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Pearl City Hawaii 9 August 2011
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Pearl City Hawaii 9 August 2011

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This three-day professional development organized by Nanakuli Elementary School and Department of Education (State of Hawaii)

This three-day professional development organized by Nanakuli Elementary School and Department of Education (State of Hawaii)

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  • 1. Professional Development for
    Singapore Math (Upper Grades)
    Day 2 Session 1
    Open Lesson
    Visualization & Generalization
  • 2. Emphasis on Visualization & Generalization
    Draw a polygon with a total of 4 dots on the sides.
    Other than visualization, the ability to see patterns and to make generalization is another core intellectual competency.
  • 3. Nanakuli Elementary School, Hawaii
  • 4.
  • 5. Nanakuli Elementary School, Hawaii
  • 6. Nanakuli Elementary School, Hawaii
  • 7. Nanakuli Elementary School, Hawaii
  • 8. Professional Development for
    Singapore Math (Upper Grades)
    Day 2 Session 2
    Focus on
    Visualization
  • 9. Focus on Thinking: Visualization
    The area of the trapezoid.
    In Singapore Math, visualization is one of the core thinking skills.
  • 10. Focus on Thinking: Visualization
  • 11.
  • 12. Focus on Thinking: Visualization
    110g
    In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
  • 13. Focus on Thinking: Visualization
    110g
    290g
    In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
  • 14. Focus on Thinking: Visualization
    110g
    290g
    In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
  • 15. Focus on Thinking: Visualization
    110g
    ?
    ?
    In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
    290g
  • 16. Focus on Thinking: Visualization
    290 g – 110 g = 180 g
    180 g ÷ 2 = 90 g
    3 x 90 g = 270 g
    Bella puts 270 g of sugar on the dish.
    110g
    ?
    ?
    In Singapore Math, bar model method is a key strategy and it emphasizes visualization.
    290g
  • 17. Professional Development for
    Singapore Math (Upper Grades)
    Day 2 Session 3
    Focus on
    Generalization
  • 18. Focus on Thinking: Generalization
    2
    3
    4
    5
    6
    1
    10
    9
    8
    7
    11
    12
    13
    14
    15
    16
    20
    19
    18
    17
    21
    22
    23
    24
    25
    26
    30
    29
    28
    27
    31
    32
    33
    34
    35
    36
    In Singapore Math, patterning and generalization is an core intellectual competency.
  • 19. Focus on Thinking: Generalization
    2
    3
    4
    5
    1
    8
    7
    6
    9
    10
    11
    12
    13
    16
    15
    14
    17
    18
    19
    20
    21
    24
    23
    22
    25
    26
    27
    28
    29
    In Singapore Math, patterning and generalization is an core intellectual competency.
  • 20.
  • 21.
  • 22. 6 is shared equally between 2.
    6 ÷ 2 = 3
    In 6, how many 2s are there?
    6 ÷ 2 = 3
  • 23.
  • 24. 1÷12=2
     
    2÷12=2  2
     
    3÷12=3  2
     
    4÷12=4  2
     
    𝑛÷12=𝑛  2
     
  • 25. 1÷34=113
     
    2÷34=2  113
     
    3÷34=3  113
     
  • 26. Skemp
    Understanding in mathematics
    • relational
    (conceptual)
    • instrumental
    (procedural)
    • conventional
    Teaching for conceptual understanding is given emphasis in Singapore Math.
    Primary Mathematics Standards Edition Grade 6
    Primary Mathematics Standards Edition Grade 6
  • 27. Primary Mathematics Standards Edition Grade 6
  • 28. Professional Development for
    Singapore Math (Upper Grades)
    Day 2 Session 4
    Focus on
    Number Sense
  • 29.
  • 30. There were several ways the value of m was established
    • First, last and middle of the numbers used
    • 31. If there are more odd numbers in the list then m are odd
    Contributions from course participants
  • 32. The value of s was established in different ways
    • First + last + middle of the numbers used to get the middle s
    • 33. Three times the middle number to get the middle s
    • 34. The middle three consecutive numbers which is essentially the same as three times the middle number to get the middle s
    • 35. The first + second + last of the numbers used to get the smallest s
    For 72, 73, 74, 75 and 76, we can use the values of s for 2, 3, 4, 5, 6 – just add 210.
    Contributions from course participants