I use these guided notes in conjunction with the Mathematics Vision Project Secondary Math 1 curriculum, Getting Ready chapter 1 lesson 2. Topics this covers are: linear growth, rates of change, table of values, constructing a linear equation given a pattern, solving linear equations, graphing a line given a point and slope, graphing a line given slope intercept form.
I have the students work in small groups or pairs and explore the linear pattern together. I give some direct instruction, but I leave it open for the students to work together to come up with an expression or equation that represents the table of values for the growing pattern.
I have also used this worksheet (separated by examples) as a centers activity. Example 1 is the first center, Example 2 is the second center, etc.