The contents are arranged in units for progressive learning. The problem solving strategies are demonstrated using the variants of recent PSLE questions (2012 – 2016) in the Numbers and Algebra Strand. The solutions will highlight the foundation mathematics, illustrate mathematical skills and applied some classic problem solving strategies.
- Unit 1 Simple Practical Problems
- Unit 2 Practical Units Problems
- Unit 3 Simple Algebraic Problems
- Unit 4 Ratio Problems
- Unit 5 Fraction Problems
- Unit 6 Percentage Problems
- Unit 7 Distributive Property Problems
- Unit 8 Challenging Distributive Problems
- Unit 9 Challenging Problems
- Unit 10 Speed Problems
Our suggested three stages of learning are as follows:
For Primary Four at Foundation Level, (Unit 1 to Unit 3)
At this level, pupils will learn to
- understand mathematical situations and construct bar models,
- recognise commonly used mathematical models;
- visualise corresponding relations between two quantities;
- perform arithmetic operations on bar models,
- apply Euclidean Division Algorithm for cycle a&remainder situations,
- have an idea of the Unitary Method,
- acquire various algebraic manipulation skills for effective algebraic approach.
The learning tales place when pupils go through the contents in the following units
Unit 1: Simple Practical Problems.
Unit 2: Practical Units Problems.
Unit 3: Simple Algebraic Problems.
For Primary Five At Immediate level (Unit 4 – Unit 7)
At this level, pupils will solve harder problems with higher mathematical knowledge, they will be able to
- construct appropriate bar models for ratio situations and apply the Unitary Method;
- relate ratio situations to fraction and percentage situations for the same Ratio Approach;
- apply cumulative difference for mathematical deduction s to deal with distributive property situations.
The learning is running together with the examples and exercises in the following units.
Unit 4: Ratio Problems.
Unit 5: Fraction Problems
Unit 6: Percentage Problems
Unit 7: Distributive Property Problem
For Primary Six at Advanced level (Unit 8 – Unit 10)
To solve challenging problems, pupils will move on to learn
- the Chicken-Rabbit Approach to solve challenging distributive property problems;
- a grouping approach with LCM property for challenging counting problems;
- the use of the Greatest Common Unit procedure (based on Euclidean Algorithm) for advanced ratio approach;
- the bar modelling approach to time-distance corresponding relations for complex speed problems involving different journeys.
Pupils will learn through challenging problems in the following units :
Unit 8: Challenging Distributive Problems
Unit 9: Challenging Problems.
Unit 10: Speed Problems
Solutions to PSLE Questions
Solutions to some selected PSLE questions will be used to showcase the use of pictorial view in a problem solving approach to challenging problems.
Beyond PSLE – Bar Model Method for Primary Olympiad Mathematics
At this level, pupils will progress to learn the advanced problem solving skills for understanding the solutions to a wide range of complex problems appeared in the website barmodelhost.com, Alpha-beyond.com, our published articles and books.