Mathematical Thinking and Modelling

What is Mathematical Thinking?

• Its a food

• IT'S A SET OF COGNITIVE SKILLS USED TO ANALYZE PROBLEMS AND SITUATIONS WITH A MATHEMATICAL LENS.

• IT'S THE PROCESS OF TRANSLATING A REAL-WORLD PROBLEM INTO A MATHEMATICAL FRAMEWORK FOR ANALYSIS AND PREDICTION.

• IT'S A SET OF COGNITIVE SKILLS USED TO ANALYZE PEPLE AND SITUATIONS WITH A MATHEMATICAL LENS

Which of the following is NOT a key step in mathematical thinking?

• Observing patterns in data

• Experimenting with different approaches

• Memorising complex formulas

• Conjecturing possible solutions

1. In the context of mathematical thinking, what does "abstraction" refer to?

• Focusing on irrelevant details

• Identifying underlying relationships in a problem

• Repeating calculations multiple times

• Using specific numbers in an equation

1. You're planning a road trip and need to estimate how much gas you'll use. You consider the distance, your car's gas mileage, and typical traffic patterns. This scenario demonstrates which aspect of mathematical thinking?

• Argumentation

• Observation

• Exploration

• Conjecturing

1. A baker notices that using a specific ratio of flour to sugar consistently results in fluffy cakes. This is an example of:

• An unproven conjecture

• A completely random outcome

• A mathematical proof

• A coincidence with no explanation

1. Which of the following statements best reflects the power of mathematical thinking?

• It allows us to solve problems with a single formula.

• It helps us think logically and creatively in various situations.

• It guarantees us the correct answer to every problem.

• It requires advanced mathematical knowledge to be useful.

What is Mathematical Modelling?

• IT'S THE PROCESS OF TRANSLATING A REAL-WORLD PROBLEM INTO A MATHEMATICAL FRAMEWORK FOR ANALYSIS AND PREDICTION.

• IT'S A SET OF COGNITIVE SKILLS USED TO ANALYZE PROBLEMS AND SITUATIONS WITH A MATHEMATICAL LENS.

• IT INVOLVES A MULTI-STEP PROCESS: OBSERVATION, ABSTRACTION, EXPLORATION, CONJECTURING, AND ARGUMENTATION

• IT'S THE FOUNDATION. WE GATHER INFORMATION THROUGH OUR SENSES (SEEING, HEARING, TOUCHING) AND ANALYZE THE SITUATION AT HAND.

1. The first step in mathematical modelling involves:

• Solving complex mathematical equations.

• Identifying a real-world problem or question

• Developing a computer simulation.

• Interpreting the mathematical solution in the real-world context.

1. Which of the following is NOT a component of a mathematical model?

• Variables representing unknown quantities.

• Parameters representing fixed values.

• Real-world data used for validation.

• A narrative describing the problem.

1. A model that predicts population growth using birth and death rates is an example of a: . . .

• Physical model (like a miniature car)

• Conceptual model (like a flow chart)

• Mathematical model (using equations)

• All of the above.