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# Seoul Foreign School Plenary Session

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This plenary session was for all teachers teaching mathematics in Grades 1 through 8. It is based on MAP101 Fundamentals of Singapore Mathematics.

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### Seoul Foreign School Plenary Session

1. 1. Professional Development Singapore Mathematics Seoul  9 – 11 July 2012 Dr Yeap Ban Har yeapbanhar@gmail.com Marshall Cavendish Institute Singapore Presentation slides are available at www.banhar.blogspot.com MAP101 www.mcinstitute.com.sg www.facebook.com/MCISingapore
2. 2. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
3. 3. IntroductionThis course is an overview of SingaporeMath. It includes the what and how ofteaching mathematics.
4. 4. Curriculum document is available at http://www.moe.gov.sg/
5. 5. THINKING SCHOOLSLEARNING NATION Singapore Ministry of Education 1997
6. 6. whatis singapore mathematics
7. 7. key focus of singaporemathematics
8. 8. problem solving
9. 9. thinking
10. 10. anexcellent vehicle for the development &improvement of a person’s intellectual competencies Ministry of Education Singapore 2006
11. 11. conceptualunderstanding
12. 12. FUNDAMENTALS of singapore math Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
13. 13. Singapore Math Visualization
14. 14. 110 g180 g 110 g Bella puts 180 g brown sugar on the dish. 290 g
15. 15. on an identical dish 110 g 2 units = 180 g 1 unit = 90 g 180 g 110 g 3 units = 270 g Bella puts 270 g brown sugar on the dish. 290 g
16. 16. Singapore Math is based on the CPA Apporach.Pictorial representations can be more concrete(pictures) or more abstract (diagrams such as barmodel).An alternate way to solve the brown sugarproblem:
17. 17. Singapore Mathematics focuses on the ability to visualize. For example, bar models are used extensively.Bar models were introduced to overcome thepervasive problems students had with word problems– even the basic ones.
18. 18. Such word problems are used to helpstudents Deal with information Handle and clarify ambiguity – one dish or two Develop visualization – bar models are used extensively Practice mental strategies – numbers used are not difficult to compute
19. 19. Singapore Math Visualization
20. 20. Procedural & Conceptual UnderstandingSingapore Math places an emphasis onboth. Procedures are explained in aconceptual way. For example, longdivision is seen simply as breakinglarge numbers into smaller ones beforedividing.
21. 21. Using number bonds to make sense of long divisionDifferentiated Instruction for advanced Over-learners – how does one get the result emphasizing of 51  3 from 60  3. procedural Balancing knowledge procedural knowledge with conceptual understanding
22. 22. Singapore MathPatterns & Generalization
24. 24. C H E R Y L
25. 25. C H E R Y L1
26. 26. C H E R Y L 2
27. 27. C H E R Y L 3
28. 28. C H E R Y L 4
29. 29. C H E R Y L 5
30. 30. C H E R Y L 6
31. 31. C H E R Y L 7
32. 32. C H E R Y L 8
33. 33. C H E R Y L 9
34. 34. C H E R Y L
35. 35. C H E R Y L
36. 36. C H E R Y L
37. 37. C H E R Y L
38. 38. C H E R Y L
39. 39. C H E R Y L Which letter is 99?
40. 40. Method 1The positions of 11, 22, 33 are at C, H, E respectively.Positions of multiples of 11 can be located. Method 4 The position for 99 can be found by writing out all the numbers Method 3 but this is not Numbers ending with 9 efficient are at E. So, 99 is at E method. Method 2 too. The positions of numbers ending with 1 and 6 can be located ta either ends. Thus 91 or 96 can be located. Subsequently, 99 can be located.
41. 41. D A V I D
42. 42. Method 1The letters under A and I areeven. So 99 cannot be there.Method 2The positions of numbers endingwith 9 form a diagonal pattern.Method 3The numbers under first Dincreases by 8. Thus 17 + 80 = 97is under first D. The position for99 can be worked out.Method 4The positions of multiples of 8 I isdefinitely under A. 8 x 12 = 96 isunder A. The position of 99 canbe worked out.Method 5Numbers under V is 1 less thanmultiples of 4. So, 2011 (1 lessthan 2012) is under V. 99 is lessthan 100.
43. 43. Method 2The positions of numbers ending with 9form a diagonal pattern.The methods were the ones thatparticipants in Chile came up with.
44. 44. Another MethodIn a course done in December 2010 with a group ofChilean teachers, there was a method that involvesdivision. For Cheryl, it was 99  10.For David, it was 99  8. Are you able to figure out thatmethod?
45. 45. Singapore MathPatterns & Generalization
46. 46. Singapore Mathematics: Focus on Problem Solving
47. 47. CPA Approach based onJerome Bruner was usedto learn division offractions – using paperfolding and subsequentdrawing.
48. 48. Singapore Mathematics: Focus on Conceptual Understanding
49. 49. Singapore MathLearn New Concept Through Problem Solving
50. 50. Textbook StudyObserve the various meanings ofmultiplication from Grade 1 to Grade3.
51. 51. Multiplication FactsWe do a case study on multiplicationfacts. We will see the use of an anchortask to engage students for anextended period of time.
52. 52. Strategy 1Get 3 x 4 from 2 x 4Strategy 2DoublingStrategy 3Get 7 x 4 from 2 x 4 and 5 x 4Strategy 4Get 9 x 4 from 10 x 4
53. 53. Strategy 1Get 3 x 4 from 2 x 4
54. 54. Strategy 3Get 9 x 4 from 4 x 4 and 5 x 4This is essentially the distributiveproperty. Do we introduce thephrase at this point?
55. 55. Strategy 2 Doubling
56. 56. Strategy 4Get 9 x 4 from 10 x 4
57. 57. Unusual ResponseGet 4 x 8 from 4 x 2. Can it be done? Does the numberof cups change? Does the number of counters per cupchange?
58. 58. Differentiated InstructionThese are examples of how the lesson can bedifferentiated for advanced learners.
59. 59. Prior to learning multiplication, studentslearn to make equal groups using concretematerials. Marbles is the suggestedmaterials.
60. 60. After that they represent these concretesituations using, first, drawings ..
61. 61. Open Lesson in Chile
62. 62. … and, later, diagrams. Students alsowrite multiplication sentences inconventional symbols.
63. 63. First, equal groups –three groups of four. Third, four multiplied three times ….Second, array –Three rows of four
64. 64. Textbook StudyObserve how equal grouprepresentation evolves into array andarea models. Also observe how themultiplication tables of 3 and 6 arerelated on the flights of stairs.
65. 65. They begin with equal group representation.
66. 66. 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 2021 22 23 24 25 26 27 28 29 30
67. 67. In Primary 2, students learnmultiplication facts of 2, 5, 10 and 3and 4. In Primary 3, they learn themultiplication facts of 6, 7, 8 and 9.
68. 68. Later, the array meaning ofmultiplication is introduced.
69. 69. Square tiles are subsequently used to lead tothe area representation of multiplication.
70. 70. Open Lesson at Broomfield, Colorado
71. 71. Students who were already good in the skill of multiplying two-digit numberwith a single-digit number were asked to make observations. They wereasked “What do you notice? Are there some digits that cannot be used taall?”
72. 72. Singapore MathDrill-and-Practice Through Problem Solving
73. 73. Singapore MathThree-Part Lesson
74. 74. Singapore MathThree-Part Lesson
75. 75. Singapore MathThree-Part Lesson
76. 76. FUNDAMENTALS of singapore math The following slides are for additional tasks that are discussed on the second day for Grades 5 – 8 Mayflower Primary School, SingaporeSlides are available atwww.banhar.blogspot.com
77. 77. Marcus gave ¼ of his coin collection to his sisterand ½ of the remainder to his brother.As a result, Marcus had 18 coins.Find the number of coins in his collection at first. 3 units = 18 8 units = ??? Marcus had 48 coins at first.