Differentiating Quadratic Functions for Mixed-Ability Classrooms (VIC, VCAA-Aligned)

Quadratics are a classic spread-point in the Victorian maths classroom: some students are ready to factorise and find roots while others are still making sense of what a parabola even represents. Differentiation is how you keep all of them progressing on the same content without leaving anyone stranded or bored. This piece offers concrete tiering — support, core and extension — for teaching quadratic functions, aligned to the Victorian Curriculum F–10 and the way the Victorian Curriculum and Assessment Authority (VCAA) structures mathematics at Levels 7–10. It builds on Quadratic Functions and Parabolas.

One concept, three entry points

Start every student at the same big idea — a quadratic describes a curved relationship, and its graph is a parabola — then vary the representation each learner works with. Support students lean on tables and graphs, core students connect graphs to equations, and extension students move fluently between all representations. This keeps the Number and Algebra target from the Victorian Curriculum constant while the scaffolding flexes.

Support: concrete before abstract

Students who struggle with quadratics usually need the visual before the symbolic. Begin with a completed table of values they plot to reveal the U-shape, so the parabola is something they build rather than are told about. Provide a partly worked factorising template and a reference card of the key features — vertex, axis of symmetry, intercepts — with a labelled diagram. Real contexts help: a ball's flight or the arc of a water jet makes the maths tangible.

• Pre-filled tables of values to plot and reveal the curve.
• Labelled parabola reference card kept in the workbook.
• Partly completed factorising steps to finish, not start from scratch.
• Real-world arc contexts to anchor the abstract relationship.

Core: connecting graph and equation

Core learners work through the main sequence in Quadratic Functions and Parabolas independently, moving between an equation, its table and its graph, and finding intercepts and the turning point. Ask them to explain how a change in the equation shifts the graph — this reasoning is exactly what VCAA rewards and what prepares students for the VCE.

Extension: modelling and connection

Stretch capable students with genuine challenge: set a modelling task where they fit a quadratic to a real situation and interpret its features in context, then justify their model. Connect the work to adjacent topics so they see structure — the sample-space reasoning in Probability – Fundamentals and Tree Diagrams and the ratio thinking behind Trigonometric Functions – Sine and Cosine both reward students who can generalise. This develops the Critical and Creative Thinking capability alongside the mathematics.

• Support: tables, labelled graphs and partly worked steps.
• Core: independent movement between equation, table and graph.
• Extension: quadratic modelling of a real situation with justification.

Assessment across the range

Use one rubric with descriptors climbing from emerging to sophisticated so every Victorian student is measured against the same criteria at their own level. Low-stakes exit tasks — sketch a parabola from an equation, or find the roots of a simple quadratic — give you a quick formative read to inform the next lesson and to feed VCAA reporting against the Levels 7–10 achievement standards. Well-pitched differentiation means your support student leaves understanding what a parabola is, and your extension student leaves modelling with one.

Related reading from the Teacher Hub

• Differentiating Music Analysis for Mixed-Ability Classrooms (VIC, VCAA-Aligned)
• A Unit Plan for Teaching The Pythagorean Theorem (VIC, VCAA-Aligned)
• A Unit Plan for Teaching Characterisation and Analysing Fiction (VIC, VCAA-Aligned)