Differentiating Quadratic Functions for Mixed-Ability Classes (England, National Curriculum)

Quadratics are one of the great dividers of a mixed-ability maths class. Some pupils see the elegant symmetry of a parabola immediately; others are still shaky on substituting a negative value into x². The National Curriculum for England expects pupils to work with quadratic graphs and expressions by the end of Key Stage 4, and GCSE tiers with AQA, Edexcel and OCR span from sketching a simple parabola to solving by completing the square. This piece offers concrete tiering — support, core and extension — so one class can work on the same idea at genuinely different depths.

Anchor everything to the parabola

Keep a shared visual anchor so the class feels like one lesson, not three: everyone works with the graph of a quadratic and its key features — roots, turning point, line of symmetry. The graded tasks in Quadratic Functions and Parabolas let you hand the same context to every pupil while varying the demand, which protects the self-esteem of pupils who would notice a “easier sheet” instantly.

Support: scaffolds that keep the mathematics intact

Support pupils need structure around the process, not a watered-down topic:

• A part-completed table of values so substitution errors do not derail the graph.
• Colour-coded steps for plotting: calculate, plot, join with a smooth curve.
• A worked example alongside the task — a faded example that removes one step at a time.
• Sentence stems for describing the graph: “The curve crosses the x-axis at… so the solutions are…”

These pupils still meet the same objective — interpreting a quadratic graph — with the cognitive load managed so they can actually reach it.

Core and extension: raising the ceiling

Core pupils plot quadratics independently and read off roots and turning points, then link the graph to a factorised equation. Extension pupils take on real challenge: connecting the completed-square form to the coordinates of the turning point, or solving problems where a quadratic models an area or a projectile. Genuine stretch means less scaffolding and more open questions — “What happens to the graph as the coefficient of x² grows?” The proportional and probabilistic reasoning in Probability – Fundamentals and Tree Diagrams offers a change-of-context problem set for fast finishers, and the trigonometric graph work in Trigonometric Functions – Sine and Cosine extends the idea of reading meaning from a curve into a new family of functions.

One lesson, one set of criteria

Differentiation only works if it does not fragment your assessment. Use a single success ladder — from “plots a quadratic accurately” to “interprets and applies the completed-square form” — and mark every pupil against their next rung rather than a fixed target. Mini-plenaries let a support pupil share a correctly plotted curve and an extension pupil share a modelling insight in the same breath, signalling that both are doing real mathematics. Handled this way, a mixed-ability quadratics unit prepares foundation and higher pupils alike for the demands of their GCSE tier without ever splitting the class into visible camps. Keep the tiers deliberately porous: a support pupil who has plotted three parabolas accurately should be invited to try reading off the turning point unaided, while an extension pupil who stumbles on completing the square is not demoted but simply handed a faded worked example for that one step. When pupils experience differentiation as movement rather than as a fixed ceiling, they take more risks, and it is that willingness to attempt the harder question that ultimately moves them up a tier.

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