Understanding Variables

Unit Context

This lesson is Lesson 2 of 30 in the unit "Algebra in Everyday Life" designed for Year 7-10 students working between Year 2 and Year 7 capability levels in a NSW Support Unit setting. The focus is on building foundational understanding of variables as symbols representing unknowns in equations.

Curriculum Links and Learning Objectives

NSW Mathematics K–10 Syllabus for Years 7-10 — Algebra Strand

Content description: Represent variables in simple algebraic expressions, sentences, and equations to solve problems in everyday contexts.
Learning outcomes:
Students understand that variables represent unknown or changing values.
Students construct simple algebraic expressions using variables.
Students interpret and explain the meaning of variables in context.

Relevant Achievement Standards:

Year 7: Use algebraic expressions to represent situations and describe relationships between variables from authentic data; substitute values into formulas to find unknown values; solve simple linear equations with natural number solutions.

Lesson Duration

45 minutes

Class Size

20 students

Lesson Overview

Learning Intentions

Understand what variables are and why they are used in mathematics.
Recognise variables as symbols that represent unknown or changing numbers.
Connect variables and expressions to real-life situations.

Success Criteria

I can explain what a variable is.
I can identify a variable in an algebraic expression.
I can create a simple expression using a variable to represent an unknown.
I can solve simple problems by substituting numbers in place of variables.

Resources Required

Whiteboard and markers
Printed cards with simple real-life problem scenarios (e.g., "Number of apples + 3 = 7")
Handouts with simple algebraic expressions (dyslexia-friendly format: clear font, large size, coloured overlays optional)
Counters or physical objects (for modelling)
Worksheets for practice
Visual aids showing variable examples (age, temperature, speed)
Laptops/tablets with simple algebra games (optional for advanced learners)

Lesson Breakdown

Time	Activity	Description	Differentiation & Supports
0–5 mins	Warm-up: What is a Variable?	Teacher introduces the term ‘variable’ with simple language. Use relatable examples (e.g., “How many apples?”)	Use visuals and physical objects to support comprehension. Simple yes/no questioning; model responses.
5–15 mins	Direct Teaching: Variables as Symbols	Explain variables symbolise unknown numbers or changing amounts. Use real-life examples (age, money, time).	Use large clear print materials; dyslexia-friendly fonts with spacing; repeat key terms; provide sentence stems.
15–25 mins	Guided Activity: Matching Game	Students match cards with scenarios to algebraic expressions, e.g., x + 3 = 7 with “number of apples + 3 = 7”.	Provide physical counters for hands-on engagement; pair students for peer support; use small group instructions.
25–35 mins	Independent Practice: Simple Substitution	Given expressions with variables, substitute numbers to find results, e.g., if x=4, what is x + 2?	Provide step-by-step examples; allow extra time; use calculators as needed; for advanced learners, include two-step expressions.
35–40 mins	Extension Challenge	Advanced learners create their own story problems involving variables and present to class.	Encourage use of digital tools or drawing. Support shy learners with sentence frames or templates.
40–45 mins	Reflection and Recap	Whole class discusses what variables are. Use exit slip: “What is a variable?”	Use verbal, written or pictorial responses. Offer alternative communication for students with language difficulties.

Differentiation Strategies for Diverse Learners

For students with Autism, Behavioural or Mental Health issues:
Predictable lesson structure with clear time frames.
Visual schedules and timers.
Use calm, explicit instructions.
Opportunities for movement breaks.
For students with Dyslexia:
Dyslexia-friendly handouts: sans-serif fonts like Arial or Comic Sans, large print, double spacing.
Colour overlays on worksheets.
Use oral instructions alongside written ones.
Provide worked examples with highlighting and chunks.
For Students with Learning Gaps:
Repetition and multiple examples linking algebra to authentic everyday life scenarios.
Use manipulatives (counters, blocks) to illustrate unknown quantities.
Simplify language; check understanding before moving on.
For Advanced Learners:
Provide challenge tasks such as creating their own problems.
Introduce two-step equations or multiple variables as extension.
Use digital algebra games or apps for enrichment.

Assessment and Feedback

Ongoing formative assessment through questioning and observation during activities.
Review exit slips to gauge student understanding of variables.
Feedback given verbally and visually; use positive reinforcement.
For individual students, targeted follow-up tasks as needed.

Real-World Connections and Careers Advice

Discuss how variables are used in real life, e.g., managing money, cooking recipes, or planning time.
Relate understanding variables to workplace skills like problem-solving and following instructions.
Briefly mention careers that use algebra (e.g., engineering, computer programming, trades) to increase student engagement and connection to future goals.

Notes for Teachers

Use consistent terms (variable, unknown, letter) and encourage students to verbalise reasoning.
Model thinking aloud using story contexts linked to students’ experiences.
Provide a calm, supportive environment mindful of students’ sensory and emotional needs.
Keep instructions clear, simple, and chunked.
Use positive behaviour support strategies as needed.

This lesson builds foundational algebra skills tightly aligned to the NSW Mathematics Curriculum for Years 7-10 and caters sensitively to students needing support with concepts, language, and engagement through authentic, practical contexts and differentiated instruction.

Teaching Instructions