Year 9

# Monte Carlo Simulations

Students use the Monte Carlo method of problem solving by randomly generating data to calculate area and estimate π.

This is a classic reSolve sequence aligned with the Australian Curriculum V8.4. It is only available as a downloadable package.

Students learn how statistical techniques that rely on randomly generated data can be used to solve problems that have a defined solution that is difficult to solve using traditional methods.

This sequence is for students who:

• are familiar with proportions.
• are familiar with area formulae for trapezia, triangles and circles.
• can solve problems using Pythagoras’ theorem.

The tasks link different mathematical concepts through the generation of random points to estimate irregular areas and π.

### Lesson 1: Oil Spills

Students compare the efficiency and accuracy of different methods for calculating the area of an irregular shape, using the context of oil spill maps. They are introduced to the concept of the Monte Carlo method for calculating area.

### Lesson 2: Estimating Pi

Students use the Monte Carlo method to estimate the area of a quadrant of a circle. By comparing this with the formula for the area of a circle, students estimate the value of π.

Last updated June 21 2020.

This is a classic reSolve sequence aligned with the Australian Curriculum V8.4. It is only available as a downloadable package.