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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 8, Year 9
|Teaching strategies and pedagogical approaches
|area, central tendency, polygons, statistical frequency, mean, median, pi
|Strand and focus
|Statistics, Build understanding, Apply understanding, Measurement
|Chance and probability, Data representation and interpretation
|AC: Mathematics (V9.0) content descriptions
Solve problems involving the area and perimeter of irregular and composite shapes using appropriate units
Use Pythagoras' theorem to solve problems involving the side lengths of right-angled triangles
Calculate relative frequencies from given or collected data to estimate probabilities of events involving "and", inclusive "or" and exclusive "or"
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
Interpreting and representing data (P8)
Multiplicative strategies (P9)
Understanding chance (P6)
Understanding geometric properties (P7)
Understanding units of measurement (P9, P10)
reSolve Maths by Inquiry
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