*PROBLEMS & SOLUTIONS*?

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.