# reSolve: Monte Carlo Simulations

TLF ID M025322

This sequence of two lessons explores how statistical techniques that rely on randomly generated data can be used to solve problems. In the first lesson, students compare different methods for calculating the area of an irregular shape, using the context of oil spill maps. They are introduced to the Monte Carlo method for statistically calculating area. In the second lesson, they 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, they estimate the value of π. The lessons are outlined in detail including curriculum links, vocabulary, sample answers, spreadsheets of data, discussion points and student resources. This sequence is part of the reSolve: Maths by Inquiry program.

#### Educational details

Educational value
• This resource is very valuable for the year 9 mathematics content descriptions about calculating areas of composite shapes. In the first lesson, students are challenged to estimate the area of a complex, irregular shape using a variety of methods including using a series of grids, a series of trapezia and radiating triangles.
• The resource is also valuable for the year 9 mathematics content description about investigating Pythagoras' Theorem and its application to solving simple problems using right angled triangles. In the second lesson, students use Pythagoras' Theorem to calculate the distances from the origin to the point outside the circle for a series of randomly generated points, as part of their investigation to estimate the value of pi.
• The lessons are also of some value for the year 9 mathematics Statistics and Probability content descriptions about calculating relative frequencies and comparing data displays using mean to interpret numerical data sets. Throughout the lessons, students use relative frequencies to estimate the probabilities of data points lying inside a given set and then aggregate their class statistics, calculating mean results for larger sets of data.
• This resource also offers opportunities to link to the Numeracy General capability, as it engages students in solving and modelling area related problems involving complex data by estimating and calculating using a variety of efficient mental, written and digital strategies.
• This resource is also of pedagogical value as it supports teachers in building an inquiry-focused learning environment with authentic application of mathematical skills and understandings. The unit aims to develop content knowledge as well as assisting students to understand the process of inquiry.
Year level

9

Learning area
• Mathematics

#### Other details

Contributors
• Contributor
• Name: Education Services Australia
• Organization: Education Services Australia
• Description: Data manager
• URL: http://www.esa.edu.au/
• Name: Australian Government Department of Education and Training
• Organization: Australian Government Department of Education and Training
• Publisher
• Name: Australian Academy of Science
• Organization: Australian Academy of Science
• Description: Publisher
• URL: https://www.science.org.au/