The following lessons were created for an 8th grade class. The lessons introduce students to arithmetic and geometric sequences. The first lesson introduces the students to the type of pattern and any new key vocabulary pertaining to the subject matter. Next, students get deeper into the sequences and derive explicit formulas. Students will not be given the abstract formulas at the beginning of these lessons. Instead they will work collaboratively to determine the patterns within the sequences to “create” the formula. This method gains the students understanding of the concept behind the formula and leads them to the abstract explicit formula for finding the nth term of a sequence.
Once students have completed their investigations they will then create x/y tables for their sequences, which will then result in ordered pairs for graphing! Students graph the ordered pairs for our sequences and will uncover in their investigations that arithmetic sequences result in linear graphs because they are linear functions. Also, that geometric sequences result in exponential changes, thus exponential functions. Students will understand the difference of exponential changes vs linear through a series of assignments and hands on activities.
This unit plan integrates literature and science and makes use of collaborative activities and oral presentations. This will assist students with further studies when calculating the partial sums and understanding the idea of limits when analyzing graphs.