Today I had the opportunity to observe Luka working with a Year 10 student on the topic of linear relationships. The session was an excellent example of how mathematical concepts can be used when they are linked to real-world applications and explained in progressive, accessible steps.
Luka began by revisiting the general form of a linear equation, y=mx+c Rather than rushing into abstract algebraic manipulation, he encouraged the student to interpret these terms visually by plotting examples on the Cartesian plane. This step was particularly effective, as it grounded the algebraic symbols in a picture the student could immediately recognise.
A highlight of the lesson was Luka’s use of contextual problems. He framed linear relationships in everyday settings, such as calculating the cost of ride-share fares or predicting phone plan charges based on a fixed rate plus usage. By doing this, he helped the student see that slope represents a rate of change while the intercept captures a starting value. The student initially struggled to articulate why the line’s steepness changed with different values of m, but through questioning and repeated sketching, Luka guided them toward understanding slope as a measure of sensitivity: the greater the slope, the faster
y changes with respect to x.
The pacing of the lesson balanced explanation and practice well. Luka would model an example, then hand over to the student to attempt a similar problem. This strategy ensured active engagement and allowed him to provide immediate feedback. Importantly, he encouraged the student to verbalise their reasoning at each step, which not only clarified their thought process but also revealed gaps in understanding that Luka could address on the spot.
What stood out most in this session was the emphasis on linking algebra to interpretation. Too often, linear relationships are treated as purely symbolic exercises. Luka showed how to integrate both the visual and practical dimensions, making the concept more intuitive and less intimidating. It was a reminder of how effective tutoring blends clarity, relevance, and patience to deepen student learning.
Tynan Philmara