It’s Hip to Be Square!

A Bounded Differentiated Problem Exploring Square Numbers

Years 3 to 6

Australian Curriculum v9.0 – Mathematics

What makes a square number square?

It’s Hip to Be Square! helps teachers develop students’ conceptual understanding of square numbers through mathematical investigation, reasoning and proof.

Rather than simply recognising or recalling square numbers, students investigate mathematical rules, test examples, represent their thinking, and justify whether a rule is always true.

It’s Hip to Be Square! is a hands-on bounded differentiated problem that invites students to explore the structure, patterns and properties of square numbers 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, arrays, equations and mathematical language, learners investigate what makes a square number square. Students explore the relationship between square numbers and equal rows and columns, factor pairs and consecutive odd numbers. 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 square numbers, 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.

Australian Curriculum v9.0 Aligned

This resource includes:

• Editable PowerPoint lesson presentation
• Learning intention and success criteria
• Bounded differentiated problem for Years 3–6
• Let’s Go, Strive for Success and Mathematician prompts
• Printable task cards
• Reflection and discussion prompts
• Student self-assessment tool
• Teacher notes
• Responsive teaching ideas, extension opportunities and common misconceptions
• Australian Curriculum Version 9 aligned materials

Students will:

• Investigate whether mathematical rules about square numbers are always true.
• Explore what makes a square number a square number.
• Represent square numbers using concrete materials, drawings, arrays and equations.
• Connect square numbers with equal rows and columns, equal factors and factor pairs.
• Investigate patterns between consecutive square numbers and consecutive odd numbers.
• Test mathematical ideas using multiple examples.
• Prove and justify their mathematical thinking.
• Develop reasoning, generalisation and mathematical communication through investigation.

Perfect for:

• Years 3 to 6 classrooms
• Multiplication and square number units
• Rich mathematical investigations
• Differentiated mathematics instruction
• Formative assessment opportunities
• Small-group support 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 structure, patterns and properties of square numbers.