Welcome to Communicating Reasoning!

In the Thinking Skills (9694) syllabus, solving a problem is only half the battle. The other half is communicating how you solved it. This chapter focuses on "Show and label working clearly." Whether you are an expert at math or find problem-solving a bit intimidating, mastering this skill is the easiest way to boost your grade in Paper 1.

Think of your working like a map. If you just tell someone "I am at the park," they don't know how you got there. If you show them the map with the route you took, they can follow your logic—and even if you took one wrong turn, they can see you had the right idea!

Note: This chapter is part of the "Communicating reasoning in problem solving" section. For more on explaining the logic behind your steps, see the chapter on "Explain reasoning."

Why Showing Your Working is a "Grade-Saver"

In Paper 1 (Problem Solving), the exam is not multiple choice. You are required to write down your answers and the steps you took. Here is why clear working is essential:

  • Method Marks: Even if your final answer is wrong (perhaps because you typed a number into your calculator incorrectly), the examiner can still give you marks for the correct steps.
  • Required Evidence: For some questions—especially those with a "Yes" or "No" answer—credit may be withheld entirely if you do not show the working that led to that conclusion.
  • The 2028 Requirement: For students taking exams in 2028 and beyond, the syllabus explicitly states that you should label values and calculations with units and words.

Quick Tip: If a question asks you to "Show that..." or "Explain why...", the "working" is actually the most important part of the answer!

How to Label Your Working

Labeling means adding context to your numbers. A string of numbers like \(50 \times 1.2 = 60\) doesn't tell the examiner much. Using words and units makes it "labeled."

The "Words and Units" Rule

When you perform a calculation, tell the examiner what that number represents. Look at the difference between these two approaches to a simple problem about buying items:

The "Messy" Way (Risky):
\(10 \times \$5 = \$50\)
\(50 + \$2 = \$52\)

The "Labeled" Way (Best Practice):
\(Cost\ of\ items: 10 \times \$5 = \$50\)
\(Total\ cost\ with\ delivery: \$50 + \$2 = \$52\)

By adding "Cost of items" and "Total cost with delivery," you have communicated your reasoning clearly. If you accidentally wrote \(\$51\) as the total, the examiner can see your "Cost of items" was correct and give you credit for that step.

Step-by-Step: The Perfect Calculation

When you are solving a problem in the exam, follow these three simple steps to ensure your working is clear:

  1. Identify the element: Give the calculation a name (e.g., "Daily Rate" or "Number of Boxes").
  2. Show the operation: Write down the numbers you are adding, subtracting, multiplying, or dividing.
  3. Include the units: Always include \(\$\), \(kg\), \(cm\), \(hours\), etc., in your final step.

Example:
If a car travels \(150\ km\) in \(3\ hours\), don't just write \(50\).
Write: \(Average\ speed = 150\ km / 3\ hours = 50\ km/h\).

Common Mistakes to Avoid

Don't worry if you find this tedious at first; it becomes second nature with practice! Avoid these common pitfalls:

  • The "Mystery Number": Writing a result down without showing where it came from. If you write \(144\) on the page, the examiner has no idea if you did \(12 \times 12\) or \(140 + 4\).
  • Calculator "Ghosting": Doing everything on your calculator and only writing the final answer. If you hit a wrong button, you get zero marks. Write the calculation down before you type it into the calculator.
  • Scratchpad Scrawl: Writing bits of math all over the page in no particular order. Try to work vertically (down the page) so the examiner can follow your "path."

Memory Aid: The "ELU" Method

Whenever you write a line of working, check for ELU:

  • Element (What is this? e.g., "Profit")
  • Logic (How is it calculated? e.g., "\(Income - Cost\)")
  • Unit (What is the measurement? e.g., "\(\$\)")

Quick Review: Key Takeaways

Key Terms:

  • Communicating Reasoning: The skill of showing how you reached a conclusion.
  • Units: Labels like \(\$\), \(m\), or \(kg\) that give meaning to numbers.
  • Working: The intermediate steps and calculations used to find a solution.

Summary:

  • Paper 1 is a written paper where method matters as much as the answer.
  • Labeling calculations with words and units is a specific requirement (especially for the 2028 syllabus).
  • Clear working protects you from losing all marks if you make a simple calculation error.
  • Always explain what a number is, not just what the number is.

Did you know? Examiners often have a "mark scheme" that specifically says "1 mark for evidence of..." followed by a specific calculation. If that calculation isn't on your paper, they can't give you the mark, even if you clearly did it in your head!