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.
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 (MP1). Solving the puzzles provides students opportunities to express regularity in repeated reasoning (MP8) when they informally state a recursive rule for generating the next term in a sequence from the previous term. If students try to convince each other that they have found the minimum number of moves to solve the puzzle, they are constructing mathematical arguments and critiquing the reasoning of others (MP3).
The second activity is optional and provided for additional practice with another context if needed, or as an alternative activity if students have familiarity with the Tower of Hanoi puzzle.
Lesson overview
 1.1 Warmup: What's Next? (5 minutes)

1.2 Activity: The Tower of Hanoi (30 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem

1.3 Optional Activity: Checker Jumping Puzzle (30 minutes)
 Digital applet in this activity
 Lesson Synthesis
 1.4 Cooldown: Next (5 minutes)
Learning goals:
 Comprehend the term "sequence" (in written and spoken language) as a list of numbers.
 Describe (orally) a recursive rule for identifying the next term of a simple sequence.
 Generate a sequence that arises from a mathematical context.
Learning goals (student facing):
 Let’s explore the Tower of Hanoi.
Learning targets (student facing):
 I can give an example of a sequence.
Required materials:
 Internetenabled device (optional)
 Objects for Tower of Hanoi (ex: coins for each partner: quarter, nickel, penny, dime)  [print version]
 Paper with 3 circles [print version]
 Coins or tokens, in 2 colors, for optional activity
Required preparation:
 Students should manipulate either physical or digital objects to experiment with the Tower of Hanoi puzzle. For physical, each group could use a quarter, nickel, penny, and dime, and a piece of paper with 3 circles drawn on it. For students using the digital version of the materials, acquire devices that can run the digital applet. It is ideal if each student has their own device.
 If you are doing the optional checker jumping puzzle, each group needs at least 3 tokens each of 2 different colors. These could be actual checkers, counting chips, pennies and nickels, or any other appropriate tokens
Glossary:
 sequence A list of numbers, possibly going on forever, such as all the odd positive integers arranged in order: 1, 3, 5, 7, . . . .
 term (of a sequence) One of the numbers in a sequence.
 Access the complete Algebra 2 Glossary.
Standards:
 This lesson builds towards the standards: CCSS.HSFBF.A.1.aMS.FBF.1aCCSS.HSFBF.A.2MS.FBF.2MO.A1.LQE.A.3MO.A1.LQE.B.4
IM Algebra 1, Geometry, Algebra 2 is copyright 2019 Illustrative Mathematics and licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.