Objective

By the end of this lesson, Jason will be able to differentiate between a relation and a function, understand the concept of ordered pairs, and identify functions using the vertical line test.

Materials and Prep

• Paper and pencil
• Graph paper (optional)
• Markers or colored pencils
• Ruler
• Prepared list of ordered pairs (to be used for activities)

Before starting the lesson, ensure that Jason understands basic coordinate systems and how to plot points on a graph.

Activities

• Activity 1: Ordered Pairs Exploration

  Jason will create a list of ordered pairs based on a real-life scenario (e.g., favorite ice cream flavors and their ratings). He will then plot these points on a graph to visualize the relation.

• Activity 2: Function or Not?

  Using the ordered pairs from Activity 1, Jason will determine whether the relation is a function. He will do this by checking if any x-values repeat.

• Activity 3: Vertical Line Test

  Jason will draw the graph of the relation on graph paper and use a ruler to perform the vertical line test, verifying if it passes the function criteria.

• Activity 4: Create Your Own Function

  Jason will invent a simple function and write its rule. He will then create a table of values and plot them on a graph to demonstrate his function visually.

Talking Points

• "A relation is simply a set of ordered pairs, while a function is a special kind of relation where each input (x-value) has exactly one output (y-value)."
• "When we plot points on a graph, we can visualize the relation. If any vertical line crosses the graph more than once, it’s not a function!"
• "An ordered pair is written as (x, y). The x-value is the input, and the y-value is the output. If the x-values are repeated, then it’s not a function."
• "Functions can often be represented with equations, but we can also express them through tables, graphs, or even real-life scenarios!"