Activity: Part 1: Table of Values
On this page, there is a series of 6 short activities that introduce linear relationships through patterns, contexts, as an arithmetic sequence, as a function, and as a graph. Definitions for discrete and continuous are also included.
For related concept, also see my page on Arithmetic Sequences.
Activity: Part 2: A Written Rule
Activity: Part 3: Arithmetic Sequence
Activity: Part 4: Functions and Function Notation
This next activity worked for me as a teacher (and for my personality). If it is too wacky for you, please feel free to skip it :)
Function Notation always seems to be tricky - I am not sure why - this narrative always worked for my students.
Activity: Part 5: Graph
Activity: Part 6: Cartesian Coordinates
As the x changes, the graph changes height
This idea of "height" works well for students still lost on the Cartesian plane without a compass. Arguably, the "height" can go "underground" as well, but it depends on context.
It is good to have a discussion after the activity about whether or not the graph of F(x) should be considered continuous or discrete. In this case, since we only know that F(x) = 3x + 10, and we haven't been given a Domain, nor do we know the context, we can't really determine whether it is continuous or discrete.