Education Technology

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  • Subject Area

    • Standard: National Curriculum 7-10: Number and Algebra: Patterns and algebra
    • Standard: National Curriculum 7-10: Statistics and Probability: Data representation and interpretation

  • Author

    Texas Instruments

  • Level

    Middle

  • Activity Time

    120 Minutes

  • Device
    • TI-Nspire™
    • TI-Nspire™ CAS
    • TI-Nspire™ Navigator™
    • TI-Nspire™ Apps for iPad®
  • Software

    TI-Nspire™
    TI-Nspire™ CAS
    TI-Nspire™ CAS Navigator™ NC System
    TI-Nspire™ Navigator™ NC System

  • TI-Nspire Version

    4.2

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Coding Hailstones

Published on 05/29/2016

Activity Overview

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.

Objectives

Data representation and interpretation Investigate techniques for collecting data, including census, sampling and observation - ACMSP284

Vocabulary

Mathematics

  • Factor
  • Prime
  • Composite
  • Even / Odd
  • Algorithm

Coding

  • IF / Then/ Else
  • While / EndWhile
  • Mod
  • Request
  • Display

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.