Education Technology

Goldbach Conjecture

Published on 03/05/2017

Activity Overview

Explore one of the great ‘unsolved mathematics’ problems.  The humble beginnings make this problem accessible to upper primary level mathematics:  “Every even number greater than two can be written as the sum of two prime numbers”.   Students start by exploring two digit numbers, then they apply some relatively simple coding commands to write a basic program that makes exploration quicker.  One of the beauties of this unsolved mathematics problem is that it is easy to escalate the mathematics and coding aspects to provide a challenge to a broad range of students.

Objectives

  • Apply STEM principles design – test – evaluate to improve coding efficiency by utilising some basic number facts.
  • Conduct an investigation into the frequency of pairs of prime numbers that produce the same sum.

Vocabulary

Mathematics

  • Prime
  • Composite
  • Even / Odd

Coding

  • isPrime
  • IF / Then/ Else
  • For/ Endfor

About the Lesson

Students get a feel for the problem by first exploring a selection of even numbers ‘by-hand’.  Using the ‘isPrime’ commend on the calculator makes checking for solutions much quicker.  The by-hand exploration also helps students see the repetitive nature of the calculations and therefore the desire to code a solution.  The 10 Minutes of Code sessions cover all the prerequisite material.  Student hand-outs and teacher notes provide enough instructional content for most beginner level programmers to construct a basic program even if they have not completed the 10 minutes of code units.  Students can attempt the challenge questions that increase the level of coding expertise and encourage use of the STEM principles: Design – Test – Evaluate to improve the efficiency and functionality of their program.