What to understand in Number System
Rational/irrational numbers, decimal representation and number-line reasoning. The goal is to understand the underlying relationship, recognise the type of problem or concept, and explain each step rather than memorising an isolated answer.
PCDS study method
- Recall prerequisite ideas and definitions.
- Study one visual or real-life representation of the concept.
- Work through a model example with reasoning shown.
- Solve a similar problem independently.
- Review the exact error and retry without looking at the solution.
Original worked example
Is √18 rational or irrational? Simplify it.
Step 1: √18 = √(9×2)
Step 2: √18 = 3√2
Step 3: √2 is irrational, and multiplying by non-zero rational 3 remains irrational.
Answer: 3√2, irrational.
What an expert tutor should check
A good tutor should verify whether the student can explain the method in their own words, apply it to a changed question, and identify common traps—not merely copy the worked steps.