This collaborative activity involves building a map of numbers using a very simple rule. The basic idea is to build a bunch of recursive sequences using the same rule, but different starting values.

The Rule

Start with any positive whole number. If the number is even, divide it by 2. Otherwise, triple it and add one. Repeat until you spot a pattern or get tired.


Apply the rule for the following starting numbers. Then, build a map of the sequences generated by the numbers and make conjectures based on what you learned.

Some Good Starting Numbers to Build the Map

10, 3, 256, 113, 35, 53, 11, 9, 341, 75, 23, 672, 201

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