National Singapore Math Summer Institute Denver 2011
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National Singapore Math Summer Institute Denver 2011 Presentation Transcript

  • 1. Core Elective
    Investigating
    Problem Solving
    DrYeap Ban Har
    Marshall Cavendish Institute
    Singapore
    banhar@sg.marshallcavendish.com
    Sculpture: Riverside Merchants
    Singapore River
    www.marshallcavendish.com/education/mci
  • 2.  
    Source: Mathematics Syllabus Primary
    Singapore Ministry of Education 2006
  • 3. St Edward School, Florida
    Princess Elizabeth Primary School, Singapore
  • 4. Archipelschool De Tweemaster – Kameleon,
    The Netherlands
  • 5. King Solomon Academy, London
  • 6. First Number
    88
    Second
    Number
    11 units = 88
    01 units = 08
    First Number = 6 x 8 = 48
    Second Number = 5 x 8 = 40
    The numbers are 40 and 48.
  • 7. National Singapore Math Summer Institute
    Denver, USA
  • 8. 2
    2
    3x = 8 + 2
    8
    8
    x = 10 ÷ 3
    10
  • 9. National Singapore Math Summer Institute
    Denver, USA
  • 10.
  • 11.
  • 12. National Singapore Math Summer Institute
    Denver, USA
  • 13. 27 x 5 = 150 – 15 = 135
    135 ÷ 3 = 40 + 5 = 45
    Each shelf had 45 books at first.
    National Singapore Math Summer Institute
    Denver, USA
  • 14. Other methods offered by participants
    Algebraic Method
    30x = 27(x + 5)
    Hence 30x = 27x + 27 x 5
    30x – 27x = 135
    3x = 135
    x = 45 where x is the number of books on each shelf at first
    Model Method
    The bar model may look rather cumbersome with one bar of 30 units and an equal bar of 27 longer units.
    5
  • 15. Draw a polygon with 4 dots on the sides and find its area.
    National Singapore Math Summer Institute
    Denver, USA
  • 16. Area
    Number of Dots
    National Singapore Math Summer Institute
    Denver, USA
  • 17. There was a hypothesis by a participant that the area is also related to dots shown by arrows – dots that are “untouched” by the polygon when the smallest possible rectangle is drawn around the polygon. Can you figure this one out?
    National Singapore Math Summer Institute
    Denver, USA
  • 18. Applying this hypothesis, the square has 4 “untouched” dots and the rhombus has 8 “untouched” dots
    National Singapore Math Summer Institute
    Denver, USA
  • 19. Archipelschool De Tweemaster – Kameleon,
    The Netherlands
  • 20. High School Attached to Tsukuba University, Japan
    Draw a polygon with no dots inside it. Investigate.
    A polygon has 4 dots on the perimeter. Find an expression for its area.
    www.marshallcavendish.com/education/mci