Understanding the difference between the average rate of change and the instantaneous rate of change can be tough for Year 9 students.

Let’s break it down:

1. Average Rate of Change: This shows how much a function changes over a certain period.

   To find it, we use this formula:

   $\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}$

   In this formula, $f(a)$ and $f(b)$ are the values of the function at points $a$ and $b$.

   The average rate of change gives a general idea of how the function behaves over that time. But, it might not always be accurate.

2. Instantaneous Rate of Change: This one is a bit more complicated. It looks at the rate of change at just one specific point.

   It's shown as the derivative $f'(c)$ at point $c$. To find this, we usually need to learn about limits, which can make it tricky.

Both of these ideas can be hard to understand because they rely on knowing about functions and limits.

But don’t worry! With some practice and by looking at graphs, students can see and understand the differences better. This will help make these basic ideas in calculus easier to grasp.