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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.

Year level(s) Year 8, Year 9
Audience Teacher
Purpose Teaching resource
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)