Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

This page supports the lesson note with a companion video and a short classroom-ready summary.

For class groups and homework, share this lesson page so learners also get the summary, objectives, and full lesson context.

Performance objectives

• Define differentiation and its role in calculating rates of change.
• Apply differentiation to find the rate of change for a function.
• Calculate average and instantaneous rates of change.
• Solve real-life problems involving rates of change.

Lesson summary

This lesson introduces one of the most powerful applications of calculus: understanding and calculating rates of change. We often talk about how fast things change in our daily lives – the speed of a car, the rate at which prices increase, or how quickly a disease spreads. While we can easily calculate an *average* speed over a journey, calculus allows us to find the *exact* speed at a single moment in time. This concept, known as the instantaneous rate of change, has wide applications in science, engineering, economics, and even public health in Ghana, from analysing the performance of our Black Stars to managing our national economy.

Lesson notes

Part 1: Revisiting the Average Rate of Change

You already know how to find the gradient (slope) of a straight line connecting two points, `(x₁, y₁)` and `(x₂, y₂)`:

``` Gradient (m) = (Change in y) / (Change in x) = (y₂ - y₁) / (x₂ - x₁) = Δy / Δx ```

This gradient represents the average rate of change of `y` with respect to `x`. For a curve, this formula gives the gradient of the *secant line* connecting two points on the curve.

Evaluation guide

• Apply differentiation to find the rate of change.
• Collaborative learning, Experiential Learning, and initiate Talk for Learning.
• change of a given function or phenomenon at certain points.
• Think -pair share: Learners in a mixed -ability group use their previous knowledge of finding the slope