In Classroom Resources, Number and Algebra, Patterns, Patterns and Algebra

This activity is designed to encourage students to engage with a problem, before they over think it. Too often in class we begin with what is familiar to students and gradually increase the challenge. This problem begins with a challenge and encourages students to work backwards to solve a simpler problem, before applying what they know to solve even more challenging problems.


  • Identify the qualities and behaviours of a good mathematician
  • Choose an appropriate strategy to attempt an unfamiliar problem
  • Explain the strategy used to solve the problem
  • Recognise and continue number patterns
  • Record solutions using a systematic approach
  • Interpret data and identify patterns
  • Develop rules to describe number sequences
  • Use symbols to record and explain rules


Curriculum Connections: VICTORIAN CURRICULUM F-10 (YEAR 6)


Number & Place value
  • Identify and describe properties of prime, composite, square and triangular numbers (VCMNA208)


Patterns & Algebra
  • Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (VCMNA219)


Data representation & interpretation
  • Construct, interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (VCMSP235)


At the end of this lesson students should be able to answer the following questions
  • What do you know about this problem?
  • How could you start this problem?
  • Can you explain the strategy you are using?
  • Could we try a simpler problem?
  • How could you record the solution? Could a table help?
  • Do you notice any patterns? Can you use this information to predict future solutions?
  • How can you demonstrate that all your solutions are correct?
  • Can you develop a rule to describe the number sequence?
  • Can you use what you have discovered to find all possible solutions?


For more information, please download the attached lesson plan.

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