Introduction: Finding the Right Fit

Welcome! In this chapter of Thinking Skills, we are looking at a skill you actually use every single day. Whether you are filtering search results for a new pair of shoes, checking which movies are playing at a time you’re free, or seeing if you qualify for a student discount, you are identifying cases that satisfy given criteria. In Paper 1 (Problem Solving), this involves looking at a set of rules (the criteria) and a list of possibilities (the cases) to find out which ones work. Don't worry if this seems a bit technical at first—it’s all about being organized and reading carefully!

1. What are "Criteria" and "Cases"?

Before we dive in, let’s make sure we understand the two main "ingredients" of these problems:
  • Criteria: These are the rules or conditions that must be met. Think of them as a "checklist." For example: "Must be aged 18 or over" or "Must cost less than \( \$20 \)."
  • Cases: These are the individual items, people, or options you are checking against the criteria.

Quick Tip: In the exam, a "case" might be a row in a table, a person in a story, or a specific time slot in a schedule.

2. The "Filter" Method: A Step-by-Step Guide

To solve these problems without getting overwhelmed, follow this systematic approach:

Step 1: List the Criteria

Read the question carefully and pull out every single rule. Sometimes a rule is hidden in the text (e.g., "The shop is closed on Sundays" is a criterion for a shopping trip!).

Step 2: Check Cases One Rule at a Time

Instead of looking at one "case" and checking all rules, it is often faster to take one "rule" and cross out all the "cases" that break it. This is called elimination.

Step 3: Watch for the "Negative"

Sometimes the syllabus asks you to identify criteria not met by a proposed solution. This means looking at a case that failed and explaining exactly why it didn’t work.
Key Takeaway
Success in this chapter depends on accuracy, not speed. Missing even one small criterion (like "at least" vs. "more than") will lead to the wrong answer.

3. Common Mathematical Tricky Bits

Even though Paper 1 isn't a "Math paper," it uses mathematical language to set criteria. Keep an eye out for these terms:
  • "At least" / "Minimum": This means the number itself is included. (\( \ge \))
  • "More than" / "Exceeding": This means the number itself is not included. (\( > \))
  • "At most" / "Maximum": This means up to and including that number. (\( \le \))
  • "Inclusive": If a range is given as "Monday to Wednesday inclusive," it means Mon, Tue, and Wed are all okay.

Example: If a club requires you to be "over 16," a person who is exactly 16 does not satisfy the criteria.

4. Working Through an Example

Imagine you are helping a friend choose a gym membership. Here are the Criteria:
  1. Monthly fee must be under \( \$50 \).
  2. Must have a swimming pool.
  3. Must be open before \( 07:00 \).
The Cases (Gyms):
  • Gym A: Fee \( \$45 \), Pool: No, Opens \( 06:00 \).
  • Gym B: Fee \( \$55 \), Pool: Yes, Opens \( 05:00 \).
  • Gym C: Fee \( \$40 \), Pool: Yes, Opens \( 08:00 \).
  • Gym D: Fee \( \$48 \), Pool: Yes, Opens \( 06:30 \).
The Solution Process:
  • Check Rule 1 (Price < \( \$50 \)): Gym B is out.
  • Check Rule 2 (Pool): Gym A is out.
  • Check Rule 3 (Open before \( 07:00 \)): Gym C is out.
  • Result: Gym D is the only case that satisfies all criteria.

5. Avoiding Common Mistakes

1. The "Almost-Right" Trap: Many students pick a case that satisfies most of the rules but misses one small detail. Always double-check the entire checklist for your final answer.

2. Misreading "Units": From 2028 onwards, the syllabus emphasizes labeling your work. If a criterion is about "Total Weight in kg" and the data is in "grams," you must convert the units before checking if the case fits.

3. Forgetting the "Optimal" Connection: While this chapter is about identifying cases, it is often the first step to Finding Optimal Solutions (which you will study in a later chapter). Once you find all cases that could work, you might be asked to find the best or cheapest one.

Quick Review

  • Identify: Pick out the specific rules mentioned in the text.
  • Eliminate: Discard cases that break any of those rules.
  • Verify: Ensure the remaining case satisfies every single condition.
  • Communicate: (Especially for 2028 exams) Explain why a case fits or fails using clear labels and units.

Did you know? In Paper 1, even if you get the final answer wrong, you can often get "working marks" for showing your steps in checking the criteria. Always show your process!

Next Steps: Now that you can identify which cases fit, you're ready to move on to Search for solutions in simple situations, where you'll use these rules to find answers from scratch!