Explore a comprehensive approach to teaching geometry and trigonometry in this 31-minute lecture from Insights into Mathematics. Begin with framing a program for young learners, starting from basic shapes and simple transformations in early years to more advanced topics. Discover how to introduce rational trigonometry to Year 9 and 10 students. Delve into circle geometry, the concept of 'pi', and angle as approximate measurements on a circle. Gain valuable insights for primary and high school mathematics teachers on structuring a progressive curriculum. Cover topics including primary school education, theorems, pre-Year 9 concepts, the Spread Law, circle geometry, and calculating the area of a circle.