Introduction to Stating Assumptions

Hello! Welcome to one of the most important parts of Thinking Skills (9694). When we solve problems, we often make "leaps" in our thinking. We start with some information, do some calculations, and reach a conclusion. But sometimes, there is a hidden piece of the puzzle that we just take for granted. In this chapter, you will learn how to identify and state assumptions clearly.

Being able to state your assumptions is a key part of Communicating Reasoning. It shows that you understand the limits of your solution and that you’ve thought about what needs to be true for your answer to work in the real world.

What is an Assumption?

In the context of problem solving, an assumption is a piece of information that is not given in the problem but is required for your reasoning to be valid. It is something you treat as true so that your method or solution makes sense.

Think of it like a bridge:
If the Information Provided is on one side of a river and your Solution is on the other, the Reasoning is the bridge you build. If there is a gap in that bridge, the Assumption is the plank you lay down to cross it. Without that plank, you can't get to the solution!

Note: This is closely related to "Justifying the solution to a problem," but while justifying explains why you did something, stating assumptions explains what else must be true for that "why" to hold up.

Why Do We Need to State Assumptions?

In your exam (especially from the 2028 syllabus onwards), you are assessed on how well you communicate reasoning. Stating assumptions is vital because:

  • Clarity: it makes your thought process transparent to the examiner.
  • Accuracy: It acknowledges that real-world problems are often messy.
  • Logical Integrity: It shows you haven't just "guessed" but have considered the conditions of the problem.

Common Types of Assumptions in Problem Solving

When you are looking for assumptions within your reasoning, they usually fall into a few categories. Don't worry if these seem tricky; they usually become obvious once you ask, "But what if...?"

1. The "Constant Rate" Assumption

If you calculate that a car traveling \( 60 \) miles at \( 30 \) mph will take \( 2 \) hours, you are assuming the speed remains constant. In reality, the car might stop at traffic lights or slow down for a cow in the road!

2. The "No External Factors" Assumption

If you are scheduling a series of tasks that take \( 10 \) minutes each, you are assuming there are no delays between the tasks and that no external events (like a power cut or a lunch break) interrupt them.

3. The "Availability" Assumption

If your solution requires three people to work on a project at the same time, you are assuming that all three people are available and not busy with other tasks.

Step-by-Step: How to State an Assumption

If a question asks you to "State an assumption made within your reasoning," follow these steps:

Step 1: Look at your final answer.
What is the "big claim" you are making? (e.g., "The project will be finished by \( 5:00 \text{ PM} \).")

Step 2: Look at the data you used.
Did you use every single piece of information? Did you add any "rules" of your own?

Step 3: Ask the "What if" question.
Ask: "What could happen that would make my answer wrong, even if my math is perfect?"
If the answer is "The machine could break down," then your assumption is: "I am assuming the machine operates without breaking down."

Step 4: State it clearly.
Use the command word State: express it in clear, simple terms. Avoid being vague.

Examples in Action

Example Scenario 1: The Delivery Driver

Information: A driver needs to deliver \( 5 \) packages. Each delivery takes \( 10 \) minutes of driving and \( 5 \) minutes to drop off. The driver starts at \( 9:00 \text{ AM} \).
Reasoning: \( 5 \times (10 + 5) = 75 \) minutes. The driver will finish at \( 10:15 \text{ AM} \).
Stated Assumption: "I am assuming there is no time lost between completing one delivery and starting the drive to the next one," or "I am assuming there is no traffic congestion that increases driving time."

Example Scenario 2: The Ticket Sales

Information: A cinema has \( 100 \) seats. Tickets cost \( \$10 \) each. The cinema expects to make \( \$1000 \) for the evening show.
Reasoning: \( 100 \times \$10 = \$1000 \).
Stated Assumption: "I am assuming that every single seat will be sold (the show is sold out)."

Common Mistakes to Avoid

  • Stating a fact instead of an assumption: Don't just repeat a number from the question. If the question says "The price is \( \$5 \)," saying "I assume the price is \( \$5 \)" is not an assumption—it's a given fact!
  • Being too "wild": Don't assume something impossible or unrelated, like "I assume aliens don't steal the packages." Stick to logical, realistic factors.
  • Speculation vs. Assumption: As per the syllabus, speculations about the "author's intent" or the "mood of the characters" are not unstated assumptions in problem solving. Keep it focused on the logic and data.
Quick Review: Key Takeaways

1. Definition: An assumption is an unstated but necessary bridge in your logic.
2. Identifying: Ask what must stay true for your calculation to work in the real world.
3. Formatting: State it clearly and concisely. Use units and labels if referring to values (especially for the 2028 syllabus).
4. Context: In Paper 1, assumptions usually involve rates, time, availability, or the consistency of a model.

Keep practicing! The more problems you solve, the easier it becomes to spot those "hidden" steps you are taking. You've got this!