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.