Introduction to Applying a Simple Model
Welcome to one of the most practical parts of the Thinking Skills syllabus! In the "Understanding and using information" section, you will often be asked to apply a simple model. Don't let the word "model" intimidate you—in this subject, a model is simply a set of rules, a formula, or a description that tells you how a system works.
Think of a model like the instructions for a board game or the pricing list at a coffee shop. Once you understand the rules, you can use them to work out the result for any situation. Mastering this skill is essential for success in Paper 1 (Problem Solving) and Paper 3 (Problem Analysis and Solution).
Note: If you need to learn how to find the data first, see the chapter on "Identify and select relevant information."
What is a "Simple Model"?
A simple model is a way of representing a real-world situation using logic or basic mathematics. It usually takes the form of:
• A Formula: For example, \( \text{Total Cost} = \text{Fixed Fee} + (\text{Price per Hour} \times \text{Hours}) \).
• A Set of Rules: For example, "A student passes if they score over 50% in the exam AND submit all their homework."
• A Process: A step-by-step method to reach a conclusion.
Your job is to take the "rules" provided in the exam text and apply them to the specific "facts" given in the question.
Step-by-Step: How to Apply a Model
Don’t worry if a problem seems complex at first. You can break it down using these three steps:
1. Identify the Model (The Rules)
Read the scenario carefully. Look for the "logic" of the situation. Is there a fixed cost? Does a rate change after a certain point?
Example: A car park charges \$5 for the first hour and \$2 for every hour after that.
2. Identify the Inputs (The Facts)
Look for the specific numbers or conditions the question is asking you to solve for.
Example: How much does it cost to park for 4 hours?
3. Execute the Calculation (The Application)
Plug your facts into the rules.
\( \text{First hour} = \$5 \)
\( \text{Remaining hours} = 4 - 1 = 3 \text{ hours} \)
\( \text{Cost for remaining hours} = 3 \times \$2 = \$6 \)
\( \text{Total} = \$5 + \$6 = \$11 \)
Real-World Example: The "Bonus Points" Model
Imagine a mobile phone company offers "Reward Points" based on this model:
"Customers receive 10 points for every \$1 spent. If a customer spends more than \$50 in a single month, they receive an additional 50 bonus points."
Question: How many points does Sarah get if she spends \$62 in June?
Applying the model:
1. Calculate standard points: \( 62 \times 10 = 620 \text{ points} \).
2. Check for the bonus: Did she spend more than \$50? Yes (\( \$62 > \$50 \)).
3. Add the bonus: \( 620 + 50 = 670 \text{ points} \).
Quick Review: If Sarah had spent only \$45, she would have received \( 45 \times 10 = 450 \text{ points} \), with no bonus added because she didn't meet the "over \$50" criteria.
Common Pitfalls to Avoid
Even top students can make small mistakes when applying models. Watch out for these:
• Mixing Units: If the model uses minutes but the question gives you hours, you must convert them first.
• Boundary Errors: Check if a rule says "more than 10" (which means 11, 12...) or "10 or more" (which includes 10).
• Ignoring the "Fixed" Element: Don't forget to add the initial fee or "starting value" if the model includes one (like the \$5 parking fee in our earlier example).
Applying Models in Paper 3
In Paper 3, the models are usually more detailed and mimic real-world scenarios more closely. You might have to combine several small rules together.
Key Advice for 2028 Exams: The syllabus now emphasizes "Communicating Reasoning." This means that even if your final answer is wrong, you can get marks for showing your working clearly. Always label your calculations (e.g., write "Cost before tax = \( \dots \)") so the examiner can follow your logic.
Key Takeaways
• A model is just a set of rules or a formula described in the text.
• To apply it, you must find the relevant data and follow the rules exactly.
• Always check for conditional rules (the "if/then" parts of the model).
• Show your working clearly to gain "partial credit" marks in longer questions.
Did you know? Computer programmers do this every day! Coding is essentially creating a complex model and then asking the computer to "apply" it to millions of pieces of data.