Welcome to Thinking Skills: Organising Information
Hello there! Welcome to the first step of becoming a master problem-solver. In the Thinking Skills (9694) syllabus, the very first thing we need to learn is how to Organise Information.
Think of this like tidying a messy room before you start looking for your car keys. If the information in your head is messy, solving the problem is much harder! In this chapter, we will learn how to pick out the important bits of a story, understand rules (models), and see how different pieces of data fit together like a puzzle. Don't worry if this seems tricky at first—once you learn the "tricks of the trade," it becomes much easier!
1.1 Understanding Information in Different Forms
In your exam, information won't always be a simple sentence. It might be hidden in a long story, a complicated table, or a confusing map. Your job is to be a "data detective."
Forms of Information
Information usually comes in three "flavours":
1. Text: A paragraph describing a situation (e.g., a story about someone catching a bus).
2. Tables: Numbers and categories arranged in rows and columns (e.g., a bus timetable).
3. Diagrams: Pictures, maps, or flowcharts (e.g., a map showing bus routes).
Extracting Relevant Information
The most important skill is ignoring distractors. These are bits of information that look important but don't actually help you solve the specific problem.
Example: If a question asks how much a bus ticket costs, and the text tells you the bus is blue, the driver's name is Bob, and the ticket is \$2.00, only the "\$2.00" is relevant. The rest is just "noise."
Combining Data Sets
Sometimes, the answer isn't in one place. You might need to take a price from a table and a discount code from a text paragraph to find the final answer.
The "Jigsaw" Rule: Treat every piece of information like a puzzle piece. You can't see the whole picture until you click them together!
Quick Review: The Filter Method
When reading a problem, ask yourself: "Does this specific number help me answer the final question?" If no, ignore it!
Key Takeaway: Problem solving starts with filtering out what you don't need and gathering the relevant bits from text, tables, and pictures.
1.2 Understanding Logical Relationships
Once you have the information, you need to understand the "rules of the game." In Thinking Skills, we call these models.
Simple Models and Thresholds
A model is just a set of instructions or rules.
Analogy: Think of a "Free Shipping" rule.
- If you spend under \$50, shipping is \$5.
- If you spend \$50 or more, shipping is \$0.
The "\$50" is called a threshold. It is the point where the rule changes. In your exam, always look for these "tipping points" where the calculation changes.
Necessary and Sufficient Conditions
This sounds like jargon, but it’s actually quite simple once you use an example:
1. Necessary Condition: Something that must happen for the result to occur.
Example: Having a battery is necessary for a mobile phone to turn on. (Without it, it’s impossible).
2. Sufficient Condition: Something that is enough to make the result occur on its own.
Example: Dropping your phone in a deep lake is sufficient to break it. (It’s not the only way to break it, but it's definitely enough to do the job!).
Mnemonic: The "N.S." Trick
Necessary = Needed.
Sufficient = So much that it's enough.
Deducing Original Data from Processed Data
Sometimes, you are given the "end result" (processed data) and have to work backwards to find the "start" (original data).
Example: If you know the average score of 3 students was 80, you can deduce the total points scored.
Using the formula: \( \text{Average} \times \text{Number of Items} = \text{Total} \)
\( 80 \times 3 = 240 \)
Even if you don't know the individual scores, you now know they must add up to 240. This is a powerful tool for solving mysteries!
Did you know? Many "logic puzzles" in magazines are just exercises in identifying necessary and sufficient conditions!
Common Mistake to Avoid: Don't confuse "Average" with "Every." If the average height in a room is 170cm, it doesn't mean everyone is 170cm. Someone could be 150cm and someone else could be 190cm!
Key Takeaway: Models are rules that often change at certain "thresholds." Understanding the difference between what is needed (necessary) and what is enough (sufficient) helps you navigate these rules.
Chapter Summary: Tips for Success
1. Read the question first: This tells you what information is relevant before you even start reading the long text.
2. Draw it out: If a model describes movement (like traffic through a junction), draw a simple sketch. It's much harder to make mistakes when you can see it.
3. Check the boundaries: When you see a rule (like a tax bracket or a shipping fee), check exactly what happens at the threshold. Is it "more than \$10" or "\$10 or more"? That one dollar makes a difference!
4. Stay calm: Some problems look scary because they have lots of numbers. Just remember: you only need a few of them to find the answer. Use your "filter"!
You've finished the first chapter! Great job. Organising information is the foundation for everything else in Problem Solving. Keep practicing picking out the "useful" from the "useless," and you'll be a pro in no time!