This activity mixes some basic programming, little or no prior experience required and a series of questions that lead into a mathematical inquiry. Students explore the popular hailstone problem manually, leading to the desire to work more efficiently and hence the construction of a quick program. After the initial investigation, students launch into their own inquiry relating to Hail Stone numbers.

Euclid's Algorithm for the Highest Common Factor is a perfect fit for students coding in mathematics. This 2000 year old algorithm finds the highest common factor of two numbers, students can however extend the algorithm to find the highest common factor of a list of numbers with the option to place this new functionality in the calculator's public library. 

What is the probability that two randomly selected integers (whole numbers) are co-prime? This is a really simple algorithm to write, the result however is very surprising! Divide 6 by the proportion, then take the square-root, what number remains?