Transformation are significantly more powerful when they are created and explored in a dynamic, digital environment. In this activity students perform a series of dilations on points on the Cartesian plane. The dilations are dynamic and provide the opportunity to consider both input and output. The point is then attached to a function, allowing students to consider the function as a family of points. Finally, students use algebra to calculate the corresponding equation to the dilated function.

Why are horizontal transformations counter intuitive? In this activity students perform a series of translations, horizontally and vertically by starting with a single point on the Cartesian plane. The point is then attached to a function, allowing students to consider the function as a family of points and examine how the image of the point moves. Finally, students use algebra to calculate the corresponding equation to the translated function.

This activity flips factorising on its head. Two linear functions are graphed and multiplied together to produce a quadratic. The dynamic nature of the linear and quadratic graphs allow students to explore connections, ranging from axis intercepts to completing the square. Students makes sense of the instruction “express the quadratic as a product of its linear factors”.

This engaging mathematics activity invites students to investigate the motion of a bouncing ball using a TI-Nspire calculator connected to a CBR2 motion sensor. As the ball bounces, the sensor captures position-time data, which students then analyse to uncover the parabolic nature of each bounce. The activity transforms abstract algebraic concepts into a dynamic, hands-on experience, fostering deeper understanding through real-world application.

Is the iconic arch of the Sydney Harbour Bridge a parabola or a catenary? In this activity students determine equations for the two arches on the Sydney Harbour bridge and the roadway using different techniques. Students perform calculations to check the accuracy of the modelling and apply the models to determine the total length of the cables.

Eastlands shopping centre is Melbourne’s east is home to beautiful series of parabolic arches. One of the main atriums is lit by vaulted ceilings in the form of parabolas. In this activity students determine the equation to some of these arches and find the variant and invariant properties.