Develop a model (2027 syllabus)

Q: What are the three main components of a logical model?

The three components are variables (changing values), constants (fixed values), and constraints (rules or limits).

Thinking Skills (9694) · Cambridge International A Level · 5 min read · Updated: 7 Sept 2026

Introduction to Developing a Model

Welcome to one of the most practical parts of the Thinking Skills course! In the context of "Analysing Information and Data," developing a model isn't about building a miniature airplane or walking a runway. Instead, it’s about creating a "mathematical or logical blueprint" of a real-world situation.

When you develop a model, you take a complex story—like a business trying to set prices or a school organizing a bus schedule—and turn it into a set of rules or equations. This allows you to predict what will happen or find the best possible solution. Don’t worry if this sounds intimidating; at its heart, modeling is just organized problem-solving.

What is a Model?

In your exam (specifically Paper 3: Problem Analysis and Solution), a model is a simplified representation of a situation. It helps you understand the logical relationships between different pieces of information.

A good model usually consists of:

Variables: The things that can change (e.g., the number of tickets sold, represented by $ n $).
Constants: The things that stay the same (e.g., the fixed cost of renting a hall, represented by $ \$200 $).
Constraints: The rules or limits you must follow (e.g., the hall can only hold $ 50 $ people).

Step-by-Step: How to Develop a Model

When you are faced with a long scenario in Paper 3, follow these steps to build your model:

1. Identify the Objective

Ask yourself: What am I trying to calculate? Is it the total cost? The minimum time? The maximum profit? Knowing your goal helps you decide which information is relevant.

2. List the "Rules of the Game" (Constraints)

Every problem has limits. Look for words like "maximum," "at least," "cannot exceed," or "must include."
Example: If a taxi can carry a maximum of $ 4 $ passengers, this is a constraint: $ \text{Passengers} \le 4 $.

3. Establish Relationships

This is where you connect the pieces. How does one piece of data affect another?
Example: If a plumber charges a call-out fee of $ \$50 $ plus $ \$30 $ per hour, the relationship for the total cost $ (C) $ based on hours $ (h) $ is:
$ C = 50 + 30h $

4. Test and Refine

Try putting a simple number into your model to see if it makes sense. If the plumber works for $ 2 $ hours, the cost should be $ 50 + (30 \times 2) = 110 $. If your calculation gives you a million dollars, you know your model needs fixing!

Quick Review: Developing a model is the process of translating a written scenario into a logical or mathematical system of variables and rules.

Applying the Model to a Situation

Once you have a model, the 2027 syllabus expects you to apply it. This means using your rules to solve the specific problem presented in the question.

Scenario Example:
A local cinema charges $ \$10 $ for adults and $ \$5 $ for children. The cinema must pay $ \$100 $ to the film distributor for every screening.
The Model: $ \text{Profit} = (10 \times \text{Adults}) + (5 \times \text{Children}) - 100 $.
The Application: If $ 15 $ adults and $ 10 $ children attend, what is the profit?
$ \text{Profit} = (10 \times 15) + (5 \times 10) - 100 $
$ \text{Profit} = 150 + 50 - 100 = 100 $

Did you know? In Paper 3, scenarios are often "progressive." This means you might develop a simple model in part (a), and then the question will ask you to adapt or refine it in part (b) by adding more complex rules!

Common Mistakes to Avoid

Ignoring Fixed Costs: Students often forget to include the "constant" (like a flat entry fee or a one-time setup cost) in their equations.
Mixing Units: Always check if the data is in different units (e.g., minutes vs. hours, or cents vs. dollars). Convert everything to a single unit before building your model.
Forgetting Constraints: It is easy to calculate a "mathematical" answer that is impossible in the "real world" (e.g., calculating that you need $ 4.2 $ buses—you can't have $ 0.2 $ of a bus, so you must round up to $ 5 $).

Pro-Tips for Exam Success (2027 Syllabus)

1. Show Your Working: The syllabus explicitly states that credit is awarded for correct steps towards a solution, even if your final answer is wrong. If you just write "Yes" or "No" without the underlying model, you might get zero marks.

2. Label Your Values: From the 2027/2028 guidance, it is highly recommended to label your calculations with words and units. Instead of just writing $ 500 $, write $ \text{Total Income} = \$500 $. This makes your reasoning clear to the examiner (and to yourself!).

3. Look for "Necessary and Sufficient" Conditions: Part of developing a model is knowing exactly what must happen (necessary) versus what is enough to make something happen (sufficient). Ensure your model reflects these logical requirements accurately.

Key Takeaway: When developing a model, start by identifying what stays the same (constants) and what changes (variables). Create a logical structure (equations or rules) that respects the limits (constraints) of the scenario. Always label your units and show every step of your reasoning.

Note: This chapter focuses on creating the model. For information on how to handle data transformations within these models, see the chapter on Transform data (2027 syllabus).

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is a model in the context of Thinking Skills?

A model is a simplified mathematical or logical blueprint of a real-world situation used to understand relationships and predict outcomes.

What are the three main components of a logical model?

The three components are variables (changing values), constants (fixed values), and constraints (rules or limits).

What is the first step in developing a model from a written scenario?

The first step is to identify the objective, which means determining exactly what you are trying to calculate (e.g., maximum profit or minimum time).

How do you identify constraints within a problem description?

Look for restrictive language such as "maximum," "at least," "cannot exceed," or "must include."

What does it mean to "establish relationships" in modeling?

It means connecting the data by determining how one piece of information mathematically affects another (e.g., creating an equation).

Why is it important to test and refine a model?

Testing helps you verify that your logic is correct by checking if simple inputs produce realistic and expected results.

What are the three common mistakes to avoid when building a model?

The three common mistakes are ignoring fixed costs, mixing units (e.g., minutes vs. hours), and forgetting real-world constraints.

Why is showing your working essential in the 2027 Thinking Skills syllabus?

Credit is awarded for correct steps towards a solution; providing only a final answer risks receiving zero marks if that answer is incorrect.

How should you label your values in the exam for maximum clarity?

Use words and units to label each calculation (e.g., writing "$ \text{Total Income} = \$500 $" instead of just "$ 500 $").

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