Education Technology

Kicking Goals

Activity Overview

Watch Paul discusses the kick, we discuss the calculus and more.

There is no doubt, a kick directly in front of goals is more likely to be successful, but where is the best place if you are near the boundary line? This activity starts with shooting for goals in soccer before heading out to the MCG and a magnificent kick from the boundary by AFL great, Paul Salmon. Did he find the best spot from where to launch his kick?


Students formulate algebraic and trigonometric expressions related to two different sporting arenas and use calculus to establish the ultimate location to kick for goals based on the circumstances provided.  


  • Ellipse
  • ArcTan
  • Derivative
  • Solve

About the Lesson

Students start by modelling shots on goal in soccer. The rectangular field shape combined with the specific shooting locations simplifies the mathematics. Once students have finished looking at soccer, they move onto the real situation one AFL player created after taking a mark near the point post. The player walked back along the boundary line, almost all the way to the 50m arc and proceeded to kick a goal! Was this the best place to kick a goal? Use differential calculus, arcTan and coordinate geometry to explore this practical problem.