A New Teacher's Guide to Teaching Quadratic Functions (WA, SCSA-Aligned)

Quadratic functions can feel like a wall for early-career teachers, because so much lands at once: parabolas, factorising, the quadratic formula, completing the square, and students who arrive with shaky algebra. Take heart. In a Western Australian Years 7 to 10 Mathematics classroom, you do not have to teach it all in the first week, and you certainly do not have to teach it perfectly. This guide sets out what to prioritise, the traps that catch new teachers, and a simple first lesson, all framed by the Western Australian Curriculum and the School Curriculum and Standards Authority (SCSA).

What to prioritise: graph before algebra

The most common misstep is starting with factorising. Lead instead with the graph. When students first meet the parabola as a shape, a ball's flight, a stream of water, a satellite dish, the algebra later has something to describe. Prioritise, in order: recognising a parabola, understanding what changes its shape and position, and only then the algebraic techniques for finding key features. A resource such as Quadratic Functions and Parabolas is built around this graph-first logic, which saves you sequencing it all from scratch in your first year.

Common traps for new teachers

Keep an eye out for these:

• Assuming secure prior algebra. Many students cannot yet expand or factorise confidently. Diagnose early and reteach as needed rather than pushing on.
• Rushing to the quadratic formula. Handed over too soon, it becomes a magic spell students apply without understanding. Build meaning first.
• Neglecting the connection between forms. Students should see that factored, standard and turning-point forms describe the same parabola. Move between them explicitly.
• Skipping the "why". Without real contexts, quadratics feel pointless. Anchor them in projectile motion and area problems.

A simple first lesson

Here is a first lesson you can teach with confidence:

1. Show a short clip or photo of a basketball shot. Ask students to sketch the ball's path. They draw a parabola without knowing the name.
2. Reveal that this shape is a quadratic, and that mathematics can predict exactly where the ball lands.
3. Using graphing software, change one number in y equals x squared and let students describe what happens to the curve.
4. Students complete a short table of values for a simple quadratic and plot it by hand.
5. Close with the question: "What real things move in this shape?" Collect answers as a hook into the unit.

This lesson builds intuition and the Numeracy and Critical and Creative Thinking capabilities before a single term is factorised, which makes the later algebra land far more easily.

Shore up the foundations

Quadratics expose earlier gaps quickly. If students struggle with the algebra, the problem is often lower down. A quick review of proportional reasoning and probability-style thinking can steady a class; resources such as Probability – Fundamentals and Tree Diagrams keep number fluency ticking over while you build the new content. Looking ahead, the same graphing and modelling skills feed directly into senior work, including the trigonometric modelling in Trigonometric Functions – Sine and Cosine, so time invested now pays dividends across the WACE ATAR and General courses.

Keep it inclusive

Quadratics are a topic where confidence gaps widen fast, so plan support in from the start: provide worked examples to refer back to, allow graphing technology to lift the load off computation, and use consistent visual conventions for every parabola. Give students who need it a partially completed table rather than a blank one. These small adjustments let more Western Australian students reach the same SCSA achievement standard, and they mean your first experience of teaching quadratics is a success for the class and for you.

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