Landing: Collatz Conjecture Exploration and Teamwork Activity

Landing: Collatz Conjecture Exploration and Teamwork Activity [∞]

Delta Pig (talk) 17:49, 6 January 2025 (MST)

Activity (20 minutes):

Collatz Conjecture Exploration and Teamwork Activity

Materials:

• Pen and paper
• Whiteboard (optional)

Instructions:

1. Group the learners into small teams of 2-4 people.
2. Challenge each team to pick a starting number (you can choose a number from 1 to 100).
3. Have the teams calculate the Collatz sequence for their number, step by step, by following the rules of the conjecture. They should write down each number in the sequence until it reaches 1.
4. After a few minutes, ask each team to present their sequence to the group and discuss whether they noticed any patterns, and how long it took to reach 1.
5. Wrap up the activity by discussing how the unpredictability of the sequences mirrors challenges in real life. Even with simple steps, we often don’t know exactly where the process will take us, and sometimes it’s the most straightforward problems that require the most effort and patience to solve.

Reflection Questions:

• What did you notice about the sequences? Did they always follow a similar pattern, or were some numbers more unpredictable than others?
• How does this relate to problems that seem easy at first, but turn out to be more complicated?
• How can we approach problems that seem hard, but have simple rules like the Collatz Conjecture?

This activity illustrates the idea that persistence and careful thinking often reveal surprising results, even in problems that seem simple at first glance.