Using the Legend of Gauss is a perfect lesson for you to use over the first day or two of school because it is accessible to multiple skills and levels of understanding. This allows the teacher to make an initial assessment of their students understanding of the foundational principles of mathematics and doing mathematics. I have also found that it is a great way to introduce your students to the norms of the classroom and to get to know each other but also to engage in some meaningful mathematics. But, that being said, it could also be used anytime throughout the year, even as a mid year re-evaluation of the basics.
This is the resources for a lesson or two dealing with Arithmetic and Geometric Sequences and Series. Depending on your goals and the sophistication of your students, you can adjust the discussions appropriately and there are some suggestions included on the slides. Here are a few I have suggested but you can make your own based on the lesson materials:
-To introduce or review functional thinking, notation and variables.
-To develop the formula for the sum of an finite number of terms of an arithmetic sequence (series).
-To introduce or review the properties of linear and exponential functions.
-To introduce or review the properties of arithmetic and geometric sequences.
-To Introduce series.
This is a lesson is designed to be a task (or sequence of tasks) rather than a lecture. This allows you the freedom to adjust the goals as you see fit and gives the students an opportunity to interact with the mathematics and each other. Because of the nature of the activities, with very few lesson slides you have built in extensions that can make the lesson a single lesson or a series of lessons.
This document includes the annotated powerpoint slides and possible homework problems you could extend over two days if you prefer to keep your homework assignments short. The powerpoint slides are not beautified but the content is good and can be easily copied onto your own slides.