Both Methods (I) & (II) below does not use Algebra, which is not taught to primary school kids until secondary school (above 12 or 13 years old).
(I) Ancient Chinese Arithmetic Method:
例2：The sister is 13 years old this year, while the brother is 9 years old.
When the total of their ages is 40, how old will they be?
Trick: Age difference does not change over time, they + or – in tandem. When 2 ages change, the multiple between them also changes.
(II) Singapore Modeling Math:
Compare the Ancient Chinese Arithmetic (I) & Singapore Modeling Math (II):
- (II) is better for young kids to understand visually the logic behind,
- (I) is more a memorised trick but poor math education pedagogy. In [例 2] it is very hard for kids to understand why the 2 steps (40+4) & (40 – 4), although they lead to the correct answer.
- Singapore Modeling Math (II) is invented by the Singapore Professor Lee Peng Yee 李秉彝 from Nanyang Technological University (National Institute of Education) in the 1980s, combining: Ancient Chinese Arithmetic [as shown in (I)], Polya Problem Solving Methodology, Visual Graphical Modeling
- French Fields Medalist Cédric Villani recommended the Singapore Modeling Math Pedagogy to all primary schools in France.
- The most famous Chinese Ancient Arithmetic “The Chicken-Rabbit Problem” (《孙子算经》，dated 3 AD – 5 AD）which had inspired Prof Lee Peng Yee. Watch video “鸡兔问题 :“.
- The Physics Noble Prize Laureate Paul Dirac’s “Coconuts & Monkeys Problem” : use Higher Math (Sequence & Linear Algebra, solved by Prof Richard Halmos) vs Singapore Modeling Math (3rd solution) .