The Hailstone Sequence What is a conjecture? The Hailstone Sequence

Unproven claim that is suspected to be true Science Hypothesis Based on observations Can be tested Cannot be proven Theory Example Chocolate may cause pimples Observation? Test? Proven? Math Conjecture Based on observations Can be tested Has potential to be proven Theorem Example The sum of two odd numbers is even Observation? Test? Proven?

The Hailstone Conjecture In 1937, mathematician Lothar Collatz made a conjecture that is still today one of the world’s unsolved problems in mathematics. It involves a sequence of numbers called the Hailstone sequence.

Why is it called the Hailstone Sequence? 20, 10, 5, 16, 8, 4, 2, 1

What is the Hailstone Conjecture? If a number is even, divide it by 2 If a number is odd, multiply it by 3 and add 1 20, 10, 5, 16, 8, 4, 2, 1 Try working with some hailstone strings that have different starting numbers. Together, make a conjecture based on your observations. Test your conjecture with more numbers

Conjectures: