Imagine you just arrived home from school, you’re really hungry. You decide the block of chocolate will help you with your homework. Pretty soon half the block is gone, so you quickly put it back in the refrigerator. Your brother arrives home, spots the half eaten block of chocolate and immediately breaks half the remaining block off for himself. Dad’s next, when he visits the refrigerator he too breaks off half the remaining block. How long will the block last you wonder?

This introduction combined with a dynamic representation and accurate mathematical notation is used for the basis of introducing and exploring Geometric sequences and series.

One of the simplest and beautiful mathematical sequences. The simplicity: 1, 1, 2, 3, 5, 8 ... is such that each term is the sum of the previous two terms. Examples of the sequence can be found in nature, architecture and number theory. In this investigation, students explore some of the patterns within the sequence such as the consecutive sum of the squared terms. What about the last digit of term 60, 61, 62 ... what pattern do these form? Don't worry, the magical phi is not left out, including amazing relationships such as 1 + phi. Check it out!

Students explore the relationship between the number of discs and moves required to solve the classic “Tower of Hanoi” problem. The TI-Nspire file contains an interactive model produced by Andy Kemp.  The interactive model allows you to change the number of disks and automatically record the total number of moves allowing students to focus on solving the problem and identifying patterns. The activity also includes a degree of scaffolding to help student identify and understand the nature of the geometric recursive relationship between the number of disks and the number of moves.

Students use trigonometric functions to model biorhythmic activity. Whilst the psuedo science of biorhythms equates approximately to astrology, the activity content is applicable to graphing simple trigonometric functions involving only transformations. The alignment of days helps students understand the period of the function.