Students use an interactive diagram of a three dimensional box to explore the relationship between the side lengths of the box and the length of the diagonal connecting opposing vertices. Students verify the length of the diagonal by using Pythagoras’s theorem in three dimensions.

Students use a number of interactive diagrams to collect data and explore the relationship between the side lengths of a triangle and its area with a view to establishing the rule A = ½ a b sin(C)

In this activity students collect data for a range of ball sizes and masses. The data is then analysed and an appropriate line of best fit is applied. Students then consider balls that don't quite fit the plot, including an AFL football. In considering an AFL football students use alternative means to create a comparison with the spherical balls. Calculations include arithmetic mean (radius), geometric mean (radius) and volume. Students are ultimately provided with a problem involving the design of a ball using a specific material and thickness leading to calculations of density.