Please note: This site contains links to websites not controlled by the Australian Government or ESA. More information here.
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 BY-NC-SA 4.0. |
Related resources
-
reSolve: Mathematical modelling – How risky is life?
This is a series of inquiry-based lessons about modelling the risk of death by various causes, using probability, statistics and proportional thinking.
Resource details -
Big ideas in statistics (Years 7 to 10)
A look at the big ideas involved in developing statistical understanding and some of the misconceptions that students might hold
Resource details -
Statistics and probability (Years 7 to 9)
These units explore the relationship between probability and the way data is represented.
Resource details -
Loaded dice
Students use different operations to predict favourable results in chance experiments and games. They record their data in different ways and make predictions about chance-related outcomes.
Resource details