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1. Teaching Fundamental
Concepts in Fractions
~ using Problem Solving Approach~
Peggy Foo
Marshall Cavendish Institute

2. Focus of Singapore Math
 The central focus is on mathematical problem solving
Reasoning,
communication
and connections

3. Exercise vs Problem
 Find the sum  How many ways can I get 3?
275 + 418 = ___
−

4. Exercise vs Problem
Exercise Problem
 Complex
 Simple, straightforward
 Novel
 Familiar
 Do not have routine
 Use routine procedures
procedures

5. Problem Solving Approach
 Does not always have to come after teaching of basic
concepts and skills
 Can take place at the beginning of a topic to teach basic
concepts
 Teaching through problem solving

6. Teaching through Problem Solving
Problem 1
 Find different ways to represent halves and quarters?

7. Who is correct?
Problem 2
Allen thinks that ¼ of the rectangle is shaded. Sherlyn
thinks that Allen is wrong because the triangles are different?

8. Learning Points
 Allen is correct.
 Each equal part can be identical (same size and shape)
 Each equal part can also be of the same size but different
shape

9. Example
 4 parts are in equal size when the shapes are different.

10. Who is correct
Problem 3:
 From the previous task, Allen concludes that ½ is bigger than
¼. Sherlyn thinks Allen is wrong again.

11. Learning Points
 Allen is wrong.
 ½ may not be bigger than ¼.
 It depends on the quantity of the whole used.

12. Equivalent Fractions
Fold a piece of paper into 4 equal parts
Show 3 fourths
Fold the same strip into 8 equal parts.
How many eighths are equal to 3 fourths?
How many twelfths are equal to 3 fourths?

13. Mixed Numbers
Share 1 cake equally among 4 children
Share 3 cakes equally among 4 children
Share 5 cakes equally among 4 children