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.

##### Purpose
• 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

##### 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
• 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?