Today, I observed Mary and Katerina working together through a practice paper on dilations and related function questions during the lesson. Together, they worked through a worksheet that included a range of questions on transformations of functions, with a strong focus on translations and dilations. At the beginning, they started with more basic transformation questions, identifying how graphs shift when values are added or subtracted either inside or outside the function.

As they moved further into the practice paper, the questions became more challenging and focused more on dilations. Mary and Katerina worked through vertical dilations first, multiplying functions by constant factors and observing how this stretched or compressed the graph. Horizontal dilations required more thought, and they occasionally paused to discuss their reasoning, particularly around the idea that changes inside the function produce an opposite effect on the graph compared to what might be expected.
Some of the later questions involved logarithms, including expressions using log base e. They attempted to simplify these expressions using basic log laws, such as expanding products into sums and turning powers into coefficients. At times they needed to revisit earlier examples, but they gradually became more confident as they progressed through similar questions.
Throughout the lesson, both students made effective use of the available materials. They referred to their textbooks to check formulas and confirm examples when they were unsure, which helped them stay on track. The whiteboard was also used to work through selected questions step-by-step, allowing them to visualise the transformations more clearly and identify small errors in their working.
Overall, Mary and Katerina made steady progress through the practice paper. They demonstrated a developing understanding of transformations, dilations, and basic logarithmic rules. The lesson highlighted how combining practice questions with textbooks and whiteboard explanations can support understanding and improve confidence with more complex mathematical problems.

David Hanna