Lesson Notes By Weeks and Term v4 - SHS 1

Lesson Video

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Performance objectives

• Explain the rate of change of a function.
• Use technology to investigate the rate of change.
• Calculate the derivative of a function using rules.
• Compare the rate of change at different points on a graph.

Lesson summary

This lesson introduces the fundamental concept of Calculus: the rate of change. We will move beyond the idea of an average rate of change (like the average speed of a bus from Accra to Kumasi) to understand the instantaneous rate of change (the speed of the bus at the exact moment it passes Nkawkaw). This idea, also known as the derivative, is crucial for understanding how things change in the world around us, from the speed of a moving object to the profit changes in a business. We will use graphs and simple technology to see and feel what rate of change means at a single point on a curve.

Lesson notes

Concept 1: Average Rate of Change

Think about a journey in a tro-tro from the 37 Station to Madina. The total distance is about 14 km, and it might take 30 minutes (0.5 hours) on a good day.

The average speed (which is an average rate of change of distance) is: `Average Speed = Total Distance / Total Time = 14 km / 0.5 hours = 28 km/h`

This doesn't mean the tro-tro was moving at exactly 28 km/h the whole time. It stopped for passengers, sped up on clear roads, and slowed down in traffic.

Evaluation guide

• Use technology or any innovative ways to investigate the rate of change of a function, h
• (u), with respect to u.
• Collaborative learning, Experiential Learning, and initiate Talk for Learning.
• function relates to its derivative.