Algebra: Number Sequences

Australian curriculum number (ACMNA055; ACMNA060)

This sequence builds students’ algebraic thinking through explorations of additive number patterns. As students solve the problems to generate the patterns, their strategies for addition and subtraction are applied and developed. A key focus of each task is to build students’ ability to reason why patterns occur and to generalise patterns to fit various situations.

This sequence is for students who:

  • have some experience with number patterns involving addition. 
  • can add and subtract one- and two-digit numbers. 
  • have or are developing flexible strategies for performing addition and subtraction.


Lesson 1: Counter Toss

Students toss four two-colour counters to explore number patterns. One colour is allocated a value of 2 and the other 5. Students are asked to consider all possible scores that can be generated by tossing the counters and why the resulting number pattern occurs. Students then explore the different number patterns generated, using different values for the colours on the counters.

Lesson 2: Letterbox Numbers

This task uses the context of house numbers on a suburban street to explore number patterns. Students add together varying sequences of house numbers to reveal different patterns. Students are asked to explain why these number patterns occur. The final investigation asks students to explore and find their own patterns and to reason mathematically as to why they occur.


Last updated June 14 2020.