There have been two topics that I’ve really enjoyed teaching recently to Year 10:
Pythagoras’ theorem and trigonometry are used in calculations involving sides and angles of right-angled triangles. We have used this to show some interesting calculations, such as finding the height of Mount Everest and calculating the distance between the Earth and Moon and the Earth and the Sun.
When we have done calculations involving volumes of shapes, we have shown how ancient Egyptians managed to calculate the volumes of their pyramids so that they knew how much stone was needed to be dug up. We also performed experiments with cylinders (by placing water in a measuring tube) to discover the volume of cylinders and used this to show the relationship that there are indeed 1000cm3 in 1 Litre.
Here is an example of how we used this idea of volume of prisms to create an algebraic expression to describe this volume: