This activity is a student centered exploration of the differences between rules and general rules when looking at number sequences. The use of "term" and "term number" are used to address differences between a number on the list (represented by the variable t) and it's location in the list (represented by the variable n).
Besides exploring the various number relationships that exist in a number sequence, students will be shown how to communicate that relationship in the form of an equation. An example portion is provided to visually assist students. Likewise, a chart is used to organize the number sequence (similar to a t-chart). This is a precursor to the x and y table used in Algebra.
Furthermore, student will be asked a series of multiple choice questions upon completion of the first page to identify correlations between the rule and general rule. There is a conclusion statement provided at the end of the exploration to provide closure and make sure everyone walks away with the same understanding.
I have personally used this activity with a diverse population of students in a small group setting and have found much success. This exploration takes a relatively complex topic and makes it accessible to everyone without the intimidation or boredom of a textbook / class lecture. The answer keys are provided.