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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 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 content descriptions 
ACMMG216
Calculate areas of composite shapes
ACMMG222
Investigate Pythagoras’ Theorem and its application to solving simple problems involving right angled triangles
ACMSP226
Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or'
ACMSP283
Compare data displays using mean, median and range to describe and interpret numerical data sets in terms of location (centre) and spread

National numeracy learning progression 
Understanding geometric properties
Interpreting and representing data  IRD5 Understanding units of measurement  UuM9 
Copyright details 

Organisation  reSolve Maths by Inquiry 
Copyright  © Australian Government Department of Education, Skills and Employment 2021. Creative Commons BYNCSA 4.0. 
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