Pythagorean triples
This lesson is one in a series of lessons on Pythagoras theorem. The purpose of this lesson is to have students undertake a mathematical exploration to find Pythagorean triples, that is, sets of positive integers {a, b, c} such that a2 + b2 = c2. Students apply trial and error to identify sets of positive integers {a, b, c} that are Pythagorean triples using a spreadsheet. They apply scaling to develop new triples from a known triple, and use a formula (Euclid’s formula) to generate Pythagorean triples. They then take a systematic approach to explore if there are any emerging patterns. This lesson is an example of an exploration within mathematics itself rather than an application of mathematics to contexts involving practical problems or other learning areas.
Additional details 

Year level(s)  Year 8 

Audience  Teacher 
Purpose  Teaching resource 
Format  Web page 
Teaching strategies and pedagogical approaches  Mathematics investigation, Questioning 
Keywords  problem solving, rightangled triangles, triangles, Maths Hub lesson plan 
Curriculum alignment 

Curriculum connections  Critical and creative thinking 
Strand and focus  Number, Measurement 
Topics  Pythagoras and trigonometry 
AC: Mathematics (V9.0) content descriptions 
AC9M8N01
Recognise irrational numbers in applied contexts, including square roots and Π
AC9M8M06
Use Pythagoras' theorem to solve problems involving the side lengths of rightangled triangles 
Numeracy progression 
Understanding geometric properties (P7)
Understanding units of measurement (P10) Multiplicative strategies (P9) 
Copyright details 

Organisation  Commonwealth of Australia 
Copyright  © 2024 Commonwealth of Australia. Creative Commons BY 4.0. 
Related resources

How old is the (Pythagorean) theorem?
This is an introductory lesson in a series of lessons on Pythagoras theorem. Students learn about Pythagoras’ theorem and its application in calculating lengths in rightangled triangles.
Resource details 
Pythagoras investigations and applications
This lesson is one in a series of lessons on Pythagoras theorem. Students work in small groups to investigate the application of Pythagoras’ theorem to problems in a practical or theoretical context.
Resource details 
Pythagoras: Cartesian coordinate plane
This lesson is one in a series of lessons on Pythagoras theorem. Students calculate the distance between any two points on the Cartesian coordinate plane using Pythagoras’ theorem and then develop a set of steps that outline the process. It combines the use of Pythagoras’ theorem with the Cartesian coordinate plane and the use of coordinates to specify position, form line segments, shapes of triangles and determine their perimeters.
Resource details