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Lesson 1: A Towering Sequence
• De ne the term "sequence."
• Develop a recursive de nition of a sequence.
• Generate a sequence that arises from a mathematical context.
Lesson Narrative
The purpose of this lesson is to introduce students to the idea of sequences and to de ning functions recursively in an informal way. In the rst activity, students experiment with the Tower of Hanoi puzzle and generate a list of numbers. Sequence and term (of a sequence) are de ned. The second activity is optional and provided for additional practice with another context if needed. It is identical in structure, but uses a di erent puzzle that generates a di erent sequence.
Solving the puzzles provides opportunities to express regularity in repeated reasoning (MP8) when they express a recursive rule for generating the next term in a sequence. If students try to convince each other that they have found the minimum number of moves to solve the puzzle, they may construct mathematical arguments and critique the reasoning of others (MP3).
Required Materials Coins
Objects for Tower of Hanoi Required Preparation
Students should manipulate physical objects to experiment with the Tower of Hanoi puzzle. Each student 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, an applet is provided.
If you are doing the optional checker jumping puzzle, each student needs 3 tokens each of 2 di erent colors. These could be actual checkers, counting chips, pennies and nickels, or any other appropriate tokens.
Student Learning Goals
• Let’s explore the Tower of Hanoi. 1.1 What’s Next?
Warm Up: 10 minutes
The purpose of this task is to get students thinking about generating a list of numbers based on a rule. In the next activity, they will try to come up with such a rule in order to continue a pattern in a list of numbers.
Unit 1 Lesson 1: A Towering Sequence 7