Catholic Education South Australia
  • Patterns exist in, and are a regular occurrence in mathematics
  • They can be recognised, extended and generalised with both words and symbols
  • The same pattern can be found in many different forms

Inquiry Question

How might I explain how patterns grow?



Youcubed is a website with many Mathematical and Numeracy resources created by Jo Boaler, Professor of Education at Stanford University. The investigation, Squares Upon Squares, asks students to reflect on questions such as “How do you see the shapes growing?”

Link: Youcubed


NRICH is a website with many Mathematical and Numeracy resources created by the University of Cambridge. The inquiry Sticky Triangles is an open-ended investigation, guiding learners to visually explore growing patterns and extending them to share their generalisations.



re(Solve) is a Mathematics and Numeracy website with many resources aligned to the Australian Curriculum created by the Australian Government Department of Education.  This link provides three tasks, The Magic V, Matchsticks and Shapeshifter, asking learners to analyse the task, form or test conjectures and explain their thinking to others.

Link: re(Solve)

Australian Curriculum Lessons

Australian Curriculum Lessons website provides learning resources aligned to the Australian Curriculum. In the investigation, "Looking at Patterns in Paving Stones", learners apply algebraic patterning concepts to describe, continue and repeat, number patterns. They apply these understandings in the real-life context of problem solving the cost of paving stones.

Link: Australian Curriculum Lessons

Advice for Teachers 

Between years 3 to 6, students begin to explore patterns which progress through steps or sequences. These are referred to as growing patterns. When exploring growing patterns encourage students to: 

  • Build their patterns with everyday materials available. If this is not possible, encourage them to draw models 
  • Build or draw each sequence or term separately  
  • Predict what they think will happen and why  
  • Talk about their pattern and what they notice 
  • Determine how each step differs from the previous one 
  • Arrange numeric components in a table to predict, analyse and prove thinking  
  • Look for and identify generalisations or algebraic relationships. 

 Adapted from: Van de Walle. J and Lovin.L, Teaching Student Centred Mathematics: Grades K-3, 2006 

Considerations and Strategies for EAL Learners 

Number sentences in mathematics introduce the passive voice, which is very difficult for EAL/D students even in the Developing and Consolidating phases of English language learning (for example When a number is added to 23 …). Reword sentences to help EAL/D students see the process required (for example ‘23 plus which number …’) and show how this instruction can also be worded as ‘When a number is added to 23 …’  

Be aware of the range of language used to explain concepts (for example multiplication can be described by: 'times', 'by', 'lots of’, ‘groups of', 'multiplied by'). Provide consistency for EAL/D students by developing a glossary of terms.