii
  13. 13. Nanakuli Elementary School, Hawaii
  14. 14. Nanakuli Elementary School, Hawaii
  15. 15. case study |
  16. 16. differentiation |
  17. 17. “The idea of differentiatinginstruction is an approach toteaching that advocates activeplanning for and attention tostudent differences inclassrooms, in the context of highquality curriculums.”| www.caroltomlinson.com
  18. 18. Goh’s Report (1978)recommended adifferentiated educationsystem for Singapore.Grade 1 to 4MathematicsFoundationMathematics
  19. 19. Grade 1Regular ProgramLearning SupportGoh’s Report (1978)recommended adifferentiated education
  20. 20. We want to make our educationsystem even more student-centric, and sharpen our focusin holistic education – centred onvalues and characterdevelopment.| Heng 2011
  21. 21. Differentiated instruction isreflected in the ProfessionalLearning Communities (PLC) fourcritical questions| DuFour 2004Educational LeadershipMay 2004 | Volume 61 | Number 8Schools as Learning Communities
  22. 22. what is it that theteacher wants studentsto learn
  23. 23. how does a teacherknow when studentshave learnt it
  24. 24. what if students do notlearn it
  25. 25. what if they alreadylearnt it
  26. 26. model ofdifferentiation |
  27. 27. What to Differentiate• Content• Process• Product
  28. 28. the content of instruction
  29. 29. Grade 1 to 4MathematicsFoundationMathematicsExampleSingapore Grade 5 and 6 Curriculum isan example of content differentiation.
  30. 30. the processes and techniquesused to help make sense of agiven topic
  31. 31. the products produced bystudents that demonstrate theirlearning
  32. 32. Levels of Differentiation• Student Level• Class Level
  33. 33. differentiation for the entire class
  34. 34. differentiation for groupswithin a class
  35. 35. Differentiation for AdvancedLearners• Acceleration model• Enrichment model
  36. 36. acceleration
  37. 37. enrichment
  38. 38. applying concepts|
  39. 39. concepts learning|
  40. 40. Cut into 4 equal parts.
  41. 41. practice|
  42. 42. Teaching of Ratioincorporating multiplication and divisionYeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available atwww.banhar.blogspot.com
  43. 43. teaching of ratio |
  44. 44. word problem|
  45. 45. The number of boys to the number ofgirls in a group was in the ratio 2 : 3.
  46. 46. 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.
  47. 47. multiplication |
  48. 48. Teaching of Rate & Speedincorporating multiplication and divisionYeap Ban Haryeapbanhar@gmail.comMarshall Cavendish InstituteSlides are available atwww.banhar.blogspot.com
  49. 49. Rate SituationsIdentify three rate situations in real-life applications.
  50. 50. Rate SituationsConstant RateConstant SpeedGraphical ApproachCalculus3 apples for $235 cents per pound

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