We are going to look at Differentiation for curves. This will help to strengthen learners understanding of substitution of both positive and negative numbers. We will revisit find equations of straight lines and apply this to tangents of quadratic and cubic curves.
Differential calculus can be challenging to teach because learners need to make a connections between graphs and their functions and also need to associate the gradient function across all points of the graph. Learners will often learn rules for finding a derivative without really understanding how they work and are then unable to apply these rules independently and in more complex, less familiar situations.
Securing an understanding of Differentiation as a rate of change will help extended learners to apply their learning to more complex situations. A good understanding of using differentiation will help learners to link to more complex differentiation in future including connected rates of change.
This unit will explore using differentiation to find the gradients of functions at specific points of a curve and will lead on to finding maximum and minimum points of real world functions as might be used within sciences.
This unit of work is just one of several approaches that you could take when teaching this topic, and you should aim to adapt the resources to match the ability level of your learners, as well as your school context.