# What can you learn from 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.

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