Singapore Modelling Math

Modelling Math versus Usual Method

Marie had 20 m of cloth. She used 3/5 of it to make some dresses. How many meters of cloth did she use?
1. Model method:

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5 units = 20 m
1 unit = 20 / 5= 4 m
3 units= 3 x 4 = 12 m

2. Usual method:

3/5 x 20 = 12 m

The 2nd method is too abstract for 8 or 9 yr-old kids who will resort to learn fraction “x” or “/” formula by rote.
Models appear 'silly' to adults who prefer abstract concept '3/5 x 20';

Note 1:  Singapore Primary School Modelling Math

Adopted since 1990 from Polya’s “How to Solve It” (1945) 4-Step Problem Solving Process

1. Understand the problem in English Word Math.
2. Devise a plan: draw models
3. Carry out the plan: solve
4. Look back: verify

The Concrete-Pictorial-Abstract Math approach is developed by Dr. Kho Tek Hong (retired in 2007) & his MOE team @ 1980s.

Note 2: Models can also help visualize & 'concretize' Abstract Algebra (Set, Group, Coset, subgroup, kernel, isomorphism ...Galois theory). Feynman invented 'model' (Feynman diagram) to visualize quantum theory.