Factoring Quadratics

Year levels

Targeting students Year 7-10 working at levels from Year 2 to Year 7, as per the support unit context.

Lesson Overview

This 45-minute lesson is Lesson 19 of 30 in the unit "Algebra in Everyday Life." The focus is on introducing and practising techniques to factor basic quadratic expressions, connecting algebraic skills to real-life contexts relevant to students' everyday experiences. The lesson is carefully scaffolded to support students with autism, behavioural and mental health challenges, emphasising repetition, breaking down steps, and linking abstract concepts to authentic scenarios.

NSW Curriculum Alignment

Mathematics K-10 Syllabus

Stage 4 (Years 7-8):
Learning Objective: Apply algebraic techniques and strategies to simplify and factorise linear and simple quadratic expressions (e.g. factorising quadratics with leading coefficient 1).
Content Descriptor: AC9M7AL01 Apply index laws and factorise algebraic expressions including monic quadratics
Stage 5 (Years 9-10):
Learning Objective: Factorise monic quadratic expressions and solve related problems
Content Descriptor: AC9M9AL05 Factorise monic quadratic expressions and solve quadratic equations by factorising

This lesson primarily links to early and middle content of these stages, adjusted to suit readiness and engagement levels of students working between Year 2 and 7 levels.

Referenced achievement standards:

Year 7 Achievement Standard includes use of algebraic expressions and solving simple equations.
Year 9 Achievement Standard expects extension to monic quadratic factorisation and algebraic problem solving.

Learning Objectives

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

Understand what a quadratic expression is (specifically monic quadratics in form (x^2 + bx + c)).
Identify factors of the constant term and use these to factor simple quadratics.
Demonstrate the factoring process step-by-step using concrete examples.
Connect factoring quadratics to real-world contexts, such as area problems or career-related examples (e.g., working in trades, finance, or design).
Show persistence and confidence in working through algebraic factoring problems with support.

Resources Needed

Whiteboard and markers
Printed worksheets with guided factoring exercises (large print, dyslexia-friendly fonts, ample spacing)
Manipulatives: Algebra tiles or square cutouts to visualise (x^2 + bx + c) (optional)
Visual aids showing stepwise factoring process
Calculator for checking answers (optional)
Real life scenario cards (e.g., "designing a garden bed", "budgeting for a square cost layout")

Lesson Breakdown

Time	Activity	Rationale/Notes
5 min	Introduction / Warm-up: Recap what a quadratic is, relate to shapes (e.g., areas of squares and rectangles). Discuss (x^2), (x) terms, and constants. Use visual aid and manipulatives.	Connects abstract algebra to visual, concrete concepts to build engagement and understanding. Supports diverse learning styles.
10 min	Explicit Teaching: Demonstrate how to factor simple monic quadratic (x^2 + bx + c). Focus on finding two numbers that multiply to (c) and add to (b). Use a think-aloud approach on the board with examples such as (x^2 + 5x + 6). Break process into steps and repeat.	Repetition and clear stepwise instruction aid those with learning difficulties.
10 min	Guided Practice: Students work in pairs or small groups on a worksheet with factoring exercises starting from very simple to slightly more challenging. Teacher circulates for support and scaffolding. Encourage discussion of strategies.	Peer support and scaffolded practice support understanding. Differentiation by giving varied difficulty problems.
10 min	Real World Application Discussion: Present a realistic scenario showing how factoring quadratics applies, for example, calculating materials for a square garden bed with an extra edging strip. Have students suggest what numbers might mean in the example, linking algebra to career/transition goals.	Builds authentic context for learning; relates maths to life skills and future goals.
5 min	Extension for Advanced Learners: Offer extension problems involving simple factorisation of non-monic quadratics or creating quadratics from area models.	Challenge advanced learners to deepen understanding.
5 min	Review and Reflect: Recap key points, answer questions, and encourage students to express what they learnt today. Celebrate effort and growth.	Reinforce learning and build confidence; helps teacher assess understanding.

Differentiation Strategies

For diverse learners and those with Autism, behaviour, or mental health challenges:
Use clear and concise instructions broken into small, manageable steps.
Include visual aids and hands-on resources like algebra tiles to illustrate concepts.
Provide printed notes summarising steps with dyslexia-friendly font (such as OpenDyslexic or Arial), large spacing and colour coding (e.g., colour code factors and terms).
Allow movement breaks if needed to maintain focus.
Use positive behaviour supports and celebrate attempts.
Pair students carefully for peer support.
For students working below Year 7 levels:
Focus on recognising and manipulating simple factors and understanding (x^2) as an area concept before symbolic factoring.
Use more concrete materials and real-world examples.
For advanced learners:
Provide factoring problems with leading coefficients other than 1.
Introduce the concept of completing the square or simple quadratic equation solving via factorisation.
Encourage creating their own quadratic expressions from factors.

Dyslexia-Friendly Reading and Writing Support

Use dyslexia-friendly fonts and backgrounds for all printed materials (e.g., off-white or pastel coloured paper to reduce glare).
Avoid dense text; use bullet points and numbered steps for clarity.
Use colour coding to highlight connections (e.g., matching factors and terms).
Allow verbal explanations and answers where possible to reduce writing barriers.
Provide audio or video alternatives demonstrating the factoring process for revision.

Assessment / Evidence of Learning

Monitor participation and accuracy during guided practice worksheets and group discussions.
Conduct a brief oral quiz at end of lesson asking students to explain the factoring steps in their own words.
Collect worksheets and provide feedback tailored to students' needs.
Use student explanations of the real-world application to gauge understanding.

Career and Life Skills Connection

Discuss how factoring relates to problem-solving in careers such as construction, landscaping, fashion design (pattern making), finance (modelling costs), and technology.
Highlight skills such as breaking down complex tasks into steps, persistence with challenging problems, and applying maths to everyday tasks.
Reinforce respect, teamwork, and patience during pair and group activities as workplace skills.

This lesson balances curriculum rigour with accessibility, supporting students with complex learning needs through real-world relevance, clear scaffolding, repetition, and multi-modal approaches. It prepares them for future lessons in algebra and practical problem solving.

Please let me know if you would like detailed worksheets or visual aids to accompany this plan!

Teaching Instructions