The purpose of this lesson is for students to work with sequences and describe them recursively in an informal way. A sequence is defined here as a list of numbers, while a term (of a sequence) is one of the numbers in the list. The lesson begins with four sequences for students to consider. Students identify common structures and specific patterns, and share the connections they see between different sequences.

Next, using the Tower of Hanoi puzzle, students first make sense of the rules of the puzzle before playing with different numbers of discs in order to generate a sequence representing the minimum number of moves needed to complete the puzzle. Looking for patterns as they solve the puzzle provides students opportunities to express regularity in repeated reasoning (MP8). Throughout both activities, students share their reasoning with classmates, attending to precision of language (MP6) as they refine their ideas and discuss the ideas of others.

The third activity is optional and provided for additional practice with another context if needed, or as an alternative activity if students are familiar with the Tower of Hanoi puzzle.

While geometric and arithmetic sequences are a focus of the unit, the sequence generated from the activity “The Tower of Hanoi” is neither. This was a deliberate choice to promote student discussion since the pattern to generate the sequence is one students are less likely to guess correctly than a more straightforward linear or exponential pattern.

Math Community
This is the first exercise that focuses on the work of building a mathematical community. Students have the opportunity to think about what a mathematical community is and to share their initial thoughts about what it looks like and sounds like to do math together in a community.