FRAC
 TION
  in singapore

 math
                                      Dr Yeap Ban Har
                          Marshall Cavendish Institute
                                            Singapore
Slides are available at      yeapbanhar@gmail.com

www.banhar.blogspot.com
This course is in two parts. Today
 FRAC                                                                we focus on pre-fraction ideas
                                                                       i.e. ideas learnt in the early

 TION                                                                grades which are important in
                                                                the learning of fraction as well as
  in singapore                                                       basic concept of fractions. We

 math                                                            will also examine fraction topics
                                                                typically taught in lower primary
                                                                     levels i.e. grades one to three.

                          MAP202 TEACHING OF FRACTIONS
Slides are available at   reviewing fundamentals of singapore math


www.banhar.blogspot.com
FRAC
 TION
  in singapore

 math
Slides are available at

www.banhar.blogspot.com
General Overview of Singapore and its
         Education System




                             Land
                               700 sq km

                             People
                               4.7 million
General Overview of Singapore and its
         Education System




 GDP per capita in current U.S. dollars
     1965      $510       2010     $43 300
General Overview of Singapore and its
              Education System
 Students
   500 000

 Teachers
   30 000

 Principals & Vice-Principals
   900

 Schools
   173 Primary Schools (Primary 1 – 6)
   155 Secondary Schools (Secondary 1 – 4)
   13 Junior Colleges (JC 1 – 2)
                                                                                          Canossa Convent Primary School Singapore
   15 Mixed-Level Schools

  The data refers to 1-12 school system. Pre-school is not part of the formal education
  system. The data excludes post-secondary education system which includes institutes
  of technical education, polytechnics and universities.
Universities

    National Examination
                                                   Institutes of
                                     Poly
                                                     Technical
                                   technics
                      Junior                        Education
                     Colleges


  Integrated
                                National Examination
 Programmes


                                  Secondary Schools



                      National Examination



                        Primary Schools


A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest
http://www.moe.gov.sg/education/education-statistics-digest/
THINKING SCHOOLS
LEARNING NATION
         Singapore Ministry of Education 1997
“Mathematics is an excellent
 vehicle for the development
and improvement of a person’s
  intellectual competencies”
                 Singapore Ministry of Education 2006
21st Century Competencies Framework
Singapore Ministry of Education 2011
FRAC
 TION
  in singapore

 math                     MAP202 TEACHING OF FRACTIONS
                          pre-numeracy
                          skills
Slides are available at

www.banhar.blogspot.com
Pre-Numeracy Skills
  Matching

  Sorting / Classifying
1
counting
 same
  units
number
 bonds




         Earlybird Kindergarten Mathematics
Photo: PCF Telok Blangah Kindergarten
adding
 same
 units
tens   ones



renaming
           1      3
1
1
1
1
1




               adding
renaming        same
                units
x + 2y      3x

            x + 2y   3y

x + 2y   3xy
FRAC
 TION
  in singapore

 math
                                      Dr Yeap Ban Har
                          Marshall Cavendish Institute
                                            Singapore
Slides are available at      yeapbanhar@gmail.com

www.banhar.blogspot.com
BASIC IDEAS OF FRACTIONS
FRAC
TION
the C P A
approach
FRAC
TION
the C P A
approach
FRAC
TION
mathematical
variability
FRAC
TION
conceptual
approach
FRAC
TION                       3
teaching for   3 fourths
                           4
meaning
St Edward’s School, Florida
St Edward’s School, Florida



Grade 2
concrete pictorial  abstract
FRAC
It does not show
half. What does it
   show then?                               TION
                                            opportunities for
                                            differentiation

                       It does not show
                     fourth. What does it
                          show then?
My Pals Are Here! Mathematics (Second Edition)
St Edward School, Florida


                  Initial
                 Concrete
                Experience


                                                  Subsequent
                                                    Pictorial
                                                 Representation
My Pals Are Here! Mathematics (Second Edition)
Eventual
  Symbolic
Representation
My Pals Are Here! Mathematics (Second Edition)
4 eighteenths




1 fourth                   8    9
                              +
                           36   36

           Singapore Examination & Assessment Board
           Primary School Leaving Examination
Primary 2   3 fifths + 1 fifth
3 fourths
            Primary 3   3 fifths + 1 tenth
3 pieces
3 pencils   Primary 4   3 fifths + 9 tenths
            Primary 5   3 fifths + 1 half
FRAC
TION
spiral
approach
COMPARING FRACTIONS
EQUIVALENT FRACTIONS
Lim Siong Guan
Head, Civil Service
        Singapore
We    discussed   teaching   We discussed   visualization
mathematics         versus   and         looking       for
teaching the ability to      patterns.   Also we discussed
learn mathematics and        generic competencies including

developing the belief        metacognition             and

that one can figure          collaboration.
things out by oneself.

MAP202a Teaching of Fractions 1

  • 1.
    FRAC TION in singapore math Dr Yeap Ban Har Marshall Cavendish Institute Singapore Slides are available at yeapbanhar@gmail.com www.banhar.blogspot.com
  • 2.
    This course isin two parts. Today FRAC we focus on pre-fraction ideas i.e. ideas learnt in the early TION grades which are important in the learning of fraction as well as in singapore basic concept of fractions. We math will also examine fraction topics typically taught in lower primary levels i.e. grades one to three. MAP202 TEACHING OF FRACTIONS Slides are available at reviewing fundamentals of singapore math www.banhar.blogspot.com
  • 3.
    FRAC TION in singapore math Slides are available at www.banhar.blogspot.com
  • 4.
    General Overview ofSingapore and its Education System  Land  700 sq km  People  4.7 million
  • 5.
    General Overview ofSingapore and its Education System  GDP per capita in current U.S. dollars 1965 $510 2010 $43 300
  • 6.
    General Overview ofSingapore and its Education System  Students  500 000  Teachers  30 000  Principals & Vice-Principals  900  Schools  173 Primary Schools (Primary 1 – 6)  155 Secondary Schools (Secondary 1 – 4)  13 Junior Colleges (JC 1 – 2) Canossa Convent Primary School Singapore  15 Mixed-Level Schools The data refers to 1-12 school system. Pre-school is not part of the formal education system. The data excludes post-secondary education system which includes institutes of technical education, polytechnics and universities.
  • 7.
    Universities National Examination Institutes of Poly Technical technics Junior Education Colleges Integrated National Examination Programmes Secondary Schools National Examination Primary Schools A detailed schematic diagram of Singapore’s education system is available in Education Statistics Digest http://www.moe.gov.sg/education/education-statistics-digest/
  • 10.
    THINKING SCHOOLS LEARNING NATION Singapore Ministry of Education 1997
  • 11.
    “Mathematics is anexcellent vehicle for the development and improvement of a person’s intellectual competencies” Singapore Ministry of Education 2006
  • 12.
    21st Century CompetenciesFramework Singapore Ministry of Education 2011
  • 14.
    FRAC TION in singapore math MAP202 TEACHING OF FRACTIONS pre-numeracy skills Slides are available at www.banhar.blogspot.com
  • 15.
    Pre-Numeracy Skills Matching Sorting / Classifying
  • 18.
  • 21.
  • 22.
    number bonds Earlybird Kindergarten Mathematics
  • 23.
    Photo: PCF TelokBlangah Kindergarten
  • 24.
  • 26.
    tens ones renaming 1 3
  • 27.
  • 28.
  • 29.
  • 30.
  • 31.
    1 adding renaming same units
  • 32.
    x + 2y 3x x + 2y 3y x + 2y 3xy
  • 33.
    FRAC TION in singapore math Dr Yeap Ban Har Marshall Cavendish Institute Singapore Slides are available at yeapbanhar@gmail.com www.banhar.blogspot.com
  • 34.
    BASIC IDEAS OFFRACTIONS
  • 35.
  • 36.
  • 37.
  • 38.
  • 39.
    FRAC TION 3 teaching for 3 fourths 4 meaning
  • 40.
  • 41.
    St Edward’s School,Florida Grade 2 concrete pictorial  abstract
  • 42.
    FRAC It does notshow half. What does it show then? TION opportunities for differentiation It does not show fourth. What does it show then?
  • 43.
    My Pals AreHere! Mathematics (Second Edition)
  • 44.
    St Edward School,Florida Initial Concrete Experience Subsequent Pictorial Representation My Pals Are Here! Mathematics (Second Edition)
  • 45.
  • 46.
    My Pals AreHere! Mathematics (Second Edition)
  • 47.
    4 eighteenths 1 fourth 8 9 + 36 36 Singapore Examination & Assessment Board Primary School Leaving Examination
  • 48.
    Primary 2 3 fifths + 1 fifth 3 fourths Primary 3 3 fifths + 1 tenth 3 pieces 3 pencils Primary 4 3 fifths + 9 tenths Primary 5 3 fifths + 1 half FRAC TION spiral approach
  • 49.
  • 52.
  • 57.
    Lim Siong Guan Head,Civil Service Singapore
  • 58.
    We discussed teaching We discussed visualization mathematics versus and looking for teaching the ability to patterns. Also we discussed learn mathematics and generic competencies including developing the belief metacognition and that one can figure collaboration. things out by oneself.