Today, I had the opportunity to observe Edward’s Year 9 Mathematics tutoring session, which focused on foundational trigonometry skills. The main concepts covered were calculating unknown angles and sides in right-angled triangles using the primary trigonometric ratios: sine, cosine, and tangent. The lesson was structured to gradually build the student’s confidence and understanding, ensuring they were not only following along but also able to apply the methods independently.

Edward began the session by revisiting the key trig ratios, reinforcing when and how each one should be used. He explained SOH-CAH-TOA clearly and provided examples that illustrated different problem types, such as finding a missing side when an angle and a side are known, as well as finding an angle when two sides are given. Throughout these demonstrations, Edward paused frequently to check for understanding, asking the student guiding questions to help them think through each step rather than simply memorise formulas.

He then worked through a series of example questions on the board. For each problem, he modelled the process of identifying the correct ratio, setting up the equation, and using a calculator accurately—an important skill at this level. Edward also highlighted common mistakes, such as mixing up opposite and adjacent sides or forgetting to use inverse trig functions when solving for angles.

After several examples, Edward shifted responsibility to the student. He provided a set of practice questions, encouraging the student to attempt them independently while he observed. Edward offered support only when needed, prompting the student to explain their reasoning or revisit the diagram when they appeared unsure. This balance of guidance and independence helped reinforce the student’s problem-solving skills and gave them the opportunity to consolidate what they had learned.

Overall, a great session to observe.

Alexander Nikitopoulos