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.
Data representation and interpretation Investigate techniques for collecting data, including census, sampling and observation - ACMSP284
Sequence, prime, composite, odd, even, algorithm
About the Lesson
This activity investigates the popular hail stone problem. Students initially explore the problem manually to help build the desire to automate the sequence generation. Students then write a simple program to generate the numbers turning the focus of the lesson away from the relatively simple and repetitive task of sequence generation into a more inquiry focused task, looking for patterns. Students can graph sequence length versus initial number and look for patterns. Other options within this task include exploring prime and composite sequence length or explorations that lead to the notion that ‘powers of two’ produce a relentless degeneration of the sequence and can also lead to a level of algebraic investigation for more able students.