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reSolve: Geometry: Lunch Lap (Trial)
In this sequence of two lessons, students apply Pythagoras' Theorem to explore a practical problem involving optimising paths to lunch carts. In the first lesson, students investigate the length of a path that touches three sides of a rectangle, starting and finishing at the same point. They model the problem, use Pythagoras' Theorem to calculate the length of the path, then work with spreadsheets and GeoGebra models to find the shortest possible path. In the second lesson, students use geometric reasoning to find the positions of the carts and justify that the parallelogram is the shortest path. 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  Pythagoras' theorem, right angled triangles, algorithm, modelling 
Curriculum alignment 

Curriculum connections  Numeracy 
Strand and focus  Measurement, Space, Build understanding, Apply understanding 
Topics  Pythagoras and trigonometry, Angles and geometric reasoning 
AC: Mathematics (V9.0) content descriptions 
AC9M8M06
Use Pythagoras' theorem to solve problems involving the side lengths of rightangled triangles 
Numeracy progression 
Understanding units of measurement (P10)
Understanding geometric properties (P7) Multiplicative strategies (P9) 
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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