Part A — Solving real-world problems with the modelling cycle
Mathematical modelling turns a real-world situation into maths, solves it, then checks the answer back in context. Follow the four stages every time.
Work through each problem using the four stages. Show your thinking at each stage, not just the answer.
Problem 1 — The class party. A class of 28 students is sharing pizzas. Each pizza is cut into 8 slices, and each student should get 2 slices.
- Analyse: What do we need to find? What information matters?
- Represent: Write an expression for the number of slices needed and the number of pizzas.
- Solve: How many pizzas must be ordered?
- Interpret: Pizzas are sold whole — does your answer need rounding? Explain.
Problem 2 — Order of operations. A shop sells pencils in packs of 6. Mr Lee buys 4 packs and 5 loose pencils, then gives 3 away. Write one number sentence (using brackets/order of operations) for how many pencils he has left, then solve it.
Problem 3 — Fractions, same denominator. A water tank is 3/8 full in the morning and 2/8 more is added at noon. Represent the situation, solve for the fraction full, and interpret: is the tank more or less than half full?