Introduction: Why Your Working Matters

Have you ever solved a complex puzzle but couldn't explain to a friend how you did it? In Thinking Skills (9694), especially in Paper 3 (Problem Analysis and Solution), arriving at the right answer is only half the battle. The examiners want to see your "map"—the steps you took to get there.

Think of your working as a conversation with the examiner. This chapter focuses on showing and labeling your working clearly. By doing this, you ensure that even if you make a small calculation error at the end, you can still earn most of the marks for your logic and method. For the 2028 syllabus edition, this is no longer just a "good idea"—it is an explicit requirement for communicating your reasoning.

Note: For more on describing the logic behind your steps, see the chapter on "Explain reasoning".

1. What Does "Show Your Working" Actually Mean?

In Thinking Skills, "working" refers to any mathematical operation, deduction, or selection process you used to reach your conclusion. It is the evidence of your thinking.

Don't worry if this seems tricky at first! You don't need to write a novel. You just need to show the numbers you used and how you combined them. If a question asks for a "Yes" or "No" answer, providing the answer alone is often worth zero marks unless the supporting working is shown.

The Golden Rule of Partial Credit

In Paper 3, scenarios are long and complex. The examiners often award marks for correct steps even if the final answer is wrong. If you write down only the final (incorrect) answer, the examiner has no way to give you those "method marks."

2. The Art of Labeling (New for 2028)

Starting with the 2028 exams, the syllabus explicitly asks candidates to label their values and calculations with units and words. It isn't enough to just write \( 10 \times 5 = 50 \). You need to tell the examiner what those numbers represent.

How to Label Correcty

A good label includes two things:

  • The Description: What is this number? (e.g., "Total cost," "Number of students," "Time remaining")
  • The Unit: What is the measurement? (e.g., \( \$ \), \( kg \), \( hours \), \( meters \))

Example: The Toy Store Scenario

Imagine a problem where you need to find the profit from selling toys.
Poor Working: \( 5 \times 10 = 50 \)
Clear, Labeled Working: Income from toys sold on Monday: \( 5 \text{ toys} \times \$10 = \$50 \)

Quick Tip: Use the words already provided in the question to create your labels. If the question asks for "the total cost of the project," your label should be "Total cost of project."

3. Structuring Your Response

When problems get complicated, your page can quickly become a mess of scribbles. To keep things clear for both you and the examiner, follow these steps:

  1. Identify the Goal: What is the specific value you are trying to find in this step?
  2. State the Operation: Show the sum, subtraction, or multiplication clearly.
  3. Label the Result: Use a word or short phrase to identify what the result means.
  4. Final Answer Highlight: Clearly state your final answer at the bottom, often with a double underline or by writing it in the designated answer space.

Did you know? Using a calculator is essential for Paper 3 and strongly recommended for Paper 1. Even though you are using a calculator, you must still write down the calculation you performed on the paper!

4. Common Mistakes to Avoid

Even the brightest students lose marks by falling into these "clarity traps":

  • The "Ghost" Number: Writing a number down without showing where it came from. If you write "Cost = \( \$450 \)", but the numbers in the text were \( \$300 \) and \( \$150 \), you should write: \( \$300 + \$150 = \$450 \).
  • The Scribble Method: Doing your rough work in a corner and then writing only the final answer in the middle. The examiner might ignore the corner! Keep your main working in the center of the response area.
  • Missing Units: Writing "50" instead of "\( 50 \text{ minutes} \)" or "\( \$50 \)". In many problems, the unit is just as important as the number.
  • The Logic Jump: Skipping a step because it seems "obvious." Nothing is obvious to an examiner who is marking hundreds of papers. Show every step.

5. Step-by-Step Demonstration

The Scenario: A bus travels at \( 60 \text{ km/h} \) for \( 2 \text{ hours} \). Fuel costs \( \$2 \) per kilometer. What is the total fuel cost?

How a top-tier student shows working:
Distance traveled: \( 60 \text{ km/h} \times 2 \text{ hours} = 120 \text{ km} \)
Total fuel cost: \( 120 \text{ km} \times \$2/\text{km} = \$240 \)
Answer: \( \$240 \)

Why this works: Even if the student accidentally typed \( 60 \times 3 \) into their calculator, the examiner sees the label "Distance traveled" and the method "\( \text{speed} \times \text{time} \)" and can award partial marks.

Key Takeaways

Summary Checklist:
- Always show the calculations, even if you used a calculator.
- Use labels (words) to explain what each number represents.
- Include units (like \( \$ \), \( kg \), or \( m \)) in your working and final answer.
- Lay out your work line-by-line so it is easy to follow.
- Remember: In Paper 3, "Yes/No" answers almost always require supporting working to get full marks.

Final Encouragement: Clear working isn't just for the examiner—it helps you stay organized. If you get stuck halfway through a problem, looking back at your clearly labeled steps will help you find your way back to the solution!