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reSolve: Monte Carlo Simulations

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 pi (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: Mathematics by Inquiry program.

Additional details
Year level(s)	Year 8, Year 9
Audience	Teacher
Purpose	Teaching resource
Format	Downloadable resources
Teaching strategies and pedagogical approaches	Mathematics investigation
Keywords	area, central tendency, polygons, statistical frequency, mean, median, pi
Curriculum alignment
Curriculum connections	Numeracy
Strand and focus	Statistics, Build understanding, Apply understanding, Measurement
Topics	Chance and probability, Data representation and interpretation
AC: Mathematics (V9.0) content descriptions	AC9M8M01 Solve problems involving the area and perimeter of irregular and composite shapes using appropriate units AC9M8M06 Use Pythagoras' theorem to solve problems involving the side lengths of right-angled triangles AC9M9P02 Calculate relative frequencies from given or collected data to estimate probabilities of events involving "and", inclusive "or" and exclusive "or" AC9M9ST03 Represent the distribution of multiple data sets for numerical variables using comparative representations; compare data distributions with consideration of centre, spread and shape, and the effect of outliers on these measures
Numeracy progression	Interpreting and representing data (P8) Multiplicative strategies (P9) Understanding chance (P6) Understanding geometric properties (P7) Understanding units of measurement (P9, P10)
Copyright details
Organisation	reSolve Maths by Inquiry
Copyright	© Australian Government Department of Education, Skills and Employment 2021. Creative Commons BY-NC-SA 4.0.