Quadratic Functions

Lesson 18 of 30: Introduction to Quadratic Functions

Year Levels

Year 7-10 (with support and modification for students working between Year 2 and Year 7 levels)

Learning Objectives

By the end of this 45-minute lesson, students will be able to:

Understand the basics of quadratic functions and identify their standard form: ( y = ax^2 + bx + c )
Recognise examples of quadratic relationships in everyday life.
Create simple tables of values for a quadratic function and plot its graph using concrete examples.
Use mathematical language to describe the shape of a parabola (e.g., "U-shaped").
Develop confidence with the vocabulary of quadratic functions: coefficient, term, constant, variable.

NSW Curriculum Links

Stage 4 – Year 7-8 Syllabus (Algebra Strand):
Recognise, model, represent and describe linear and simple non-linear relations, including quadratic functions.
Use tables and graphs to investigate quadratic relationships and identify features such as turning points and symmetries.
Mathematics K-10 Syllabus Content Descriptions:
AC9M7N01: Recognise and describe quadratic functions.
AC9M7N03: Create tables and graphs for quadratic functions.
Mathematics Achievement Standards Year 7-9:
Students use algebraic expressions to represent relationships and graph quadratic functions to solve problems.

Lesson Structure (45 minutes)

Time	Activity	Purpose & Notes
0-5 minutes	Warm-up & Review (Oral and visual)	Quick revision of algebraic expressions and graphs of linear functions. Use real-life examples such as speed vs time graphs to engage students. Use whiteboard or chart paper. Introduce the word "quadratic".
5-15 minutes	Introduction to Quadratic Functions	Present the standard form ( y = ax^2 + bx + c ) using large, clear fonts on visual aids. Explain terms: coefficient, variable, constant. Use colour-coding for each term (e.g., blue for ( ax^2 ), green for ( bx ), red for ( c )). Relate to a simple example, e.g., ( y = x^2 ) or ( y = 2x^2 + 3 ). Use graphs to show "U" shape.
15-25 minutes	Group Activity: Create Table of Values & Plot	Students work in pairs to fill a table of values for a quadratic function like ( y = x^2 - 2x + 1 ) with ( x = 0,1,2,3 ). Provide a printed worksheet with large fonts and dyslexia-friendly spacing. Then plot these points on graph paper (colourful, large-grid) to see the parabola forming. Teacher circulates to scaffold and provide repetition for students needing support. Use step-by-step instructions with visual icons.
25-35 minutes	Real-World Connection and Discussion	Show authentic examples showing quadratic patterns: trajectories (throwing a ball), area problems, or design patterns. Use simple video or images. Discuss where quadratic models appear in students’ lives. Encourage sharing ideas verbally in a supportive environment.
35-42 minutes	Individual Practice & Differentiation	Students complete an easy worksheet with 3 quadratic functions. For weaker learners: fill-in-the-blanks and matching terms to parts of the equation. For advanced learners: identify coefficients and sketch graphs on their own or explore changing values of ( a ) to see how the graph shape changes.
42-45 minutes	Review and Reflect	Recap main points collectively using flashcards or an interactive whiteboard quiz. Ask students to name parts of the equation or describe the shape of the graph. Provide positive reinforcement and clarify misunderstandings. Outline next lesson focus (solving quadratic equations).

Differentiation Strategies

For students with Autism, behaviour or mental health challenges:
Use clear, consistent routines.
Break tasks into small, manageable steps with visual cues.
Provide calm, distraction-reduced workspace options.
Use repetitive and scaffolded questions.
Incorporate movement breaks or sensory tools as needed.
For students with learning gaps (working at lower levels):
Offer simplified, concrete examples only (e.g., ( y = x^2 )).
Provide one-to-one or small group support during activities.
Use physical manipulatives (number tiles, counters) to illustrate concept of squaring.
Dyslexia-friendly elements:
Use clear fonts (e.g., Arial, Comic Sans).
Use large spacing and bullet points.
Provide colour-coded key terms and diagrams.
Supply oral instructions alongside written ones.
Use dyslexia-friendly coloured overlays or backgrounds if needed.
Extension for advanced learners:
Explore how changing ( a ), ( b ), and ( c ) affect the parabola's graph.
Begin investigation of vertex form of a quadratic ( y = a(x-h)^2 + k ).
Challenge students to find maximum or minimum points by inspection.

Resources Required

Whiteboard/Markers
Printed worksheets with tables for plotting values (large font, colour-coded)
Graph paper with clear grids
Visual aids showing quadratic graphs
Real-world images/videos demonstrating quadratic functions (e.g., sports throws, architecture)
Manipulatives (optional)
Interactive quiz tool or flashcards for review

Assessment for Learning

Observe students' participation in group table activities and their plotting accuracy.
Use questioning during plenary to check understanding of terms in quadratic standard form.
Review worksheets completed individually for conceptual grasp.
Provide feedback verbally to encourage effort and clarify misconceptions.

Notes for the Teacher

Focus on making abstract algebraic concepts concrete through multiple representations (symbolic, graphical, verbal, and physical).
Allow plenty of repetition and revisit key ideas throughout the lesson.
Encourage respectful, kind peer support to build confidence and social skills, critical for your students’ development and post-school success.
Highlight the relevance of algebra to everyday situations and possible career pathways (as Careers Advisor).
Adjust pacing and complexity dynamically based on the group’s needs.

This lesson balances curriculum rigor with sensitivity to diverse learner needs in a supportive classroom environment, aiming to build foundational understanding and confidence in algebraic thinking.

Teaching Instructions