Double Trouble | Investigating the Rules

Foundation to Year 6

Looking for a mathematics task that develops conceptual understanding, reveals student thinking, and supports differentiation?

Double Trouble: Investigating the Rules helps teachers develop students' understanding of doubling through mathematical investigation, reasoning and proof.

Rather than simply practising doubles, students investigate mathematical rules, test examples, represent their thinking, and justify whether a rule is always true.

Double Trouble: Investigating the Rules is a hands-on bounded differentiated problem that invites students to explore mathematical ideas through purposeful investigation. A bounded differentiated problem is a worthwhile mathematical experience with intentional supports, constraints and extensions that reveal student thinking. Rather than creating multiple tasks for different learners, all students engage with the same rich mathematical investigation while accessing it at an appropriate level of challenge.

Using concrete materials, drawings, numbers and mathematical language, learners investigate rules about doubling by testing examples, searching for patterns and representing their thinking in different ways. As the learning progresses, students move beyond identifying patterns to proving mathematical ideas, justifying their reasoning and making generalisations.

Rather than providing another worksheet to practise doubles, this resource encourages students to think like mathematicians. Learners investigate whether mathematical rules are always true, communicate their reasoning, and deepen their conceptual understanding through purposeful discussion and problem-solving. The built-in supports, constraints and extensions allow every learner to access the same worthwhile mathematical investigation while making their thinking visible for assessment and responsive teaching.

This resource includes:

✔ Editable PowerPoint lesson presentations

✔ Learning intentions and success criteria

✔ Three differentiated bounded mathematical investigations (Foundation–Year 1, Years 2–4 and Years 5–6)

✔ Let's Go, Strive for Success and Mathematician prompts

✔ Reflection and discussion prompts

✔ Student self-assessment tools

✔ Teacher notes

✔ Responsive teaching ideas, extension opportunities and common misconceptions

✔ Australian Curriculum Version 9 aligned materials

Students will:

• Investigate whether mathematical rules about doubling are always true.
• Represent their thinking using concrete materials, drawings, numbers and mathematical language.
• Test mathematical ideas using multiple examples.
• Recognise patterns and relationships.
• Prove and justify their mathematical thinking.
• Develop reasoning and mathematical communication through investigation.

Perfect for:

• Foundation to Year 6 classrooms
• Multiplication and doubling units
• Rich mathematical investigations
• Differentiated mathematics instruction
• Formative assessment opportunities
• Small-group intervention and extension
• Developing mathematical reasoning, problem-solving and communication

This resource promotes conceptual understanding, reasoning, problem-solving and mathematical communication through purposeful investigation of the mathematical properties of doubling.