1. The Hailstone Sequence
What is a conjecture?
The Hailstone Sequence

2. 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?

3. 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.

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

5. 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

6. Conjectures: