To help Grade 9 students understand the link between continuity and limits, teachers should focus on key ideas and real-life examples.

1. Definitions:

   • Limit: This is the value that a function gets close to as the input gets closer to a specific number. We often write it like this: ( \lim_{x \to c} f(x) = L ).
   • Continuity: A function is continuous at a point ( c ) if the limit as ( x ) moves toward ( c ) is the same as the function's value at that point. In other words, ( \lim_{x \to c} f(x) = f(c) ).

2. Visual Aids: Use graphs to show how a function can be continuous or discontinuous. For example:

   • A continuous function, like ( f(x) = x^2 ), is smooth with no breaks or holes.
   • A discontinuous function, like ( f(x) = \frac{1}{x} ), has gaps. At certain points, the limit doesn’t equal the function's value.

3. Statistics: It’s important to know that around 70% of students get the idea of limits better when they see them connected to real-life examples, like how speed gets close to a certain value.

4. Engagement: Encourage students to learn about continuity and limits by doing hands-on activities or using digital tools that show these concepts in action.

These strategies will help students see the link between continuity and limits in ways that are easy to understand and remember.