Welcome to Explaining Reasoning!

In Thinking Skills, finding the correct answer is only half the battle. To get full marks, especially in Paper 1 (Problem Solving), you need to show the examiner how you got there. This chapter focuses on the skill of explaining reasoning—making the "why" and the "how" of your solution crystal clear.

Don't worry if you find communicating your thoughts a bit tricky. Many students find it easier to do the math in their head than to write it down! These notes will help you turn those "head-calculations" into high-scoring exam answers.

What does "Explain" Actually Mean?

According to the official syllabus, the command word Explain requires you to do two things:

1. Set out purposes or reasons: Tell the examiner why you are doing a specific step.
2. Make relationships clear: Show how different pieces of information connect to each other.

In short: Don't just give the answer; tell the "story" of the solution using words, numbers, and units.

The Golden Rule: Labels and Units

One of the most important parts of explaining reasoning (especially for exams from 2028 onwards) is labelling your work. You should never have "naked numbers" floating on your page.

Bad Example:
\(10 \times 5 = 50\)

Good Example (with labels and units):
\(Price \times Quantity = Total\ Income\)
\(\$10 \times 5\ items = \$50\)

Why does this matter? If you make a small calculation error but your labels show that you had the right logic, the examiner can still give you "method marks." If you only provide a wrong number with no explanation, you get zero!

Quick Tip: The "Recipe" Analogy

Think of explaining reasoning like writing a recipe. If you just show someone a finished cake (the answer), they don't know how you made it. If you give them the ingredients and the steps (the reasoning), they can follow your logic from start to finish.

How to Construct an Explanation

When a question asks you to "Explain how..." or "Explain why...", follow these three steps:

1. Identify the Relevant Information

Before calculating, state which facts from the scenario you are using. This shows the examiner you have understood the information provided.

2. Show the Calculation/Step

Perform the logical or mathematical step. Always use the correct notation. For example, if you are finding a remainder, show the subtraction: \(Total\ (100) - Used\ (85) = Remainder\ (15)\).

3. Connect it to the Goal

Finish by saying what that result means for the problem. "Since 15 is less than the 20 required, the plan will not work."

The "Why" vs. The "How"

Sometimes you need to explain how a result is reached (the process), and sometimes you need to explain why a certain trend or pattern exists.

Example - Explaining a Trend:
If a shop's profit goes down even though they sold more items, your explanation might look like this:
"The profit decreased because the cost of materials rose by \(20\%\), which was greater than the \(10\%\) increase in sales revenue."

Key Takeaway

An explanation is Words + Math + Context. If you are missing any of those three, your explanation isn't fully "comprehensive."

Common Mistakes to Avoid

1. The "Silent Genius" Mistake: Writing down only the final answer. In Paper 1, credit is often withheld if the explanation needed to support the answer is missing—even if your answer is "Yes" or "No" and you got it right!

2. Mislabeling Units: Be careful with units like time. If your calculation results in \(1.5\ hours\), don't accidentally write it as \(1\ hour\ and\ 5\ minutes\). It should be \(1\ hour\ and\ 30\ minutes\).

3. Jumping Steps: If you use a complex model, don't skip to the end. Show the intermediate values. (Note: You can learn more about this in the chapter on "Show and label working clearly".)

Quick Review: Check your Explanations

Ask yourself these questions before moving to the next exam question:

  • Did I use words to describe what the numbers represent?
  • Did I include units (like \(\$\), \(kg\), or \(minutes\))?
  • Did I show the relationship between the pieces of data (e.g., "This is more than that, so...")?
  • If I got the final answer wrong, would a stranger still understand what I was trying to do?

Note: For more details on supporting your final choice, see the chapter on "Justify the solution to a problem with logical reasoning." If you need to mention things you've taken for granted, check "State assumptions made within reasoning."

Summary Key Points

- Explain means showing the "why" and "how" using evidence.
- Labels are essential for calculations (e.g., \(Income = items \times price\)).
- Logic is often worth more than the final number.
- Clarity helps the examiner award you marks even if you make a calculation error.